A compendium on beam transport and beam ... - IRUVX-PP – the...
A compendium on beam transport and beam ... - IRUVX-PP – the...
A compendium on beam transport and beam ... - IRUVX-PP – the...
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A <str<strong>on</strong>g>compendium</str<strong>on</strong>g> <strong>on</strong> <strong>beam</strong> <strong>transport</strong><br />
<strong>and</strong> <strong>beam</strong> diagnostic methods for<br />
Free Electr<strong>on</strong> Lasers<br />
<strong>IRUVX</strong>-<strong>PP</strong> Experts’ Report<br />
A. Lindblad, S. Svenss<strong>on</strong>, K. Tiedtke<br />
Partners of <strong>IRUVX</strong>-<strong>PP</strong> <strong>–</strong> <strong>the</strong> preparatory phase of EuroFEL
Imprint<br />
Publishing <strong>and</strong> c<strong>on</strong>tact:<br />
Deutsches Elektr<strong>on</strong>en-Synchrotr<strong>on</strong> DESY<br />
<strong>IRUVX</strong>-<strong>PP</strong> Project Coordinator<br />
Notkestr. 85, 22607 Hamburg, Germany<br />
Tel.: +49 40 8998-4130<br />
www.eurofel.eu<br />
ISBN 978-3-935702-45-4<br />
This <str<strong>on</strong>g>compendium</str<strong>on</strong>g> is nei<strong>the</strong>r for sale nor may be resold.<br />
Editors:<br />
Dr. Andreas Lindblad , Prof. Dr. Svante Svenss<strong>on</strong>, Dr. Kai Tiedtke<br />
Copy deadline: March 2011<br />
Cover layout: M<strong>on</strong>ika Illenseer<br />
Printing: K<strong>on</strong>rad Triltsch GmbH, Ochsenfurt-Hohestadt<br />
Editorial note:<br />
The authors of <strong>the</strong> individual scientific c<strong>on</strong>tributi<strong>on</strong>s published<br />
in this <str<strong>on</strong>g>compendium</str<strong>on</strong>g> are fully resp<strong>on</strong>sible for <strong>the</strong> c<strong>on</strong>tents.<br />
Cover:<br />
FLASH experimental hall at DESY in Hamburg <strong>and</strong> diffracti<strong>on</strong> image.<br />
(Photos: © Heiner Mueller-Elsner / Agentur-Focus.de; DESY)
A <str<strong>on</strong>g>compendium</str<strong>on</strong>g> <strong>on</strong> <strong>beam</strong> <strong>transport</strong><br />
<strong>and</strong> <strong>beam</strong> diagnostic methods for<br />
Free Electr<strong>on</strong> Lasers<br />
<strong>IRUVX</strong>-<strong>PP</strong> Experts’ Report<br />
A. Lindblad, S. Svenss<strong>on</strong>, K. Tiedtke<br />
Partners of <strong>IRUVX</strong>-<strong>PP</strong> <strong>–</strong> <strong>the</strong> preparatory phase of EuroFEL
This book was set with L ATEX using <strong>the</strong> memoir class
Foreword<br />
The development <strong>and</strong> use of X-ray free electr<strong>on</strong> lasers have underg<strong>on</strong>e a remarkable<br />
development during <strong>the</strong> last decade: <strong>the</strong> first lasing in <strong>the</strong> VUVat 100 nm wavelength<br />
was achieved in <strong>the</strong> year 2000; in Europe <strong>the</strong> soft X-ray free electr<strong>on</strong> laser Flash<br />
started operati<strong>on</strong>s in 2005 followed by <strong>the</strong> hard X-ray facility Lcls in <strong>the</strong> USA;<br />
during <strong>the</strong> time of writing of this book <strong>the</strong> first seeded X-ray free electr<strong>on</strong> laser has<br />
been commissi<strong>on</strong>ed, <strong>the</strong> Fermi@Elettra. During <strong>the</strong> following decade we will see<br />
upgrades to <strong>the</strong> currently operating facilities, as well as <strong>the</strong> emergence of new sources.<br />
Within <strong>the</strong> coming years <strong>the</strong>re will be hard X-ray free electr<strong>on</strong> laser operating<br />
<strong>on</strong> three c<strong>on</strong>tinents: The European X-Fel, Lcls in North America <strong>and</strong> Scss in<br />
Japan. The progress in accelerator technology <strong>and</strong> in free electr<strong>on</strong> laser science has<br />
resulted in emerging c<strong>on</strong>cepts for more compact <strong>and</strong> more efficient sources, which<br />
can make it feasible for nati<strong>on</strong>al laboratories to build such facilities; In more or<br />
less advanced planning <strong>and</strong> design stages, this is under c<strong>on</strong>siderati<strong>on</strong> in Sweden,<br />
Switzerl<strong>and</strong> (SwissFEL), South Korea (PAL X-Fel) <strong>and</strong> o<strong>the</strong>r countries.<br />
Freeelectr<strong>on</strong>lasers haveunprecedented<strong>beam</strong> properties<strong>and</strong>arecurrently<strong>the</strong>most<br />
intense <strong>and</strong> well collimated man-made phot<strong>on</strong> source in <strong>the</strong> UV to <strong>the</strong> hard X-ray<br />
range. A pulsed X-ray source like this allows for investigati<strong>on</strong> of matter <strong>on</strong> <strong>the</strong> scales<br />
natural to <strong>the</strong> nano-world: femtosec<strong>on</strong>ds <strong>and</strong> nanometers <strong>–</strong> current development aims<br />
for X-rays <strong>on</strong> <strong>the</strong> natural atomic scales: attosec<strong>on</strong>ds <strong>and</strong> ˚Angströms. As access to<br />
this type of source is becoming easier to gain <strong>the</strong> enthusiastic user community is ever<br />
exp<strong>and</strong>ing <strong>–</strong> a significant step essential for lowering <strong>the</strong> threshold for scientists, often<br />
coming from <strong>the</strong> synchrotr<strong>on</strong> or laser communities but not experts in <strong>the</strong> free electr<strong>on</strong><br />
laser field, to c<strong>on</strong>duct experimental work utilizing <strong>the</strong> sources’ unique capabilities. As<br />
<strong>the</strong> field is relatively young (at least for <strong>the</strong> X-ray regime) <strong>the</strong> forthcoming decade(s)<br />
will see <strong>the</strong> field mature bey<strong>on</strong>d pi<strong>on</strong>eering experiments into a broad plethora of<br />
experimental applicati<strong>on</strong>s with an equally broad <strong>and</strong> diverse user community from<br />
many different fields.<br />
Although obviously attractive with regards to phot<strong>on</strong> <strong>beam</strong> quality, <strong>the</strong> c<strong>on</strong>structi<strong>on</strong>,<br />
commissi<strong>on</strong>ing <strong>and</strong> operati<strong>on</strong> of a free electr<strong>on</strong> laser facility is technically very<br />
challenging. The accelerated electr<strong>on</strong> <strong>beam</strong> needs to have very high quality from <strong>the</strong><br />
very start, <strong>and</strong> throughout <strong>the</strong> accelerator <strong>and</strong> <strong>the</strong> magnet array of <strong>the</strong> undulator(s)<br />
requiring specific knowledge in, l<strong>and</strong> development, <strong>beam</strong> dynamics <strong>and</strong> simulati<strong>on</strong>s,<br />
electr<strong>on</strong><strong>beam</strong>diagnostics, synchr<strong>on</strong>izati<strong>on</strong>technology, undulatortechnology<strong>and</strong>laser<br />
seeding. The <strong>beam</strong> of X-rays with extremely high fluence needs to be <strong>transport</strong>ed to<br />
i
ii Foreword<br />
<strong>the</strong> user experiment with <strong>the</strong> resulting dem<strong>and</strong>s <strong>on</strong> X-ray optics with regard to surface<br />
characteristics, damage etc.In additi<strong>on</strong>, each phot<strong>on</strong>pulse needs to be diagnosed<br />
<strong>and</strong> its characteristics stored for later inclusi<strong>on</strong> in data-analysis, for poly-color experiments<br />
(involving o<strong>the</strong>r laser pulses) informati<strong>on</strong> for pulse-synchr<strong>on</strong>izati<strong>on</strong> needs to<br />
be available <strong>and</strong> so forth.<br />
In this phase, <strong>the</strong> funding programmes of <strong>the</strong> European Commissi<strong>on</strong> (EC) for <strong>the</strong><br />
development of new research infrastructures helped interested European instituti<strong>on</strong>s<br />
enormously to join <strong>the</strong>ir forces for developing key technologies required for <strong>the</strong> design<br />
<strong>and</strong> c<strong>on</strong>structi<strong>on</strong> of <strong>the</strong> next generati<strong>on</strong> free electr<strong>on</strong> laser sources in Europe:<br />
• The European Fel design study project EUROFEL funded by <strong>the</strong> 6 th Framework<br />
Programme for a period of three years, 2005<strong>–</strong>2007, focused <strong>on</strong> comp<strong>on</strong>ents<br />
<strong>the</strong> electr<strong>on</strong> accelerator <strong>and</strong> <strong>the</strong> free electr<strong>on</strong> laser itself.<br />
• This project was followed by Iruvx-<strong>PP</strong>, <strong>the</strong> preparatory project for a sustainable<br />
future European FEL c<strong>on</strong>sortium called EuroFEL. Iruvx-<strong>PP</strong> includes<br />
significant funding for fur<strong>the</strong>r technical developments regarding both <strong>the</strong> electr<strong>on</strong><br />
<strong>and</strong> phot<strong>on</strong> <strong>beam</strong>s.<br />
This <str<strong>on</strong>g>compendium</str<strong>on</strong>g> is an amalgamati<strong>on</strong> of <strong>the</strong> collaborative efforts of two of Iruvx-<br />
<strong>PP</strong>’s workpackes, <strong>the</strong> third <strong>and</strong> seventh <strong>–</strong> whose efforts were focused <strong>on</strong> X-ray phot<strong>on</strong><br />
<strong>beam</strong> optics <strong>and</strong> diagnostics. C<strong>on</strong>trasting <strong>the</strong> mainly political <strong>and</strong> structural objectives<br />
of Iruvx-<strong>PP</strong>, it provides an immediate practical result <strong>and</strong> delivers timely <strong>–</strong><br />
toge<strong>the</strong>r with an introducti<strong>on</strong> to free electr<strong>on</strong> laser technology <strong>and</strong> science <strong>–</strong> an urgently<br />
needed text which details <strong>the</strong> latest developments in <strong>the</strong> field in a manner also<br />
accessible for n<strong>on</strong>-experts.<br />
Ithasnotbeenintendedtoprovideacomplete indepthaccountof<strong>the</strong>whole fieldof<br />
free electr<strong>on</strong> laser science but ra<strong>the</strong>r to provide: (i: a presentati<strong>on</strong> of key technologies<br />
<strong>and</strong> c<strong>on</strong>cepts needed to underst<strong>and</strong> <strong>the</strong> various requirements that are imposed <strong>on</strong> <strong>the</strong><br />
electr<strong>on</strong> <strong>and</strong> phot<strong>on</strong> <strong>beam</strong>s, which limitati<strong>on</strong>s different technology choices impose <strong>on</strong><br />
<strong>the</strong> final output of <strong>the</strong> free electr<strong>on</strong> laser; (ii, detail, sometimes exp<strong>and</strong> <strong>and</strong> put into<br />
c<strong>on</strong>text <strong>the</strong> various internal reports generated in <strong>the</strong> workpackages. Taken toge<strong>the</strong>r<br />
both ambiti<strong>on</strong>s have generated a nice recollecti<strong>on</strong> of <strong>the</strong> collaborative efforts of <strong>the</strong><br />
members c<strong>on</strong>stituting <strong>the</strong> workpackages in an accessible form that hopefully will help<br />
future students <strong>and</strong> colleagues to get acquainted with <strong>the</strong> exciting field of free electr<strong>on</strong><br />
laser science.<br />
Josef Feldhaus, Hamburg, 25 th February, 2011.<br />
Scientific coordinator of <strong>the</strong> Iruvx-<strong>PP</strong> project
Preface<br />
Caveat Lector<br />
This book’s humble beginning was as a summarizing report of <strong>the</strong> collective efforts<br />
within <strong>the</strong> 3 rd & 7 th workpackage of <strong>the</strong> Iruvx-<strong>PP</strong> programme. During <strong>the</strong> time of<br />
writing (<strong>the</strong> last twelve m<strong>on</strong>ths of <strong>the</strong> programme) <strong>the</strong> members of <strong>the</strong> workpackages<br />
produced reports <strong>on</strong> <strong>the</strong>ir findings <strong>–</strong> often c<strong>on</strong>taining reviews of <strong>the</strong> various fields<br />
where <strong>the</strong> undertakings took place.<br />
Each such report have been, more or less, basis for secti<strong>on</strong>s <strong>and</strong> indeed whole<br />
chapters in this book, notably in <strong>the</strong> sec<strong>on</strong>d part. The reports’ titles <strong>and</strong> <strong>the</strong>ir authors<br />
are menti<strong>on</strong>ed in <strong>the</strong> very beginning of <strong>the</strong> chapters where material from <strong>the</strong>m have<br />
been used.<br />
A summarizing report may be interesting in itself, but to heighten <strong>the</strong> appeal to<br />
a broader audience <strong>and</strong> to future students <strong>and</strong> colleagues it was thought that when<br />
adding c<strong>on</strong>text to <strong>the</strong> reports (who by <strong>the</strong>mselves deal mainly with X-ray optics<br />
<strong>and</strong> phot<strong>on</strong> diagnostic methods) a good introductory textbook describing <strong>the</strong> various<br />
challenges pertainingtowork<strong>and</strong>developmentoffree electr<strong>on</strong> lasers couldberealized.<br />
Hence <strong>the</strong> first part of <strong>the</strong> book describes <strong>the</strong> physics <strong>and</strong> c<strong>on</strong>cepts that govern<br />
free electr<strong>on</strong> lasers. The various comp<strong>on</strong>ents of a free electr<strong>on</strong> laser are also described<br />
<strong>–</strong> from <strong>the</strong> electr<strong>on</strong> gun to <strong>the</strong> undulators, <strong>and</strong> some X-ray optics. The sec<strong>on</strong>d part<br />
of <strong>the</strong> book focuses heavily <strong>on</strong> diagnostic methods that can be used to quantify <strong>the</strong><br />
properties of <strong>the</strong> free electr<strong>on</strong> laser phot<strong>on</strong> <strong>beam</strong>. In <strong>the</strong> last chapters of part two<br />
<strong>the</strong> current running <strong>and</strong> planned facilities are described in <strong>the</strong> light of what we have<br />
learned in <strong>the</strong> firstpart of <strong>the</strong> book, planned <strong>and</strong>performed experiments are described<br />
as to give an orientati<strong>on</strong> of what scientists are trying to achieve with <strong>the</strong> facilities.<br />
The bibliography of this book c<strong>on</strong>tains both references to books <strong>and</strong> articles that<br />
reflect <strong>the</strong> current state of <strong>the</strong> art, at least for part two of <strong>the</strong> book, at <strong>the</strong> time of<br />
writing (February 2011). No such list is ever complete <strong>and</strong> will so<strong>on</strong> become dated<br />
<strong>–</strong> however through citati<strong>on</strong>s to those papers <strong>the</strong> reader will so<strong>on</strong> find where <strong>the</strong> field<br />
have developed. Without any doubt many of <strong>the</strong> references will remain key references<br />
for quite a foreseeable time.<br />
iii
iv Preface<br />
Acknowledgements<br />
I would like to extend my gratitude to my co-editors Prof. Df. Svante Svenss<strong>on</strong><br />
<strong>and</strong> Dr. Kai Tiedkte for giving me <strong>the</strong> opportunity to work with this book. I also<br />
thank <strong>the</strong>m for <strong>the</strong> many nice discussi<strong>on</strong>s <strong>and</strong> <strong>the</strong> good criticism during <strong>the</strong> authoring<br />
process. Naturally I also like to thank <strong>the</strong> authors of <strong>the</strong> reports which c<strong>on</strong>stitute<br />
parts of this book without which I would literally have started with a blank page.<br />
Thanksto<strong>the</strong>manynicepresentati<strong>on</strong>s<strong>on</strong><strong>the</strong>workshops<strong>and</strong>freeelectr<strong>on</strong>laser c<strong>on</strong>ference<br />
last year I have been kindly introduced to <strong>the</strong> fantastic subject of free electr<strong>on</strong><br />
laser science. Again, for <strong>the</strong> opportunity to work with it <strong>and</strong> writing a book about it<br />
I will be forever grateful.<br />
Andréas Lindblad, Uppsala, 28 th February, 2011.
C<strong>on</strong>tents<br />
Foreword i<br />
Preface iii<br />
C<strong>on</strong>tents v<br />
I Free electr<strong>on</strong> lasers <strong>–</strong> a primer<br />
1 Introducti<strong>on</strong> 3<br />
1.1 Historical exposé & scientific background . . . . . . . . . . . . . . . . 3<br />
1.2 Laboratory X-ray <strong>and</strong> UV/Vis phot<strong>on</strong> sources . . . . . . . . . . . . . . 7<br />
X-ray tube <strong>and</strong> anode sources . . . . . . . . . . . . . . . . . . . . . . . 8<br />
Synchrotr<strong>on</strong> light sources . . . . . . . . . . . . . . . . . . . . . . . . . 9<br />
Lasers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10<br />
High Harm<strong>on</strong>ic Generati<strong>on</strong> Lasers . . . . . . . . . . . . . . . . . . . . 11<br />
1.3 Free electr<strong>on</strong> Lasers . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12<br />
1.4 Development of X-ray free electr<strong>on</strong> lasers . . . . . . . . . . . . . . . . 15<br />
1.5 Seeding schemes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15<br />
eSase . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17<br />
HGHG . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17<br />
EEHG . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18<br />
Harm<strong>on</strong>ic afterburners . . . . . . . . . . . . . . . . . . . . . . . . . . . 18<br />
1.6 Definiti<strong>on</strong>s used throughout <strong>the</strong> book . . . . . . . . . . . . . . . . . . . 19<br />
Brilliance <strong>and</strong> Brightness . . . . . . . . . . . . . . . . . . . . . . . . . 19<br />
Emittance . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19<br />
2 Synchrotr<strong>on</strong> radiati<strong>on</strong> <strong>and</strong> its properties 23<br />
2.1 Radiati<strong>on</strong> from a moving charge . . . . . . . . . . . . . . . . . . . . . 23<br />
Maxwell’s laws . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23<br />
Charged particle at rest or moving with c<strong>on</strong>stant velocity . . . . . . . 24<br />
The fields from a charge in arbitrary moti<strong>on</strong> . . . . . . . . . . . . . . . 25<br />
Frequency <strong>and</strong> coherence of synchrotr<strong>on</strong> radiati<strong>on</strong> . . . . . . . . . . . 27<br />
v
vi C<strong>on</strong>tents<br />
2.2 Radiati<strong>on</strong> from a bending magnet . . . . . . . . . . . . . . . . . . . . . 29<br />
2.3 Undulator radiati<strong>on</strong> . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30<br />
The undulator equati<strong>on</strong> . . . . . . . . . . . . . . . . . . . . . . . . . . 30<br />
2.4 Microbunching . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37<br />
Interacti<strong>on</strong> between <strong>the</strong> electr<strong>on</strong> <strong>beam</strong> <strong>and</strong> <strong>the</strong> radiati<strong>on</strong> field . . . . . 37<br />
Exp<strong>on</strong>ential gain . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39<br />
Scaled free electr<strong>on</strong> laser equati<strong>on</strong>s . . . . . . . . . . . . . . . . . . . . 41<br />
2.5 Sase . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 44<br />
Coherence properties . . . . . . . . . . . . . . . . . . . . . . . . . . . . 45<br />
3 Free electr<strong>on</strong> laser ”hardware” 47<br />
3.1 A prototypical FEL amplifier . . . . . . . . . . . . . . . . . . . . . . . 47<br />
3.2 Electr<strong>on</strong> guns . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 47<br />
General requirements . . . . . . . . . . . . . . . . . . . . . . . . . . . . 48<br />
Thermi<strong>on</strong>ic emitters . . . . . . . . . . . . . . . . . . . . . . . . . . . . 49<br />
Photocathode emitters . . . . . . . . . . . . . . . . . . . . . . . . . . . 50<br />
Normally c<strong>on</strong>ducting guns . . . . . . . . . . . . . . . . . . . . . . . . . 50<br />
Superc<strong>on</strong>ducting guns . . . . . . . . . . . . . . . . . . . . . . . . . . . 51<br />
Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 52<br />
3.3 Radio-frequency driven accelerators . . . . . . . . . . . . . . . . . . . . 52<br />
The accelerating RF-field . . . . . . . . . . . . . . . . . . . . . . . . . 54<br />
Energy gain in a radiofrequency driven accelerating cavity . . . . . . . 57<br />
Warm technology: Copper . . . . . . . . . . . . . . . . . . . . . . . . . 58<br />
Superc<strong>on</strong>ducting technology . . . . . . . . . . . . . . . . . . . . . . . . 58<br />
3.4 Undulators . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 59<br />
Undulator tolerances example . . . . . . . . . . . . . . . . . . . . . . . 60<br />
4 X-ray optics 63<br />
4.1 Dem<strong>and</strong>s <strong>on</strong> optics precisi<strong>on</strong> at free electr<strong>on</strong> lasers . . . . . . . . . . . 63<br />
4.2 Focussing mirrors <strong>–</strong> back-reflecting geometry example . . . . . . . . . 65<br />
4.3 Damage . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 65<br />
4.4 Diffracti<strong>on</strong> gratings . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 66<br />
4.5 M<strong>on</strong>ochromators . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 67<br />
4.6 Beam attenuators . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 69<br />
5 Beam-splitting methods 73<br />
5.1 Introducti<strong>on</strong> . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 73<br />
5.2 Beam-splitter specificati<strong>on</strong> . . . . . . . . . . . . . . . . . . . . . . . . . 74<br />
5.3 Amplitude divisi<strong>on</strong> <strong>beam</strong> splitters . . . . . . . . . . . . . . . . . . . . 76<br />
Partially transmitting materials . . . . . . . . . . . . . . . . . . . . . . 76<br />
Crystal diffracti<strong>on</strong> <strong>beam</strong> splitters . . . . . . . . . . . . . . . . . . . . . 78<br />
Gratings . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 80<br />
Grids . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 83<br />
5.4 Wavefr<strong>on</strong>t divisi<strong>on</strong> <strong>beam</strong>splitters . . . . . . . . . . . . . . . . . . . . . 83<br />
Beamline apertures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 83<br />
Knife-edge mirrors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 84<br />
Knife-edge crystals . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 84<br />
Fresnel bi-mirror . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 85<br />
Slotted or perforated mirrors . . . . . . . . . . . . . . . . . . . . . . . 85
C<strong>on</strong>tents vii<br />
Structured arrays . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 87<br />
5.5 Time-based splitting . . . . . . . . . . . . . . . . . . . . . . . . . . . . 88<br />
5.6 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 89<br />
Techniques requiring <strong>the</strong> least development . . . . . . . . . . . . . . . 89<br />
Techniques requiring more development . . . . . . . . . . . . . . . . . 90<br />
II Beam diagnostics<br />
6 Introducti<strong>on</strong> 95<br />
6.1 Diagnostics categorizati<strong>on</strong> . . . . . . . . . . . . . . . . . . . . . . . . . 95<br />
Subcategorizati<strong>on</strong>s . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 96<br />
6.2 C<strong>on</strong>clusi<strong>on</strong> . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 97<br />
7 Spectral diagnostics: Intensity & Energy 99<br />
7.1 X-ray spectrometry . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 99<br />
7.2 Intensity/Beam energy . . . . . . . . . . . . . . . . . . . . . . . . . . . 100<br />
Gas m<strong>on</strong>itor detectors . . . . . . . . . . . . . . . . . . . . . . . . . . . 101<br />
Calorimeters . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 102<br />
Solid state devices . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 103<br />
7.3 Phot<strong>on</strong>-energy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 104<br />
I<strong>on</strong> time-of-flight . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 104<br />
Electr<strong>on</strong> time-of-flight . . . . . . . . . . . . . . . . . . . . . . . . . . . 106<br />
8 Beam cross-secti<strong>on</strong> diagnostics 109<br />
8.1 Introducti<strong>on</strong> . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 109<br />
The ideal cross-secti<strong>on</strong> diagnostic . . . . . . . . . . . . . . . . . . . . . 109<br />
Distributi<strong>on</strong> of diagnostics al<strong>on</strong>g <strong>the</strong> <strong>beam</strong> . . . . . . . . . . . . . . . . 110<br />
C<strong>on</strong>tent of this chapter . . . . . . . . . . . . . . . . . . . . . . . . . . . 111<br />
8.2 Definiti<strong>on</strong>s . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 112<br />
8.3 Direct imaging of <strong>the</strong> <strong>beam</strong> . . . . . . . . . . . . . . . . . . . . . . . . 113<br />
Imaging a replica of <strong>the</strong> <strong>beam</strong> . . . . . . . . . . . . . . . . . . . . . . . 114<br />
Summary of imaging techniques . . . . . . . . . . . . . . . . . . . . . . 117<br />
8.4 Scanning techniques . . . . . . . . . . . . . . . . . . . . . . . . . . . . 117<br />
Scanning wire . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 117<br />
Scanning crossed wires . . . . . . . . . . . . . . . . . . . . . . . . . . . 118<br />
Scanning slit . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 118<br />
Scanning pinhole . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 119<br />
Scanning knife-edge . . . . . . . . . . . . . . . . . . . . . . . . . . . . 119<br />
Summary of scanning techniques . . . . . . . . . . . . . . . . . . . . . 119<br />
8.5 I<strong>on</strong>izati<strong>on</strong> <strong>beam</strong>profile detectors . . . . . . . . . . . . . . . . . . . . . . 120<br />
8.6 Imaging i<strong>on</strong> chambers . . . . . . . . . . . . . . . . . . . . . . . . . . . 120<br />
Fluorescence detecti<strong>on</strong> in residual gas m<strong>on</strong>itors . . . . . . . . . . . . . 124<br />
8.7 Sampling techniques . . . . . . . . . . . . . . . . . . . . . . . . . . . . 126<br />
8.8 Spot size . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 129<br />
Techniques useable with unattenuated <strong>beam</strong>s . . . . . . . . . . . . . . 129<br />
Photoi<strong>on</strong>isati<strong>on</strong> saturati<strong>on</strong> of rare gases . . . . . . . . . . . . . . . . . 130<br />
8.9 Techniques requiring attenuated <strong>beam</strong>s . . . . . . . . . . . . . . . . . . 131<br />
Wire, knife-edge <strong>and</strong> slit scans . . . . . . . . . . . . . . . . . . . . . . 131
viii C<strong>on</strong>tents<br />
Photographic film . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 131<br />
Gas-filled detectors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 132<br />
Charge coupled device (CCD) . . . . . . . . . . . . . . . . . . . . . . . 132<br />
Multichannel plate (MCP) . . . . . . . . . . . . . . . . . . . . . . . . . 133<br />
Solid State Detectors . . . . . . . . . . . . . . . . . . . . . . . . . . . . 133<br />
8.10 Positi<strong>on</strong> <strong>and</strong> centroiding . . . . . . . . . . . . . . . . . . . . . . . . . . 133<br />
Sampling techniques . . . . . . . . . . . . . . . . . . . . . . . . . . . . 133<br />
8.11 Wavefr<strong>on</strong>t measurements . . . . . . . . . . . . . . . . . . . . . . . . . . 141<br />
8.12 THz/IR techniques . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 142<br />
Thermal detecti<strong>on</strong> . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 143<br />
Phot<strong>on</strong>ic detecti<strong>on</strong> . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 144<br />
New detectors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 145<br />
IR <strong>and</strong> THz <strong>beam</strong> profiling . . . . . . . . . . . . . . . . . . . . . . . . 145<br />
8.13 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 148<br />
9 Pulse length, profile <strong>and</strong> jitter 151<br />
9.1 Introducti<strong>on</strong> . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 151<br />
9.2 Cross-correlati<strong>on</strong> techniques . . . . . . . . . . . . . . . . . . . . . . . . 153<br />
9.3 Electro-optic techniques . . . . . . . . . . . . . . . . . . . . . . . . . . 155<br />
9.4 Autocorrelati<strong>on</strong> techniques . . . . . . . . . . . . . . . . . . . . . . . . 155<br />
Intensity autocorrelati<strong>on</strong> . . . . . . . . . . . . . . . . . . . . . . . . . . 156<br />
Autocorrelati<strong>on</strong> techniques for complete pulse characterizati<strong>on</strong> . . . . 159<br />
Frequency Resolved Optical Gating (FROG) . . . . . . . . . . . . . . 160<br />
Polarizati<strong>on</strong>-gate FROG (PG FROG) . . . . . . . . . . . . . . . . . . 162<br />
Self-diffracti<strong>on</strong> FROG (SD FROG) . . . . . . . . . . . . . . . . . . . . 163<br />
Transient-grating FROG (TG FROG) . . . . . . . . . . . . . . . . . . 163<br />
Sec<strong>on</strong>d-harm<strong>on</strong>ic-generati<strong>on</strong> FROG (SHG FROG) . . . . . . . . . . . 163<br />
Third-harm<strong>on</strong>ic-generati<strong>on</strong> FROG (THG FROG) . . . . . . . . . . . . 164<br />
9.5 Spectral Phase Interferometry for Direct Electric-field Rec<strong>on</strong>structi<strong>on</strong> 165<br />
9.6 Reflectivity modulati<strong>on</strong> . . . . . . . . . . . . . . . . . . . . . . . . . . 166<br />
9.7 Streak cameras . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 167<br />
9.8 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 168<br />
10 Free electr<strong>on</strong> laser experiments 173<br />
10.1 The ”holy grails” of free electr<strong>on</strong> laser experiments . . . . . . . . . . . 173<br />
”Molecular movies” . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 173<br />
”Single-molecule/nanostructure imaging” . . . . . . . . . . . . . . . . 174<br />
”Single-shot spectroscopy/imaging” . . . . . . . . . . . . . . . . . . . . 174<br />
10.2 Time-resolved spectroscopies . . . . . . . . . . . . . . . . . . . . . . . 174<br />
UV/Vis pump-X-ray probe spectroscopy . . . . . . . . . . . . . . . . . 174<br />
Nexafs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 175<br />
10.3 Imaging <strong>and</strong> Crystallography . . . . . . . . . . . . . . . . . . . . . . . 175<br />
10.4 N<strong>on</strong>-linear X-ray science . . . . . . . . . . . . . . . . . . . . . . . . . . 176<br />
Photoi<strong>on</strong>izati<strong>on</strong> . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 176<br />
11 Free Electr<strong>on</strong> Laser facilities 179<br />
11.1 Operating facilities . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 180<br />
11.2 Flash . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 180<br />
Injector <strong>and</strong> accelerator . . . . . . . . . . . . . . . . . . . . . . . . . . 181
C<strong>on</strong>tents ix<br />
Undulators . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 181<br />
sFlash . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 181<br />
Flash-II . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 181<br />
Experimental stati<strong>on</strong>s: . . . . . . . . . . . . . . . . . . . . . . . . . . . 182<br />
11.3 Scss <strong>–</strong> X-fel . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 183<br />
Scss . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 183<br />
Injector & accelerator . . . . . . . . . . . . . . . . . . . . . . . . . . . 183<br />
Undulators . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 183<br />
X-ray free electr<strong>on</strong> laser/ Spring-8 . . . . . . . . . . . . . . . . . . . . 183<br />
Injector & accelerator . . . . . . . . . . . . . . . . . . . . . . . . . . . 183<br />
Undulators . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 184<br />
11.4 Fermi@Elettra . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 184<br />
Injector & accelerator . . . . . . . . . . . . . . . . . . . . . . . . . . . 184<br />
Undulators . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 184<br />
Experiments: . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 185<br />
11.5 Lcls <strong>–</strong> Linac Coherent Light Source . . . . . . . . . . . . . . . . 186<br />
Injector <strong>and</strong> accelerator . . . . . . . . . . . . . . . . . . . . . . . . . . 186<br />
Undulators . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 186<br />
Lcls-II proposal . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 186<br />
Experiments: . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 187<br />
11.6 Facilities under c<strong>on</strong>structi<strong>on</strong> . . . . . . . . . . . . . . . . . . . . . . . . 188<br />
11.7 The European Xfel . . . . . . . . . . . . . . . . . . . . . . . . . . . 188<br />
Injector <strong>and</strong> accelerator . . . . . . . . . . . . . . . . . . . . . . . . . . 188<br />
Undulators . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 188<br />
Experiments: . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 189<br />
11.8 SwissFEL . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 190<br />
SwissFEL injector test facility . . . . . . . . . . . . . . . . . . . . . . 190<br />
<strong>the</strong> SwissFEL proposal . . . . . . . . . . . . . . . . . . . . . . . . . . 190<br />
Injector & accelerator . . . . . . . . . . . . . . . . . . . . . . . . . . . 191<br />
Undulators . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 191<br />
Experiments . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 191<br />
11.9 Proposed facilities . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 192<br />
11.10PAL-X-fel . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 192<br />
Accelerator . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 192<br />
Undulators . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 192<br />
12 Outlook & C<strong>on</strong>clusi<strong>on</strong>s 195<br />
12.1 Current trends . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 195<br />
More compact sources <strong>and</strong> alternative approaches . . . . . . . . . . . . 195<br />
Higher repetiti<strong>on</strong> rates . . . . . . . . . . . . . . . . . . . . . . . . . . . 196<br />
Polarizati<strong>on</strong> c<strong>on</strong>trol . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 196<br />
Coherence & Seeding . . . . . . . . . . . . . . . . . . . . . . . . . . . . 197<br />
Harder X-rays . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 198<br />
12.2 C<strong>on</strong>clusi<strong>on</strong> . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 199<br />
Bibliography 201
Part I<br />
Free electr<strong>on</strong> lasers <strong>–</strong> a primer
1. Introducti<strong>on</strong><br />
Written by: A. Lindblad<br />
1.1 Historical exposé & scientific background<br />
Ever since <strong>the</strong> advent of electricity it has been possible for humankind to produce<br />
artificial light sources not emanating from chemical processes, i.e. different from c<strong>and</strong>les,<br />
b<strong>on</strong>-fires, <strong>and</strong> <strong>the</strong> like. With <strong>the</strong> discovery of X-rays by Wilhelm Röntgen in<br />
1895 1 for which he subsequently got <strong>the</strong> first Nobel prize in physics 1901.<br />
Hisdiscovery was made possible with <strong>the</strong>adventof vacuum<br />
tube discharge sources in <strong>the</strong> end of <strong>the</strong> 19 th century <strong>–</strong> in<br />
a discharge tube (invented by William Crookes <strong>and</strong> o<strong>the</strong>rs,<br />
Figure 1.1) electr<strong>on</strong>s travel between two electrodes in a gas<br />
tube between which a high electric voltage have been applied,<br />
Röntgen discovered that, even though he covered <strong>the</strong> cathode,<br />
using cardboard, wood, books (<strong>and</strong> seemingly whatever came<br />
in h<strong>and</strong>y) a phosphorous screen placed in <strong>the</strong> o<strong>the</strong>r end of<br />
his laboratory room still glowed. In part II of this book we<br />
will see how such screens are still in use to characterize X-ray<br />
sources 2 .<br />
Figure 1.1: A Crookes tube<br />
from 1910’s.<br />
The interacti<strong>on</strong> of X-ray phot<strong>on</strong>s with matter can generate many answers in <strong>the</strong><br />
scientific inquiry <strong>–</strong> spurred by <strong>the</strong> rapid development of quantum <strong>the</strong>ory <strong>–</strong> <strong>and</strong> thus<br />
our underst<strong>and</strong>ing of atoms <strong>and</strong> matter, combined with <strong>the</strong> development of X-ray<br />
lightsources with ever-increasing quality (Figure 1.3). As evident in <strong>the</strong> short list<br />
below both scientific topics ranging from biology, chemistry <strong>and</strong> physics <strong>and</strong> industrial<br />
research <strong>and</strong> development (notably <strong>the</strong> pharmaceutical industry) have greatly<br />
benefitted from <strong>the</strong> development of this area of science.<br />
• X-ray imaging <strong>–</strong> medical imaging, materials’ science, safety<br />
1 Reported in Über eine neue Art v<strong>on</strong> Strahlen (http://de.wikisource.org/wiki/Ueber eine<br />
neue Art v<strong>on</strong> Strahlen) <strong>–</strong> published <strong>the</strong> December 28, 1895, where Röntgen refers his discovery as<br />
”X-rays” (a noti<strong>on</strong> which <strong>the</strong> modest Röntgen preferred, in many languages this type of radiati<strong>on</strong> is<br />
still known as Röntgen-rays). An english translati<strong>on</strong> can be found in Nature 53, 274<strong>–</strong>276 (January<br />
23, 1886). The discovery was deemed important enough to be translated <strong>and</strong> communicated within<br />
a m<strong>on</strong>th of <strong>the</strong> original publicati<strong>on</strong>.<br />
2 For instance, Secti<strong>on</strong> 8.3, (see page 113)<br />
3
4 1. Introducti<strong>on</strong><br />
• X-ray diffracti<strong>on</strong> <strong>–</strong> crystallography, materials’ science<br />
• X-ray absorpti<strong>on</strong> <strong>and</strong> emissi<strong>on</strong> spectroscopies <strong>–</strong> materials’ science, l<strong>on</strong>g range<br />
order.<br />
• X-ray photoelectr<strong>on</strong> spectroscopies <strong>–</strong> materials’ science, chemical b<strong>on</strong>ds, spinresolved<br />
Ofcourse <strong>the</strong>technological developmentoftechniquesfor particle accelerators, sample<br />
h<strong>and</strong>ling, radiati<strong>on</strong> detecti<strong>on</strong>, vacuum have both received <strong>and</strong> given synergetic effects<br />
in society at large.<br />
High energy phot<strong>on</strong>s or particles from radioactive sources 3 is an alternative as<br />
particle sources, though <strong>the</strong>y lack tunability <strong>and</strong> <strong>the</strong> energy is often too high to be<br />
used for many of <strong>the</strong> important applicati<strong>on</strong>s of X-rays. Applicati<strong>on</strong>s of radioactive<br />
radiati<strong>on</strong> have been found elsewhere, notably in radiati<strong>on</strong> <strong>the</strong>rapy, as gene-markers,<br />
<strong>the</strong> carb<strong>on</strong>-14 age-determinati<strong>on</strong> method etc.<br />
In Ernest Ru<strong>the</strong>rford’s laboratory (1909), Hans Geiger <strong>and</strong> Ernest Marsded used<br />
a <strong>beam</strong> of alpha particles generated from a radioactive decay of <strong>the</strong> element radium<br />
impinging <strong>on</strong> a gold foil to find out how charge was distributed within atoms. They<br />
intended to investigate <strong>the</strong> prevailing plum pudding model 4 where <strong>the</strong> positive charge<br />
was delocalized (<strong>the</strong> pudding) <strong>and</strong> <strong>the</strong> electr<strong>on</strong>s submerged (as <strong>the</strong> plums). The gold<br />
foil was surrounded by a sheet of zinc sulfide which would fluoresce when hit by alpha<br />
particles. From <strong>the</strong> plum model it was expected that <strong>the</strong> alpha particles would not<br />
scatter at all, however it was observed that a significant fracti<strong>on</strong> of <strong>the</strong> alphaparticles<br />
was backscattered by very small c<strong>on</strong>centrated positive charged objects in <strong>the</strong> gold<br />
film <strong>–</strong> this was taken as a str<strong>on</strong>g indicati<strong>on</strong> of <strong>the</strong> existence of an atomic nucleus, a<br />
result which was not expected. In 1911 Ru<strong>the</strong>rford explained <strong>the</strong> experiment in terms<br />
of scattering which resulted in <strong>the</strong> Ru<strong>the</strong>rford ”planetary” model of <strong>the</strong> atom.<br />
In Ru<strong>the</strong>rford’s laboratory significant developments followed this, especially <strong>the</strong><br />
development of particle accelerators with <strong>the</strong> purpose of splitting <strong>the</strong> atom. A note<br />
<strong>on</strong> <strong>the</strong> development of some particle accelerator techniques <strong>and</strong> c<strong>on</strong>cepts emanating<br />
from Ru<strong>the</strong>rford <strong>and</strong> his students, relevant for this book, can be found <strong>on</strong> page 52.<br />
For a lot of medical purposes (<strong>the</strong>rapeutic <strong>and</strong> o<strong>the</strong>rwise) radioactive materials<br />
are increasingly phased out to <strong>the</strong> benefit of particle accelerators where c<strong>on</strong>trol of <strong>the</strong><br />
particle energy is possible <strong>and</strong> thus <strong>the</strong> interacti<strong>on</strong> length <strong>and</strong> dose can be c<strong>on</strong>trolled.<br />
Theories <strong>on</strong> <strong>the</strong> nature of light <strong>–</strong> a small historical primer<br />
In <strong>the</strong> 17 th century investigati<strong>on</strong>s into <strong>the</strong> nature of light were pursued by means<br />
of <strong>the</strong> modern scientific method. Light was thought of as waves or particles <strong>–</strong> both<br />
with <strong>the</strong>ir shortcomings. The discourse between <strong>the</strong> two, seemingly incommensurate,<br />
st<strong>and</strong>points were ultimately resolved by <strong>the</strong> advent of quantum mechanics in <strong>the</strong><br />
beginning of <strong>the</strong> 20 th century <strong>–</strong> which argue that light (<strong>and</strong> matter) can behave both<br />
as waves <strong>and</strong> particles.<br />
3 That is: phot<strong>on</strong>s, electr<strong>on</strong>s or <strong>the</strong>ir antiparticles: positr<strong>on</strong>s, or 4 He nuclei <strong>–</strong> gamma, γ, beta,<br />
β ± <strong>and</strong> alpha, α radiati<strong>on</strong>, respectively. The greek names for radiati<strong>on</strong> were all coined by <strong>the</strong><br />
english physicist Ernest Ru<strong>the</strong>rford. For his work <strong>on</strong> radioactivity <strong>–</strong> transmutati<strong>on</strong>, <strong>the</strong> noti<strong>on</strong><br />
of half-life, <strong>and</strong> <strong>the</strong> differentiati<strong>on</strong> between alpha <strong>and</strong> beta rays <strong>–</strong> he received <strong>the</strong> Nobel prize in<br />
chemistry 1908.<br />
4 The plum pudding model of <strong>the</strong> atom was proposed by J. J. Thoms<strong>on</strong> in 1904.
1.1. Historical exposé & scientific background 5<br />
Robert Hooke <strong>and</strong> Christiaan Huygens both published <strong>the</strong>ories (In <strong>the</strong> 1660s <strong>and</strong><br />
late 1670s respectively) <strong>on</strong> light that built <strong>on</strong> light rays being waves. The main<br />
propositi<strong>on</strong> was that light, being waves, would not be affected by gravity <strong>–</strong> thus<br />
slowing down up<strong>on</strong> entering a denser medium. The wave <strong>the</strong>ory though assumed <strong>the</strong><br />
existence of a medium in which <strong>the</strong> waves could propagate through: <strong>the</strong> luminiferous<br />
æ<strong>the</strong>r 5 .<br />
Isaac Newt<strong>on</strong> described light as particles (corpuscles) to explain reflecti<strong>on</strong> of light<br />
(Opticks, 1704). Perhaps owing to his work <strong>on</strong> gravity, he postulated that <strong>the</strong> corpuscles<br />
were accelerated when <strong>the</strong>y entered a denser medium, because of <strong>the</strong> larger<br />
gravitati<strong>on</strong>al influence <strong>on</strong> <strong>the</strong> particles from <strong>the</strong> medium, which helped explain refracti<strong>on</strong>.<br />
Nowadays we know that this was a step in <strong>the</strong> wr<strong>on</strong>g directi<strong>on</strong> since <strong>the</strong><br />
speed of light is slower in a denser medium than in a dilute medium.<br />
Investigati<strong>on</strong>s into <strong>the</strong> various properties of light such as refracti<strong>on</strong>, reflecti<strong>on</strong>,<br />
polarizati<strong>on</strong> <strong>and</strong> diffracti<strong>on</strong> undertaken in <strong>the</strong> beginning of <strong>the</strong> 19 th century tilted<br />
<strong>the</strong> balance in favor of <strong>the</strong> wave <strong>the</strong>ory. However <strong>–</strong> as both <strong>the</strong>ories made different<br />
predicti<strong>on</strong>s <strong>on</strong> how <strong>the</strong> speed of light changed up<strong>on</strong> entering a denser medium <strong>–</strong> <strong>the</strong><br />
most c<strong>on</strong>vincing test to be made, i.e. measuring <strong>the</strong> actual speed of light had to wait<br />
until 1850 <strong>and</strong> Lé<strong>on</strong> Focault for a precise enough experiment to be performed 6 . His<br />
results favored <strong>the</strong> wave <strong>the</strong>ory of light <strong>and</strong> thus put <strong>the</strong> particle <strong>the</strong>ory of light out<br />
of <strong>the</strong> scientific limelight<br />
In <strong>the</strong> later part of <strong>the</strong> 19 th century James Clerk Maxwell formulated <strong>the</strong> governing<br />
equati<strong>on</strong>s of electromagnetism. His <strong>the</strong>ory built <strong>on</strong> that electromagnetic waves<br />
travelled at a c<strong>on</strong>stant speed <strong>–</strong> equal to <strong>the</strong> speed of light. 1862 he published <strong>the</strong><br />
noti<strong>on</strong> that light was a form of electromagnetic wave in On <strong>the</strong> physical lines of force.<br />
A full <strong>the</strong>ory, describing ma<strong>the</strong>matically <strong>the</strong> behavior of electric <strong>and</strong> magnetic fields <strong>–</strong><br />
<strong>the</strong> celebrated Maxwell’s equati<strong>on</strong>s 7 <strong>–</strong> was published in 1873 by Maxwell in A treatise<br />
<strong>on</strong> electricity <strong>and</strong> magnetism 8 . Heinrich Hertz c<strong>on</strong>firmed Maxwell’s <strong>the</strong>ory by generating<br />
<strong>and</strong> detecting radiowaves in a laboratory setting <strong>and</strong> proving that radiowaves<br />
5<br />
The existence of <strong>the</strong> æ<strong>the</strong>r medium was cast into str<strong>on</strong>g doubt by <strong>the</strong> famous Michels<strong>on</strong>-<br />
Morley experiment (this is <strong>the</strong> Michels<strong>on</strong> with <strong>the</strong> interferometer setup). They reas<strong>on</strong>ed al<strong>on</strong>g <strong>the</strong><br />
following lines: when <strong>the</strong> earth revolves around <strong>the</strong> sun it should produce a substantial wind in <strong>the</strong><br />
æ<strong>the</strong>r medium <strong>–</strong> thus, <strong>the</strong> speed of light would be slightly different depending <strong>on</strong> <strong>the</strong> experiment<br />
(at <strong>the</strong> earth surface) was facing <strong>the</strong> wind (foul wind) or facing from <strong>the</strong> wind (fair wind). The<br />
changes in speed of light, both daily <strong>and</strong> seas<strong>on</strong>al, was expected to be very small <strong>–</strong> hence <strong>the</strong> need<br />
for an interferometer which would split up a <strong>beam</strong> <strong>and</strong> propagate <strong>the</strong> <strong>beam</strong>s al<strong>on</strong>g l<strong>on</strong>g arms <strong>and</strong><br />
recombine <strong>the</strong>m, which would produce a interference pattern if <strong>the</strong> <strong>beam</strong>s did not propagate in<br />
<strong>the</strong> same manner, i.e. a <strong>beam</strong> propagating parallel to <strong>the</strong> æ<strong>the</strong>r wind would propagate slower than<br />
<strong>on</strong>e propagating perpendicular. Michels<strong>on</strong> <strong>and</strong> Morley combined <strong>the</strong>ir efforts in 1887 <strong>and</strong> <strong>the</strong>ir<br />
experiments cast doubt <strong>on</strong>, but did not disprove, <strong>the</strong> existence of <strong>the</strong> æ<strong>the</strong>r medium; <strong>the</strong>ir most<br />
important c<strong>on</strong>tributi<strong>on</strong> remains <strong>the</strong> interferometer that bears <strong>the</strong>ir names.<br />
6<br />
The Fizeau-Focault apparatus c<strong>on</strong>sisted of a light source <strong>and</strong> a two mirrors spaced 35 kilometers<br />
apart. The mirror closet to <strong>the</strong> lightsource was rotating at a c<strong>on</strong>stant angular rate. The elapsed<br />
time for <strong>the</strong> light to pass <strong>the</strong> distance ℓ between <strong>the</strong> mirrors is 2ℓ/c (c being <strong>the</strong> speed of light).<br />
During <strong>the</strong> flight of <strong>the</strong> light <strong>the</strong> moving mirror will have rotated away from its original positi<strong>on</strong>.<br />
The angle at which <strong>the</strong> returning light is observed is <strong>the</strong>n α = dα 2h<br />
dt c . A drawing of <strong>the</strong> original<br />
experiment can be found at: http://imgbase-scd-ulp.u-strasbg.fr/displayimage.php?pos=-212905<br />
(From his collected works Volume Two - Recueil des travaux scientifiques de Lé<strong>on</strong> Foucault,<br />
1878).<br />
7<br />
Stated in detail below (see page 23).<br />
8<br />
The basic equati<strong>on</strong>s was in fact published already in 1865 in a paper entitled A dynamical<br />
<strong>the</strong>ory of <strong>the</strong> electromagnetic field[1].
6 1. Introducti<strong>on</strong><br />
exhibited <strong>the</strong> same properties as light waves, e.g. reflecti<strong>on</strong>, refracti<strong>on</strong>, interference<br />
<strong>and</strong> diffracti<strong>on</strong>.<br />
Electromagnetic radiati<strong>on</strong> can i<strong>on</strong>ize atoms. This was discoveredbyHeinrich Hertz<br />
in 1886 in <strong>the</strong> course of <strong>the</strong> inquires described above.<br />
The apparatus Hertz used was a high voltage inducti<strong>on</strong> coil to create a discharge<br />
between two pieces of brass <strong>and</strong> a piece of copper wire with a brass sphere <strong>on</strong> <strong>on</strong>e end<br />
<strong>and</strong> <strong>on</strong> <strong>the</strong> o<strong>the</strong>r a sharp point directed towards <strong>the</strong> sphere. The basic idea is that<br />
<strong>the</strong> charges in <strong>the</strong> discharge oscillate back <strong>and</strong> forth thus emitting electromagnetic<br />
radiati<strong>on</strong>; if <strong>the</strong> emitted light would create ano<strong>the</strong>r spark between <strong>the</strong> tip of <strong>the</strong> wire<br />
<strong>and</strong> <strong>the</strong> brass sphere light would <strong>the</strong>n be proven to be electromagnetic waves.<br />
The photoelectric effect<br />
During 1886, Hertz carried out a series of experiments with his apparatus showing<br />
that electromagnetic waves were reflected through prisms, that it was polarized etc.,<br />
just <strong>the</strong> same properties as light waves. The <strong>on</strong>ly snag was that it sometimes was very<br />
hard to see <strong>the</strong> tiny spark created at <strong>the</strong> wire tip 9 , to improve this Hertz enclosed<br />
<strong>the</strong> wire in a dark casing <strong>–</strong> which reduced <strong>the</strong> intensity of <strong>the</strong> spark. He so<strong>on</strong> found<br />
out that if <strong>the</strong> part of <strong>the</strong> casing shielding <strong>the</strong> discharge was removed <strong>the</strong> intensity<br />
was not reduced <strong>and</strong> that glass, but not quartz, reduced <strong>the</strong> intensity <strong>–</strong> quartz being<br />
transparent to ultra-violet light.<br />
By using a quartz prism to disperse <strong>the</strong> electromagneticwaves<br />
it was also foundthat<strong>the</strong>greatest intensity<br />
of <strong>the</strong> detected spark was obtained in parts of <strong>the</strong> dispersed<br />
light which were above <strong>the</strong> visible range. Hertz<br />
reported his observati<strong>on</strong>s in Annalen der Physik 10 but<br />
offered noexplanati<strong>on</strong>s of <strong>the</strong>phenomena 11 <strong>–</strong> hera<strong>the</strong>r<br />
c<strong>on</strong>cluded that this phenomen<strong>on</strong> was probably of no<br />
practical use whatsoever <strong>–</strong> as we will see below this<br />
was a ra<strong>the</strong>r pessimistic c<strong>on</strong>clusi<strong>on</strong>.<br />
In 1899, J.J. Thomps<strong>on</strong> observed that negative particles<br />
were emitted when a metal surface was exposed<br />
to ultra-violet light. Later, in 1902, P. v<strong>on</strong> Lenard observed<br />
that <strong>the</strong> emitted particles’ kinetic energy 12 did<br />
E kin<br />
f0<br />
frequency f<br />
Figure 1.2: A minimum frequency of<br />
<strong>the</strong> phot<strong>on</strong>s are required to i<strong>on</strong>ize a<br />
material.<br />
depend <strong>on</strong> <strong>the</strong> color (frequency) of <strong>the</strong> light <strong>and</strong> not <strong>on</strong> <strong>the</strong> intensity of <strong>the</strong> light.<br />
In <strong>on</strong>e of his annus mirabilis (1905) papers Einstein gave a ma<strong>the</strong>matical descripti<strong>on</strong><br />
of <strong>the</strong> photoelectric effect[3]. The i<strong>on</strong>izati<strong>on</strong> was described to be caused by <strong>the</strong><br />
absorpti<strong>on</strong> of a ‘light quantum’ <strong>and</strong> that different materials had different <strong>on</strong>set frequencies<br />
f0 for electr<strong>on</strong> emissi<strong>on</strong> was explained by that <strong>the</strong> size of <strong>the</strong> energy packet<br />
needed to be large enough to overcome <strong>the</strong> first i<strong>on</strong>izati<strong>on</strong> potential of <strong>the</strong> material.<br />
9<br />
As <strong>on</strong>e remedy it was suggested that a suitably prepared frog’s leg would serve equally well<br />
as a detector.<br />
10<br />
In, Über einen Einfluss des ultravioletten Lichtes auf die electrische Entladung[2].<br />
11<br />
The spark in <strong>the</strong> detector was enhanced by charges knocked out from <strong>the</strong> material in <strong>the</strong><br />
detector by phot<strong>on</strong>s from <strong>the</strong> ultra-violet parts of <strong>the</strong> spectrum emitted from <strong>the</strong> discharge.<br />
12<br />
More exactly he measured <strong>the</strong> stopping potential of <strong>the</strong> emitted electr<strong>on</strong>s. He performed<br />
<strong>the</strong> experiment by shining light <strong>on</strong> <strong>the</strong> positively charged plate of a parallel plate capacitor <strong>and</strong><br />
observing <strong>the</strong> potential that causes <strong>the</strong> induced current to become zero.
1.2. Laboratory X-ray <strong>and</strong> UV/Vis phot<strong>on</strong> sources 7<br />
For this work he was awarded <strong>the</strong> Nobel prize of physics 1921 “for his services<br />
to Theoretical Physics, <strong>and</strong> especially for his discovery of <strong>the</strong> law of <strong>the</strong> photoelectric<br />
effect”.<br />
The use of quantized energy-levels was used in 1900 by Max Planck to explain <strong>the</strong><br />
distributi<strong>on</strong> of radiati<strong>on</strong> from a black body. To avoid <strong>the</strong> ultra-violet catastrophe of<br />
classical electrodynamics, i.e. that <strong>the</strong> radiati<strong>on</strong> energy distributi<strong>on</strong> tends to infinity<br />
for short wavelengths, he assumed that <strong>the</strong> energy of <strong>the</strong> emitting oscillators was<br />
quantized. By stating that light c<strong>on</strong>sists of discrete energy packets, Einstein could<br />
formulate an equati<strong>on</strong> that explained <strong>the</strong> photoelectric effect:<br />
εkin = �ω −φ<br />
where <strong>the</strong> kinetic energy of <strong>the</strong> photoelectr<strong>on</strong> is related to <strong>the</strong> frequency of <strong>the</strong> light<br />
<strong>and</strong> <strong>the</strong> work needed to escape <strong>the</strong> material. � is Planck’s c<strong>on</strong>stant (divided by 2π)<br />
<strong>and</strong> ω = 2πf is <strong>the</strong> angular frequency of <strong>the</strong> light. The slope of <strong>the</strong> line in Figure 1.2<br />
is thus Planck’s c<strong>on</strong>stant.<br />
In secti<strong>on</strong> 3.2, we will see how <strong>the</strong> photoelectric effect is utilized as <strong>on</strong>e way to<br />
provide a high quality source of electr<strong>on</strong>s to be used in accelerators. The effect also<br />
forms <strong>the</strong> basis for electr<strong>on</strong> spectroscopy which is an important experimental field as<br />
well as a diagnostic possibility for free electr<strong>on</strong> laser light sources (as elaborated up<strong>on</strong><br />
in Secti<strong>on</strong> 7.3).<br />
1.2 Laboratory X-ray <strong>and</strong> UV/Vis phot<strong>on</strong> sources<br />
Peak brilliance [Phot./(s⋅ mrad 2 ⋅ mm 2 ⋅ 0.1% b<strong>and</strong>w.)]<br />
10 35<br />
10 30<br />
10 25<br />
10 20<br />
10 15<br />
10 10<br />
X-ray tubes<br />
Peak Brilliance of X−ray sources<br />
3rd gen. synchrotr<strong>on</strong>s<br />
2nd gen. synchrotr<strong>on</strong>s<br />
X-FEL<br />
10<br />
1850 1900 1950 2000 2050<br />
5<br />
Time<br />
Average brilliance [Phot./(s ⋅ mrad 2 ⋅ mm 2 ⋅ 0.1% b<strong>and</strong>w.)]<br />
10 30<br />
10 25<br />
10 20<br />
10 15<br />
10 10<br />
X-ray tubes<br />
Average brilliance of X−ray sources<br />
3rd gen. synchrotr<strong>on</strong>s<br />
2nd gen. synchrotr<strong>on</strong>s<br />
1st gen. synchrotr<strong>on</strong>s 1st gen. synchrotr<strong>on</strong>s<br />
X-FEL<br />
10<br />
1850 1900 1950 2000 2050<br />
5<br />
Time<br />
Figure 1.3: Development of <strong>the</strong> brilliance of man-made X-ray sources. The brilliance is a measurement of <strong>beam</strong><br />
quality that measures how directi<strong>on</strong>al <strong>and</strong> pointy a source in combinati<strong>on</strong> by how str<strong>on</strong>gly it emits light within<br />
a certain b<strong>and</strong>width, (see page 19).
8 1. Introducti<strong>on</strong><br />
Vanode<br />
V<br />
- +<br />
X-rays<br />
Figure 1.5: A schematic of an improved Crooks tube Figure 1.1.<br />
Water out<br />
Water in<br />
ThedevelopmentofX-raysources withrespectintensity<strong>and</strong>source qualityhave, as<br />
shown in Figure 1.3 developed superexp<strong>on</strong>entially 13 since <strong>the</strong> end of <strong>the</strong> 19 th century.<br />
A technological development like this is logical, when <strong>on</strong>e c<strong>on</strong>siders <strong>the</strong> accumulated<br />
knowledge of relevant physics <strong>and</strong> related areas 14 .<br />
When <strong>the</strong> X-ray tubes reached <strong>the</strong>ir optimum potential,<br />
that is when <strong>the</strong> effort in terms of time <strong>and</strong> m<strong>on</strong>ey did not<br />
yield enough payback to develop <strong>the</strong> technology fur<strong>the</strong>r <strong>–</strong> accelerator<br />
based synchrotr<strong>on</strong> light sources took over as <strong>the</strong> developingtechnology.<br />
Currentlybothsynchrotr<strong>on</strong>storage rings<br />
<strong>and</strong> free electr<strong>on</strong> laser develop in parallel since <strong>the</strong>y satisfies<br />
different dem<strong>and</strong>s from <strong>the</strong> user community.<br />
1 10<br />
�ω [keV]<br />
Figure 1.4: Generic spec-<br />
X-ray tube <strong>and</strong> anode sources<br />
trum of X-rays from a tube<br />
source.<br />
The X-ray tubes used by Wilhelm Röntgen <strong>and</strong> o<strong>the</strong>rs in <strong>the</strong><br />
years leading up to <strong>and</strong> <strong>the</strong> first years into <strong>the</strong> 1900’s was<br />
limited in intensity (<strong>and</strong> brightness) largely by <strong>the</strong> power that<br />
<strong>the</strong> anode could dissipate without melting.<br />
In Figure 1.5 a schematic of an X-ray tube of a model dating from 1913 is shown.<br />
The electr<strong>on</strong>s are produced by <strong>the</strong>rmi<strong>on</strong>ic emissi<strong>on</strong> 15 from a heated tungsten filament<br />
serving as <strong>the</strong> cathode; <strong>the</strong> electr<strong>on</strong>s are accelerated towards an anode target which<br />
is watercooled. This type of tube can produce powers up to 18 kW.<br />
ThegenericX-rayspectrumfrom asourcewhichgeneratesX-raysbybombardment<br />
of a target with electr<strong>on</strong>s is presented in Figure 1.4. On top of a broad feature ranging<br />
over several keV of phot<strong>on</strong>-energies sharp features emanating from discrete atomic<br />
13 That is, for instance, faster than Moore’s law for <strong>the</strong> transistor density of integrated circuits.<br />
14 The rate of publicati<strong>on</strong> in physics <strong>and</strong> chemistry was also growing faster than an exp<strong>on</strong>ential<br />
curve during <strong>the</strong> first part of <strong>the</strong> 20 th century[4].<br />
15 Discussed fur<strong>the</strong>r in <strong>the</strong> c<strong>on</strong>text of electr<strong>on</strong> guns for free electr<strong>on</strong> laser below in Secti<strong>on</strong> 3.2<br />
(see page 47).
1.2. Laboratory X-ray <strong>and</strong> UV/Vis phot<strong>on</strong> sources 9<br />
transiti<strong>on</strong>s in <strong>the</strong> target which generates X-rays with precisely determined energies.<br />
The broad smooth feature arises from bremsstrahlung from electr<strong>on</strong>s that decelerate<br />
in <strong>the</strong> target <strong>and</strong> <strong>the</strong>reby emits X-rays.<br />
An improvement still up<strong>on</strong> this is <strong>the</strong> rotating anode source where <strong>the</strong> area of<br />
illuminati<strong>on</strong> is increased to allow more efficient cooling of <strong>the</strong> anode by letting it<br />
rotate in vacuum. It is desirable to keep <strong>the</strong> illuminated spot as small as possible<br />
to increase <strong>the</strong> brilliance of <strong>the</strong> source. Since <strong>the</strong> surface temperature of <strong>the</strong> anode<br />
can easily reach above 2000 ◦ C <strong>the</strong> cooling needs to be very efficient <strong>and</strong> <strong>the</strong> rotati<strong>on</strong><br />
speed kept high. Modern rotating anode sources can produce up to 100 kW of X-ray<br />
power thanks to this development.<br />
Rotatinganode sources are amature technology which <strong>the</strong>refore is used for medical<br />
purposes (imaging <strong>and</strong> <strong>the</strong>rapy) <strong>and</strong> as laboratory sources both for scientific research<br />
<strong>and</strong> in industry for material diagnostic purposes.<br />
Synchrotr<strong>on</strong> light sources<br />
First generati<strong>on</strong> synchrotr<strong>on</strong> light sources were particle physics electr<strong>on</strong> storage rings<br />
where <strong>the</strong> synchrotr<strong>on</strong>light producedin <strong>the</strong>dipole magnets (usedtobend<strong>the</strong> electr<strong>on</strong><br />
<strong>beam</strong> in a quasicircular orbit) was used by o<strong>the</strong>rs in a parasitic fashi<strong>on</strong>. For particle<br />
physics experiments, <strong>the</strong> producti<strong>on</strong> of light in <strong>the</strong> accelerating structures is a, more<br />
or less significant, problem. The first observati<strong>on</strong> of man-made synchrotr<strong>on</strong> light was<br />
published in 1947 [5].<br />
Sec<strong>on</strong>d generati<strong>on</strong> synchrotr<strong>on</strong>s were built in <strong>the</strong> early 1970s to dedicatedly supply<br />
synchrotr<strong>on</strong> radiati<strong>on</strong> for a growing number of researchers from various fields; <strong>the</strong><br />
multitude of scientific disciplines attracted by synchrotr<strong>on</strong> radiati<strong>on</strong> can in part be<br />
explained by that <strong>the</strong> emitted spectrum is from <strong>the</strong> infrared to <strong>the</strong> hard x-rays with<br />
an well defined polarisati<strong>on</strong>. The light was still produced in <strong>the</strong> bending magnets<br />
that accelerates <strong>the</strong> electr<strong>on</strong>s so that <strong>the</strong> electr<strong>on</strong>s can be stored in a quasi-circular<br />
orbit.<br />
Third generati<strong>on</strong> synchrotr<strong>on</strong>s are used today<br />
<strong>and</strong> use inserti<strong>on</strong> devices, such as wigglers<br />
<strong>and</strong> undulators[6] to produce radiati<strong>on</strong> with<br />
even higher brilliance <strong>and</strong> power. The inserti<strong>on</strong><br />
devices are periodic magnetic structures (Figure<br />
1.8) which, stated bluntly, makes <strong>the</strong> electr<strong>on</strong>s<br />
turn more often which produces a higher<br />
radiati<strong>on</strong> power than just <strong>on</strong>e bending magnet.<br />
However, since a wiggler do not need to bend<br />
<strong>the</strong> orbit <strong>–</strong> <strong>and</strong> thus ideally should not influence<br />
it <strong>–</strong> <strong>the</strong> magnetic field can be much higher<br />
which not <strong>on</strong>ly increases <strong>the</strong> radiati<strong>on</strong> power<br />
but also shifts <strong>the</strong> wavelength of <strong>the</strong> phot<strong>on</strong>s<br />
upward (which is why wigglers are sometimes<br />
called wavelength shifters). An undulator has<br />
generally a lot more magnetic periods than a<br />
Intensity<br />
Phot<strong>on</strong> energy<br />
Figure 1.6: Typical intensity distributi<strong>on</strong>s from<br />
dipole (dashed), wiggler (red, solid) <strong>and</strong> undulator<br />
(filled) radiati<strong>on</strong>.<br />
wiggler with weaker magnetic fields which keeps <strong>the</strong> deflecti<strong>on</strong>s from <strong>the</strong> central orbit<br />
small such that phot<strong>on</strong>s emitted at an earlier instant can interfere with phot<strong>on</strong>s<br />
emitted at future times which produces a build up of emitted power at certain frequencies.<br />
In chapter 2, we will investigate with some detail <strong>and</strong> rigor <strong>the</strong> properties
10 1. Introducti<strong>on</strong><br />
of undulator radiati<strong>on</strong> <strong>–</strong> as this is a prerequisite for <strong>the</strong> underst<strong>and</strong>ing of <strong>the</strong> free<br />
electr<strong>on</strong> laser formalism.<br />
Figure 1.6 presents how <strong>the</strong> general appearance of <strong>the</strong> spectra from different inserti<strong>on</strong><br />
devices can look like. In <strong>the</strong> case of <strong>the</strong> undulator <strong>the</strong>re is sharp peaks where <strong>the</strong><br />
c<strong>on</strong>diti<strong>on</strong> for positive interference is fulfilled. The peaks are distributed at multiples<br />
of <strong>the</strong> first res<strong>on</strong>ance (i.e. harm<strong>on</strong>ics of <strong>the</strong> fundamental energy where <strong>the</strong> c<strong>on</strong>diti<strong>on</strong><br />
is first fulfilled).<br />
Synchrotr<strong>on</strong> storage rings provide almost a c<strong>on</strong>tinuous source of radiati<strong>on</strong> with<br />
repetiti<strong>on</strong> rates in <strong>the</strong> 100’s of MHz something which gives rise to high average power.<br />
The high repetiti<strong>on</strong> rate is often too much for time-resolved measurements which<br />
is why synchrotr<strong>on</strong>s are sometimes run in ”low filling modes” where <strong>on</strong>ly <strong>on</strong>e or a few<br />
bunches of electr<strong>on</strong>s travel around <strong>the</strong> orbit which brings down <strong>the</strong> repetiti<strong>on</strong> rate to<br />
<strong>the</strong> order of 1 MHz. The bunches are still relatively l<strong>on</strong>g (in <strong>the</strong> order of picosec<strong>on</strong>ds);<br />
experiments dem<strong>and</strong>ing short pulses can use femtosec<strong>on</strong>d laser slicing of <strong>the</strong> electr<strong>on</strong><br />
bunches before <strong>the</strong>y pass through a bending magnet, or undulator, this modulates<br />
part of <strong>the</strong> electr<strong>on</strong> <strong>beam</strong> <strong>and</strong> causes that part of <strong>the</strong> <strong>beam</strong> to emit a short pulse<br />
which is separated from <strong>the</strong> radiati<strong>on</strong> fro <strong>the</strong> majority part of <strong>the</strong> bunch.<br />
Onecan c<strong>on</strong>cludethat synchrotr<strong>on</strong>radiati<strong>on</strong> hasmany attractive properties which,<br />
as menti<strong>on</strong>ed, have made its use widespread over a broad range of scientific communities,<br />
i.e. tunable light with an (extremely) well defined polarizati<strong>on</strong> (which can be<br />
linear, circular or elliptical) available over a very large range of energies. It also have<br />
an inherent timestructure that can be manipulated to provide relatively l<strong>on</strong>g x-ray<br />
pulses in <strong>the</strong> MHz repetiti<strong>on</strong> rate domain; in combinati<strong>on</strong> with lasers o<strong>the</strong>r timestrutures<br />
o<strong>the</strong>r types of time-resolved experiments are enables. A (significant) fracti<strong>on</strong> of<br />
<strong>the</strong> light is also transversely coherent, which enable imaging experiments making use<br />
of <strong>–</strong> for instance <strong>–</strong> phase c<strong>on</strong>trast at X-ray wavelengths.<br />
Lasers<br />
The <strong>the</strong>oretical framework for <strong>the</strong> Laser was laid down by Albert Einstein in his<br />
Zur Quanten<strong>the</strong>orie der Strahlung [7] from 1917. In this paper he detailed how light<br />
quanta are absorbed <strong>and</strong> emitted by atoms 16 . By introducing probabilities for <strong>the</strong><br />
processes of absorpti<strong>on</strong>, sp<strong>on</strong>taneous emissi<strong>on</strong> <strong>and</strong> stimulated emissi<strong>on</strong> he was able<br />
to quantify how atomic spectral lines was formed.<br />
The processes of absorpti<strong>on</strong> <strong>and</strong> emissi<strong>on</strong> of light works in <strong>the</strong> intuitive way; Stimulated<br />
emissi<strong>on</strong> describes how <strong>the</strong> presence of electromagnetic radiati<strong>on</strong> causes atoms<br />
in a higher energy state to decay into a lower <strong>on</strong>e. One can <strong>the</strong>n imagine a process<br />
where, if we were to pump atoms to a higher energy state, decays from this state will<br />
<strong>the</strong>n in turn stimulate o<strong>the</strong>r atoms in <strong>the</strong> ensemble to decay to.<br />
If, in a medium, <strong>the</strong> number of atoms in <strong>the</strong> higher energy state is larger than<br />
<strong>the</strong> number in <strong>the</strong> lower energy state <strong>the</strong> amount of stimulated emissi<strong>on</strong> is larger<br />
than that absorbed in <strong>the</strong> ensable <strong>–</strong> <strong>the</strong> amount of light in <strong>the</strong> medium is amplified.<br />
By placing this medium between two mirrors, an optical res<strong>on</strong>ator, <strong>the</strong> light passes<br />
through <strong>the</strong> gain medium many times before it is extracted somehow, this gives rise to<br />
an even more efficient amplficati<strong>on</strong>: we have a proper laser. The word (or acr<strong>on</strong>ym)<br />
Laser can be spelled out to Light Amplificati<strong>on</strong> by Stimulated Emissi<strong>on</strong> of Radiati<strong>on</strong>.<br />
16 Building <strong>on</strong> Max Planck’s seminal paper from 1901 Ueber das Gesetz der Energieverteilung<br />
im Normalspectrum[8] c<strong>on</strong>sidered to be <strong>on</strong>e of <strong>the</strong> birthplaces for quantum <strong>the</strong>ory.
1.2. Laboratory X-ray <strong>and</strong> UV/Vis phot<strong>on</strong> sources 11<br />
The first laser was built in 1960 by T. H. Maiman <strong>and</strong> c<strong>on</strong>sisted of an solid stateflashlamp<br />
pumped artificially grown ruby crystal (emitting red laser light at 694<br />
nanometer wavelength)[9]. Shortly <strong>the</strong>reafter a laser with a gasmixture as a gain<br />
medium was dem<strong>on</strong>strated.<br />
The number of available laser media is large 17 <strong>and</strong> currently covers a wavelength<br />
range between millimeters down to below 200 nm.<br />
There is a multitude of n<strong>on</strong>-linear optical processes that can be used to manipulate<br />
laser light. Of particular interest for <strong>the</strong> lasers to use toge<strong>the</strong>r with free electr<strong>on</strong> lasers<br />
is harm<strong>on</strong>ic generati<strong>on</strong> of shorter wavelengths. This phenomen<strong>on</strong> was first discovered<br />
in a quartz crystal in 1961[10], where integer multiples of <strong>the</strong> driving laser’s frequency<br />
was observed.<br />
Third harm<strong>on</strong>ic generati<strong>on</strong> using a gas as a medium was observed a few years<br />
later[11]. The intensity of <strong>the</strong> generated harm<strong>on</strong>ics drops very fast <strong>–</strong> <strong>the</strong> process can<br />
be understood (in <strong>the</strong> regime of weak fields) as an atom absorbs several phot<strong>on</strong>s which<br />
in turn are emitted as <strong>on</strong>e; <strong>the</strong> probability of absorbing n phot<strong>on</strong>s drops with n.<br />
High Harm<strong>on</strong>ic Generati<strong>on</strong> Lasers<br />
If <strong>on</strong>e ventures out of <strong>the</strong> weak field regime <strong>the</strong>re is a possibility for ano<strong>the</strong>r process<br />
to occur: high harm<strong>on</strong>ic generati<strong>on</strong>. Laser light is sh<strong>on</strong>e into a gas sustaining high<br />
enough energy density (typically in <strong>the</strong> order of 10 14 W/cm 2 a fracti<strong>on</strong> of <strong>the</strong> laser<br />
power can be c<strong>on</strong>verted into (odd) higher harm<strong>on</strong>ics of <strong>the</strong> original laser pulse. This<br />
allows for <strong>the</strong> creati<strong>on</strong> of UV <strong>and</strong> even soft X-ray pulses. Typically <strong>the</strong> repetiti<strong>on</strong><br />
rates for such systems range from a few Hz to KHz (<strong>the</strong> same as <strong>the</strong> driving laser)<br />
<strong>and</strong> even attosec<strong>on</strong>d pulses can be created.<br />
High harm<strong>on</strong>ic generati<strong>on</strong> can be understood via a semi-classical picture[12]: A<br />
sufficiently str<strong>on</strong>g laser field can perturb atomic potentials enough to allow <strong>the</strong> outermost<br />
electr<strong>on</strong>s (illustrated as a red wave-packet in Figure 1.7).<br />
This allows <strong>the</strong> electr<strong>on</strong> wave-functi<strong>on</strong> to tunnel out of <strong>the</strong> atomic potential into<br />
<strong>the</strong> c<strong>on</strong>tinuum (2 in <strong>the</strong> figure) during <strong>the</strong> first half cycle of <strong>the</strong> laser pulse; during<br />
<strong>the</strong> sec<strong>on</strong>d part of <strong>the</strong> laser cycle <strong>the</strong> electr<strong>on</strong> wavefuncti<strong>on</strong> finds itself <strong>on</strong> a str<strong>on</strong>gly<br />
attractive potential leading back to <strong>the</strong> atom where it came from <strong>–</strong> up<strong>on</strong> recombinati<strong>on</strong><br />
<strong>the</strong> system will emit <strong>the</strong> excess energy as a high energy phot<strong>on</strong> with significantly<br />
higher energy than that of <strong>the</strong> driving laser. There is also <strong>the</strong> possibility of higher<br />
harm<strong>on</strong>ics of this moti<strong>on</strong> to occur <strong>and</strong> <strong>the</strong>nce higher phot<strong>on</strong> energies.<br />
Unlike in <strong>the</strong> weak field regime <strong>the</strong> intensity of <strong>the</strong> higher harm<strong>on</strong>ics do not drop<br />
with <strong>the</strong> harm<strong>on</strong>ic number in a simple decreasing manner. Indeed, <strong>the</strong> higher harm<strong>on</strong>ics<br />
have roughly <strong>the</strong> same intensities up until a cut-off energy.<br />
This cut-off energy can be understood from <strong>the</strong> recombinati<strong>on</strong> model menti<strong>on</strong>ed<br />
above, with <strong>the</strong> i<strong>on</strong>izati<strong>on</strong> potential of <strong>the</strong> medium being Ip:<br />
Ecut-off = Ip +3.17·Up<br />
<strong>and</strong> <strong>the</strong> p<strong>on</strong>dermotive energy being <strong>the</strong> average energy of a free electr<strong>on</strong> in <strong>the</strong> linearly<br />
polarized laser field E (with angular frequency ω.<br />
Up = e2 E 2<br />
4meω 2<br />
17 Diagram of laser lines from commercially available sources:<br />
http://en.wikipedia.org/wiki/File:Commercial laser lines.svg
12 1. Introducti<strong>on</strong><br />
Laser field<br />
1<br />
3<br />
X-ray phot<strong>on</strong><br />
Figure 1.7: Illusrati<strong>on</strong> of <strong>the</strong> high harm<strong>on</strong>ic generati<strong>on</strong> process.<br />
This process is effective (that is, it works) for linearly polarized light <strong>–</strong> elliptically<br />
polarized light accelerates <strong>the</strong> electr<strong>on</strong>s in such a way that it misses <strong>the</strong> i<strong>on</strong>ized atom<br />
<strong>on</strong> <strong>on</strong> <strong>the</strong> returning path so no recombinati<strong>on</strong> occur. At very high energy densities<br />
(10 16 W/cm 2 ) <strong>the</strong> ”magnetic” term in <strong>the</strong> Lorentz force equati<strong>on</strong> (Equati<strong>on</strong> 2.5)<br />
becomes significant, which causes <strong>the</strong> accelerati<strong>on</strong> to deviate from <strong>the</strong> intended return<br />
path.<br />
In <strong>the</strong> c<strong>on</strong>text of free electr<strong>on</strong> lasers, ordinary lasers <strong>and</strong> high harm<strong>on</strong>ic generati<strong>on</strong><br />
lasers are interesting both for experiments in combinati<strong>on</strong> with free electr<strong>on</strong> laser radiati<strong>on</strong>,i.e.<br />
two-color experiments as discussed in chapter 10, <strong>and</strong> as a way to increase<br />
<strong>the</strong> quality of <strong>the</strong> free electr<strong>on</strong> laser light in ways that will be elaborated up<strong>on</strong> below<br />
(see page 15).<br />
1.3 Free electr<strong>on</strong> Lasers<br />
In a c<strong>on</strong>venti<strong>on</strong>al laser <strong>the</strong> average output power is limited by how much of <strong>the</strong> unused<br />
power (which is significantly larger than <strong>the</strong> output power) that can be dissipated by<br />
<strong>the</strong> active medium. Moreover <strong>the</strong> light from a laser is seldom diffracti<strong>on</strong> limited<br />
owing to heat effects in <strong>the</strong> lasing medium <strong>and</strong> n<strong>on</strong>-linear processes taking place in<br />
<strong>the</strong> medium.<br />
C<strong>on</strong>trasting this is <strong>the</strong> free electr<strong>on</strong> laser process which can be close to unity in<br />
efficiency. In a free electr<strong>on</strong> laser <strong>the</strong> amplificati<strong>on</strong> of <strong>the</strong> electromagnetic field occurs<br />
by <strong>the</strong> interacti<strong>on</strong> between an electr<strong>on</strong> <strong>beam</strong> <strong>and</strong> <strong>the</strong> radiati<strong>on</strong> field it creates when<br />
moving through a periodic magnetic structure. Hence <strong>the</strong> operating wavelength is<br />
tunable via machine parameters such as electr<strong>on</strong> <strong>beam</strong> energy, <strong>and</strong> magnetic field<br />
strength.<br />
Figure 1.8 depicts three different ways of producing free electr<strong>on</strong> laser radiati<strong>on</strong>:<br />
bunches in a storage ring passes through a l<strong>on</strong>g undulator; an oscillator where <strong>the</strong><br />
interacti<strong>on</strong> where <strong>the</strong> electromagnetic radiati<strong>on</strong> interacts with <strong>the</strong> electr<strong>on</strong> bunches<br />
many times; an amplifier, where <strong>the</strong> electr<strong>on</strong>s pass <strong>on</strong>ce through an l<strong>on</strong>g undulator<br />
structure <strong>–</strong> <strong>the</strong> interacti<strong>on</strong> between <strong>the</strong> electromagnetic field <strong>and</strong> <strong>the</strong> electr<strong>on</strong> <strong>beam</strong><br />
is str<strong>on</strong>g enough for <strong>on</strong>e pass to be sufficient.<br />
2
1.3. Free electr<strong>on</strong> Lasers 13<br />
Figure 1.8: Different ways of generating coherent laser radiati<strong>on</strong>. From left to right, electr<strong>on</strong>s are fed into a<br />
l<strong>on</strong>g undulator ei<strong>the</strong>r from a storage ring or in a storage ring but with mirrors that reflect part of <strong>the</strong> pulse to<br />
modulate <strong>the</strong> electr<strong>on</strong> bunch even fur<strong>the</strong>r, or from a linear accelerator where <strong>the</strong> electr<strong>on</strong> bunch gets modulated<br />
by <strong>the</strong> light field it generates.<br />
There is a number of free electr<strong>on</strong> lasers operating in <strong>the</strong> world today (chapter 11),<br />
covering light wavelengths from <strong>the</strong> infrared to <strong>the</strong> x-ray regi<strong>on</strong>s. This book will cover<br />
free electr<strong>on</strong> lasers that are providing light in <strong>the</strong> X-ray range, which are amplifiers<br />
operating in <strong>the</strong> high-gain regime.<br />
Sase<br />
The physical process that governs <strong>the</strong> functi<strong>on</strong> of a free electr<strong>on</strong> laser is abbreviates<br />
Sase <strong>–</strong> Self-Amplified Sp<strong>on</strong>taneous Emissi<strong>on</strong>. In <strong>the</strong> next chapter we will discuss this<br />
in more detail, here follows a short introducti<strong>on</strong>.<br />
The spectrum from <strong>the</strong> phot<strong>on</strong>s emitted from an electr<strong>on</strong> bunch traveling through<br />
an undulator will c<strong>on</strong>tain a large degree of incoherent radiati<strong>on</strong> <strong>and</strong> a small part of<br />
coherent radiati<strong>on</strong>. The latter occurs since a small number of electr<strong>on</strong>s, by chance,<br />
happentoberadiatingcoherently. In<strong>the</strong>undulatorspectrumthus, anumberofspikes<br />
will be seen <strong>on</strong> top of <strong>the</strong> broad sp<strong>on</strong>taneous emissi<strong>on</strong> spectrum. As <strong>the</strong> occurrence<br />
Log radiati<strong>on</strong> power<br />
Distance<br />
Figure 1.9: Growth of <strong>the</strong> radiated power in a Sase-mode as a functi<strong>on</strong> of travelled distance in <strong>the</strong> undulator.<br />
The process saturates when <strong>the</strong> microbunching is maximal.
14 1. Introducti<strong>on</strong><br />
Phot<strong>on</strong>s/s 0.03% BW<br />
10 25<br />
10 23<br />
10 21<br />
10 19<br />
1 10 100 1000<br />
Phot<strong>on</strong> energy [eV]<br />
Figure 1.10: Computed Phot<strong>on</strong> flux into 0.03% b<strong>and</strong>width at 3.63 kA at <strong>the</strong> Lcls at 1.5 ˚A wavelength. The<br />
two spikes are <strong>the</strong> 1 st <strong>and</strong> 3 rd harm<strong>on</strong>ics of <strong>the</strong> fundamental Sase mode, which sits <strong>on</strong> a broad sp<strong>on</strong>taneous<br />
radiati<strong>on</strong> background.<br />
of <strong>the</strong> coherent radiati<strong>on</strong> is r<strong>and</strong>om <strong>the</strong> number of coherently radiating modes per<br />
electr<strong>on</strong> bunch will follow a Poiss<strong>on</strong> distributi<strong>on</strong>.<br />
The radiati<strong>on</strong> field that is created from <strong>the</strong> accelerati<strong>on</strong> of <strong>the</strong> electr<strong>on</strong> bunch<br />
through an undulator in a storage ring is often c<strong>on</strong>sidered to be weak enough as to<br />
not have an effect <strong>on</strong> <strong>the</strong> electr<strong>on</strong> bunch, i.e. <strong>the</strong> electr<strong>on</strong> bunches do not interact<br />
with <strong>the</strong> radiati<strong>on</strong> field. This is true if <strong>the</strong> electr<strong>on</strong> density is low enough <strong>and</strong> if <strong>the</strong><br />
overlap between <strong>the</strong> radiati<strong>on</strong> field <strong>and</strong> <strong>the</strong> electr<strong>on</strong> <strong>beam</strong> is small.<br />
However, if <strong>the</strong> electr<strong>on</strong> density is high enough <strong>and</strong> if <strong>the</strong> quality, (called emittance<br />
18 ), of <strong>the</strong> electr<strong>on</strong> <strong>beam</strong> is high <strong>the</strong> interacti<strong>on</strong> between <strong>the</strong> electr<strong>on</strong> <strong>beam</strong> <strong>and</strong><br />
<strong>the</strong> radiated field can become substantial.<br />
If<strong>the</strong>interacti<strong>on</strong>between<strong>the</strong>electr<strong>on</strong>s in<strong>the</strong>bunch<strong>and</strong><strong>the</strong>radiati<strong>on</strong>fieldisstr<strong>on</strong>g<br />
enough amicrobunchingof <strong>the</strong> electr<strong>on</strong> bunchoccurs. This means that as <strong>the</strong> electr<strong>on</strong><br />
travelsal<strong>on</strong>g <strong>the</strong>undulatorstructure<strong>the</strong>electr<strong>on</strong> densitybecomes modulatedwith <strong>the</strong><br />
wavelength of <strong>the</strong> radiati<strong>on</strong> field. This enhances <strong>the</strong> coherent emissi<strong>on</strong> fur<strong>the</strong>r, which<br />
in turn enhances <strong>the</strong> micro-bunching <strong>and</strong> amplifies <strong>the</strong> radiati<strong>on</strong> field. The radiati<strong>on</strong><br />
mode thus gets amplified <strong>and</strong> <strong>the</strong> degree of coherence increases. The growth of <strong>the</strong><br />
radiati<strong>on</strong> mode’s strength is exp<strong>on</strong>ential until <strong>the</strong> process saturates.<br />
Free electr<strong>on</strong> laser radiati<strong>on</strong> has a number of unique features owing to <strong>the</strong> amplificati<strong>on</strong><br />
process outlined above. In Figure 1.10 an example of <strong>the</strong> brilliance from <strong>the</strong><br />
Lcls free electr<strong>on</strong> laser source is shown. The peak intensity <strong>and</strong> brilliance is many<br />
orders of magnitude larger than can be produced by o<strong>the</strong>r sources (Figure 1.3). The<br />
18 See <strong>the</strong> discussi<strong>on</strong> <strong>on</strong> emittance below.
1.4. Development of X-ray free electr<strong>on</strong> lasers 15<br />
average brilliance, which is limited by<strong>the</strong> (generally) low repetiti<strong>on</strong> rate of <strong>the</strong> driving<br />
linear accelerators are still orders of magnitudes above that of synchrotr<strong>on</strong> storage<br />
rings. In <strong>the</strong> figure <strong>the</strong> two sharp spikes mark <strong>the</strong> fundamental <strong>and</strong> third harm<strong>on</strong>ics<br />
of <strong>the</strong> Sase radiati<strong>on</strong> modes. Those spikes sit <strong>on</strong> top of a significant sp<strong>on</strong>taneous radiati<strong>on</strong><br />
background that encompasses several orders of magnitude of phot<strong>on</strong> energies.<br />
• Pulse lengths down to tens of femtosec<strong>on</strong>ds are also orders of magnitude shorter<br />
than those of a synchrotr<strong>on</strong>. Ordinary lasers <strong>and</strong> high harm<strong>on</strong>ic generati<strong>on</strong><br />
lasers can surpass this figure but can not deliver <strong>the</strong> brilliance at X-ray wavelengths<br />
c<strong>on</strong>sidered here.<br />
• Free electr<strong>on</strong> laser radiati<strong>on</strong> has full transverse coherence (if <strong>the</strong> Sase process<br />
has reached saturati<strong>on</strong>), i.e. it is diffracti<strong>on</strong> limited.<br />
The Sase process <strong>on</strong>ly amplifies certain modes at <strong>the</strong> time (<strong>and</strong> possibly <strong>the</strong>ir harm<strong>on</strong>ics)<br />
The sp<strong>on</strong>taneous radiati<strong>on</strong> spectrum extends very high up in phot<strong>on</strong> energy,<br />
towards 1 MeV.<br />
1.4 Development of X-ray free electr<strong>on</strong> lasers<br />
The c<strong>on</strong>cept of free electr<strong>on</strong> lasing was developed in <strong>the</strong> early 1970s[13]. The predicti<strong>on</strong><br />
that sp<strong>on</strong>taneous emissi<strong>on</strong> from electr<strong>on</strong> bunches traveling through a periodic<br />
magnetic fieldcould experience exp<strong>on</strong>ential gain was dem<strong>on</strong>strated 1977[14]. The first<br />
free electr<strong>on</strong> laser to reach saturati<strong>on</strong> was <strong>the</strong> Leutl free electr<strong>on</strong> laser located at <strong>the</strong><br />
Advanced Phot<strong>on</strong> Source at <strong>the</strong> Arg<strong>on</strong>ne Nati<strong>on</strong>al Laboratory, Illinois, USA[15].<br />
During<strong>the</strong>1980s <strong>and</strong>1990s asignificantresearcheffortwas c<strong>on</strong>ductedastodevelop<br />
<strong>the</strong> <strong>the</strong>ory for free electr<strong>on</strong> laser as to investigate <strong>the</strong> feasibility of increasing <strong>the</strong><br />
phot<strong>on</strong> energies into <strong>the</strong> UV <strong>and</strong> X-ray ranges[16<strong>–</strong>18]. The first lasing of a hard<br />
X-ray free electr<strong>on</strong> laser occurred in 2009[19].<br />
Around <strong>the</strong> world <strong>the</strong>re is a number of laboratories harboring free electr<strong>on</strong> lasers<br />
operating with phot<strong>on</strong> energies across <strong>the</strong> electromagnetic spectrum, from <strong>the</strong> microwave<br />
regi<strong>on</strong> to <strong>the</strong> hard X-ray regi<strong>on</strong>s.<br />
Facilities for <strong>the</strong> VUV/X-ray regi<strong>on</strong> dem<strong>and</strong> ra<strong>the</strong>r high electr<strong>on</strong> <strong>beam</strong> energies,<br />
thus linear electr<strong>on</strong> accelerators (retired from use for particle physics experiments)<br />
have been fitted with undulators <strong>and</strong> hence c<strong>on</strong>verted to free electr<strong>on</strong> laser; Flash<br />
in Hamburg <strong>and</strong> Lcls in Stanford are from this category. Dedicated facilites for <strong>the</strong><br />
X-ray range are also being deployed, for instance <strong>the</strong> Fermi@Elettra in Italy <strong>and</strong> <strong>the</strong><br />
Scss in Japan. In chapter 11 currently operating facilites <strong>and</strong> some of those under<br />
various stages of commissi<strong>on</strong>ing <strong>and</strong> planning are described in more detail.<br />
1.5 Seeding schemes<br />
As discussed previously, <strong>the</strong> Sase process starts up from shot-noise in <strong>the</strong> electr<strong>on</strong><br />
<strong>beam</strong> <strong>–</strong> thus, even though <strong>the</strong> transverse coherence is very good (optimal) <strong>the</strong> l<strong>on</strong>gitudinal<br />
coherence is poor. This means that <strong>the</strong> phot<strong>on</strong> spectrum is different for<br />
each pulse, both regarding <strong>the</strong> number of modes that are radiating, which frequencies<br />
dominate <strong>the</strong> spectrum <strong>and</strong> <strong>the</strong> <strong>beam</strong> energy.<br />
This can be seen in Figure 1.12: <strong>the</strong> frequency <strong>and</strong> intensity distributi<strong>on</strong> vary <strong>on</strong> a<br />
shot-to-shot basis. Intuitively this phenomen<strong>on</strong> can be understood by c<strong>on</strong>sidering <strong>the</strong>
16 1. Introducti<strong>on</strong><br />
10 3<br />
10 −2<br />
10 −5<br />
0.5×10 −6<br />
10 −8<br />
10 −10<br />
10 −12<br />
Name Radio Microwave Infrared Visible UV X-ray Gamma<br />
Wavelength [m]<br />
Frequency [Hz]<br />
Corresp<strong>on</strong>ding<br />
temperature of<br />
radiating blackbody<br />
Buildings Humans Butterflies Needle Point Protozoans Molecules Atoms Atomic Nuclei<br />
10 4<br />
10 8<br />
10 12<br />
10 15<br />
10 16<br />
10 18<br />
1 K 100 K 10,000 K 10,000,000 K<br />
−272 °C −173 °C 9,727 °C ~10,000,000 °C<br />
Figure 1.11: Wavelengths <strong>and</strong> frequencies in <strong>the</strong> electromagnetic spectrum.<br />
Figure 1.12: The Sase phot<strong>on</strong> spectrum from <strong>the</strong> Flash free electr<strong>on</strong> laser.<br />
stochastic start of <strong>the</strong> amplificati<strong>on</strong> process; in <strong>the</strong> beginning of <strong>the</strong> undulator many<br />
modes radiate energy, those serve as seeding radiati<strong>on</strong> for <strong>the</strong> durati<strong>on</strong> of <strong>the</strong> traversing<br />
of <strong>the</strong> (l<strong>on</strong>g) remainder of <strong>the</strong> undulator. The modes that ”fit” <strong>the</strong> res<strong>on</strong>ance<br />
c<strong>on</strong>diti<strong>on</strong> for <strong>the</strong> undulator spectrum will get progressively more amplified whereas<br />
those modes that are not radiating res<strong>on</strong>antly do not gain in energy. The res<strong>on</strong>ance<br />
c<strong>on</strong>diti<strong>on</strong> may be fulfilled by several modes simultaneously, more or less well which<br />
give rise to many spikes in <strong>the</strong> final spectrum. For each new bunch <strong>the</strong> process start<br />
10 20
1.5. Seeding schemes 17<br />
over again <strong>and</strong> thus a new set of modes arise from <strong>the</strong> stochastic start-up.<br />
Naturally <strong>the</strong>re is a desire to have a more stable free electr<strong>on</strong> laser phot<strong>on</strong> spectrum.<br />
Both <strong>the</strong> jitter in time between pulses, <strong>the</strong> pulse energy <strong>and</strong> <strong>the</strong> spectral<br />
c<strong>on</strong>tent prohibit <strong>the</strong> maximum performance of both <strong>the</strong> free electr<strong>on</strong> laser itself <strong>and</strong><br />
<strong>the</strong> possible experiments that can be performed.<br />
To circumvent <strong>the</strong> stochastic startup of <strong>the</strong> radiati<strong>on</strong>-field amplificati<strong>on</strong> <strong>the</strong> most<br />
straightforward way <strong>–</strong> at least c<strong>on</strong>ceptually <strong>–</strong> is to pre-modulate <strong>the</strong> electr<strong>on</strong> <strong>beam</strong>’s<br />
energy with a str<strong>on</strong>g laser field, <strong>the</strong>n c<strong>on</strong>vert this energy modulati<strong>on</strong> into a density<br />
modulati<strong>on</strong>. The c<strong>on</strong>versi<strong>on</strong> between energy <strong>and</strong> density modulati<strong>on</strong> can be d<strong>on</strong>e in<br />
a magnetic structure (chicane or wiggler/undulator) since <strong>the</strong> different parts of <strong>the</strong><br />
bunch take different paths through such a structure.<br />
eSase<br />
Figure 1.13: Energy modulati<strong>on</strong> of an electr<strong>on</strong> bunch.<br />
If <strong>the</strong> electr<strong>on</strong> bunch are modulated with a laser in a wiggler <strong>and</strong> subsequently pass<br />
through an undulator structure significantly shorter gain length (<strong>and</strong> thus shorter<br />
undulators) can be achieved as compared to normal Sase operati<strong>on</strong> (hence Enhanced-<br />
Sase)[20].<br />
HGHG<br />
ESASE<br />
Modulator Radiator<br />
High-Gain Harm<strong>on</strong>ic-Generati<strong>on</strong> is a frequency upc<strong>on</strong>versi<strong>on</strong> scheme, designed to upc<strong>on</strong>vert<br />
<strong>the</strong> fundamental frequency of <strong>the</strong> laser to a much higher frequency[21].<br />
This scheme has been dem<strong>on</strong>strated[22] <strong>and</strong> it includes a short modulator where<br />
<strong>the</strong> energy-densityc<strong>on</strong>versi<strong>on</strong> starts, followed by a chicane (two bendingmagnets that<br />
bends away <strong>and</strong> returns <strong>the</strong> <strong>beam</strong> al<strong>on</strong>g <strong>the</strong> orignal path). The chicane compresses<br />
<strong>the</strong> bunch fur<strong>the</strong>r which enhances <strong>the</strong> density modulati<strong>on</strong> even more before <strong>the</strong> <strong>beam</strong><br />
enters <strong>the</strong> sec<strong>on</strong>d undulator (<strong>the</strong> radiator) where <strong>the</strong> free electr<strong>on</strong> laser process takes<br />
place. Since <strong>the</strong> electr<strong>on</strong> bunch is pre-modulated when it enters <strong>the</strong> radiator <strong>the</strong><br />
spectrum from this type of free electr<strong>on</strong> laser is significantly more intense in <strong>the</strong><br />
fundamental mode (up to 10 6 times) <strong>and</strong> narrow (since, ideally, all <strong>the</strong> spectral intensity<br />
is put into <strong>on</strong>e mode <strong>and</strong> its harm<strong>on</strong>ics). The shot to shot repeatability is also
18 1. Introducti<strong>on</strong><br />
much better as <strong>the</strong> free electr<strong>on</strong> laser pulse is a up-c<strong>on</strong>verted versi<strong>on</strong> of <strong>the</strong> original<br />
laser pulse (at least <strong>the</strong> part of <strong>the</strong> spectrum arising from <strong>the</strong> part of <strong>the</strong> electr<strong>on</strong><br />
bunch that became modulated)[22]. The Hghg scheme can of course be cascaded,<br />
HGHG<br />
Dispersive secti<strong>on</strong><br />
Modulator Radiator<br />
that is putting several stages in fr<strong>on</strong>t of each o<strong>the</strong>r, to achieve increasingly shorter<br />
wavelengths.<br />
EEHG<br />
The Echo-Enabled Harm<strong>on</strong>ic Generati<strong>on</strong> free electr<strong>on</strong> laser scheme[23] have recently<br />
been dem<strong>on</strong>strated experimentally at <strong>the</strong> Next Linear Collider Test Accelerator at<br />
<strong>the</strong> SLAC Nati<strong>on</strong>al Accelerator Laboratory, Stanford, USA[24].<br />
The principle is similar to that of <strong>the</strong> Hghg scheme above with <strong>the</strong> important<br />
difference that two modulators with two different laser seedings is used before <strong>the</strong> undulator.<br />
This enables more intricate c<strong>on</strong>trol of <strong>the</strong> path differences <strong>the</strong> particles with<br />
different energies takes in <strong>the</strong> two different chicanes <strong>–</strong> allowing <strong>the</strong> density modulati<strong>on</strong><br />
of <strong>the</strong> electr<strong>on</strong>s to occur at a shorter frequency than <strong>the</strong> original laser pulses; at <strong>the</strong><br />
entrance of <strong>the</strong> radiator <strong>on</strong>e can get a pre-bunched electr<strong>on</strong> <strong>beam</strong> for a significantly<br />
shorter wavelength than any of those of <strong>the</strong> seed-lasers.<br />
Harm<strong>on</strong>ic afterburners<br />
Harm<strong>on</strong>ic afterburners c<strong>on</strong>sist of <strong>on</strong>e or more undulators placed after <strong>the</strong> main radiator.<br />
They are ei<strong>the</strong>r used to enhance <strong>the</strong> radiated power in a harm<strong>on</strong>ic of <strong>the</strong><br />
fundamental <strong>–</strong> thus reaching shorter wavelengths[25]. Extra undulators can also be<br />
used to c<strong>on</strong>trol <strong>the</strong> polarizati<strong>on</strong> of <strong>the</strong> emitted light to some degree[26, 27].
1.6. Definiti<strong>on</strong>s used throughout <strong>the</strong> book 19<br />
1.6 Definiti<strong>on</strong>s used throughout <strong>the</strong> book<br />
Brilliance <strong>and</strong> Brightness<br />
The intensity of a source can be regarded as <strong>the</strong> flow of energy per unit time per unit<br />
source area<br />
I = dE<br />
dtdxdy<br />
The flux of a source Φ<br />
Φ =<br />
�<br />
1 dI<br />
ω dω dω<br />
is defined as <strong>the</strong> number of phot<strong>on</strong>s per unit time, per unit surface area of <strong>the</strong> source.<br />
As figures of merit for a light source <strong>the</strong> intensity <strong>and</strong> flux are ra<strong>the</strong>r blunt tools<br />
since <strong>the</strong>y say nothing about <strong>the</strong> directi<strong>on</strong>ality of <strong>the</strong> source. If we differentiate <strong>the</strong><br />
flux with respect to <strong>the</strong> solid angle dΩ we obtain <strong>the</strong> brightness:<br />
B = dΦ<br />
dΩ<br />
with units [phot<strong>on</strong>s/s/mm 2 /mrad].<br />
Brilliance, or spectral brightness[28] is defined as <strong>the</strong> number of phot<strong>on</strong>s emitted<br />
per unit time, per unit solid angle, per unit source area inside a b<strong>and</strong>width chosen to<br />
be 0.1%<br />
Br = d2 Φ<br />
dωdΩ<br />
thus <strong>the</strong> unit [phot<strong>on</strong>s/s/mm 2 /mrad/0.1%BW]. This defines <strong>the</strong> brightness of a<br />
source inside a certain frequency envelope centered around a certain frequency ω.<br />
Spectral brightness is closely related to <strong>the</strong> emittance of <strong>the</strong> of <strong>the</strong> electr<strong>on</strong> <strong>beam</strong><br />
source. The emittance is <strong>the</strong> product of <strong>the</strong> <strong>beam</strong> divergence <strong>and</strong> <strong>the</strong> transverse size<br />
of <strong>the</strong> <strong>beam</strong> al<strong>on</strong>g each directi<strong>on</strong> perpendicular to <strong>the</strong> propagati<strong>on</strong> of <strong>the</strong> electr<strong>on</strong>s.<br />
Emittance<br />
When an ensemble of charged particles propagates through an accelerator <strong>the</strong>y move<br />
al<strong>on</strong>g an orbit through <strong>the</strong> accelerator structure (composed of guiding magnets <strong>and</strong><br />
accelerating cavities etc.). Each particle in <strong>the</strong> ensemble move al<strong>on</strong>g a trajectory,<br />
i.e. <strong>the</strong> orbit is described by <strong>the</strong> ensemble moti<strong>on</strong> is an average of <strong>the</strong> individual<br />
trajectories.<br />
The instantaneous positi<strong>on</strong> of an particle can be described by <strong>the</strong> tripple [x,y,s]<br />
(as defined in Figure 1.15). In a linear accelerator <strong>the</strong> ˆs directi<strong>on</strong> coincides with <strong>the</strong><br />
ˆz coordinate. For a complete descripti<strong>on</strong> of <strong>the</strong> particle’s state we also need to define<br />
coordinates that are proporti<strong>on</strong>al to <strong>the</strong> <strong>the</strong> momentum of <strong>the</strong> particles: [x ′ ,y ′ ,E],<br />
with x ′ = px/p, y ′ = py/p which describe <strong>the</strong> angular deviati<strong>on</strong>, perpendicular to<br />
<strong>the</strong> directi<strong>on</strong> of moti<strong>on</strong>, from <strong>the</strong> ideal orbit. For relativistic particles <strong>the</strong> energy is<br />
approximately equal to <strong>the</strong> particle momentum E ≈ cp. In some instances it is more<br />
c<strong>on</strong>venient to define <strong>the</strong> energy in terms of its deviati<strong>on</strong> from <strong>the</strong> ensemble average,<br />
as this gives a measure which is independent of <strong>the</strong> total energy.
20 1. Introducti<strong>on</strong><br />
10<br />
8<br />
6<br />
4<br />
2<br />
0<br />
2<br />
1<br />
Potential energy surface <strong>and</strong> phase plot<br />
0<br />
X’<br />
−1<br />
Figure 1.14: Part of a quadratic potential energy surface with a phase portrait. The circles describe orbits with<br />
c<strong>on</strong>stant energy, i.e. a particle would move al<strong>on</strong>g those circles.<br />
−2<br />
A <strong>beam</strong> can thus be defined as occupying a certain volume in a 6-dimensi<strong>on</strong>al<br />
phase space. This volume stays c<strong>on</strong>stant if <strong>the</strong> ensemble’s moti<strong>on</strong> is such that <strong>the</strong> total<br />
energy of <strong>the</strong> system do not change (i.e. evolves according to Hamilt<strong>on</strong>’s equati<strong>on</strong>s<br />
of moti<strong>on</strong>) 19 . For c<strong>on</strong>venience <strong>the</strong> phase space of <strong>the</strong> ensemble is usually represented<br />
by two-dimensi<strong>on</strong>al projecti<strong>on</strong>s x,x ′ ; Figure 1.14 shows a phaseportrait <strong>and</strong> a potential<br />
energy surface for a particle moving in a quadratic potential (for instance a<br />
gravitati<strong>on</strong>al force), <strong>the</strong> circles represent orbits with c<strong>on</strong>stant energy.<br />
Horiz<strong>on</strong>tal emittance (for instance al<strong>on</strong>g <strong>the</strong> x directi<strong>on</strong>) εx is <strong>the</strong> area of an ellipse<br />
encompassing <strong>the</strong> majority of <strong>the</strong> particles (usually this is taken to be <strong>the</strong> area of a<br />
root-mean-square (rms) sense). A measure of <strong>the</strong> average phase space area covered by<br />
<strong>the</strong> particles in <strong>the</strong> x,x ′ -plane can <strong>the</strong>n be computed, assuming a distributi<strong>on</strong> al<strong>on</strong>g<br />
<strong>the</strong> ideal orbit such that 〈x〉 = 〈x ′ 〉 = 0<br />
−2<br />
−1<br />
εx = � 〈x 2 〉〈x ′2 〉−〈xx ′ 〉 2<br />
This quantity is c<strong>on</strong>served as l<strong>on</strong>g as <strong>the</strong> moti<strong>on</strong> in this directi<strong>on</strong> is independent from<br />
<strong>the</strong> moti<strong>on</strong> in <strong>the</strong> o<strong>the</strong>r directi<strong>on</strong>s (something which is comm<strong>on</strong> in accelerators)[29].<br />
19 As a c<strong>on</strong>sequence of Liouville’s <strong>the</strong>orem, i.e. that <strong>the</strong> volume in phase space stays c<strong>on</strong>stant if<br />
<strong>the</strong> system evolves under <strong>the</strong> influence of c<strong>on</strong>servative forces <strong>on</strong>ly. Forces that depend <strong>on</strong> positi<strong>on</strong><br />
<strong>on</strong>ly are c<strong>on</strong>servative, e.g. gravity <strong>and</strong> Coloumb forces. It is less comm<strong>on</strong> that forces that depend<br />
<strong>on</strong> <strong>the</strong> momentum are c<strong>on</strong>servative, an important excepti<strong>on</strong> to <strong>the</strong> latter is magnetic forces which<br />
do not change <strong>the</strong> momentum magnitude, <strong>on</strong>ly its directi<strong>on</strong>; thus magnetic forces are c<strong>on</strong>servative.<br />
0<br />
X<br />
1<br />
2
1.6. Definiti<strong>on</strong>s used throughout <strong>the</strong> book 21<br />
ˆx<br />
ˆy<br />
ˆs<br />
� 〈x〉 2<br />
� 〈x ′ 〉 2<br />
Figure 1.15: Definiti<strong>on</strong> of <strong>the</strong> rms width <strong>and</strong> angular spread of particles in a bunch.<br />
In Figure 1.15 <strong>the</strong> quantities inside <strong>the</strong> square-root are depicted.<br />
The emittance, as defined above, is also preserved as l<strong>on</strong>g as <strong>the</strong> particles are not<br />
accelerated. It is <strong>the</strong>refore customary to use <strong>the</strong> normalized emittance which makes<br />
<strong>the</strong> emittance comparable even if <strong>the</strong> <strong>beam</strong> has underg<strong>on</strong>e accelerati<strong>on</strong>[30].<br />
The normalized emittance is related to <strong>the</strong> <strong>beam</strong> energy via <strong>the</strong> relativistic factors<br />
β = v<br />
<strong>and</strong> γ = √ 1<br />
c<br />
1−β2 :<br />
εn = βγε<br />
which is invariant al<strong>on</strong>g <strong>the</strong> accelerator structure in <strong>the</strong> absence of radiati<strong>on</strong>. C<strong>on</strong>sequently,<br />
<strong>the</strong> transverse size of a charged particle <strong>beam</strong> shrinks as it gets accelerated<br />
as √ βγ. As will be seen below, <strong>the</strong> emittance needs to be very low for a free electr<strong>on</strong><br />
laser as <strong>the</strong> generated radiati<strong>on</strong> needs to overlap substantially with <strong>the</strong> electr<strong>on</strong><br />
<strong>beam</strong> for <strong>the</strong> lasing process to occur. Toge<strong>the</strong>r with <strong>the</strong> current <strong>and</strong> <strong>the</strong> <strong>beam</strong> energy<br />
<strong>the</strong> transverse <strong>and</strong> l<strong>on</strong>gitudinal emittances are very important figures of merit for<br />
accelerators.
22 1. Introducti<strong>on</strong><br />
Summary<br />
• X-rays can be used to investigate <strong>the</strong> electr<strong>on</strong>ic <strong>and</strong> geometrical<br />
structure of matter <strong>–</strong> by spectroscopic or scattering experiments<br />
respectively. Thus <strong>the</strong>y are used by a broad scientific<br />
community for experiments, i.e. for both fundamental <strong>and</strong><br />
applied investigati<strong>on</strong>s in medicince, biology, chemistry <strong>and</strong><br />
physics.<br />
• The brilliance (quality) of X-ray sources have developed exp<strong>on</strong>entially<br />
since <strong>the</strong> discovery of X-ray radiati<strong>on</strong>.<br />
• Today <strong>the</strong> most brilliant, man-made, X-ray source is <strong>the</strong> free<br />
electr<strong>on</strong> laser. O<strong>the</strong>r X-ray sources are X-ray tubes, anodes,<br />
synchrotr<strong>on</strong> storage rings <strong>and</strong> high-harm<strong>on</strong>ic generati<strong>on</strong><br />
(HHG) lasers.<br />
• Compared to solid state lasers <strong>and</strong> HHG lasers a free electr<strong>on</strong><br />
laser do not have any limit <strong>on</strong> <strong>the</strong> output power imposed by<br />
<strong>the</strong> laser medium, it being an electr<strong>on</strong> <strong>beam</strong> in vacuum <strong>and</strong><br />
not a gas or a solid.<br />
• Thebasic process thatgovernsfree electr<strong>on</strong>laser amplificati<strong>on</strong><br />
is abbreviated Sase <strong>–</strong> Self Amplified Sp<strong>on</strong>taneous Emissi<strong>on</strong>.<br />
This process describes how <strong>the</strong> radiati<strong>on</strong> field is amplified bya<br />
relativistic electr<strong>on</strong> <strong>beam</strong> moving through aperiodic magnetic<br />
field (i.e. in an undulator) when <strong>the</strong> radiati<strong>on</strong> field modulates<br />
<strong>the</strong> electr<strong>on</strong> <strong>beam</strong> density (microbunching). A nice introductory<br />
descripti<strong>on</strong> of <strong>the</strong> free electr<strong>on</strong> laser process can be found<br />
in Ref. [31].<br />
• Sase is a positive feedback process <strong>and</strong> <strong>the</strong> amplificati<strong>on</strong> of<br />
<strong>the</strong> radiati<strong>on</strong> field can be exp<strong>on</strong>ential. The process reach saturati<strong>on</strong><br />
when <strong>the</strong> electr<strong>on</strong> <strong>beam</strong> is microbunched with <strong>the</strong><br />
periodicity of emitted radiati<strong>on</strong>. The process starts up from<br />
electr<strong>on</strong> shot-noise in <strong>the</strong> <strong>beam</strong>, thus <strong>the</strong> number of radiati<strong>on</strong><br />
modes follow a Poiss<strong>on</strong> distributi<strong>on</strong>.<br />
• The spectrum of <strong>the</strong> emitted phot<strong>on</strong>s is broad (from incoherent<br />
sp<strong>on</strong>taneous undulator radiati<strong>on</strong>) with a number of<br />
sharp spikes corresp<strong>on</strong>ding to <strong>the</strong> coherent radiati<strong>on</strong> from<br />
Sase-modes. The radiati<strong>on</strong> in <strong>the</strong> modes have full transverse<br />
coherence <strong>and</strong> each mode is diffracti<strong>on</strong> limited.<br />
• The energy <strong>and</strong> intensity distributi<strong>on</strong> from each pulse is<br />
unique since <strong>the</strong> process starts up from noise. Methods to manipulate<br />
<strong>the</strong> electr<strong>on</strong> <strong>beam</strong> serving to enhance <strong>the</strong> shot toshot<br />
repeatability of <strong>the</strong> spectrum utilize lasers to seed <strong>the</strong> <strong>beam</strong><br />
before entering <strong>the</strong> periodic magnetic structure (undulator).<br />
In fortuitous cases this can lock <strong>the</strong> radiati<strong>on</strong> into a single<br />
Sase-mode which <strong>the</strong>n becomes <strong>on</strong>e milli<strong>on</strong> times more intense<br />
<strong>the</strong>n <strong>the</strong> corresp<strong>on</strong>ding unmanipulated Sase-spectrum.
2. Synchrotr<strong>on</strong> radiati<strong>on</strong> <strong>and</strong> its properties<br />
Written by: A. Lindblad<br />
2.1 Radiati<strong>on</strong> from a moving charge<br />
This chapter c<strong>on</strong>tains certain elements of classical electrodynamics, which is needed<br />
in <strong>the</strong> following chapters. For <strong>the</strong> underlying framework <strong>and</strong> definiti<strong>on</strong>s see <strong>the</strong> book<br />
of Jacks<strong>on</strong> <strong>and</strong> Schwinger’s article from 1949[32, 33].<br />
Maxwell’s laws<br />
Gauss’ law for <strong>the</strong> electric field states that <strong>the</strong> flux of <strong>the</strong> electric field through a<br />
closed surface S is proporti<strong>on</strong>al to <strong>the</strong> enclosed total charge:<br />
�<br />
E·dA =<br />
S<br />
Q<br />
ǫ0<br />
(2.1)<br />
Analogously <strong>the</strong>re is a Gauss’ law for <strong>the</strong> magnetic field B; <strong>the</strong> field lines of <strong>the</strong><br />
magnetic field must be closed <strong>–</strong> thus <strong>the</strong> net flux through a closed surface must be<br />
zero, i.e. �<br />
B·dA = 0 (2.2)<br />
S<br />
This implies that <strong>the</strong>re are no magnetic m<strong>on</strong>opoles, if <strong>the</strong>re were this equati<strong>on</strong> would<br />
also have a source term as <strong>the</strong> equati<strong>on</strong> for <strong>the</strong> electric field.<br />
For <strong>the</strong> electric <strong>and</strong> magnetic fields to be coupled<br />
<strong>the</strong> flux of ei<strong>the</strong>r <strong>the</strong> electric or <strong>the</strong> magnetic fields<br />
needs to change; if <strong>the</strong> flux of <strong>the</strong> magnetic field<br />
changes over time, <strong>the</strong>n <strong>the</strong> electromotive force al<strong>on</strong>g<br />
a closed loop <strong>on</strong> <strong>the</strong> surface S is proporti<strong>on</strong>al to <strong>the</strong><br />
flux:<br />
S1<br />
I<br />
∂S S2<br />
E<br />
I<br />
�<br />
E·dℓ = −<br />
∂S<br />
B<br />
Figure2.1: Surfacessharing<strong>the</strong> same<br />
bounding c<strong>on</strong>tour ∂S.<br />
∂ΦB<br />
∂t<br />
(2.3)<br />
The sum of <strong>the</strong> magnetic fields through a closed<br />
loop <strong>on</strong> a surface enclosing a current is proporti<strong>on</strong>al<br />
23
24 2. Synchrotr<strong>on</strong> radiati<strong>on</strong> <strong>and</strong> its properties<br />
to that current (Ampere’s law): �<br />
B · dℓ = µ0I. However, as seen in Figure 2.1 it<br />
∂S<br />
is easy to c<strong>on</strong>struct a situati<strong>on</strong> where <strong>the</strong> same bounding c<strong>on</strong>tour is shared by two<br />
surfaces where <strong>on</strong>ly <strong>on</strong>e of <strong>the</strong> surfaces c<strong>on</strong>tain <strong>the</strong> current in Ampère’s law, whereas<br />
<strong>the</strong> o<strong>the</strong>r <strong>on</strong>e c<strong>on</strong>tains a changing electric field <strong>–</strong> here we use a discharging parallelplate<br />
capacitor for this purpose; even though no charge flows between <strong>the</strong> capacitor<br />
plates <strong>the</strong>re is still a current ID flowing inside <strong>the</strong> capacitor (although <strong>the</strong>re is a<br />
vacuum between <strong>the</strong> plates here), by Ampère’s law we have just stated <strong>the</strong>re should<br />
be an induced magnetic field.<br />
Using Gauss’ law for <strong>the</strong> electric field, assuming a static surface, we can get:<br />
�<br />
dQ<br />
= I = ǫ0 dS ·<br />
dt ∂E ∂E<br />
≈ −Sǫ0<br />
∂t ∂t<br />
S<br />
This current <strong>and</strong> <strong>the</strong> c<strong>on</strong>ducti<strong>on</strong> current must be equal since <strong>the</strong>y must sum to zero.<br />
We divide by <strong>the</strong> area of <strong>the</strong> surface element S <strong>and</strong> use current densities (i.e. divide<br />
I by <strong>the</strong> area as well, I/S = J) <strong>and</strong> we get <strong>the</strong> result: <strong>the</strong> Ampère-Maxwell equati<strong>on</strong>:<br />
�<br />
∂S<br />
B ·dℓ = µ0<br />
�<br />
S<br />
�<br />
J+ǫ0<br />
∂E<br />
∂t<br />
�<br />
·dS (2.4)<br />
Equati<strong>on</strong>s 2.1, 2.2, 2.3, <strong>and</strong> 2.4 are <strong>the</strong> Maxwell equati<strong>on</strong>s that c<strong>on</strong>situte <strong>the</strong> basis<br />
for classical electrodynamics; via Gauss’ <strong>and</strong> Stoke’s <strong>the</strong>orems we can formulate <strong>the</strong>m<br />
also in differential form as<br />
Gauss’ law ∇·E = ρ<br />
ǫ0<br />
Gauss’ law for magnetic field ∇·B = 0<br />
Maxwell-Faraday equati<strong>on</strong> ∇×E = − ∂B<br />
∂t<br />
Ampère-Maxwell equati<strong>on</strong> ∇×B = µ0J+µ0ǫ0 ∂E<br />
∂t<br />
The electric <strong>and</strong> magnetic fields also couple via <strong>the</strong> force <strong>the</strong> fields exert <strong>on</strong> a<br />
charge moving in <strong>the</strong>m in <strong>the</strong> expressi<strong>on</strong> for <strong>the</strong> Lorentz force equati<strong>on</strong>:<br />
F = −q[E+v×B] (2.5)<br />
The energy flux of <strong>the</strong> fields can be found via <strong>the</strong> expressi<strong>on</strong> for Poynting’s vector:<br />
S = 1<br />
Charged particle at rest or moving with c<strong>on</strong>stant velocity<br />
µ0<br />
(E×B) = 1<br />
|E|<br />
cµ0<br />
2 ˆz (2.6)<br />
A charged particle at rest surrounds itself with an electric field that can be written<br />
(Coulomb’s law):<br />
E = 1 q<br />
4πǫ0 r2ˆr This is a special case of Gauss’ law for <strong>the</strong> electric field, Equati<strong>on</strong> 2.1.<br />
Since <strong>the</strong> electric field is static in <strong>the</strong> situati<strong>on</strong> when <strong>the</strong> particle is at rest no<br />
magnetic field is induced (Ampére-Maxwell equati<strong>on</strong> 2.4. In <strong>the</strong> case of a uniformly
2.1. Radiati<strong>on</strong> from a moving charge 25<br />
moving charge we have a c<strong>on</strong>stant current which creates a static magnetic field (Equati<strong>on</strong><br />
2.4 again) <strong>–</strong> no electric field is induced (Equati<strong>on</strong> 2.3).<br />
In both cases c<strong>on</strong>sidered here nochange in <strong>the</strong> kinetic energy of <strong>the</strong> particle occurs,<br />
thus no energy exists that can be transferred to <strong>the</strong> electromagnetic radiati<strong>on</strong> field.<br />
The fields from a charge in arbitrary moti<strong>on</strong><br />
Following Feynman[34, 35] we write <strong>the</strong>electric field from acharge in arbitrary moti<strong>on</strong><br />
as<br />
E = q<br />
� � ′ ′<br />
ˆr r′ d ˆr<br />
+<br />
4πǫ0 r ′2 c dt r ′2<br />
�<br />
+ 1<br />
c2 d 2<br />
dt2ˆr′ �<br />
(2.7)<br />
<strong>and</strong> <strong>the</strong> magnetic field cB = ˆr ′ × E. The primed quantites is to remember that we<br />
have to evaluate <strong>the</strong>se quantites at retarded time t ′ = t− r′<br />
<strong>–</strong> this is a c<strong>on</strong>sequence<br />
c<br />
of <strong>the</strong> finite speed of light, at <strong>the</strong> observati<strong>on</strong> point p in Figure 2.2 signals observed<br />
at time t was created when <strong>the</strong> charge was at t ′ . The sec<strong>on</strong>d term corresp<strong>on</strong>ds to a<br />
linear extrapolati<strong>on</strong> of <strong>the</strong> Coulomb field (velocity times <strong>the</strong> time-delay r ′ /c), such<br />
that when <strong>the</strong> velocity tends to zero we retain <strong>the</strong> normal Coulomb field.<br />
The first two terms are both proporti<strong>on</strong>al to <strong>the</strong> inverse squared distance <strong>and</strong> thus<br />
decays fast with respect to <strong>the</strong> distance, at least compared to <strong>the</strong> third term which is<br />
proporti<strong>on</strong>al to <strong>the</strong> inverse distance. Therefore, <strong>the</strong> last term in <strong>the</strong> equati<strong>on</strong> above<br />
is called <strong>the</strong> radiati<strong>on</strong> field since it survives even when r → ∞.<br />
Electric <strong>and</strong> magnetic field lines must be to be c<strong>on</strong>tinuous; looking at <strong>the</strong> right-side<br />
of Figure 2.2 we can c<strong>on</strong>sider a charge that get accelerated a very short time towards<br />
a n<strong>on</strong>-relativistic velocity (v ≪ c). The signal at X that was emitted at time t = 0<br />
have its fr<strong>on</strong>t at a distance c∆t from <strong>the</strong> signal that was emitted at t = ∆t; for <strong>the</strong><br />
electric field lines to be c<strong>on</strong>tinuous <strong>the</strong>re must exist a perpendicular comp<strong>on</strong>ent of<br />
<strong>the</strong> electric field which is proporti<strong>on</strong>al to <strong>the</strong> velocity in that directi<strong>on</strong> (<strong>and</strong> thus <strong>the</strong><br />
acellerati<strong>on</strong>). The parallel comp<strong>on</strong>ent is given by <strong>the</strong> first two terms in <strong>the</strong> equati<strong>on</strong><br />
for <strong>the</strong> electric field above.<br />
1<br />
˙x<br />
r ′<br />
r ′<br />
c 2<br />
˙x ˙ xt<br />
Figure 2.2: Signalsreceived at <strong>the</strong> observati<strong>on</strong>pointp attime twascreated at<strong>the</strong> retarded time t’. Equati<strong>on</strong>2.7<br />
attempts to account for <strong>the</strong> particles moti<strong>on</strong> by linearly extrapolating <strong>the</strong> Coulomb-field to guess <strong>the</strong> particles<br />
current positi<strong>on</strong>.<br />
r<br />
p<br />
2<br />
1<br />
ϑ<br />
˙x⊥<br />
˙x�<br />
c∆t<br />
E⊥<br />
E�
26 2. Synchrotr<strong>on</strong> radiati<strong>on</strong> <strong>and</strong> its properties<br />
|E⊥/E�| = ˙x⊥t<br />
c∆t = ¨x⊥ ·∆t·t<br />
=<br />
c∆t<br />
¨x⊥ ·t<br />
c = {t = r/c} = ¨x⊥ ·r<br />
c2 The magnitude of <strong>the</strong> electric field outside <strong>the</strong> sphere is given by Gauss’ law, which<br />
gives <strong>the</strong> parallel comp<strong>on</strong>ent: E� = q<br />
4πǫ0<br />
1<br />
r 2, yielding <strong>the</strong> perpendicular comp<strong>on</strong>ent<br />
we seek:<br />
E⊥ = q ¨x⊥<br />
4πǫ0 c2 q 1<br />
sinϑˆr =<br />
r 4πǫ0 c2 d 2<br />
dt2ˆr (2.8)<br />
in <strong>the</strong> relativistic case we must take care to evaluate <strong>the</strong> derivative at retarded time.<br />
Radiated power from a charged particle in n<strong>on</strong>-relativistic moti<strong>on</strong><br />
Equipped with <strong>the</strong> expressi<strong>on</strong> for <strong>the</strong> Poynting vector <strong>and</strong> <strong>the</strong> expressi<strong>on</strong> for <strong>the</strong><br />
electric <strong>and</strong> magnetic fields for a charge in accelerated moti<strong>on</strong> we are now equipped<br />
to find <strong>the</strong> expressi<strong>on</strong> for <strong>the</strong> radiated power.<br />
In Figure 2.2 we can see that we can write <strong>the</strong> radiati<strong>on</strong> part of <strong>the</strong> electric field<br />
(<strong>the</strong> o<strong>the</strong>r terms will fall off as 1/r 4 in <strong>the</strong> expressi<strong>on</strong> for <strong>the</strong> Poynting vector <strong>and</strong><br />
thus carry an insignificant energy flux compared to <strong>the</strong> radiati<strong>on</strong> field)<br />
E⊥ =<br />
q<br />
4πǫ0c2 1<br />
¨xsinϑ (2.9)<br />
r<br />
with directi<strong>on</strong> ˆr×(ˆr× ˆx). <strong>the</strong> magnetic field we get straightforwardly cB = ˆr×E⊥.<br />
Inserting this into Equati<strong>on</strong> 2.6 we get:<br />
|S| = 1<br />
c4 q 2<br />
(4πǫ0) 2<br />
¨x 2<br />
r2 sin2ϑ (2.10)<br />
To get <strong>the</strong> total radiated power we integrate over all angles<br />
��<br />
P = |S|dS =<br />
� π<br />
0<br />
|S|2πr 2 sinϑdϑ = q2<br />
6πǫ0c 3¨x<br />
This is <strong>the</strong> Larmor formula[36] for <strong>the</strong> total radiati<strong>on</strong> power 1 .<br />
Radiated power from a relativistic charged particle<br />
(2.11)<br />
Equati<strong>on</strong> 2.10 describes <strong>the</strong> radiati<strong>on</strong> field from a charge in n<strong>on</strong>-relativistic moti<strong>on</strong>,<br />
with <strong>the</strong> typical sin 2 ϑ look of <strong>the</strong> power distributi<strong>on</strong> (which is similar to that of<br />
a dipole-antenna); <strong>the</strong> left-side of Figure 2.3 shows <strong>the</strong> radiati<strong>on</strong> lobes from a n<strong>on</strong>relativistic<br />
charge moving al<strong>on</strong>g <strong>the</strong> z-axis that gets accelerated in <strong>the</strong> directi<strong>on</strong> of<br />
1<br />
The Larmor formula is <strong>the</strong> result <strong>on</strong>e obtains within <strong>the</strong> framework of classical electrodynamics.<br />
If <strong>on</strong>e accounts for <strong>the</strong> quantum nature of <strong>the</strong> emitted phot<strong>on</strong>, <strong>and</strong> thus <strong>the</strong> resulting recoil<br />
exerted <strong>on</strong> <strong>the</strong> electr<strong>on</strong>, <strong>the</strong> radiated power is slightly less[33]:<br />
�<br />
P = PLarmor 1 − 55<br />
16 √ �<br />
ε<br />
3 E<br />
with ε as <strong>the</strong> classical phot<strong>on</strong> energy <strong>and</strong> E <strong>the</strong> total energy.
2.1. Radiati<strong>on</strong> from a moving charge 27<br />
<strong>the</strong> x-axis. We will now try to get a look-<strong>and</strong>-feel for how <strong>the</strong> radiati<strong>on</strong> power is<br />
distributed up<strong>on</strong> accelerati<strong>on</strong> at relativistic velocities.<br />
In <strong>the</strong> rest-frame of <strong>the</strong> particle (i.e. a reference frame moving with <strong>the</strong> same speed<br />
as <strong>the</strong> particle) S ⋆ <strong>the</strong> radiati<strong>on</strong> flux will look as in <strong>the</strong> n<strong>on</strong>-relativistic case described<br />
above, that is a dipole-field; this is shown in <strong>the</strong> left side of Figure 2.3. A radiated<br />
electromagnetic wave with wavelength λ in a certain directi<strong>on</strong> in <strong>the</strong> rest-frame will,<br />
will have a wavevector k ⋆ in that frame. To see how this wavevector looks in ”our”<br />
laboratory frame we must do a Lorentz-transformati<strong>on</strong>.<br />
If we c<strong>on</strong>sider <strong>the</strong> velocity to be solely in <strong>the</strong> ˆz directi<strong>on</strong> we can write <strong>the</strong> Lorentztransformati<strong>on</strong><br />
from <strong>the</strong> starred to <strong>the</strong> unstarred system as kz = 2γk ⋆ z, where γ is<br />
<strong>the</strong> relativistic factor<br />
1<br />
�<br />
1− v2<br />
c 2<br />
1<br />
= √ . As we approach more <strong>and</strong> more relativistic<br />
1−β2 velocities more <strong>and</strong> more of <strong>the</strong> radiati<strong>on</strong> is focussed in <strong>the</strong> forward directi<strong>on</strong>; <strong>the</strong><br />
opening angle of <strong>the</strong> radiati<strong>on</strong> c<strong>on</strong>e shrinks:<br />
θ ≈ kx<br />
kz<br />
≈ k⋆ x<br />
2γk ⋆ z<br />
= tanθ⋆<br />
2γ<br />
≈ 1<br />
2γ<br />
This is a very important property from <strong>the</strong> point of view of light producing accelerators,<br />
<strong>the</strong> more <strong>the</strong> particles get accelerated, <strong>the</strong> more focussed <strong>the</strong> radiati<strong>on</strong> gets.<br />
It can also be seen from <strong>the</strong> bottom in <strong>the</strong> figure that smaller opening angles get<br />
shifted to higher frequencies than those with larger opening angles <strong>–</strong> thus <strong>the</strong>re will<br />
be a spatial frequency distributi<strong>on</strong> of <strong>the</strong> electromagnetic radiati<strong>on</strong> with <strong>the</strong> highest<br />
frequencies in <strong>the</strong> middle; this is a angle dependent Doppler shift of <strong>the</strong> radiati<strong>on</strong>.<br />
To find <strong>the</strong> magnitude of <strong>the</strong> radiated power <strong>on</strong>e must generalize Larmor’s formula<br />
to take into account relativistic effects (see e.g.[32]); for <strong>the</strong> treatment here it suffices<br />
to know that for <strong>the</strong> same accelerating force leads to a factor γ 2 higher radiati<strong>on</strong><br />
power <strong>–</strong> it is thus more ec<strong>on</strong>omical to have light producing structures that accelerate<br />
<strong>the</strong> particles transversely ra<strong>the</strong>r than accelerating <strong>the</strong>m l<strong>on</strong>gitudinally (at least from<br />
<strong>the</strong> light producti<strong>on</strong> point-of-view). This is also <strong>the</strong> reas<strong>on</strong> as to why linear colliders<br />
are historically <strong>the</strong> weap<strong>on</strong> of choice for particle physics experiments where, notably<br />
for light particles, synchrotr<strong>on</strong> radiati<strong>on</strong> losses is undesirable since <strong>the</strong> particle energy<br />
is <strong>the</strong> critical parameter.<br />
If we let rcmc 2 = e 2 define <strong>the</strong> classical particle radius rc <strong>and</strong> ρ <strong>the</strong> bending radius<br />
of <strong>the</strong> orbit caused by <strong>the</strong> deflecting magnetic field, <strong>the</strong> total radiated power becomes:<br />
Pγ = 2<br />
3 rcmc2cβ 4 γ 4<br />
ρ2 (2.12)<br />
InFigure 2.3 we see thatmost of<strong>the</strong> radiati<strong>on</strong> will beradiated in <strong>the</strong>forward directi<strong>on</strong><br />
with a polarisati<strong>on</strong> perpendicular to <strong>the</strong> bending magnetic field (σ mode) <strong>–</strong> however,<br />
some of <strong>the</strong> power will be emitted in a mode off axis with circular polarizati<strong>on</strong> (π<br />
mode). It can be shown [37] that <strong>the</strong> relative power between <strong>the</strong> modes are:<br />
Pσ = 7 1<br />
Pγ, Pπ =<br />
8 8 Pγ<br />
Frequency <strong>and</strong> coherence of synchrotr<strong>on</strong> radiati<strong>on</strong><br />
Synchrotr<strong>on</strong> radiati<strong>on</strong> from a charged particle in a circular orbit at relativistic speeds<br />
= φ, this angular<br />
is characterized by a searchlightlike lobe of radiati<strong>on</strong> of width 1<br />
γ
28 2. Synchrotr<strong>on</strong> radiati<strong>on</strong> <strong>and</strong> its properties<br />
a ⋆ a<br />
Θ ⋆<br />
v ≪ c v � c<br />
k ⋆<br />
θ ⋆<br />
k ⋆ z<br />
k ⋆ x<br />
ˆx<br />
L<br />
ˆz<br />
k<br />
θ<br />
kz<br />
θ<br />
kx ≈ k ⋆ x<br />
Figure 2.3: N<strong>on</strong>relativistic (left, starred quantities) <strong>and</strong> relativistic (right) dipole radiati<strong>on</strong> fields. With k =<br />
2π/λ we get from <strong>the</strong> starred reference frame to <strong>the</strong> laboratory (observers’) frame via a Lorentz transformati<strong>on</strong><br />
L.<br />
interval is swept during <strong>the</strong> time ∆t ⋆ during which <strong>the</strong> particle moves <strong>the</strong> length<br />
∆ℓ ⋆ = v ⋆ ∆t ⋆ ⋆ φ<br />
= v <strong>–</strong> all in <strong>the</strong> particles frame of reference.<br />
ω0<br />
Due to <strong>the</strong> relativistic effects in play (length c<strong>on</strong>tracti<strong>on</strong> <strong>and</strong> time dilati<strong>on</strong>) an<br />
observer will measure a compressed pulse width of length:<br />
≈<br />
∆t = ∆t ⋆ − ∆ℓ⋆<br />
c = ∆t⋆ − v⋆∆t ⋆<br />
c =<br />
�<br />
1− v⋆<br />
�<br />
∆t<br />
c<br />
⋆ �<br />
= 1− v⋆<br />
�<br />
φ<br />
≈<br />
c ω0<br />
�<br />
1− v⋆<br />
�<br />
�<br />
1<br />
=<br />
c γω0<br />
1− v⋆<br />
c<br />
��<br />
1+ v⋆<br />
c<br />
1+ v⋆<br />
c<br />
�<br />
� � � �<br />
⋆ 2<br />
1 v 1<br />
≈ 1−<br />
γω0 c 2γω0<br />
= 1<br />
2γ 3 ω0<br />
In <strong>the</strong> last steps we have, since v ⋆ ≈ c in an accelerator, made <strong>the</strong> approximati<strong>on</strong><br />
1+v ⋆ /c = 2. The spectral width of a pulse of durati<strong>on</strong> ∆t is ∆ω � 1/∆t. Thus, in<br />
<strong>the</strong> case of synchrotr<strong>on</strong> radiati<strong>on</strong> we can expect to observe radiati<strong>on</strong> with frequencies<br />
up to about<br />
ωMax ≈ 2γ 3 ω0<br />
The spectrum will c<strong>on</strong>sist of Fourier comp<strong>on</strong>ents nω0 from n = 1 to n ≈ 2γ 3 . A<br />
spectrum from a bending magnet in a storage ring will thus be a broad spectrum<br />
peaked at <strong>the</strong> critical frequency (see e.g. [32, 38]). The critical frequency is usually<br />
defined as <strong>the</strong> frequency where half <strong>the</strong> integral power lies below <strong>and</strong> half lies above<br />
this frequency.<br />
In a storage ring, or linear accelerator <strong>the</strong>re also exist collective effects since <strong>the</strong>re<br />
is a number of particles in <strong>the</strong> <strong>beam</strong>, say N; how <strong>the</strong> particles are distributed have a<br />
large impact <strong>on</strong> <strong>the</strong> emitted radiati<strong>on</strong>. If we c<strong>on</strong>sider <strong>the</strong> case of a storage ring three<br />
cases can be discerned.
2.2. Radiati<strong>on</strong> from a bending magnet 29<br />
e −<br />
1<br />
γ<br />
1<br />
γ<br />
∆t<br />
Figure 2.4: The time during which an observer is illuminated...<br />
• The particles are evenly distributed in a c<strong>on</strong>stant current al<strong>on</strong>g <strong>the</strong> ring <strong>–</strong> this<br />
leads to perfect cancellati<strong>on</strong> of <strong>the</strong> radiati<strong>on</strong> fields since <strong>the</strong>ir phases are evenly<br />
distributed.<br />
• If every particle is closer than a typical wavelength (in a short ”bunch”) <strong>the</strong>n<br />
<strong>the</strong>ir individual phase differences will be small <strong>and</strong> <strong>the</strong> field from each particle<br />
will be amplified N times <strong>–</strong> leading to a N 2 fold increase in <strong>the</strong> radiated power.<br />
This is coherent radiati<strong>on</strong>.<br />
• If <strong>the</strong> particles are unevenly distributed in <strong>the</strong> ring <strong>the</strong>n √ N of <strong>the</strong> particles<br />
will have phases that are not perfectly r<strong>and</strong>om 2 . Then <strong>the</strong> fields from those √ N<br />
particles will amplify that of <strong>the</strong> √ N o<strong>the</strong>rs which leads to that <strong>the</strong> incoherent<br />
radiati<strong>on</strong> is proporti<strong>on</strong>al to N.<br />
In a synchrotr<strong>on</strong> <strong>beam</strong> from a storage ring with bunches of N particles both incoherent<br />
<strong>and</strong> coherent parts of <strong>the</strong> radiati<strong>on</strong> field are normally present (Equati<strong>on</strong> 2.32).<br />
2.2 Radiati<strong>on</strong> from a bending magnet<br />
Asseen abovein Equati<strong>on</strong>2.12, <strong>the</strong>power is inverselyproporti<strong>on</strong>al to<strong>the</strong>radiusof <strong>the</strong><br />
orbit squared. The upper limit for a single magnet is thus set by <strong>the</strong> strength of <strong>the</strong><br />
deflecting magnetic field <strong>and</strong> <strong>the</strong> <strong>beam</strong> energy. To maximize <strong>the</strong> radiated power <strong>on</strong>e<br />
thus needs to have smaller magnet gaps <strong>and</strong> higher magnetic field strengths combined<br />
with a high <strong>beam</strong> energy. Thus <strong>the</strong>re exist a limit as of how intense radiati<strong>on</strong> <strong>on</strong>e can<br />
create with a bending magnet.<br />
For a single bending magnet <strong>the</strong>re exist ano<strong>the</strong>r side-c<strong>on</strong>diti<strong>on</strong> <strong>–</strong> that is that <strong>the</strong><br />
magnet should not bend <strong>the</strong> electr<strong>on</strong>s away from <strong>the</strong> orbit in <strong>the</strong> storage ring, thus a<br />
2 Imagine that <strong>the</strong> emitted radiati<strong>on</strong> is shot-noise <strong>–</strong> thus characterizedby a Poiss<strong>on</strong> distributi<strong>on</strong>,<br />
<strong>the</strong>n for a sufficiently large number of particles <strong>the</strong> signal to noise ratio will be <strong>the</strong> square root of <strong>the</strong><br />
number of emitters, since <strong>the</strong> variance is √ N for a normal distributi<strong>on</strong> <strong>–</strong> which can be c<strong>on</strong>sidered<br />
applicable since for large N <strong>the</strong> Poiss<strong>on</strong>-distributi<strong>on</strong> tends towards <strong>the</strong> normal distributi<strong>on</strong>.
30 2. Synchrotr<strong>on</strong> radiati<strong>on</strong> <strong>and</strong> its properties<br />
too str<strong>on</strong>g magnetic field can not be utilized. To circumvent this we can imagine an<br />
array of str<strong>on</strong>g magnets that eventually returns <strong>the</strong> electr<strong>on</strong> to <strong>the</strong> intended orbit.<br />
If <strong>the</strong> array of magnets are str<strong>on</strong>g, such that <strong>the</strong> deflecti<strong>on</strong> from <strong>the</strong> central orbit<br />
is large so that <strong>the</strong> light pulses from different bunches do not overlap, we will get a<br />
spectrum similar to that of a single bending magnet but more intense <strong>and</strong> <strong>–</strong> with <strong>the</strong><br />
now str<strong>on</strong>ger magnetic field <strong>–</strong> shorter critical wavelength. Such a device is called a<br />
wiggler or wavelength shifter. The output power exceeds that of a bending magnet<br />
by twice <strong>the</strong> number of periods, i.e. 2·N.<br />
We can also imagine a device with a smaller magnetic field strength where <strong>the</strong><br />
deflecti<strong>on</strong>s from <strong>the</strong> central orbit is not too large, instead we employ many more<br />
poles to get <strong>the</strong> intensity str<strong>on</strong>ger. In this type of scheme <strong>the</strong> emitted radiati<strong>on</strong> field<br />
can positively interfere for certain wavelengths (this c<strong>on</strong>diti<strong>on</strong> will be specified below)<br />
resulting in a spectrum with a fundamental radiati<strong>on</strong> mode <strong>and</strong> its harm<strong>on</strong>ics whose<br />
wavelength corresp<strong>on</strong>ds to a given combinati<strong>on</strong> of magnetic field strengths <strong>and</strong> <strong>beam</strong><br />
energy. This type of device is called an undulator. In a free electr<strong>on</strong> laser this device<br />
is a critical comp<strong>on</strong>ent which ultimately sets <strong>the</strong> properties of <strong>the</strong> emitted radiati<strong>on</strong>.<br />
The output power exceeds that of a bending magnet by <strong>the</strong> square of <strong>the</strong> number of<br />
periods: N 2 .<br />
2.3 Undulator radiati<strong>on</strong><br />
The undulator was described already in 1951 as a source for synchrotr<strong>on</strong> X-ray radiati<strong>on</strong><br />
[6]. In Figure 2.5 a schematic of <strong>the</strong> alternating-magnetic pole scheme of a<br />
permanent magnet undulator is shown <strong>–</strong> usually <strong>the</strong> number of poles is much larger<br />
since <strong>the</strong> number of deflecti<strong>on</strong>s for <strong>the</strong> electr<strong>on</strong> bunch dictates <strong>the</strong> intensity <strong>and</strong> spectral<br />
quality of <strong>the</strong> radiati<strong>on</strong> emitted (as we will derive below).<br />
λu<br />
Figure 2.5: A schematic of <strong>the</strong> periodic magnet structure of an undulator. In yellow <strong>the</strong> electr<strong>on</strong> path is shown.<br />
The undulator equati<strong>on</strong><br />
The undulator strength parameter K<br />
The magnetic field in an periodic magnet structure can be written, if we c<strong>on</strong>sider that<br />
we look at <strong>the</strong> structure from above as in Figure 2.5:<br />
� �<br />
2π<br />
B(z) = B0cos ˆy = B0cos(kuz) ˆy (2.13)<br />
z<br />
λu<br />
θ<br />
ˆz
2.3. Undulator radiati<strong>on</strong> 31<br />
Remembering <strong>the</strong> expressi<strong>on</strong> for <strong>the</strong> Lorentz force (Equati<strong>on</strong> 2.5) <strong>and</strong> Newt<strong>on</strong>’s<br />
sec<strong>on</strong>d law we can write<br />
dp<br />
dt<br />
= [˙p] = e(v×B) ⇒ ˙px = −evzBy<br />
where in <strong>the</strong> last step we have used v = vzˆz; we have also used <strong>the</strong> approximati<strong>on</strong><br />
that <strong>the</strong> electric field created is weak enough so that <strong>the</strong> interacti<strong>on</strong> is negligible <strong>–</strong><br />
later we will see what c<strong>on</strong>sequences occur when this is not <strong>the</strong> case (see secti<strong>on</strong> 2.5<br />
at (see page 44)).<br />
this is <strong>the</strong> equati<strong>on</strong> of moti<strong>on</strong> for <strong>the</strong> electr<strong>on</strong> in <strong>the</strong> periodic magnetic structure 3 .<br />
If we insert Equati<strong>on</strong> 2.13 into <strong>the</strong> equati<strong>on</strong> of moti<strong>on</strong> we get<br />
˙px = −e dz<br />
dt B0cos[kuz]<br />
which after integrati<strong>on</strong> with respect to time gives:<br />
mγvx = − eB0<br />
sin(kuz)<br />
ku<br />
(<strong>the</strong> relativistic factor γ enters from <strong>the</strong> expressi<strong>on</strong> for relativistic momentum) which<br />
defines <strong>the</strong> undulator strength parameter K:<br />
vx = − eB0<br />
sin(kuz) = −Kc sin(kuz) (2.14)<br />
mekuγ γ<br />
If <strong>the</strong> deflecti<strong>on</strong> from <strong>the</strong> ˆz directi<strong>on</strong> can be c<strong>on</strong>sidered small we can use tanθ ≈ θ<br />
toge<strong>the</strong>r with <strong>the</strong> approximati<strong>on</strong> that vz = c to obtain:<br />
�<br />
tanθ = vx<br />
vz<br />
≈ vx<br />
�<br />
≈ θ = −<br />
c<br />
K<br />
γ sin(kuz)<br />
Usually <strong>the</strong> n<strong>on</strong>-dimensi<strong>on</strong>al parameter K is written as:<br />
K = λueB0<br />
2πmec<br />
≈ 0.9337B0λu<br />
(2.15)<br />
where <strong>the</strong> latter holds true if <strong>the</strong> magnetic field strength is measured in Tesla <strong>and</strong> <strong>the</strong><br />
undulator period in centimeters.<br />
The c<strong>on</strong>diti<strong>on</strong> of coherent emissi<strong>on</strong><br />
In an undulator <strong>the</strong> transverse moti<strong>on</strong> is small, thus significant parts of <strong>the</strong> radiati<strong>on</strong><br />
field emitted at different times will overlap as <strong>the</strong> electr<strong>on</strong> transverse <strong>the</strong> undulator.<br />
This will result in positive <strong>and</strong> negative interference of certain wavelengths which<br />
are <strong>on</strong> or off res<strong>on</strong>ance with <strong>the</strong> period of <strong>the</strong> magnetic field. The c<strong>on</strong>diti<strong>on</strong> for<br />
a wavelength to experience positive interference can be derived without too much<br />
effort in terms of <strong>the</strong> undulator strength parameter, <strong>the</strong> relativistic factor γ <strong>and</strong> <strong>the</strong><br />
deflecti<strong>on</strong> angle.
32 2. Synchrotr<strong>on</strong> radiati<strong>on</strong> <strong>and</strong> its properties<br />
A<br />
λu<br />
λucosθ<br />
Figure 2.6: Light traveling <strong>the</strong> path AB interferes with light emitted from A at an angle θ (path AB’).<br />
C<strong>on</strong>siderthat<strong>the</strong>electr<strong>on</strong> emitradiati<strong>on</strong>at<strong>the</strong>wave-crest 4 labelled AinFigure2.6<br />
<strong>and</strong> at some later instance τ emit radiati<strong>on</strong> at crest B.<br />
In Figure 2.6 <strong>the</strong> path through an undulator for an electr<strong>on</strong> moving in <strong>the</strong> field<br />
described by Equati<strong>on</strong> 2.13. The relati<strong>on</strong>ship between <strong>the</strong> emitted wavelength λs<br />
<strong>and</strong> <strong>the</strong> period of <strong>the</strong> undulator λu can be found by c<strong>on</strong>sidering <strong>the</strong> c<strong>on</strong>diti<strong>on</strong> for<br />
c<strong>on</strong>structive interference of <strong>the</strong> wavefr<strong>on</strong>ts emitted at A <strong>and</strong> B respectively.<br />
If we denote <strong>the</strong> average l<strong>on</strong>gitudinal velocity ˜vz <strong>the</strong>n <strong>the</strong> time difference between<br />
<strong>the</strong>topoints of emissi<strong>on</strong> is τ = λu/˜vz. The pathdifference between <strong>the</strong>twopoints will<br />
be a multiple of some wavelength λs of <strong>the</strong> emitted light; multiples of this wavelength<br />
will experience positive interference <strong>and</strong> will dominate <strong>the</strong> spectrum.<br />
c λu<br />
˜vz<br />
����<br />
AB<br />
θ<br />
B<br />
−λucosθ = nλs<br />
� �� �<br />
AB’<br />
n ∈ Z+ (2.16)<br />
We now need to seek <strong>the</strong> average l<strong>on</strong>gitudinal velocity. Remembering Equati<strong>on</strong><br />
2.14, we have an expressi<strong>on</strong> for <strong>the</strong> velocity in <strong>the</strong> transverse directi<strong>on</strong> <strong>–</strong> thus we<br />
can write:<br />
�<br />
vz = � v 2 −v 2 x =<br />
v2 c2<br />
−K 2<br />
γ2 sin2kuz where, by using β = v/c <strong>and</strong> γ = 1/ � 1−β 2 , <strong>on</strong>e can by breaking c out of <strong>the</strong><br />
square-root find:<br />
�<br />
vz = c 1− 1 1<br />
−<br />
γ2 γ2K2 sin2 �<br />
kuz = c 1− 1<br />
γ2 � �<br />
K2 2 sin kuz<br />
Knowing that γ >> 1 <strong>and</strong> <strong>the</strong> McLaurin series for √ 1+x = 1+ 1<br />
2<br />
�<br />
vz ≈ c 1− 1<br />
2γ2 � � 2 2<br />
1+K sin kuz �<br />
θ<br />
ˆz<br />
x− 1<br />
8 x2 +...<br />
3 In an helical undulator <strong>the</strong> magnetic field can be written B = Bu [ˆxcos(kuz) + ûsin(kuz)].<br />
4 The strength of <strong>the</strong> radiati<strong>on</strong> is proporti<strong>on</strong>al to <strong>the</strong> accelerati<strong>on</strong>, Equati<strong>on</strong> 2.11.
2.3. Undulator radiati<strong>on</strong> 33<br />
which averaged over <strong>on</strong>e half oscillati<strong>on</strong> gives <strong>the</strong> sought average velocity 5 :<br />
�<br />
˜vz ≈ c 1− 1<br />
2γ2 �<br />
1+ K2<br />
��<br />
2<br />
which, inserted into Equati<strong>on</strong> 2.16, gives:<br />
⎡<br />
nλs = λu⎣<br />
1<br />
1− 1<br />
2γ2 �<br />
1+ K2<br />
�<br />
� − 1−<br />
2<br />
θ2<br />
�<br />
2<br />
⎤<br />
⎦<br />
(2.17)<br />
where we have exp<strong>and</strong>ed <strong>the</strong> cosine for small θ, for <strong>the</strong> first term we again use <strong>the</strong><br />
1<br />
fact that 1/γ is very small: 1−x = 1+x+x2 +..., which gives <strong>the</strong> final result, for<br />
n = 1:<br />
λs = λu<br />
2γ2 �<br />
1+ 1<br />
2 K2 +(γθ) 2<br />
�<br />
(2.18)<br />
In a helical undulator <strong>the</strong> 1<br />
2 K2 term becomes K 2 . This equati<strong>on</strong> is usually referred to<br />
as <strong>the</strong> undulator equati<strong>on</strong> which defines <strong>the</strong> wavelength which satisfies <strong>the</strong> res<strong>on</strong>ance<br />
c<strong>on</strong>diti<strong>on</strong> up<strong>on</strong> which <strong>the</strong> radiati<strong>on</strong> is experiencing positive interference.<br />
On axis (θ = 0) <strong>the</strong> total time of travel through <strong>the</strong> magnetic structure will be<br />
∆t = Nu∆T, with Nu being <strong>the</strong> number of poles <strong>–</strong> this yields a linewidth of <strong>the</strong><br />
radiati<strong>on</strong> given by: ∆ω<br />
ω<br />
= 1<br />
Nu .<br />
For future reference we note that owing to <strong>the</strong> properties of <strong>the</strong> Fourier transform:<br />
The pulse length will be increased if it is larger than λNu <strong>and</strong> <strong>the</strong> line width will be<br />
increased if <strong>the</strong> energy spread of <strong>the</strong> <strong>beam</strong> superseeds<br />
A detailed look at <strong>the</strong> equati<strong>on</strong>s of moti<strong>on</strong> in an undulator<br />
1<br />
2Nu .<br />
To derive <strong>the</strong> frequency spectrum of undulator radiati<strong>on</strong> it is c<strong>on</strong>venient to know a bit<br />
more about <strong>the</strong> trajectories of <strong>the</strong> particles in <strong>the</strong> undulator, so far we <strong>on</strong>ly c<strong>on</strong>cerned<br />
ourselves with <strong>the</strong> transverse comp<strong>on</strong>ent of <strong>the</strong> moti<strong>on</strong> as this gives us expressi<strong>on</strong>s<br />
for <strong>the</strong> wiggler/undulator strength parameter K <strong>and</strong> <strong>the</strong> res<strong>on</strong>ance c<strong>on</strong>diti<strong>on</strong> for <strong>the</strong><br />
emitted radiati<strong>on</strong>.<br />
It is here c<strong>on</strong>venient to use Hamilt<strong>on</strong>ian dynamics, as this will simplify our discussi<strong>on</strong><br />
later when we c<strong>on</strong>sider what happens when we can no l<strong>on</strong>ger make <strong>the</strong> approximati<strong>on</strong><br />
that <strong>the</strong> radiated electric field is de-coupled from <strong>the</strong> moti<strong>on</strong> of <strong>the</strong> electr<strong>on</strong>s.<br />
The Hamilt<strong>on</strong>ian for an electr<strong>on</strong> in an electromagnetic field with vector potential A<br />
can be written: �<br />
H = (p−eA) 2 c2 +(mc2 ) 4 (2.19)<br />
From Maxwell’s equati<strong>on</strong>s it can be inferred that, since we know <strong>the</strong> rotati<strong>on</strong> <strong>and</strong><br />
curl of <strong>the</strong> electric <strong>and</strong> magnetic fields <strong>on</strong>e can formulate <strong>the</strong>m in terms of a vector<br />
potential A <strong>and</strong> a scalar potential φ. This is Helmholtz <strong>the</strong>orem of vector calculus;<br />
for <strong>the</strong> B field this relati<strong>on</strong> is particularly simple B = ∇×A <strong>–</strong> thus (with <strong>the</strong> aid of<br />
Equati<strong>on</strong> 2.13)<br />
π� 5 1<br />
π<br />
0<br />
sin 2 xdx = 1<br />
2
34 2. Synchrotr<strong>on</strong> radiati<strong>on</strong> <strong>and</strong> its properties<br />
A = B<br />
sin(kuz)ˆx<br />
ku<br />
is <strong>the</strong> vector potential defining <strong>the</strong> undulator field. The Hamilt<strong>on</strong>ian described<br />
above do not have any explicit time dependence in <strong>the</strong> coordinates; for such a system<br />
<strong>the</strong> Hamilt<strong>on</strong>ian describes <strong>the</strong> total energy of <strong>the</strong> system, i.e. H = γmc 2 . Moreover,<br />
as <strong>the</strong> magnetic field d<strong>on</strong>ot perform any work <strong>on</strong> <strong>the</strong> particles, as it <strong>on</strong>ly changes <strong>the</strong>ir<br />
trajectory <strong>–</strong> we get an added b<strong>on</strong>us in that <strong>the</strong> can<strong>on</strong>ical momenta in <strong>the</strong> transverse<br />
directi<strong>on</strong>s of <strong>the</strong> system is c<strong>on</strong>served, hence[39]:<br />
˙px = − ∂H<br />
∂x<br />
˙py = − ∂H<br />
∂y<br />
Both momenta are thus c<strong>on</strong>stant <strong>and</strong> we can choose this c<strong>on</strong>stant to be zero if<br />
we c<strong>on</strong>sider <strong>the</strong> electr<strong>on</strong>’s velocity up<strong>on</strong> its entrance in <strong>the</strong> magnetic structure to be<br />
completely axial. The trajectories are given by<br />
˙x = ∂H<br />
∂px<br />
˙y = ∂H<br />
∂py<br />
= px −eAx<br />
= py −eAy<br />
= 0,<br />
= 0<br />
γm ,<br />
γm<br />
We use <strong>the</strong> definiti<strong>on</strong> of <strong>the</strong> undulator strength parameter K <strong>and</strong> divide by c to<br />
obtain expressi<strong>on</strong>s for <strong>the</strong> velocities<br />
βx = − K<br />
γ<br />
sin(kuz), βy = 0<br />
from <strong>the</strong> definiti<strong>on</strong> of <strong>the</strong> relativistic parameter γ = 1/ � 1−β 2 we can get an<br />
expressi<strong>on</strong> for <strong>the</strong> axial velocity βz as well:<br />
βz = K2<br />
4γ2β0 cos(2kuβ0ct)+β0<br />
(2.20)<br />
where β0 is <strong>the</strong> average l<strong>on</strong>gitudinal velocity (Equati<strong>on</strong> 2.17). The l<strong>on</strong>gitudinal velocity<br />
is thus slowed down since a part of <strong>the</strong> kinetic energy is transferred to <strong>the</strong><br />
transverse moti<strong>on</strong>.<br />
It can be expected that <strong>the</strong> velocity in <strong>the</strong> forward directi<strong>on</strong> will be much greater<br />
than <strong>the</strong> transverse deviati<strong>on</strong>s, thus we can c<strong>on</strong>sider <strong>the</strong> l<strong>on</strong>gitudinal trajectory as<br />
approximately given by βoct+z0 in <strong>the</strong> integrati<strong>on</strong> of Equati<strong>on</strong> 2.20<br />
K 2<br />
z(t) = 1<br />
8β2 sin(2kuβ0ct)+β0ct+z0 (2.21)<br />
0 kuγ2 The transverse comp<strong>on</strong>ent can be obtained similarily as was d<strong>on</strong>e above:<br />
x(t) = 1<br />
β0<br />
K<br />
kuγ coskuβ0ct+x0<br />
In <strong>the</strong> rest frame of <strong>the</strong> electr<strong>on</strong> it will <strong>the</strong>refore describe a figure eight moti<strong>on</strong>.
2.3. Undulator radiati<strong>on</strong> 35<br />
Frequency distributi<strong>on</strong> of undulator radiati<strong>on</strong><br />
Using <strong>the</strong> vector potential introduced above we are now equipped to derive <strong>the</strong> frequency<br />
spectrum from a relativistic electr<strong>on</strong> in an undulator field.<br />
Ano<strong>the</strong>r way to express <strong>the</strong> radiated power per unit solid angle is[32]:<br />
dP(t)<br />
dΩ<br />
= |A(t)|2<br />
<strong>the</strong>nce <strong>the</strong> total radiated energy becomes <strong>the</strong> time-integral (assuming that <strong>the</strong> radiati<strong>on</strong><br />
field drops sufficiently fast for large times, past <strong>and</strong> future, so that <strong>the</strong> radiated<br />
energy is finite)<br />
dW<br />
dΩ =<br />
�<br />
|A(t)| 2 dt<br />
The relativistic fields can be derived from <strong>the</strong> vector potential A <strong>and</strong> <strong>the</strong> scalar<br />
potential ψ, <strong>the</strong> Liénard-Wiechert potentials[32, 40] which takes care of <strong>the</strong> fact that<br />
<strong>the</strong> radiati<strong>on</strong> perceived by an observer was generated at an earlier instant (i.e. at<br />
retarded time t ′ = t−R/c).<br />
�<br />
c<br />
A(t) =<br />
4π [RErad]<br />
⎡<br />
�<br />
c<br />
ret = ⎣<br />
4π<br />
ˆn×<br />
�<br />
(ˆn−β)× ˙ �<br />
β<br />
(1−β · ˆn) 3<br />
⎤<br />
⎦<br />
<strong>the</strong> electric field here have some resemblance to <strong>the</strong> <strong>on</strong>e described by Equati<strong>on</strong> 2.8,<br />
however in <strong>the</strong> present case all <strong>the</strong> c<strong>on</strong>sequences of <strong>the</strong> relativistic velocity of <strong>the</strong><br />
moti<strong>on</strong> have been manifested.<br />
To analyze <strong>the</strong> frequency spectrum of <strong>the</strong> radiati<strong>on</strong> it is c<strong>on</strong>venient to express <strong>the</strong><br />
radiated energy in terms of <strong>the</strong> Fourier transform, where we can make use of <strong>the</strong><br />
Parseval <strong>the</strong>orem 6<br />
dW<br />
dΩ =<br />
∞�<br />
−∞<br />
|A(ω)| 2 dω<br />
If integrati<strong>on</strong> is taken for positive values of <strong>the</strong> frequencies, since negative <strong>on</strong>es do<br />
not have any physical meaning, we can write, as <strong>the</strong> integr<strong>and</strong>:<br />
|A(ω)| 2 +|A(−ω)| 2 = 2|A(ω)| 2<br />
where <strong>the</strong>last equality hold if A(t)is real so thatA(−ω) = A ∗ (ω). Wemay formulate<br />
<strong>the</strong> argument of <strong>the</strong> integral as <strong>the</strong> intensity as <strong>the</strong> double derivative of <strong>the</strong> intensity,<br />
as perceived <strong>on</strong> <strong>the</strong> directi<strong>on</strong> ˆn from <strong>the</strong> source<br />
dW<br />
dΩ =<br />
∞�<br />
0<br />
d 2 I(ω,ˆn)<br />
dΩdω dω<br />
6 Loosely stated: <strong>the</strong> integral of <strong>the</strong> square of a functi<strong>on</strong> is identical to <strong>the</strong> integral of <strong>the</strong> square<br />
of its Fourier series, i.e. with appropriate units: <strong>the</strong> energy c<strong>on</strong>tained in a waveform is identical<br />
to <strong>the</strong> energy c<strong>on</strong>tained in <strong>the</strong> sum of its various frequency comp<strong>on</strong>ents.<br />
ret
36 2. Synchrotr<strong>on</strong> radiati<strong>on</strong> <strong>and</strong> its properties<br />
We need to find <strong>the</strong> Fourier transform of <strong>the</strong> vector potential to proceed<br />
�<br />
e2 A(ω) =<br />
8π2 ∞�<br />
e<br />
c<br />
iωt<br />
⎡<br />
⎣ ˆn×<br />
�<br />
(ˆn−β)× ˙ �<br />
β<br />
(1−β · ˆn) 3<br />
⎤<br />
⎦ dt<br />
−∞<br />
we should now change variables as to take explicit care of <strong>the</strong> retarded time, t ′ +<br />
R(t ′ )/c = t, we also assume that <strong>the</strong> unit vector ˆn stays c<strong>on</strong>stant in time <strong>–</strong> that<br />
is, our observati<strong>on</strong> point is sufficiently far away from <strong>the</strong> regi<strong>on</strong> in space where <strong>the</strong><br />
accelerati<strong>on</strong> takes place. The distance R(t ′ ) ≈ x− ˆn· ˆr(t ′ ).<br />
A(ω) =<br />
� e 2<br />
8π 2 c<br />
∞�<br />
−∞<br />
e iω(t′ −ˆn·ˆr(t ′ )/c) ˆn×<br />
ret<br />
�<br />
(ˆn−β)× ˙ �<br />
β<br />
(1−β · ˆn) 2<br />
dt ′<br />
it can be shown that <strong>on</strong>e can rewrite <strong>the</strong> integr<strong>and</strong> in terms of time derivative<br />
�<br />
ˆn× (ˆn−β)× ˙ �<br />
β<br />
(1−β · ˆn) 2 = d<br />
dt ′<br />
� �<br />
ˆn×(ˆn×β)<br />
1−β · ˆn<br />
with this in mind <strong>on</strong>e can integrate Equati<strong>on</strong><br />
2.22 by parts to obtain a significantly simpler<br />
expressi<strong>on</strong> for <strong>the</strong> frequency distributi<strong>on</strong><br />
e 2 ω 2<br />
4π 2 c<br />
�<br />
� ∞�<br />
�<br />
�<br />
�<br />
�<br />
−∞<br />
ˆn×(ˆn×β)e iω(t′ −ˆn·ˆr(t ′ )/c) dt ′<br />
(2.23)<br />
On axis, <strong>the</strong> fundamental harm<strong>on</strong>ic of <strong>the</strong><br />
undulator will thus have a frequency distributi<strong>on</strong><br />
given by:<br />
d 2 I<br />
dωdΩ = e2N 2 uγ 2 K 2<br />
�<br />
c 1+ K2<br />
� �2 sinx1<br />
� F1(K) 2<br />
x1<br />
2<br />
(2.24)<br />
where F1 is a difference between Bessel functi<strong>on</strong>s<br />
such that<br />
F1(K) = [J0(κ)−J1(κ)] 2<br />
where <strong>the</strong> arguments are written as κ =<br />
Fur<strong>the</strong>rmore<br />
�<br />
�<br />
�<br />
�<br />
�<br />
�<br />
2<br />
K 2<br />
�<br />
4 1+ K2<br />
2<br />
1<br />
0.9<br />
0.8<br />
0.7<br />
0.6<br />
0.5<br />
0.4<br />
0.3<br />
0.2<br />
0.1<br />
0<br />
−30 −20 −10 0 10 20 30<br />
(2.22)<br />
Figure 2.7: Undulator-radiati<strong>on</strong> in frequencyspace<br />
(amplitude scaled to unity) shows an oscillatory<br />
behaviour dominated by <strong>the</strong> sinx/x<br />
term.<br />
ω −ωr<br />
x1 = πNu<br />
ωr<br />
where ωr is <strong>the</strong> res<strong>on</strong>ant frequency obtained from <strong>the</strong> undulator equati<strong>on</strong> above:<br />
ωr = 2ckuγ2<br />
1+ K2<br />
2<br />
�.
2.4. Microbunching 37<br />
2.4 Microbunching<br />
Interacti<strong>on</strong> between <strong>the</strong> electr<strong>on</strong> <strong>beam</strong> <strong>and</strong> <strong>the</strong> radiati<strong>on</strong> field<br />
Up until now we have c<strong>on</strong>sidered <strong>the</strong> coupling between <strong>the</strong> electr<strong>on</strong>s’ moti<strong>on</strong> <strong>and</strong><br />
<strong>the</strong> radiati<strong>on</strong> field to be negligible. If we c<strong>on</strong>sider <strong>the</strong> possibility for energy to be<br />
transferredback<strong>and</strong>forthbetween<strong>the</strong>electr<strong>on</strong><strong>beam</strong>inanundulator<strong>and</strong><strong>the</strong>radiated<br />
electromagnetic field we will find that free electr<strong>on</strong> laser amplificati<strong>on</strong> can occur. In<br />
<strong>the</strong> following we will entertain this possibility <strong>and</strong> find out <strong>the</strong> c<strong>on</strong>diti<strong>on</strong>s that enables<br />
this amplificati<strong>on</strong> to happen.<br />
An energy-modulati<strong>on</strong> to occur al<strong>on</strong>g an electr<strong>on</strong> bunch can be accounted for via<br />
<strong>the</strong> acti<strong>on</strong> of <strong>the</strong> part of <strong>the</strong> Lorentz force (Equati<strong>on</strong> 2.5) c<strong>on</strong>taining <strong>the</strong> electric field:<br />
dW = F·ds = −eE·ds = −E ·v ·ds (2.25)<br />
In an undulator <strong>the</strong> electr<strong>on</strong> velocity have comp<strong>on</strong>ents parallel to <strong>the</strong> electric field.<br />
Ex(z,t) = Ecos(kz −ωt+φ0) (2.26)<br />
To find <strong>the</strong> flow of energy per time we need an expressi<strong>on</strong> for <strong>the</strong> electr<strong>on</strong> velocity<br />
in an undulator <strong>–</strong> this is given by Equati<strong>on</strong> 2.14, hence:<br />
= ecE0K<br />
2γ<br />
dW<br />
dt<br />
cK<br />
= −eE0cos(ks−ωt+φ0)<br />
γ sin(kus) =<br />
� �� �<br />
Eq. 2.14<br />
{sin([k +ku]s−ωt+φ0)−sin([k −ku]s−ωt+φ0)} =<br />
= − ecE0K<br />
2γ<br />
[sinΨ+ −sinΨ−] (2.27)<br />
For <strong>the</strong> energy transfer between <strong>the</strong> electr<strong>on</strong> <strong>beam</strong> <strong>and</strong> <strong>the</strong> radiati<strong>on</strong> field to be<br />
efficient over <strong>the</strong> whole undulator structure, <strong>the</strong> phase between <strong>the</strong> sinosoidal terms<br />
within <strong>the</strong> brackets in Equati<strong>on</strong> 2.27 needs to be c<strong>on</strong>stant, i.e.:<br />
0 = dΨ±<br />
dt<br />
= −[k ±ku] ds<br />
dt<br />
The resulting wavelength can thus be calculated:<br />
λ = 2π<br />
k<br />
= ± 2π<br />
2kuγ 2<br />
�<br />
1+ K2<br />
2<br />
K2<br />
2<br />
−ω ≈ −kc1+ ±kuc (2.28)<br />
2γ2 �<br />
= λu<br />
2γ 2<br />
�<br />
1+ K2<br />
�<br />
2<br />
(2.29)<br />
in <strong>the</strong> last step, <strong>the</strong> negative branch of soluti<strong>on</strong>s have been dropped since <strong>on</strong>ly wavelengths<br />
larger than zero make physical sense. Our hope is to make Ψ+ c<strong>on</strong>stant to<br />
fulfill <strong>the</strong> res<strong>on</strong>ance c<strong>on</strong>diti<strong>on</strong> defined by Equati<strong>on</strong> 2.28. This is fulfilled if <strong>the</strong> electr<strong>on</strong>s<br />
lag behind <strong>the</strong> radiati<strong>on</strong> field <strong>on</strong>e λu per undulator period. The energy between<br />
<strong>the</strong> electr<strong>on</strong> <strong>beam</strong> <strong>and</strong> <strong>the</strong> radiati<strong>on</strong> field is exchanged with <strong>the</strong> same wavelength as<br />
sp<strong>on</strong>taneous undulator radiati<strong>on</strong>.
38 2. Synchrotr<strong>on</strong> radiati<strong>on</strong> <strong>and</strong> its properties<br />
ˆy<br />
ˆy<br />
ˆy<br />
ˆy<br />
ˆx<br />
ˆx<br />
ˆx<br />
ˆx<br />
v<br />
E<br />
0<br />
0<br />
λu<br />
Figure 2.8: The interacti<strong>on</strong> between <strong>the</strong> electr<strong>on</strong>s in <strong>the</strong> <strong>beam</strong> <strong>and</strong> <strong>the</strong> radiati<strong>on</strong> field give rise to a density<br />
modulati<strong>on</strong> of <strong>the</strong> electr<strong>on</strong> bunches. This occurs most efficiently if <strong>the</strong> <strong>the</strong> electr<strong>on</strong> bunch lags behind <strong>the</strong><br />
radiati<strong>on</strong> field with <strong>on</strong>e λu per period.<br />
dW<br />
dt<br />
v<br />
The electr<strong>on</strong> velocity is parallel with <strong>the</strong> electric field twice per period <strong>–</strong> <strong>the</strong>re<br />
= 0. The p<strong>on</strong>dermotive phase Ψ+, related to <strong>the</strong> negative branch as Ψ− =<br />
Ψ+ − 2kus when dΨ ±<br />
dt<br />
E<br />
= 0, oscillates twice per period <strong>and</strong> <strong>on</strong> average cancels out,<br />
i.e. for a homogeneous e - -distributi<strong>on</strong> half <strong>the</strong> electr<strong>on</strong>s gain energy while <strong>the</strong> o<strong>the</strong>r<br />
half looses it.<br />
As a result <strong>the</strong> electr<strong>on</strong>s, if bunched from <strong>the</strong> start, tend to become density modulated<br />
with <strong>the</strong> periodicity of <strong>the</strong> radiati<strong>on</strong> field <strong>–</strong> this process is called microbunching.<br />
The wavelength of <strong>the</strong> density modulati<strong>on</strong> is thus given also by Equati<strong>on</strong> 2.29.<br />
With <strong>the</strong> res<strong>on</strong>ant c<strong>on</strong>diti<strong>on</strong> fulfilled <strong>the</strong> electr<strong>on</strong> <strong>beam</strong> <strong>and</strong> <strong>the</strong> radiati<strong>on</strong> field can<br />
exchange energy over several (many) undulator periods which, taken toge<strong>the</strong>r with<br />
<strong>the</strong> microbunching, can lead to a net gain of energy in <strong>the</strong> radiati<strong>on</strong> field.<br />
So far we have c<strong>on</strong>sidered <strong>the</strong> electr<strong>on</strong> <strong>beam</strong> to be m<strong>on</strong>oenergetic <strong>–</strong> it is instructive<br />
to c<strong>on</strong>sider also a <strong>beam</strong> with an energy spread (which will later be seen to relate to<br />
v<br />
E<br />
λr<br />
ˆz<br />
ˆz<br />
ˆz<br />
ˆz
2.4. Microbunching 39<br />
o<strong>the</strong>r figures of merit for free electr<strong>on</strong> laser <strong>beam</strong>). We denote <strong>the</strong> energy spread by<br />
∆γ, <strong>the</strong>n we can write <strong>the</strong> p<strong>on</strong>dermotive phase change as:<br />
dΨ+<br />
dt<br />
K2<br />
2<br />
= −kc1+<br />
2<br />
�<br />
1 1<br />
−<br />
(γ +∆γ) 2 γ2 �<br />
≈ 2kuc ∆γ<br />
γ<br />
����<br />
=η<br />
(2.30)<br />
where in <strong>the</strong> last step <strong>the</strong> relative energy spread has been defined. Knowing this we<br />
can formulate <strong>the</strong> energy transfer rate:<br />
dW<br />
dt<br />
= dη<br />
dt γmec2<br />
(2.31)<br />
Using <strong>the</strong> two relati<strong>on</strong>ships found above we can write an equati<strong>on</strong> system in <strong>the</strong> two<br />
variables Ψ <strong>and</strong> η: ⎧<br />
⎪⎨ dΨ+<br />
dt<br />
⎪⎩<br />
dη<br />
dt<br />
= 2kucη<br />
= − eE0K<br />
2mecγ2 sinΨ<br />
with Ψ = Ψ+ as <strong>the</strong> phase of <strong>the</strong> radiati<strong>on</strong> field compared to <strong>the</strong> electr<strong>on</strong>s with<br />
∆γ = 0 somewhere where dW<br />
= 0. The system of differential equati<strong>on</strong>s can be<br />
dt<br />
combined to a single sec<strong>on</strong>d order differential equati<strong>on</strong>:<br />
¨Ψ+Ω 2 sinΨ = 0, Ω 2 = eE0kuK<br />
meγ 2<br />
For small oscillati<strong>on</strong>s (i.e. sinx ≈ x) this is nothing but an harm<strong>on</strong>ic oscillator:<br />
¨x+ω 2 x = 0. Large oscillati<strong>on</strong>s, where <strong>on</strong>e needs to keep <strong>the</strong> sine-term intact, cause<br />
<strong>the</strong> frequency to decrease; analogous to, for instance, a swing that can make a full<br />
loop.<br />
For <strong>the</strong> electr<strong>on</strong>s that deviate from <strong>the</strong> ”central” energy more energy is lost than<br />
gained. This fur<strong>the</strong>r drives <strong>the</strong> bunching since ”fast” electr<strong>on</strong>s slow down <strong>and</strong> ”slow”<br />
electr<strong>on</strong>s get accelerated. This l<strong>on</strong>gitudinal moti<strong>on</strong> of <strong>the</strong> electr<strong>on</strong>s reduce <strong>the</strong> coupling(c<strong>on</strong>tained<br />
in K)between <strong>the</strong> electr<strong>on</strong> bunch<strong>and</strong> <strong>the</strong>radiati<strong>on</strong> field, acorrecti<strong>on</strong><br />
need thus to be made, i.e.<br />
� � 2<br />
K<br />
K −→ K J0<br />
4+2K 2<br />
� � 2<br />
K<br />
−J1<br />
4+2K 2<br />
��<br />
For K close to unity <strong>the</strong> reducti<strong>on</strong> caused by <strong>the</strong> Bessel functi<strong>on</strong>s within <strong>the</strong> brackets<br />
is 0.9 <strong>and</strong> tends toward 0.7 for large K. This correcti<strong>on</strong> is comm<strong>on</strong>ly written as [JJ]<br />
in free electr<strong>on</strong> laser litterature.<br />
Exp<strong>on</strong>ential gain<br />
The radiated power in a spectrum emanating from sp<strong>on</strong>taneous radiati<strong>on</strong> is proporti<strong>on</strong>al<br />
to <strong>the</strong> number of emitters, i.e. no phase correlati<strong>on</strong> exist. In a free electr<strong>on</strong><br />
laser <strong>beam</strong> ideally all electr<strong>on</strong>s in <strong>the</strong> <strong>beam</strong> emit in phase, as stated previously such<br />
an ensamble’s radiated power is proporti<strong>on</strong>al to <strong>the</strong> square of <strong>the</strong> number of emitters.
40 2. Synchrotr<strong>on</strong> radiati<strong>on</strong> <strong>and</strong> its properties<br />
In a storage ring, part of <strong>the</strong> electr<strong>on</strong>s in a bunch emit in phase <strong>–</strong> <strong>the</strong> number of<br />
such emitters can be enhanced by various laser slicing schemes, all striving to increase<br />
<strong>the</strong> number of coherent emitters. � In general � <strong>the</strong> power from such a mixed ensamble<br />
2<br />
can be described by P = P0 Ne +NeFe ;<br />
��<br />
Fe =<br />
�2 cos(2πz/λ)S(z)dz<br />
(2.32)<br />
where S(z) is <strong>the</strong> l<strong>on</strong>gitudinal density distributi<strong>on</strong> of <strong>the</strong> electr<strong>on</strong>s, The number of<br />
electr<strong>on</strong>s in <strong>the</strong> storage ring case is Ne ∼ 10 10 .<br />
In a free electr<strong>on</strong> laser amplifier three collective phenomena c<strong>on</strong>tribute towards <strong>the</strong><br />
quadratic dependence <strong>on</strong> <strong>the</strong> number of emitters:<br />
1. Modulati<strong>on</strong> of <strong>the</strong> electr<strong>on</strong>s’ energies due to <strong>the</strong> interacti<strong>on</strong> with <strong>the</strong> radiati<strong>on</strong><br />
field.<br />
2. Change in <strong>the</strong> electr<strong>on</strong>s’ l<strong>on</strong>gitudinal positi<strong>on</strong>s from path length differences in<br />
<strong>the</strong> combined potential created by <strong>the</strong> radiati<strong>on</strong> field <strong>and</strong> <strong>the</strong> undulator field.<br />
3. A, so far, ignored growth of <strong>the</strong> radiati<strong>on</strong> field which enhance <strong>the</strong> two aforementi<strong>on</strong>ed<br />
effects.<br />
If we let e i2πz/λ−iωt describe <strong>the</strong> radiati<strong>on</strong> field (which develops according to <strong>the</strong><br />
wave equati<strong>on</strong>) <strong>and</strong> E = E0e iΦ describe <strong>the</strong> transverse oscillati<strong>on</strong>s of <strong>the</strong> electr<strong>on</strong>s,<br />
<strong>on</strong>e may formulate <strong>the</strong> three cooperating processes in a more specific language:<br />
� �<br />
∂ ∂<br />
+ E = i<br />
c∂t ∂z<br />
µ0<br />
2 aw<br />
�<br />
j<br />
e iΦ j<br />
γj<br />
(2.33)<br />
The right h<strong>and</strong> side of this expressi<strong>on</strong> clearly have a maximum when <strong>the</strong> phases Φj<br />
are <strong>the</strong> same, i.e. when <strong>the</strong> electr<strong>on</strong>s emit in phase. Fur<strong>the</strong>rmore, <strong>the</strong> strength of this<br />
maximum is clearly larger with increasing number of electr<strong>on</strong>s j.<br />
mc 2dγ<br />
dt<br />
aw<br />
= eE0 sin(Φ+Ψ) (2.34)<br />
γ<br />
This equati<strong>on</strong> describes how <strong>the</strong> energy transfer occurs between <strong>the</strong> electr<strong>on</strong>s <strong>and</strong> <strong>the</strong><br />
radiati<strong>on</strong> field. Here aw describes <strong>the</strong> coupling <strong>on</strong>-axis in <strong>the</strong> undulator so that for<br />
a planar undulator λu = λ0<br />
2γ2 � 2<br />
1+a w +γ 2 θ 2� , for a planar undulator a 2 w = K 2 /2.<br />
Lastly, <strong>the</strong> equati<strong>on</strong> below describes <strong>the</strong> energy modulati<strong>on</strong> of <strong>the</strong> electr<strong>on</strong> <strong>beam</strong><br />
which give rise to <strong>the</strong> microbunching of <strong>the</strong> electr<strong>on</strong>s. If <strong>the</strong> l<strong>on</strong>gitudinal velocity<br />
βz differs from <strong>the</strong> res<strong>on</strong>ant velocity ˜ βz <strong>the</strong> electr<strong>on</strong> slips in p<strong>on</strong>dermotive phase,<br />
electr<strong>on</strong>s with higher velocity move forward while slower <strong>on</strong>es are retarded.<br />
dΦ<br />
dt<br />
= 2πc<br />
λ<br />
� βz<br />
˜βz<br />
�<br />
−1<br />
(2.35)
2.4. Microbunching 41<br />
Scaled free electr<strong>on</strong> laser equati<strong>on</strong>s<br />
The equati<strong>on</strong>s above can be formulated compactly by utilizing <strong>the</strong> Pierce parameter:<br />
ρ = λu 4π<br />
4π<br />
2 ·j0 ·K 2 rms ·A 2 jj<br />
IA ·λu ·γ 3<br />
(2.36)<br />
where j0 is <strong>the</strong> <strong>beam</strong>’s current density, IA = mc 3 /e = 17 kA (<strong>the</strong> Alfvén current). Ajj<br />
is <strong>the</strong> coupling coefficient between <strong>the</strong> electr<strong>on</strong> <strong>and</strong> phot<strong>on</strong> <strong>beam</strong>s <strong>–</strong> for a helical field<br />
it is equal to unity, whereas for a planar sinusoidal magnetic field it is a combinati<strong>on</strong><br />
of Bessel functi<strong>on</strong>s of <strong>the</strong> first kind: Ajj = [J0(κ) − J1(κ)] with argument κ =<br />
K 2 rms/[2·(1+K 2 rms)]. To c<strong>on</strong>nect it str<strong>on</strong>ger with <strong>the</strong> results above we may write it<br />
as functi<strong>on</strong> of <strong>the</strong> undulator parameters <strong>and</strong> properties of <strong>the</strong> electr<strong>on</strong> <strong>beam</strong>:<br />
� �2/3 F1Kγ0Ωf<br />
ρ =<br />
4cγ 2 rku<br />
with this we can write a detuning parameter describing how <strong>the</strong> electr<strong>on</strong> <strong>beam</strong>’s<br />
energy relates to <strong>the</strong> res<strong>on</strong>ant energy of <strong>the</strong> radiated field:<br />
δ = γ2 0 −γ 2 r<br />
2γ 2 rρ<br />
≈ ∆γ<br />
γρ<br />
= η<br />
ρ<br />
where <strong>the</strong> approximati<strong>on</strong> holds for small deviati<strong>on</strong>s from <strong>the</strong> res<strong>on</strong>ant energy. The<br />
res<strong>on</strong>ant energy is given by <strong>the</strong> undulator equati<strong>on</strong> as:<br />
γr = kr<br />
2ku<br />
� µ0Nee 2 c 2<br />
1+K 2 /2<br />
2<br />
The Ωf is <strong>the</strong> plasma frequency which enters as a parameter in <strong>the</strong> space<br />
γme<br />
charge coefficient which describes <strong>the</strong> repulsi<strong>on</strong> forces between <strong>the</strong> electr<strong>on</strong>s in <strong>the</strong><br />
<strong>beam</strong> <strong>–</strong> something which counteracts <strong>the</strong> micro-bunching. The balance between <strong>the</strong><br />
space charge effects <strong>and</strong> micro-bunching is <strong>on</strong>e of <strong>the</strong> reas<strong>on</strong>s why <strong>the</strong> amplificati<strong>on</strong><br />
eventually saturates. The space charge coefficient is defined as:<br />
σ = Ωfγ0<br />
�<br />
1<br />
ckrρ 1+K 2 /2<br />
We write our new set of variables, describing <strong>the</strong> energy-spread, field amplitude <strong>and</strong><br />
positi<strong>on</strong>-time, following[41]:<br />
η ′ = η<br />
ρ<br />
A = F1Kkr<br />
4γrkuρ2 �<br />
−iKre iΨ�<br />
˜z = 2ckrργ2 r<br />
γ2 t<br />
0<br />
where in <strong>the</strong> sec<strong>on</strong>d equati<strong>on</strong> we have introduced <strong>the</strong> complex amplitude of <strong>the</strong> vector<br />
potential. For <strong>the</strong> details <strong>on</strong> <strong>the</strong> derivati<strong>on</strong> <strong>–</strong> not important for <strong>the</strong> following
42 2. Synchrotr<strong>on</strong> radiati<strong>on</strong> <strong>and</strong> its properties<br />
<strong>–</strong> <strong>the</strong> reader is referred to B<strong>on</strong>ifacio et al. [41]. With <strong>the</strong> new variables above our<br />
equati<strong>on</strong>s 2.35, 2.35 <strong>and</strong> 2.35 can be normalized to <strong>the</strong> system of equati<strong>on</strong>s:<br />
˙θ = δ +η ′<br />
˙η ′ = − � A+iσ 2� e −θ�� e iθ −c.c.<br />
˙<br />
A = � e −θ�<br />
This 1-D system of equati<strong>on</strong>s can be solved analytically for a few idealized cases,<br />
o<strong>the</strong>rwise we have to utilize numerical methods to solve <strong>the</strong>m. Without energyspread<br />
<strong>and</strong> using <strong>the</strong> reas<strong>on</strong>able ansatz A ∝ e iΛ˜z we find that <strong>the</strong> cubic dispersi<strong>on</strong> relati<strong>on</strong>:<br />
� (Λ+δ) 2 −σ 2 � Λ = −1<br />
reduces to Λ 3 = −1.<br />
This equati<strong>on</strong> have three soluti<strong>on</strong>s describing <strong>the</strong> free electr<strong>on</strong> laser collective instability:<br />
<strong>the</strong> real soluti<strong>on</strong>, which is oscillatory, <strong>and</strong> two complex soluti<strong>on</strong>s which is<br />
decaying <strong>and</strong> growing respectively. In <strong>the</strong> start-up phase <strong>the</strong> three soluti<strong>on</strong>s have<br />
comparable magnitudes, after a certain time <strong>the</strong> growing soluti<strong>on</strong> will dominate, <strong>and</strong><br />
<strong>the</strong> field amplitude grows exp<strong>on</strong>entially. Within <strong>the</strong> linear <strong>on</strong>e dimensi<strong>on</strong>al framework<br />
we can not explain where this growth process ends (for instance via <strong>beam</strong> blow-up<br />
due to space-charge effects) as it is a n<strong>on</strong>-linear process.<br />
Inserting ˜z = 2kuρz (using z = ct <strong>and</strong> no energy spread) into our ansatz gives <strong>the</strong><br />
scales soluti<strong>on</strong> A ∝ e iΛz/Lg , defining <strong>the</strong> <strong>on</strong>e-dimensi<strong>on</strong>al gain-length 7 :<br />
Lg = λu<br />
2 √ 3πρ<br />
which is <strong>the</strong> undulator-length needed for <strong>the</strong> field to grow a factor e. As will discussed<br />
below, differentfactors combinetolimit<strong>the</strong>gainafteracertainlengthin<strong>the</strong>undulator<br />
<strong>–</strong> it can be shown that this length is[31]:<br />
Ls ≈ 22Lg<br />
Significant effort is put to keep <strong>the</strong> gain-length (<strong>and</strong> thus saturati<strong>on</strong>-length) as short<br />
as possible for ec<strong>on</strong>omical reas<strong>on</strong>s.<br />
The results here is valid for a m<strong>on</strong>o-energetic <strong>beam</strong>, introducing energy-spread<br />
effects <strong>the</strong> gain negatively as it prevents <strong>the</strong> bunching of <strong>the</strong> electr<strong>on</strong>s at <strong>the</strong> proper<br />
phase.<br />
The output power at saturati<strong>on</strong> of <strong>the</strong> free electr<strong>on</strong> laser can also be expressed in<br />
terms of ρ:<br />
�<br />
〈γ〉Ipeakmc<br />
Psat = ρP<strong>beam</strong> = ρ<br />
2�<br />
e<br />
Besides maximizing ρ to shorten <strong>the</strong> undulator, a large value of <strong>the</strong> parameter also<br />
give greater radiati<strong>on</strong> output power.<br />
7 By solving −ℜe (iΛ) = √ 3/2
2.4. Microbunching 43<br />
Saturati<strong>on</strong> <strong>–</strong> limiting factors for <strong>the</strong> gain<br />
The Pierce parameter defined above shows up in several relati<strong>on</strong>s highlighting <strong>the</strong><br />
dem<strong>and</strong>s <strong>on</strong> <strong>the</strong> quality of <strong>the</strong> electr<strong>on</strong> <strong>beam</strong> for <strong>the</strong> free electr<strong>on</strong> laser amplificati<strong>on</strong><br />
to be efficient. Electr<strong>on</strong>s transfer energy to <strong>the</strong> radiati<strong>on</strong> field until <strong>the</strong>y fall out of<br />
<strong>the</strong> b<strong>and</strong>width of <strong>the</strong> free electr<strong>on</strong> laser <strong>and</strong> <strong>the</strong> synchr<strong>on</strong>ism c<strong>on</strong>diti<strong>on</strong> is no l<strong>on</strong>ger<br />
fulfilled. We may thus formulate <strong>the</strong> efficiency of a free electr<strong>on</strong> laser simply by<br />
restating <strong>the</strong> last equati<strong>on</strong> as ρ = Psat/P<strong>beam</strong> <strong>–</strong> <strong>the</strong> Pierce parameter is thus a measure<br />
<strong>on</strong> how good a machine is when it comes to c<strong>on</strong>verting electr<strong>on</strong> <strong>beam</strong> energy to<br />
radiati<strong>on</strong> energy.<br />
Am<strong>on</strong>g <strong>the</strong> limiting factors for <strong>the</strong> gain process (<strong>and</strong> indeed <strong>the</strong> free electr<strong>on</strong><br />
laser process as a whole) is:<br />
• Energy spread around <strong>the</strong> res<strong>on</strong>ant energy<br />
• Deviati<strong>on</strong> of <strong>the</strong> mean energy from <strong>the</strong> res<strong>on</strong>ant energy<br />
• The size <strong>and</strong> divergence of <strong>the</strong> electr<strong>on</strong> <strong>beam</strong>, that is normalized emittance.<br />
• Diffracti<strong>on</strong> effects in <strong>the</strong> <strong>beam</strong>.<br />
In Equati<strong>on</strong> 2.24 we found that <strong>the</strong> frequency spectrum of undulator radiati<strong>on</strong><br />
is proporti<strong>on</strong>al to � �<br />
sinw 2<br />
with w ∝ (γ − γr)/γr. The gain curve, showing how a<br />
w<br />
mode with arbitrary energy will get amplified in <strong>the</strong> undulator, for <strong>the</strong> free electr<strong>on</strong><br />
laser process can be shown to be proporti<strong>on</strong>al to <strong>the</strong> derivative of that functi<strong>on</strong>, i.e.<br />
G(ω) ∝ − d<br />
� �2 sinw<br />
dω w<br />
The proporti<strong>on</strong>ality c<strong>on</strong>stant c<strong>on</strong>tains parameters that define <strong>the</strong> electr<strong>on</strong> <strong>beam</strong> <strong>and</strong><br />
radiati<strong>on</strong> field properties as dictated by <strong>the</strong> list above <strong>–</strong> a detailed treatment requires<br />
assumpti<strong>on</strong>s <strong>on</strong> <strong>the</strong> electr<strong>on</strong> <strong>beam</strong> <strong>and</strong> <strong>the</strong> details would vary 8 .<br />
8 See for instance <strong>the</strong> books by Saldin <strong>and</strong> co-workers, or Wiedemann[42, 43], or for a more<br />
compact account <strong>the</strong> review in Ref. [44]. Said references also serve as good general references for<br />
this chapter for readers who want a more detailed <strong>and</strong> perhaps more stringent account of matters<br />
than presented in this introductory text to <strong>the</strong> subject at h<strong>and</strong>.<br />
Gain<br />
1<br />
0.5<br />
−10 −5 5 10<br />
−0.5<br />
−1<br />
Figure 2.9: The small-signal gain functi<strong>on</strong> for a free electr<strong>on</strong> laser amplifier.<br />
w
44 2. Synchrotr<strong>on</strong> radiati<strong>on</strong> <strong>and</strong> its properties<br />
In Figure 2.9 <strong>the</strong> derivative of <strong>the</strong> negative cardinal sine functi<strong>on</strong> is plotted, this<br />
is <strong>the</strong> functi<strong>on</strong>al dependence <strong>on</strong> <strong>the</strong> <strong>beam</strong>’s energy for <strong>the</strong> gain curve as given by <strong>the</strong><br />
equati<strong>on</strong> above. It can be seen that a <strong>beam</strong> must have a certain, not too large, energy<br />
spread <strong>and</strong> ideally a small shift towards higher energies than <strong>the</strong> res<strong>on</strong>ance energy<br />
to have a positive gain (for a nearly m<strong>on</strong>ochromatic <strong>beam</strong> <strong>the</strong> optimal shift is about<br />
+1.2 <strong>on</strong> <strong>the</strong> gain curve).<br />
An energy spread prevents efficient microbunching of all electr<strong>on</strong>s with <strong>the</strong> same<br />
p<strong>on</strong>dermotivephase, this smears out <strong>the</strong>electr<strong>on</strong> bunchwhich preventsefficient transfer<br />
of energy into <strong>the</strong> res<strong>on</strong>ant mode with (fundamental) wavelength λr. The res<strong>on</strong>ant<br />
energy being γr = � (λu/2λ)·(1+a 2 w) <strong>the</strong> initial energy spread σ ′ of <strong>the</strong> electr<strong>on</strong><br />
<strong>beam</strong> should be kept<br />
σ ′<br />
≪ ρ<br />
γr<br />
The undulator res<strong>on</strong>ant energy needs, of course, to be tuned to <strong>the</strong> <strong>beam</strong> energy,<br />
i.e. <strong>the</strong> energies needs to be matched:<br />
� �<br />
�〈γ〉−γr<br />
�<br />
� �<br />
� � ≪ ρ<br />
γr<br />
Greater efficiency is obtained if <strong>the</strong> electr<strong>on</strong> <strong>beam</strong> <strong>and</strong> <strong>the</strong> phot<strong>on</strong> <strong>beam</strong> overlap<br />
exactly. An electr<strong>on</strong> oscillates around <strong>the</strong> central path through <strong>and</strong> undulator with a<br />
period that is muchl<strong>on</strong>ger than<strong>the</strong> undulator’s period; this moti<strong>on</strong> is called abetatr<strong>on</strong><br />
moti<strong>on</strong>. Part of <strong>the</strong> electr<strong>on</strong>’s kinetic energy is <strong>the</strong>nce partiti<strong>on</strong>ed into <strong>the</strong> executi<strong>on</strong><br />
of this betatr<strong>on</strong> moti<strong>on</strong> which slows down <strong>the</strong> electr<strong>on</strong>, effectively acting as an energy<br />
spread. The betatr<strong>on</strong> amplitude functi<strong>on</strong> β ′ have a direct effect <strong>on</strong> <strong>the</strong> normalized<br />
transverse emittance of <strong>the</strong> phot<strong>on</strong> <strong>beam</strong> which dictates <strong>the</strong> following dem<strong>and</strong>:<br />
ǫn ≪ 4γβ′ 〈γ〉<br />
ρ<br />
The beta oscillati<strong>on</strong> needs to be optimized to strike a balance between a high electr<strong>on</strong><br />
density <strong>and</strong> space charge effects which degrades <strong>the</strong> emittance <strong>–</strong> a good starting point<br />
is to set it equal to <strong>the</strong> gain length, β ′ ≈ Lg ≈ λ<br />
ρ. This gives us a c<strong>on</strong>diti<strong>on</strong> <strong>on</strong> how<br />
4π<br />
<strong>the</strong> emittances of <strong>the</strong> electr<strong>on</strong> (ǫ) <strong>and</strong> <strong>the</strong> phot<strong>on</strong> <strong>beam</strong> (diffracti<strong>on</strong> limited λ/4π)<br />
should be matched:<br />
ǫ = ǫn λ<br />
<<br />
γ 4π<br />
If this c<strong>on</strong>diti<strong>on</strong> is fulfilled nei<strong>the</strong>r <strong>beam</strong> diverges faster than <strong>the</strong> o<strong>the</strong>r.<br />
Diffracti<strong>on</strong> effects in <strong>the</strong> <strong>beam</strong> softens <strong>the</strong> coupling between <strong>the</strong> radiati<strong>on</strong> field <strong>and</strong><br />
<strong>the</strong> electr<strong>on</strong> <strong>beam</strong>, to account for those properly a more intricate three-dimensi<strong>on</strong>al<br />
model needs to be c<strong>on</strong>structed[17]. A 3-d analogue to our <strong>on</strong>e dimensi<strong>on</strong>al Pierce<br />
parameter can be found where <strong>the</strong> relati<strong>on</strong>s states are still fulfilled.<br />
2.5 Sase<br />
So far our treatment of <strong>the</strong> free electr<strong>on</strong> laser problem have been d<strong>on</strong>e without any<br />
assumpti<strong>on</strong> <strong>on</strong> <strong>the</strong> nature of <strong>the</strong> radiati<strong>on</strong> mode(s) that are amplified. In <strong>the</strong> previous<br />
chapter, schemes aimed to create c<strong>on</strong>diti<strong>on</strong>s for amplificati<strong>on</strong> of already coherently<br />
λu
2.5. Sase 45<br />
radiati<strong>on</strong> modes from <strong>the</strong> start were discussed. Such schemes were not employed in<br />
<strong>the</strong> X-ray range until recently <strong>–</strong> at <strong>the</strong> Fermi@Elettra free electr<strong>on</strong> laser in Italy,<br />
which successfully dem<strong>on</strong>strated Hghg seeding in december 2010.<br />
The process of Sase utilizes <strong>the</strong> broadb<strong>and</strong> sp<strong>on</strong>taneous undulator radiati<strong>on</strong> from<br />
<strong>the</strong> first few gain-lengths of <strong>the</strong> undulator secti<strong>on</strong> as a seed for <strong>the</strong> remainder of <strong>the</strong><br />
amplificati<strong>on</strong> process. Owing to this <strong>the</strong> res<strong>on</strong>ance c<strong>on</strong>diti<strong>on</strong> is always fulfilled for<br />
some modes of <strong>the</strong> radiati<strong>on</strong>, thus <strong>the</strong> number of radiati<strong>on</strong> modes <strong>and</strong> <strong>the</strong>ir energy is<br />
sampled from a r<strong>and</strong>om distributi<strong>on</strong> (within <strong>the</strong> b<strong>and</strong>width of <strong>the</strong> amplifier which is<br />
also related to <strong>the</strong> Pierce parameter: ∆ω<br />
= ρ) <strong>on</strong> a shot-to-shot basis.<br />
ω<br />
The shot-to-shot fluctuati<strong>on</strong>s of <strong>the</strong> radiati<strong>on</strong> pulse energy follows a Gamma distributi<strong>on</strong><br />
[45] whose free parameter M can be interpreted as <strong>the</strong> number of spikes<br />
in <strong>the</strong> final frequency spectrum. The length of <strong>the</strong> individual spikes is proporti<strong>on</strong>al<br />
to <strong>the</strong> gain-length <strong>and</strong> <strong>the</strong> wavelength of <strong>the</strong> radiati<strong>on</strong> as λ/λuLg. Shorter pulses<br />
increases <strong>the</strong> number of spikes as <strong>the</strong> energy c<strong>on</strong>tent of such pulse is broader. The<br />
width of <strong>the</strong> Gamma distributi<strong>on</strong> is inversly proporti<strong>on</strong>al to √ M; <strong>the</strong> fluctuati<strong>on</strong> of<br />
<strong>the</strong> power is distributed as a negative exp<strong>on</strong>ential[42].<br />
Coherence properties<br />
Coherence means that <strong>the</strong> relative phase of waves is fixed. Spatial coherence between<br />
two radiati<strong>on</strong> sources means that <strong>the</strong> phot<strong>on</strong>s originating from <strong>the</strong>m occupy<br />
<strong>the</strong> same volume in phase space. In practice this means that emitters within <strong>the</strong><br />
coherence-length/area can amplify each o<strong>the</strong>r by c<strong>on</strong>structive interference if <strong>the</strong> phase<br />
relati<strong>on</strong>ship means that <strong>the</strong>y are equal.<br />
Temporal coherence can be thought of in <strong>the</strong> same manner: waves emitted at<br />
different times have a phase-correlati<strong>on</strong> that is predictable. The time during which<br />
<strong>the</strong> phase-relati<strong>on</strong>ship remains locked is referred to as <strong>the</strong> coherence-time. Waves<br />
emitted during this time interval (e.g. from electr<strong>on</strong>s al<strong>on</strong>g <strong>the</strong> electr<strong>on</strong> bunch) can<br />
c<strong>on</strong>structively interfere with each o<strong>the</strong>r if <strong>the</strong> phases are equal. The coherence time<br />
τ is intimately related to <strong>the</strong> spectral width ∆λ of <strong>the</strong> source via:<br />
∆λ = λ2<br />
cτ<br />
A l<strong>on</strong>g coherence time thus ensures a narrow spectral b<strong>and</strong>width of <strong>the</strong> source. This<br />
is <strong>the</strong> case for a normal Laser. In a Sase free electr<strong>on</strong> laser many modes are excited<br />
with various coherence-times for each meaning that each mode give rise to a narrow<br />
spike in <strong>the</strong> spectrum, whereas <strong>the</strong> compound spectrum is broad[45].<br />
Sase ensures very high transverse (spatial) coherence at <strong>the</strong> saturati<strong>on</strong> point[45<strong>–</strong><br />
47]; towards <strong>the</strong> end of <strong>the</strong> linear gain regime ideally all electr<strong>on</strong>s in <strong>the</strong> <strong>beam</strong> radiate<br />
in c<strong>on</strong>cert. This makes <strong>the</strong> free electr<strong>on</strong> laser extremely attractive for diffractive<br />
imaging[48] <strong>and</strong> o<strong>the</strong>r experiments relying heavily <strong>on</strong> this property of <strong>the</strong> X-ray<br />
source[49]. As we have seen earlier <strong>the</strong> ratio between <strong>the</strong> coherent radiati<strong>on</strong> part of<br />
<strong>the</strong> radiati<strong>on</strong> spectrum <strong>and</strong> <strong>the</strong> in-coherent (sp<strong>on</strong>taneous) radiati<strong>on</strong> can be extremely<br />
high in a free electr<strong>on</strong> laser whereas in a storage ring <strong>the</strong> relati<strong>on</strong>ship <strong>the</strong> coherent<br />
part of <strong>the</strong> undulator spectrum is significantly lower[50].
46 2. Synchrotr<strong>on</strong> radiati<strong>on</strong> <strong>and</strong> its properties<br />
Summary<br />
• Synchrotr<strong>on</strong> radiati<strong>on</strong> is radiati<strong>on</strong> emitted from accelerated<br />
relativistic charged particles.<br />
• This type of radiati<strong>on</strong> can be produced in bending magnets in<br />
storage rings. The number of phot<strong>on</strong>s emitted <strong>and</strong> <strong>the</strong> quality<br />
of <strong>the</strong> phot<strong>on</strong> <strong>beam</strong> can be optimized with magnetic arrays.<br />
<strong>–</strong> Bending magnet <strong>–</strong> magnetic field strength limited by <strong>the</strong><br />
c<strong>on</strong>diti<strong>on</strong> that <strong>the</strong> electr<strong>on</strong>s should stay in orbit in <strong>the</strong><br />
storage ring. The number of emitted phot<strong>on</strong>s is proporti<strong>on</strong>al<br />
to <strong>the</strong> <strong>beam</strong> energy <strong>and</strong> <strong>the</strong> curvature of <strong>the</strong> bend<br />
(denote this flux Φ).<br />
<strong>–</strong> A wiggler can have a str<strong>on</strong>ger magnetic field since it returns<br />
<strong>the</strong> electr<strong>on</strong> <strong>beam</strong> to its original path <strong>–</strong> it is a sequence<br />
of bending magnets. The phot<strong>on</strong> flux is proporti<strong>on</strong>al<br />
to <strong>the</strong> numberof magnetic periods, i.e. ∝ Nw×Φ.<br />
<strong>–</strong> An undulator have many magnetic periods that have<br />
smaller field strengths than <strong>the</strong> wigglers <strong>–</strong> however <strong>the</strong><br />
sp<strong>on</strong>taneous emissi<strong>on</strong> can c<strong>on</strong>structively interfere for certain<br />
wavelengths yielding a dependence of <strong>the</strong> flux that<br />
is proporti<strong>on</strong>al to <strong>the</strong> square of <strong>the</strong> number of magnetic<br />
periods, i.e. ∝ N 2 u ×Φ.<br />
• In a free electr<strong>on</strong> laser <strong>the</strong> electr<strong>on</strong> bunches become density<br />
modulated with <strong>the</strong> period of <strong>the</strong> radiati<strong>on</strong> field. The phot<strong>on</strong><br />
flux is <strong>the</strong>refore proporti<strong>on</strong>al to <strong>the</strong> number of cooperating<br />
electr<strong>on</strong>s in <strong>the</strong> <strong>beam</strong> in additi<strong>on</strong> to <strong>the</strong> undulator flux: ∝<br />
N 2 u ×Ne ×Φ.<br />
• Anundulatorhasaspectrumwithharm<strong>on</strong>icsofafundamental<br />
frequency. The frequency spectrum is dominated by <strong>the</strong> sinc<br />
functi<strong>on</strong> ∼ sinx<br />
. The b<strong>and</strong>width of an undulator is inversely<br />
x<br />
proporti<strong>on</strong>al to <strong>the</strong> number of periods.<br />
• The gain-functi<strong>on</strong> for a free electr<strong>on</strong> laser amplifier can be described<br />
by<strong>the</strong> derivative of <strong>the</strong> sinc functi<strong>on</strong>: we must have an<br />
electr<strong>on</strong> <strong>beam</strong> with slightly higher energy than <strong>the</strong> res<strong>on</strong>ance<br />
energy with a small energy spread for optimal gain.<br />
• Sase starts up from noise in <strong>the</strong> <strong>beam</strong> resulting in a r<strong>and</strong>om<br />
selecti<strong>on</strong> of radiating modes <strong>–</strong> giving rise to a broad<br />
spectrum with many spikes with poor l<strong>on</strong>gitudinal coherence.<br />
Each spike is diffracti<strong>on</strong> limited.<br />
• Short-pulses <strong>and</strong> low charge gives fewer radiating modes[51].<br />
Am<strong>on</strong>ochromator betweentwoundulatorsecti<strong>on</strong>s canbeused<br />
to select a desired mode[52].<br />
• Seeding schemes serves to increase <strong>the</strong> micro-bunching before<br />
<strong>the</strong>freeelectr<strong>on</strong>laseramplificati<strong>on</strong> takesplacewhichincreases<br />
<strong>the</strong> degree of l<strong>on</strong>gitudinal coherence.<br />
• Simulati<strong>on</strong>s Genesis[53], Fast[54]. See for instance <strong>the</strong> start<br />
to end simulati<strong>on</strong>s of <strong>the</strong> Lcls facility described in Ref. [55].
3. Free electr<strong>on</strong> laser ”hardware”<br />
Written by: A. Lindblad<br />
3.1 A prototypical FEL amplifier<br />
In this chapter we will have a closer look at what is actually inside <strong>the</strong> tunnel of a<br />
free electr<strong>on</strong> laser facility. Key technologies will be presented <strong>and</strong> at which facilities<br />
<strong>the</strong>y are utilized.<br />
A free electr<strong>on</strong> laser c<strong>on</strong>sists, in principle, of four parts before <strong>the</strong> user experiments<br />
(<strong>and</strong> <strong>the</strong>ir optics): (1) an electr<strong>on</strong> gun optimized for low emittance which injects a<br />
short intense electr<strong>on</strong> bunch into (2) a linear accelerator structure followed by (3) <strong>on</strong>e<br />
or more undulator secti<strong>on</strong>(s) where <strong>the</strong> free electr<strong>on</strong> laser process takes place; in some<br />
cases <strong>the</strong> three first principal secti<strong>on</strong>s are followed in turn by an (4) gas-attenuator<br />
secti<strong>on</strong>.<br />
e - -gun<br />
3.2 Electr<strong>on</strong> guns<br />
Accelerating structure<br />
Figure 3.1: Schematic of a free electr<strong>on</strong> laser facility.<br />
Undulator(s) Gas attenuator<br />
The electr<strong>on</strong> emitter source at <strong>the</strong> start of <strong>the</strong> accelerator is comm<strong>on</strong>ly referred to<br />
as an electr<strong>on</strong> gun. In <strong>the</strong> ideal case it produce a m<strong>on</strong>oenergetic current spike with<br />
minimal spatial extent. This current spike (see Figure 3.2), produced with electr<strong>on</strong><br />
emissi<strong>on</strong>, is <strong>transport</strong>ed <strong>and</strong> focussed with an electric field (sometimes in combinati<strong>on</strong><br />
with a magnetic field) to <strong>the</strong> exit of <strong>the</strong> gun.<br />
Since electr<strong>on</strong>s carry charge <strong>the</strong>y can not be compressed into an arbitrarily small<br />
<strong>beam</strong>. Space charge effects effectively limits <strong>the</strong> minimal size of <strong>the</strong> electr<strong>on</strong> <strong>beam</strong>.<br />
As will be seen below this is <strong>on</strong>e of <strong>the</strong> principal limitati<strong>on</strong>s when c<strong>on</strong>structing guns<br />
for free electr<strong>on</strong> lasers.<br />
47
48 3. Free electr<strong>on</strong> laser ”hardware”<br />
I [A]<br />
Time [t]<br />
y<br />
x<br />
I [A]<br />
Time [t]<br />
Figure 3.2: Ideal properties of an electr<strong>on</strong> gun (left) compared to real life properties.<br />
Electr<strong>on</strong> guns can be divided into categories by <strong>the</strong> method of electric field generati<strong>on</strong><br />
(direct current (DC) radiofrequency (RF)), by <strong>the</strong> method of electr<strong>on</strong> emissi<strong>on</strong>,<br />
i.e. <strong>the</strong>rmi<strong>on</strong>ic, photocathode, cold emissi<strong>on</strong> or plasma source. A general divisi<strong>on</strong> also<br />
exist for accelerators between hot <strong>and</strong> cold technology, i.e. normally c<strong>on</strong>ducting vs.<br />
superc<strong>on</strong>ducting <strong>–</strong> both of which have <strong>the</strong>ir pros <strong>and</strong> c<strong>on</strong>s.<br />
A direct current electrostatic <strong>the</strong>rmi<strong>on</strong>ic gun is arguably <strong>the</strong> simplest: a hot cathode<br />
emits electr<strong>on</strong>s through <strong>the</strong>rmi<strong>on</strong>ic emissi<strong>on</strong> (i.e. <strong>the</strong> cathode is hot enough so<br />
that electr<strong>on</strong>s can escape from <strong>the</strong> surface) cased by <strong>the</strong> heating from <strong>the</strong> direct current<br />
going through <strong>the</strong> cathode <strong>–</strong> <strong>the</strong> electr<strong>on</strong>s from <strong>the</strong> cathode are <strong>the</strong>n accelerated<br />
away via an electrostatic field.<br />
Of course <strong>the</strong> accelerating field need not be static. Ei<strong>the</strong>r an RF pulse provide<br />
<strong>the</strong> accelerating potential or a pulsed DC field can provide <strong>the</strong> same. For instance,<br />
<strong>the</strong> Scss free electr<strong>on</strong> laser at <strong>the</strong> Spring-8 site in Japan a <strong>the</strong>rmi<strong>on</strong>ic gun is used<br />
toge<strong>the</strong>r with a pulsed DC field of 500 kV with a CeB6 cathode[56, 57].<br />
Nei<strong>the</strong>r cold emissi<strong>on</strong> (also called field emissi<strong>on</strong>) nor plasma source electrodes are<br />
used for free electr<strong>on</strong> laser electr<strong>on</strong> guns. Field emissi<strong>on</strong> emitters are though an area<br />
of currentresearch[58]. Photocathode guns <strong>on</strong> <strong>the</strong>o<strong>the</strong>r h<strong>and</strong> are used bothat Flash,<br />
Fermi <strong>and</strong> at <strong>the</strong> Lcls. A photocathode gun is c<strong>on</strong>structed from a laser that can<br />
photoi<strong>on</strong>ize a cathode.<br />
General requirements<br />
Generally, <strong>the</strong> <strong>beam</strong> dynamics throughout <strong>the</strong> accelerator downstream from <strong>the</strong> electr<strong>on</strong><br />
gun can be described by independent l<strong>on</strong>gitudinal <strong>and</strong> transverse parts. In this<br />
approximati<strong>on</strong> a few parameters are critical at <strong>the</strong> start of <strong>the</strong> undulator: charge per<br />
bunch, <strong>the</strong> geometrical transverse emittance <strong>and</strong> <strong>the</strong> l<strong>on</strong>gitudinal emittance.<br />
For lasing at X-ray wavelengts, <strong>the</strong> geometric emittance must be smaller than<br />
λ/4π (where λ is <strong>the</strong> phot<strong>on</strong> wavelength), i.e.that <strong>the</strong> electr<strong>on</strong> <strong>beam</strong> must overlap<br />
sufficiently/totally with <strong>the</strong> generated phot<strong>on</strong>-<strong>beam</strong>.<br />
The geometric emittance is proporti<strong>on</strong>al to <strong>the</strong> normalized emittance divided by<br />
<strong>the</strong> <strong>beam</strong> energy[59]<br />
εg = εn<br />
E<br />
thus, a small normalized emittance allow for a lowering of <strong>the</strong> <strong>beam</strong> energy of <strong>the</strong><br />
accelerator <strong>–</strong> which in turn lowers <strong>the</strong> total cost for <strong>the</strong> facility.<br />
The emittance of <strong>the</strong> electr<strong>on</strong> <strong>beam</strong> is defined by <strong>the</strong> electr<strong>on</strong> gun where <strong>the</strong> charge<br />
cloud to be accelerated is created. The ultimate performance of a free electr<strong>on</strong> laser is<br />
ultimately determined by quality of <strong>the</strong> electr<strong>on</strong> <strong>beam</strong> at <strong>the</strong> start of <strong>the</strong> accelerating<br />
y<br />
x
3.2. Electr<strong>on</strong> guns 49<br />
structure. More precisely <strong>the</strong> emittance of <strong>the</strong> electr<strong>on</strong> <strong>beam</strong> needs to be low, as this<br />
quantity can <strong>–</strong> in <strong>the</strong> best case scenario <strong>–</strong> be c<strong>on</strong>served throughout <strong>the</strong> accelerator.<br />
Since performance (<strong>and</strong> cost efficiency) can be gained by c<strong>on</strong>structing an low emittance<br />
electr<strong>on</strong> gun a lot of effort have been (<strong>and</strong> still is) put into research <strong>and</strong> development<br />
in this area (for a recent overview see W. A. Ferrario[60]).<br />
The l<strong>on</strong>gitudinal emittance <strong>and</strong> <strong>the</strong> bunch charge define two important parameters<br />
for <strong>the</strong> lasing process: <strong>the</strong> energy spread <strong>and</strong> <strong>the</strong> peak current. The path difference<br />
of <strong>the</strong> electr<strong>on</strong>s (caused by, for instance energy spread) in <strong>the</strong> undulator over <strong>on</strong>e<br />
gain-length must be very small (very much smaller than <strong>the</strong> radiati<strong>on</strong> wavelength)<br />
allow microbunching to occur.<br />
Table 3.1, c<strong>on</strong>stitutes a wish-list for electr<strong>on</strong> guns suitable for X-ray free electr<strong>on</strong><br />
lasers. As will become evident, it is hard to find guns that simultaneously fulfill all of<br />
<strong>the</strong> menti<strong>on</strong>ed points. The accelerator structure (normal c<strong>on</strong>ducting, superc<strong>on</strong>ducting)<br />
<strong>and</strong> user dem<strong>and</strong>s <strong>on</strong> <strong>the</strong> facility will guide <strong>the</strong> choices.<br />
Parameter Value & Comments<br />
Repetiti<strong>on</strong> rate Hz to 100’s of MHz<br />
Charge per bunch Tens of pC to ∼ nC<br />
Normalized emittance ∼ 0.1 to ∼ 1 µm<br />
Energy at gun exit ≥∼ 0.5 MeV<br />
E-field at <strong>the</strong> cathode ≥∼ 10 MV/m<br />
B-field compatibility emittance compensati<strong>on</strong><br />
Spatial distributi<strong>on</strong> c<strong>on</strong>trollable<br />
Bunch length (rms) fs to 10’s of ps<br />
Vacuum 10 −9 −10 −11 mbar<br />
Load-lock compatibility Facilitate cathode replacement<br />
High reliability User facility operati<strong>on</strong><br />
Table 3.1: Some requirements for X-ray free electr<strong>on</strong> laser electr<strong>on</strong> guns.<br />
The design parameters of a facility vis-à-vis average brightness <strong>and</strong> flux sets <strong>the</strong><br />
repetiti<strong>on</strong> rate <strong>and</strong> peak current; <strong>the</strong> desired radiati<strong>on</strong> wavelength sets <strong>the</strong> electr<strong>on</strong><br />
energy <strong>and</strong> undulator energy <strong>and</strong> field; phot<strong>on</strong> pulse length <strong>and</strong> radiati<strong>on</strong> field intensity<br />
c<strong>on</strong>strain choices of seeding schemes, peak current, total charge, etc.<br />
Choice of cathode materials range from pure metals to various semic<strong>on</strong>ductor compounds<br />
(e.g. CeB6[56], ZrC[61]). They are chosen with respect to <strong>the</strong>ir stability <strong>and</strong><br />
quantum efficiency. With low repetiti<strong>on</strong> rates (up to about 1 kHz) presently available<br />
lasers can in combinati<strong>on</strong> with a low quantum efficiency material (i.e. QE ≈<br />
10 −5 −10 −4 ) achieve a high enough photocurrent to be employed. Megahertz repetiti<strong>on</strong><br />
rates require materials with higher efficiency in <strong>the</strong> order of percents.<br />
Thermi<strong>on</strong>ic emitters<br />
The normalized rms emittance of electr<strong>on</strong>s emitted from a hot cathode of radius rc<br />
can be described by[62]:<br />
εn = βγ � 〈x2 〉〈x ′2 〉 = γ rc<br />
�<br />
kBT<br />
2 mc2
50 3. Free electr<strong>on</strong> laser ”hardware”<br />
-<br />
-<br />
-<br />
-<br />
- - - -<br />
-<br />
- - - - -<br />
+<br />
+<br />
+<br />
+<br />
-<br />
-<br />
-<br />
-<br />
-<br />
- - - -<br />
- - - - -<br />
Figure 3.3: Thermi<strong>on</strong>ic emitter (left) <strong>and</strong> photocathode emitter (right) with a static accelerating gradient.<br />
with T being <strong>the</strong> cathode temperature <strong>and</strong> kB Boltzman’s c<strong>on</strong>stant. Clearly <strong>the</strong> key<br />
to a low emittance is to have a small cathode to begin with. At <strong>the</strong> SCSS (Spring-8)<br />
a <strong>the</strong>rmi<strong>on</strong>ic gun using a CeB6 cathode operating at 1450 ◦ C produces a 3 A peak<br />
current with a emittance as low as 0.4π mm mrad[56].<br />
Photocathode emitters<br />
The emittance from a photo-cathode depends str<strong>on</strong>gly <strong>on</strong> material properties, thus<br />
materials incombinati<strong>on</strong>withlasertechnologyis<strong>the</strong>reforeanactiveareaofresearch[63,<br />
64].<br />
Photocathode guns are used at <strong>the</strong> majority of free electr<strong>on</strong> laser facilities around<br />
<strong>the</strong> world.<br />
• Lcls: currently polycrystaline Cu, CsBr coated Cu being c<strong>on</strong>sidered as a future<br />
alternative[65].<br />
• Flash: Cs2Te.<br />
Semi-c<strong>on</strong>ductor cathode materials are more sensitive to degrading processes such<br />
as i<strong>on</strong> backscattering <strong>and</strong> surface degradati<strong>on</strong> than <strong>the</strong>ir metal low efficiency counterparts.<br />
Never<strong>the</strong>less, by asserting proper vacuum c<strong>on</strong>diti<strong>on</strong>s Cs : GaAs <strong>and</strong> Cs2Te<br />
are operating at user facilities .<br />
For an comprehensive investigati<strong>on</strong> <strong>on</strong> different cathode materials <strong>and</strong> a perspective<br />
of <strong>the</strong> current research efforts see[66]. The emittance can be reduced by cooling<br />
of <strong>the</strong> cathode[62].<br />
Normally c<strong>on</strong>ducting guns<br />
Static (DC) accelerati<strong>on</strong><br />
In this type of electr<strong>on</strong> gun <strong>the</strong> particles are accelerated by a static 1 (or pulsed field<br />
that is static during <strong>the</strong> duty cycle, i.e. when an electr<strong>on</strong> bunch is to be accelerated<br />
into <strong>the</strong> accelerator structure), as depicted in Figure 3.3.<br />
1 Cockcroft & Walt<strong>on</strong> used an electrostatic linear acceleratorwhere an alternatingcurrentsource<br />
is rectified by diodes <strong>and</strong> capacitors to achieve a voltage multiplicati<strong>on</strong> over several stages. They<br />
used <strong>the</strong> machine to split lithium atoms with 400 keV prot<strong>on</strong>s <strong>–</strong> <strong>the</strong> results were published 1932[67];<br />
for this achievement <strong>the</strong>y were rewarded <strong>the</strong> Nobel prize in physics 1951 for ”Transmutati<strong>on</strong> of<br />
atomic nuclei by artificially accelerated atomic particles”.<br />
+<br />
+<br />
+<br />
+
3.2. Electr<strong>on</strong> guns 51<br />
The charges are accelerated byaforce proporti<strong>on</strong>al to <strong>the</strong> gradient of <strong>the</strong> potential,<br />
i.e. <strong>the</strong> voltage difference F = −q∇φ. The energy gained is ∆E = qU with <strong>the</strong> unit<br />
often givenin electr<strong>on</strong> volts (eV).Withthis typeof voltage multiplicati<strong>on</strong> itis possible<br />
to reach voltages of 1-2 MV.<br />
Radio frequency (RF) accelerati<strong>on</strong><br />
An oscillating electromagnetic field can be used to accelerate charged particles. If <strong>the</strong><br />
particles moti<strong>on</strong> is matched so that <strong>the</strong>y interact res<strong>on</strong>antly with <strong>the</strong> rf-field a very<br />
high amount of accelerati<strong>on</strong> can be achieved (see page 52).<br />
Guns operating in <strong>the</strong> L- <strong>and</strong> S-b<strong>and</strong>s 2 (∼ 1−2 GHz <strong>and</strong> 2−4 GHz) have already<br />
been c<strong>on</strong>structed <strong>and</strong> successfully employed in photoinjector schemes, notably <strong>the</strong><br />
Lcls gun at SLAC[68]. Normally c<strong>on</strong>ducting RF-guns can be c<strong>on</strong>sidered a mature<br />
technology that exhibit several important performance parameters in-line with what<br />
is dem<strong>and</strong>ed from a free electr<strong>on</strong> laser point-of-view: <strong>the</strong>y are capable of producing a<br />
high field gradient (up to150 MV/m) which allow <strong>the</strong>extracti<strong>on</strong> of high peak currents<br />
in short bunches; <strong>the</strong>y permit <strong>the</strong> use of emittance compensati<strong>on</strong> through <strong>the</strong> use of<br />
solenoidal magnetic fields; <strong>the</strong>y are compatible with a large numberof various cathode<br />
materials.<br />
The limiting factor is <strong>the</strong> power density exerted <strong>on</strong> <strong>the</strong> cavity walls when <strong>the</strong>y are<br />
submitted to a high accelerating field gradient. A high radio frequency implies that<br />
<strong>the</strong> cavities are comparatively small which makes efficient dissipati<strong>on</strong> of <strong>the</strong> generated<br />
heat through a cooling system technically challenging. Hence <strong>the</strong> repetiti<strong>on</strong> rate for<br />
is limited to a maximum somewhere between 100 Hz <strong>and</strong> about 10 kHz (depending <strong>on</strong><br />
<strong>the</strong> RF-frequency). The small cavities also imply that <strong>the</strong> apertures are small which<br />
can also impair pumping which may generate vacuum quality c<strong>on</strong>cerns.<br />
Below a certain frequency <strong>the</strong> heat load <strong>on</strong> <strong>the</strong> cavity walls becomes manageable<br />
in such a way (with lower RF frequency <strong>the</strong> cavities become larger which decreases<br />
<strong>the</strong> power density) that a c<strong>on</strong>tinuous wave (CW) operati<strong>on</strong> mode can be allowed[69].<br />
Lower frequency implies a lower accelerating gradient which are still higher than <strong>the</strong><br />
alternative ”varm technology” direct current counter parts.<br />
The interest for this type of operati<strong>on</strong> is large from <strong>the</strong> user community since it<br />
allows a higher repetiti<strong>on</strong> rate than stated above, even for a n<strong>on</strong>-superc<strong>on</strong>ducting<br />
apparatus. Owing to <strong>the</strong> corresp<strong>on</strong>dence to RF technology employed at storage ring<br />
this technology is well matured which ensures reliability <strong>and</strong> simplicity hard to find<br />
in o<strong>the</strong>r schemes.<br />
Superc<strong>on</strong>ducting guns<br />
A scheme where superc<strong>on</strong>ducting radiofrequency (SRF) accelerator cavities are combined<br />
with photocathode laser electr<strong>on</strong> guns can potentially allow for <strong>the</strong> producti<strong>on</strong><br />
of electr<strong>on</strong> <strong>beam</strong>s of sufficient quality for usage in free electr<strong>on</strong> lasers at very high<br />
repetiti<strong>on</strong> rates[70].<br />
An overview of <strong>the</strong> current research <strong>and</strong> developments have been published by A.<br />
Arnold <strong>and</strong> co-workers[71].<br />
2 RF sources are classified into VHF, UHF, microwave <strong>and</strong> millimetre waveb<strong>and</strong>s. The microwave<br />
b<strong>and</strong>s are divided into <strong>the</strong> following categories: <strong>the</strong> L b<strong>and</strong>, 1.12-1.7 GHz; S b<strong>and</strong>, 2.6-3.95<br />
GHz; C b<strong>and</strong>, 3.95-5.85 GHz; X b<strong>and</strong>, 8.2-12.4 GHz; K b<strong>and</strong>, 18.0-26.5 GHz. The millimetre wave<br />
b<strong>and</strong> is between 30 <strong>and</strong> 300 GHz.
52 3. Free electr<strong>on</strong> laser ”hardware”<br />
The Meissner effect (exclusi<strong>on</strong> of B-field from superc<strong>on</strong>ducting cavity walls) makes<br />
<strong>the</strong> inclusi<strong>on</strong> of emittance reducing B-fields in <strong>the</strong> source regi<strong>on</strong> problematic. The<br />
use of higher order cavity modes that generate a magnetic comp<strong>on</strong>ent achieving <strong>the</strong><br />
emittance reducti<strong>on</strong> have been proposed <strong>and</strong> are under investigati<strong>on</strong>[72, 73].<br />
Summary<br />
Table 3.2 presents <strong>the</strong> current best <strong>beam</strong> performance as obtained from different<br />
gun technologies. The low emittance of <strong>the</strong> Lcls gun is achieved thanks to <strong>the</strong> low<br />
peak current operati<strong>on</strong>. The PITZ gun has a 10 Hz structure with 1 MHz pulse<br />
substructure. The Rossendorf setup apparently suffers from a damaged cavity <strong>–</strong><br />
impairing <strong>the</strong> strength of <strong>the</strong>ir accelerating field.<br />
Gun Technology Rate Acc. Field E εn C<br />
[Hz] [MV/m] [MeV] [µm] [pC]<br />
Lcls NC RF 120 140 6 0.5 250<br />
3 GHz 0.14 20<br />
PITZ NC RF 10 60 > 5 1.3 1000<br />
(Flash) 1.3 GHz<br />
JLab DC 75·10 6<br />
6 0.35 3 140<br />
Scss Pulsed DC 60 ∼ 60 0.5 0.6 300<br />
Rossendorf SRF 125·10 6<br />
5 ˜1 3 80<br />
Table 3.2: Performances of existing guns employing different technologies. Table obtained from W. A. Barletta<br />
et al. [74].<br />
3.3 Radio-frequency driven accelerators<br />
RF RF RF<br />
RF RF RF RF RF<br />
Figure3.4: Different rfaccelerati<strong>on</strong>schemes. From lefttoright: in<strong>the</strong> betatr<strong>on</strong>chargedparticlesare accelerated<br />
in a spiral path in a static magnetic field; in <strong>the</strong> microtr<strong>on</strong> <strong>the</strong> magnetic field is static but <strong>the</strong> orbit is stretched<br />
l<strong>on</strong>ger for each pass to adapt to <strong>the</strong> particles’ higher kinetic energy; in <strong>the</strong> synchrotr<strong>on</strong> <strong>the</strong> magnetic field<br />
strength is risen per turn to compensate for <strong>the</strong> higher kinetic energy (in a storage ring <strong>the</strong> rf power is matched<br />
to <strong>the</strong> synchrotr<strong>on</strong> radiati<strong>on</strong> losses, hence <strong>the</strong> orbit is kept stable with a c<strong>on</strong>stant magnetic field strength). A<br />
linear accelerator successively accelerate <strong>the</strong> particles without bending <strong>the</strong>ir orbit.<br />
A radio-frequency (RF) accelerator use power from a single RF generator to create<br />
an alternating electric field gradient over <strong>the</strong> gaps of <strong>the</strong> accelerating secti<strong>on</strong>s. Figure<br />
3.4 different particle accelerati<strong>on</strong> schemes are presented, all can be understood<br />
from <strong>the</strong> Lorentz force equati<strong>on</strong> (Equati<strong>on</strong> 2.5): <strong>on</strong>ly an electric field can change
3.3. Radio-frequency driven accelerators 53<br />
<strong>the</strong> kinetic energy of a particle, whereas an magnetic field can change <strong>the</strong> orbit of a<br />
particle (since it exerts a force perpendicular to <strong>the</strong> particle’s velocity) 3 .<br />
In 1924 G. Ising suggested that time-varying electric fields could be used for <strong>the</strong><br />
accelerati<strong>on</strong> of charged particles through a periodic structure of drift-tubes[75]. The<br />
first successful operati<strong>on</strong> of a radio frequency driven linear accelerator was dem<strong>on</strong>strated<br />
in 1928 by R. Wiederöe[76].<br />
In Figure 3.5 an accelerator of this type is outlined. The lengths of <strong>the</strong> drift tubes<br />
needs to be progressively l<strong>on</strong>ger as <strong>the</strong> particles’ velocity increases al<strong>on</strong>g <strong>the</strong>structure.<br />
However, when <strong>the</strong>ir velocity is sufficiently close to <strong>the</strong> speed of light <strong>the</strong>y mainly pick<br />
up energy, thus after a while <strong>the</strong> length of <strong>the</strong> drift tubes need not to be increased.<br />
Since <strong>the</strong> length of <strong>the</strong> structures in a Wiederöe linac is βλ/2 it makes ec<strong>on</strong>omical<br />
sense to choose higher radio frequency <strong>–</strong> since <strong>the</strong> overall accelerator would become<br />
shorter. However, <strong>the</strong> structure radiates energy as P = ωrfCV 2<br />
rf <strong>–</strong> <strong>the</strong> losses thus<br />
increase with <strong>the</strong> radio-frequency ωrf, <strong>the</strong> gap capacitance C <strong>and</strong> <strong>the</strong> voltage squared.<br />
If <strong>the</strong> drift tube is placed in a cavity <strong>the</strong> electromagnetic energy is also stored within<br />
<strong>the</strong> structure in a magnetic field (owing to <strong>the</strong> cavities inductive properties). The<br />
res<strong>on</strong>ant frequency of <strong>the</strong> cavity can of course be tuned (via <strong>the</strong> cavity radius) to<br />
match that of <strong>the</strong> accelerating field.<br />
The mass of an electr<strong>on</strong> is 1832 times smaller than a prot<strong>on</strong>, an electr<strong>on</strong> thus<br />
achieves relativistic velocities much faster with <strong>the</strong> same accelerating force. Therefore<br />
linear accelerators for electr<strong>on</strong>s generally have structures that have equal length since<br />
<strong>the</strong> velocity factor is β ≈ 1 already after <strong>the</strong> electr<strong>on</strong> gun accelerating structure.<br />
The governing principles for linear accelerators using res<strong>on</strong>ant accelerati<strong>on</strong> are<br />
slightlymorec<strong>on</strong>volutedthanthoseof<strong>the</strong>electrostatic accelerators menti<strong>on</strong>edabove[77].<br />
We will c<strong>on</strong>sider here <strong>on</strong>ly a few key features of <strong>the</strong>ir comp<strong>on</strong>ents necessary for underst<strong>and</strong>ing<br />
of accelerator parameters necessary for free electr<strong>on</strong> laser.<br />
3 At relativistic speeds v ≈ c <strong>the</strong> sec<strong>on</strong>d term in F = −q[E + v × B] may be about 300 times<br />
larger than <strong>the</strong> first term already at 1 T magnetic strength (which is readily achievable technologically).<br />
+ - + -<br />
+<br />
βλ/2<br />
Figure 3.5: Schematic of <strong>the</strong> cavity structure of a Wiederöe accelerator. To <strong>the</strong> right <strong>the</strong>re is a source for <strong>the</strong><br />
particles to be accelerated.
54 3. Free electr<strong>on</strong> laser ”hardware”<br />
The accelerating RF-field<br />
A good starting point to get a feeling for how <strong>the</strong> accelerating electric field within<br />
a accelerator cavity looks is to c<strong>on</strong>sider <strong>the</strong> field within a capacitor. If we, initially,<br />
assume <strong>the</strong> field to vary very slowly with <strong>the</strong> angular frequency ω we can write <strong>the</strong><br />
field as:<br />
E = E0e iωt<br />
(3.1)<br />
i.e. with <strong>the</strong> alternating field <strong>the</strong> charges <strong>on</strong> <strong>the</strong> plates gets depleted <strong>and</strong> accumulated<br />
sequentially.<br />
Γ<br />
E<br />
B<br />
Figure 3.6: A capacitor c<strong>on</strong>nected to an alternating current source stores both an electric <strong>and</strong> a magnetic field.<br />
The Γ c<strong>on</strong>tour (dashed) is an integrati<strong>on</strong> path.<br />
We know that a varying electric field induces a magnetic field (from <strong>the</strong> Ampère-<br />
Maxwell equati<strong>on</strong>, eq. 2.4). Inside <strong>the</strong> capacitor we have no stored current <strong>and</strong> thus<br />
(Figure 3.6):<br />
c 2<br />
�<br />
Γ<br />
B·dℓ = ∂<br />
�<br />
E·dS (3.2)<br />
∂t S<br />
where S is <strong>the</strong> area enclosed within Γ. The c<strong>on</strong>tour is a circle with radius r.<br />
c 2 B2πr = ∂<br />
∂t Eπr2 , thus B = iωr<br />
2c 2E0eiωt<br />
(3.3)<br />
Where we have made use of our definiti<strong>on</strong> of <strong>the</strong> oscillating electric field.<br />
If <strong>the</strong> time derivative of <strong>the</strong> electric field is identically zero (i.e. a static electric<br />
field) all energy in <strong>the</strong> capacitor was stored in <strong>the</strong> electric field. Now with a<br />
time-varying field <strong>the</strong>re is <strong>the</strong> additi<strong>on</strong>al possibility of storing energy in <strong>the</strong> induced<br />
magnetic field.<br />
In <strong>the</strong> center of <strong>the</strong> capacitor (r = 0) <strong>the</strong>re is no magnetic field, elsewhere <strong>the</strong>re is<br />
an induced field that varies with <strong>the</strong> distance from <strong>the</strong> center. Since such a magnetic<br />
field is present <strong>the</strong>re is a increasing perturbati<strong>on</strong> of <strong>the</strong> electric field with increasing
3.3. Radio-frequency driven accelerators 55<br />
r. It is now possible to c<strong>on</strong>struct a correcti<strong>on</strong> to <strong>the</strong> electric field that takes this into<br />
account using Faraday’s law eq. 2.3:<br />
E = E1 +E2<br />
Γ2<br />
S0<br />
(3.4)<br />
Figure 3.7: The capacitor viewed from <strong>the</strong> side, depicting <strong>the</strong> surface <strong>and</strong> integrati<strong>on</strong> path used for Faraday’s<br />
law.<br />
The sec<strong>on</strong>d term in <strong>the</strong> superpositi<strong>on</strong> is required to be zero in <strong>the</strong> center, it is also<br />
<strong>the</strong> <strong>on</strong>ly term c<strong>on</strong>tributing to <strong>the</strong> line integral in (Figure 3.7):<br />
�<br />
Γ2<br />
E·dℓ = − ∂ΦB<br />
∂t<br />
The flux of <strong>the</strong> magnetic field in a vertical strip of width dr is B(r)hdr (imagine that<br />
we split <strong>the</strong> surface S0 into strips). The right h<strong>and</strong> side boils down to −E2(r)h:<br />
�<br />
−hE2(r) = −h B(r)dr<br />
Here it can be seen that <strong>the</strong> correcti<strong>on</strong> field does not depend <strong>on</strong> <strong>the</strong> separati<strong>on</strong> of<br />
<strong>the</strong> fields, <strong>on</strong>ly <strong>on</strong> <strong>the</strong> distance from <strong>the</strong> center. The equati<strong>on</strong> above gives E2(r) =<br />
− ω2 r 2<br />
4c 2 E0e iωt , this gives us <strong>the</strong> corrected electric field in <strong>the</strong> capacitor<br />
E = E1 +E2 =<br />
�<br />
1− ω2 r 2<br />
4c 2<br />
�<br />
E0e iωt<br />
(3.5)<br />
Our obtained electric field now differs significantly from <strong>the</strong> <strong>on</strong>e we started out<br />
with to obtain <strong>the</strong> magnetic field above. Since we are dealing with fields we can<br />
repeat <strong>the</strong> same procedure for <strong>the</strong> magnetic field, i.e. use <strong>the</strong> ansatz that<br />
B = B1 +B2<br />
With B1 = iωr<br />
2c 2E0e iωt . To find <strong>the</strong> correcti<strong>on</strong> term we may use <strong>the</strong> Ampère-Maxwell<br />
equati<strong>on</strong> again (as we did above in eq. 3.2):<br />
c 2 B22πr = ∂<br />
∂t<br />
�<br />
S<br />
E·dS
56 3. Free electr<strong>on</strong> laser ”hardware”<br />
The flux of <strong>the</strong> electric field is taken through <strong>the</strong> circle enclosed by Γ in Figure 3.6<br />
<strong>and</strong> we get:<br />
B2(r) = − iω3r 3<br />
16c4 This gives us a new correcti<strong>on</strong> to <strong>the</strong> electric field via<br />
E3(r) = ∂<br />
∂t<br />
�<br />
B2(r)dr<br />
We obtain a new term in <strong>the</strong> expansi<strong>on</strong> of <strong>the</strong> electric field as:<br />
�<br />
E = 1− 1<br />
22 �<br />
ωr<br />
�2 +<br />
c<br />
1<br />
22 ·42 �<br />
ωr<br />
� �<br />
4<br />
E0e<br />
c<br />
iωt<br />
if we were to c<strong>on</strong>tinue we would get an increasingly large expansi<strong>on</strong> within <strong>the</strong> paren<strong>the</strong>sis<br />
which c<strong>on</strong>tinues as (slightly rewritten):<br />
�<br />
1− 1<br />
(1!) 2<br />
�<br />
ωr<br />
�2 +<br />
2c<br />
1<br />
(2!) 2<br />
�<br />
ωr<br />
�4 −<br />
2c<br />
1<br />
(3!) 2<br />
�<br />
ωr<br />
� �<br />
6<br />
+...<br />
2c<br />
This series is, bydefiniti<strong>on</strong>, <strong>the</strong>Bessel functi<strong>on</strong> of <strong>the</strong> first kind(J0) with argument<br />
ωr/c. The oscillating electric field in <strong>the</strong> capacitor can thus be written in <strong>the</strong> very<br />
compact form:<br />
E = J0(ωr/c)E0e iωt<br />
Bessel’s functi<strong>on</strong>s are soluti<strong>on</strong>s to <strong>the</strong> wave equati<strong>on</strong> in a cylindrical geometry. The<br />
subscript zero denotes that this soluti<strong>on</strong> is independent of <strong>the</strong> polar coordinate. In<br />
Figure 3.8 we can see that <strong>the</strong> functi<strong>on</strong> have a zero around 2.4 (it is actually 2.405).<br />
This implies that a pair of plates have a res<strong>on</strong>ant<br />
frequency2.405c/r <strong>–</strong>ofcourse <strong>the</strong>reisalso <strong>the</strong>possibility<br />
for harm<strong>on</strong>ics of this frequency, functi<strong>on</strong>s that will<br />
haveadditi<strong>on</strong>al nodes inside <strong>the</strong>cavity <strong>–</strong>meaningthat,<br />
<strong>the</strong> electric field <strong>and</strong> magnetic fields will exchange en-<br />
ergy in an oscillating manner indefinitely (as a capac-<br />
itor <strong>and</strong> an inductance coupled toge<strong>the</strong>r). If <strong>the</strong> fields<br />
were enclosed in a cylinder with c<strong>on</strong>ducting walls this<br />
would hold if <strong>the</strong> walls were perfect c<strong>on</strong>ductors.<br />
Imperfect c<strong>on</strong>ducting walls implies that <strong>the</strong> oscillating<br />
fields gradually gets drained of <strong>the</strong>ir energy due<br />
to resistive losses.<br />
To describe a res<strong>on</strong>ating cavity, we may imagine<br />
that <strong>the</strong> oscillating field occur in a hollow cylinder<br />
c<strong>on</strong>taining <strong>the</strong> same oscillating field as above (<strong>the</strong> so-<br />
J0(x)<br />
1<br />
0. 8<br />
0. 6<br />
0. 4<br />
0. 2<br />
0<br />
0 1 2 3<br />
r[c/ω]<br />
Figure 3.8: The Bessel functi<strong>on</strong> of<br />
<strong>the</strong> first kind.<br />
luti<strong>on</strong>s are basically <strong>the</strong> same). The lowest mode in such a cylinder is usually denoted<br />
TM010 which can be written:<br />
Ez = E0J0(kcr)cos(ωt−kzz)<br />
The wave numberkz describes <strong>the</strong> dependenceof <strong>the</strong> field up<strong>on</strong> <strong>the</strong> cut-offwavelength<br />
λc of <strong>the</strong> cavity <strong>–</strong> <strong>on</strong>ly electromagnetic waves with wavelengths shorter than <strong>the</strong>
3.3. Radio-frequency driven accelerators 57<br />
cylinder diameter can propagate through <strong>the</strong> structure: kz = √ k2 −k2 c, where kc =<br />
2π/λc <strong>and</strong> <strong>the</strong> free space wavenumber k = ω/c. We require that <strong>the</strong> field vanish at<br />
<strong>the</strong> surface of <strong>the</strong> cylinder, letting <strong>the</strong> radius of <strong>the</strong> cylinder be ρ, thus kc = 2.405/ρ<br />
must hold (2.405 being <strong>the</strong> first zero of <strong>the</strong> Bessel functi<strong>on</strong> J0).<br />
Ifanelectr<strong>on</strong> wouldhave<strong>the</strong>same speedas <strong>the</strong>phasevelocityof<strong>the</strong>wavedescribed<br />
above it would be accelerated, however <strong>the</strong> phase velocity of <strong>the</strong> wave is:<br />
vphase = ω c<br />
= �<br />
kz 1− λ2<br />
λ2 > c<br />
c<br />
The c<strong>on</strong>diti<strong>on</strong> of accelerati<strong>on</strong> is thus possible to fulfill for a very short distance <strong>on</strong>ly<br />
after which <strong>the</strong> wave would reverse <strong>the</strong> field orientati<strong>on</strong> <strong>and</strong> decelerate <strong>the</strong> electr<strong>on</strong><br />
again <strong>–</strong> <strong>on</strong> average no net gain in energy would be possible.<br />
To overcome this, i.e. to make a working accelerating structure, <strong>the</strong> phase velocity<br />
of <strong>the</strong> wave can be slowed down for a certain frequency to match <strong>the</strong> speed of light<br />
by introducing irises al<strong>on</strong>g <strong>the</strong> cavity. Such a structure will naturally perturb <strong>the</strong><br />
fields of <strong>the</strong> perfect cylinder, a working accelerating structure is obtained when <strong>the</strong><br />
wavelength is chosen such that it is a multiple of <strong>the</strong> distances between <strong>the</strong> iris-discs,<br />
λ = nd (see Figure 3.9). The modes inside <strong>the</strong> disc-loaded cavities are usually named<br />
after <strong>the</strong> phase advance kzd = 2π/n of <strong>the</strong> wave per sub-cavity.<br />
Beam<br />
2π/3 mode π mode<br />
Figure 3.9: Two comm<strong>on</strong> modes used in disc-loaded cavities.<br />
Energy gain in a radiofrequency driven accelerating cavity<br />
If U0 ≫ mec 2 <strong>the</strong> electr<strong>on</strong> speed is close to <strong>the</strong> speed of light. Let z = −d/2 be <strong>the</strong><br />
entrance of <strong>the</strong> cavity (corresp<strong>on</strong>ding to a time ωt = −π/2), a particle entering <strong>the</strong><br />
cavity may experience <strong>the</strong> electric field at a phase φ relative to <strong>the</strong> peak field (defining<br />
zero phase).<br />
Then <strong>the</strong> field <strong>on</strong> axis (in <strong>the</strong> ˆz directi<strong>on</strong> with r = 0 in cylindrical coordinates)<br />
can be written:<br />
Ez = E0cos(ωt(z)−φ)<br />
since, <strong>on</strong> axis <strong>the</strong> Bessel functi<strong>on</strong> J0 is equal to unity. If <strong>the</strong> particle is at z <strong>the</strong> time<br />
is given by t(z) = � z<br />
dzv(z). The energy gain is <strong>the</strong>n:<br />
0<br />
�<br />
∆U = −qE·z = q<br />
d/2<br />
−d/2<br />
E0cos(ωt(z)−φ)dz<br />
We know that during <strong>the</strong> passage <strong>the</strong> change in velocity is small <strong>–</strong> we may set t(z) ≈<br />
z/v. With <strong>the</strong> use of a trig<strong>on</strong>ometric identity we can have <strong>the</strong> phase angle outside<br />
<strong>the</strong> integrati<strong>on</strong>. Defining <strong>the</strong> accelerating gradient V = E0d <strong>and</strong> transit time T<br />
∆U = qE0dT cosφ = qVT cosφ<br />
d
58 3. Free electr<strong>on</strong> laser ”hardware”<br />
<strong>the</strong> transit time T = sin(ωd/(2v))<br />
ωd/(2v) is a correcti<strong>on</strong> to <strong>the</strong> particle accelerati<strong>on</strong> owing to<br />
<strong>the</strong> time variati<strong>on</strong> of <strong>the</strong> field while <strong>the</strong> particles transverse <strong>the</strong> cavity.<br />
is <strong>the</strong> energy gain of an electr<strong>on</strong> passing an accelerator of length L. The phase φ<br />
is measured relative to that of <strong>the</strong> traveling wave.<br />
Often <strong>on</strong>e does not operate <strong>the</strong> accelerators at <strong>the</strong> point of maximum accelerati<strong>on</strong><br />
since <strong>on</strong>e wants to introduce a energy chirp (gradient) al<strong>on</strong>g <strong>the</strong> particle bunch to<br />
achieve a shorter bunch.<br />
Warm technology: Copper<br />
Accelerating structures built in Copper have been used for decades in both storage<br />
rings <strong>and</strong> linear accelerators, thusthis technology can be c<strong>on</strong>sidered to be verymature<br />
<strong>and</strong> soluti<strong>on</strong>s are often available commercially. Copper is chosen for its good electric<br />
c<strong>on</strong>ductivity coupled with a high <strong>the</strong>rmal c<strong>on</strong>ductivity.<br />
The cheap cost per GeV (about 15 Milli<strong>on</strong> USD) must though be put against <strong>the</strong><br />
limited average brightness that can be delivered to <strong>the</strong> users.<br />
Cavity structures for <strong>the</strong> L, S, C <strong>and</strong> X b<strong>and</strong>s are currently being used for different<br />
purposes. Thanks to <strong>the</strong> cheap cost <strong>the</strong> technique is being developed for 100-150<br />
MV/m for <strong>the</strong> X-b<strong>and</strong>, mainly for <strong>the</strong> TeV lept<strong>on</strong> linear collider but with obvious<br />
synergetic effects for linear accelerators for X-ray producti<strong>on</strong>[78].<br />
C-b<strong>and</strong> normally c<strong>on</strong>ducting copper structures operating at accelerating gradients<br />
of 35 MV/m are used at <strong>the</strong> Scss free electr<strong>on</strong> laser.<br />
Superc<strong>on</strong>ducting technology<br />
Superc<strong>on</strong>ducting technology is vastly more expensive than <strong>the</strong> warm counterpart;<br />
however, <strong>the</strong> high average brightness required for larger facilities (especially those<br />
where it is envisi<strong>on</strong>ed that many experimental stati<strong>on</strong>s are served simultaneously,<br />
e.g. <strong>the</strong> European X-Fel) this might be <strong>the</strong> <strong>on</strong>ly way forward.<br />
Since <strong>the</strong> short durati<strong>on</strong> <strong>and</strong> low emittance of <strong>the</strong> electr<strong>on</strong> bunches would not be<br />
preserved in a synchrotr<strong>on</strong>, Sase free electr<strong>on</strong> lasers are based <strong>on</strong> linear accelerators,<br />
ei<strong>the</strong>r employing normally c<strong>on</strong>ducting or superc<strong>on</strong>ducting rf structures as sketched<br />
in Figure 3.9. In c<strong>on</strong>trast to <strong>the</strong> case of a c<strong>on</strong>stant current, <strong>the</strong> resistance of a<br />
superc<strong>on</strong>ductor does not completely vanish in <strong>the</strong> presence of an radiofrequency field,<br />
see e.g.[79]. It is never<strong>the</strong>less much smaller in superc<strong>on</strong>ducting niobium at e.g. 2 K<br />
than for copper at room temperature.<br />
Therefore, <strong>the</strong> quality factor Q of a superc<strong>on</strong>ducting cavity (where Q/2π is <strong>the</strong><br />
ratio of<strong>the</strong> energy stored in <strong>the</strong>system <strong>and</strong> <strong>the</strong>energy dissipated per oscillati<strong>on</strong> cycle)<br />
is of <strong>the</strong> order of 10 1 0, compared to below 10 5 for copper cavities. On <strong>the</strong> o<strong>the</strong>r h<strong>and</strong>,<br />
for 1Wof power lost in asuperc<strong>on</strong>ductingcavity at 2K, <strong>the</strong>cryogenic system requires<br />
almost 1 kW to keep <strong>the</strong> temperature c<strong>on</strong>stant. This toge<strong>the</strong>r with <strong>the</strong> technological<br />
complexity <strong>and</strong> a fundamental limitati<strong>on</strong> given by <strong>the</strong> critical magnetic field makes<br />
<strong>the</strong> choice not so obvious.<br />
It required a committee of internati<strong>on</strong>al experts in 2004 to identify <strong>the</strong> superc<strong>on</strong>ducting<br />
TESLA technology as <strong>the</strong> best soluti<strong>on</strong> for <strong>the</strong> Internati<strong>on</strong>al Linear Collider<br />
[80].<br />
At Flash, six accelerati<strong>on</strong> stages, each accommodating eight nine-cell<br />
TESLA cavities used to accelerate <strong>the</strong> electr<strong>on</strong> <strong>beam</strong> to 1 GeV[81]. The average
3.4. Undulators 59<br />
h<br />
D<br />
Figure 3.10: Schematic of an Apple-I variable polarizati<strong>on</strong> undulator. The short magnet in <strong>the</strong> start have λu/8.<br />
electric field is about 20 MV/m with <strong>on</strong>e meter cavity lengths. By optimizing cavity<br />
design <strong>and</strong> with <strong>the</strong> advent of new techniques to clean <strong>the</strong> cavity surfaces, fields larger<br />
than 50 MV/m have been dem<strong>on</strong>strated[82].<br />
The European X-ray free electr<strong>on</strong> laser will employ TESLA cavities with a field of<br />
21 MV/m. Lcls at Stanford, <strong>on</strong> <strong>the</strong> o<strong>the</strong>r h<strong>and</strong>, is based <strong>on</strong> <strong>the</strong> normal-c<strong>on</strong>ducting<br />
SLAC linac, <strong>and</strong> some o<strong>the</strong>r projects, like <strong>the</strong> Scss XFEL in Japan for example, have<br />
opted for normal-c<strong>on</strong>ducting rf structures as well.<br />
C<strong>on</strong>tinuoswaveoperati<strong>on</strong> withTESLAcavitieshaverecentlybeendem<strong>on</strong>strated[83]<br />
3.4 Undulators<br />
Most free electr<strong>on</strong> lasers use planar undulators with a fixed undulator period, which<br />
<strong>the</strong>n provide linearly polarized light c<strong>on</strong>taining a fundamental wavelength <strong>and</strong> its<br />
harm<strong>on</strong>ics. If <strong>on</strong>e desires to suppress <strong>the</strong> higher harm<strong>on</strong>ics, for some reas<strong>on</strong>, a<br />
quasiperiodic scheme can be employed[84]. A quasiperiodic undulator scheme generally<br />
degrade <strong>the</strong> performance of <strong>the</strong> undulator for <strong>the</strong> fundamental which makes<br />
such devices unattractive for <strong>the</strong> use in, at least, Sase free electr<strong>on</strong> laser, since <strong>the</strong><br />
cost is highly dependent <strong>on</strong> <strong>the</strong> undulator length <strong>and</strong> an decrease in phot<strong>on</strong> density<br />
necessitates a l<strong>on</strong>ger gain length.<br />
However, oftenpolarizati<strong>on</strong>s o<strong>the</strong>rthan<strong>the</strong>linearisdesiredby<strong>the</strong>usercommunity.<br />
By introducing a magnetic field parallel to <strong>the</strong> central path through <strong>the</strong> undulator<br />
(superimposing <strong>the</strong> vertical field) it is, in principle, possible to generate arbitrary<br />
polarizati<strong>on</strong> directi<strong>on</strong>s[85].<br />
InFigure3.10(adaptedfromRef.[86])aschematicofanApple-1(AdvancedPlanar<br />
Polarized Light Emitter) undulator. Two magnetic fields (sinusoidal <strong>and</strong> helical) are<br />
superimposed <strong>on</strong> each o<strong>the</strong>r with variable strength <strong>and</strong> phase. The type II <strong>and</strong> III<br />
varieties looks similar but have different pole geometries[87, 88].<br />
By placing a variable polarizati<strong>on</strong> device after <strong>the</strong> Sase undulator or using it<br />
directly as <strong>the</strong> primary undulator in <strong>the</strong> free electr<strong>on</strong> laser elliptically polarized light<br />
can be delivered to <strong>the</strong> user experiments.<br />
The res<strong>on</strong>ance wavelength in this type (Apple-1) of undulator looks slightly differ-<br />
y<br />
x<br />
z
60 3. Free electr<strong>on</strong> laser ”hardware”<br />
ent than our expressi<strong>on</strong> found earlier as we now have two fields in <strong>the</strong> undulator:<br />
λr = λu<br />
E2 �<br />
1+ K2 x +K 2� y<br />
2<br />
Here we obtain <strong>the</strong> res<strong>on</strong>ance wavlength in ˚Angström if <strong>the</strong> undulator period is given<br />
in millimeters <strong>and</strong> <strong>the</strong> <strong>beam</strong>’s energy in GeV. The coupling parameter between <strong>the</strong><br />
undulator field <strong>and</strong> <strong>the</strong> radiati<strong>on</strong> fields is also different with <strong>the</strong> [JJ] Bessel-functi<strong>on</strong><br />
factor reducing to unity[17].<br />
Undulator tolerances example<br />
Using <strong>the</strong> Pierce parameter ρ (Equati<strong>on</strong> 2.36) <strong>on</strong>e can estimate <strong>the</strong> accuracy needed<br />
to be achieved, with errors from different sources: temperature, alignment, undulator<br />
gap accuracy <strong>and</strong> flatness change up<strong>on</strong> undulator gap changes.<br />
The fundamental wavelength have to be tuned within<br />
ρ ≥ ∆λ<br />
λ<br />
(3.6)<br />
For an error to have a large impact <strong>on</strong> <strong>the</strong> amplificati<strong>on</strong> process it has to be in<br />
effect for at least <strong>on</strong>e gain length. As an example we can use <strong>the</strong> European Xfel<br />
which has a gain length of 10 meters <strong>and</strong> undulator secti<strong>on</strong>s that are 5 meters l<strong>on</strong>g <strong>–</strong><br />
<strong>the</strong> ρ = 3·10 −3 at 0.1 nm for this facility. If all error sources are equally severe, <strong>the</strong>n<br />
<strong>on</strong>e can obtain an idea of <strong>the</strong> tolerances required for an free electr<strong>on</strong> laser undulator<br />
system[89]. We can express <strong>the</strong> b<strong>and</strong>width as a functi<strong>on</strong> of different errors impacting<br />
<strong>the</strong> magnetic field in <strong>the</strong> undulators:<br />
�<br />
�<br />
∆λ = �<br />
� ∂λ<br />
�<br />
��<br />
�<br />
∂B�<br />
∆B2 temp. +∆B 2 gap +∆B 2 flat (3.7)<br />
from this <strong>on</strong>e obtains that<strong>–</strong>for Equati<strong>on</strong> 3.6 tobe fulfilled <strong>–</strong><strong>the</strong> alignment between<br />
undulator secti<strong>on</strong>s needs to be within ±100 µm; <strong>the</strong> temperature stability of <strong>the</strong><br />
whole undulator system within ±0.08 K <strong>–</strong> <strong>and</strong> that <strong>the</strong> gap adjustment accuracy <strong>and</strong><br />
<strong>the</strong> flatness preservati<strong>on</strong> up<strong>on</strong> gap changes needs to be better than ±1 µm.
3.4. Undulators 61<br />
Summary<br />
• The basic comp<strong>on</strong>ents of a free electr<strong>on</strong> laser before <strong>the</strong> user’s<br />
experiments are:<br />
<strong>–</strong> An electr<strong>on</strong>-gun. Which can be of <strong>the</strong>rmi<strong>on</strong>ic, photocathode<br />
or field emissi<strong>on</strong> type. The electr<strong>on</strong> gun defines<br />
<strong>the</strong> emittance <strong>and</strong> <strong>the</strong> number of electr<strong>on</strong>s in <strong>the</strong><br />
bunches.<br />
<strong>–</strong> A linear accelerator. Defines <strong>the</strong> repetiti<strong>on</strong> rate of <strong>the</strong><br />
system. Superc<strong>on</strong>ducting accelerators have higher repetiti<strong>on</strong><br />
rates (kHz-MHz) than normally c<strong>on</strong>ducting (100’s<br />
of Hz).<br />
<strong>–</strong> Undulator(s) sets <strong>the</strong> wavelength <strong>and</strong> polarizati<strong>on</strong> of <strong>the</strong><br />
X-rays.<br />
<strong>–</strong> (Gas attenuator) - can be used to limit <strong>the</strong> intensity at<br />
<strong>the</strong> experiments.
4. X-ray optics<br />
The material presented here in this chapter is partly adapted from ”Survey of<br />
in situ metrology for <strong>the</strong> measurement of damage to FEL phot<strong>on</strong> <strong>transport</strong><br />
optics” by A. J. Glees<strong>on</strong>, Iruvx WP7, 2010 by A. Lindblad.<br />
It is a challenge to c<strong>on</strong>struct any optical system for X-rays. The requirements <strong>on</strong><br />
optical elements at free electr<strong>on</strong> laser is often different than those imposed at synchrotr<strong>on</strong><br />
X-ray sources because of <strong>the</strong> high peak-power ra<strong>the</strong>r than <strong>the</strong> high average<br />
power. The dem<strong>and</strong>s <strong>on</strong> precisi<strong>on</strong> is also higher since <strong>the</strong> phot<strong>on</strong> <strong>beam</strong> from <strong>the</strong> free<br />
electr<strong>on</strong> laser undulator(s) have a very high brilliance that <strong>on</strong>e wishes to preserve to<br />
as high degree as possible. In <strong>the</strong> following secti<strong>on</strong>s we will investigate how stringent<br />
those dem<strong>and</strong>s are <strong>and</strong> <strong>the</strong> techniques that can be used to achieve this.<br />
Also c<strong>on</strong>nected to <strong>the</strong> high brilliance <strong>and</strong> fluence is damage to optical elements <strong>and</strong><br />
methods to minimize/prevent it. This will be discussed below before <strong>the</strong> chapter end,<br />
c<strong>on</strong>taining descripti<strong>on</strong>s of dispersive optics, m<strong>on</strong>ochromators <strong>and</strong> <strong>beam</strong> attenuators.<br />
If we write <strong>the</strong> index of refracti<strong>on</strong> for X-rays in matter as:<br />
n = 1−δ −iβ<br />
with δ <strong>and</strong> β as <strong>the</strong> refracti<strong>on</strong> <strong>and</strong> absorpti<strong>on</strong> coefficients respectively a number of<br />
c<strong>on</strong>clusi<strong>on</strong>s can be drawn. In <strong>the</strong> X-ray regime <strong>the</strong> reflecti<strong>on</strong> coefficient δ is in <strong>the</strong><br />
order of 10 -5 to 10 -7 , generally thus a refractive optic would not be very effective. The<br />
absorpti<strong>on</strong> coefficient is very high in <strong>the</strong> UV-soft X-ray regi<strong>on</strong> for all elements which<br />
present yet ano<strong>the</strong>r tamper, however for materials c<strong>on</strong>stituted of elements with low<br />
mass (<strong>and</strong> thus small nuclear charge) this coefficient is small above 1.5 keV <strong>–</strong> since<br />
<strong>the</strong> photoi<strong>on</strong>izati<strong>on</strong> cross-secti<strong>on</strong>s become very low <strong>the</strong>re. For instance, <strong>the</strong> deepest<br />
laying single-i<strong>on</strong>izati<strong>on</strong> threshold for carb<strong>on</strong> is around 300 eV.<br />
Absorpti<strong>on</strong> can be fur<strong>the</strong>r traded into reflecti<strong>on</strong> by having a grazing incidence of<br />
<strong>the</strong> X-rays <strong>on</strong>to <strong>the</strong> optical elements[90]. In <strong>the</strong> soft X-ray regi<strong>on</strong> this is <strong>the</strong> general<br />
approach utilized. For hard X-rays reflecti<strong>on</strong> planes in crystals of low Z materials can<br />
be used.<br />
4.1 Dem<strong>and</strong>s <strong>on</strong> optics precisi<strong>on</strong> at free electr<strong>on</strong> lasers<br />
A real-life mirror is not perfect <strong>and</strong> imperfecti<strong>on</strong>s of various kinds distort <strong>and</strong> degrades<br />
<strong>the</strong> mirror’s performance. To analyze <strong>the</strong> impact of various errors <strong>on</strong>e usually<br />
63
64 4. X-ray optics<br />
compares with an idealized surface which perfectly transfer <strong>the</strong> source point to <strong>the</strong><br />
image point.<br />
It can be shown that low frequency surface errors, between millimeters <strong>and</strong> λ,<br />
distort <strong>the</strong> wavefr<strong>on</strong>t but still image <strong>the</strong> incident wave into <strong>the</strong> image plane (often<br />
taken to be within <strong>the</strong> 1/e intensity points in a Gaussian spot). Higher frequency<br />
errors scatter <strong>the</strong> incident waves outside <strong>the</strong> image plane[91].<br />
The authors of Ref. [91] have developed a model classifying an optical systems<br />
performance in terms of <strong>the</strong> slope error (deviati<strong>on</strong> from ideal shape) <strong>and</strong> surface<br />
roughness <strong>–</strong> <strong>the</strong> system coherence length describes <strong>the</strong> limit between ’high’ <strong>and</strong> ’low’<br />
frequencies in a natural way:<br />
λ<br />
W = √ 2<br />
Θcosϑi<br />
treating Θ as <strong>the</strong> given angular radius for <strong>the</strong> image <strong>and</strong> ϑi <strong>the</strong> incident angle relative<br />
to <strong>the</strong> surface parallel we have, as a functi<strong>on</strong> of <strong>the</strong> operating wavelength λ <strong>the</strong><br />
wavelength W which is <strong>the</strong> surface spatial wavelength that diffracts intensity into <strong>the</strong><br />
1/e radius of a Gaussian spot.<br />
For a diffracti<strong>on</strong> limited source (as is free electr<strong>on</strong> laser <strong>and</strong> modern synchrotr<strong>on</strong><br />
storage rings) <strong>the</strong> W is roughly equal to <strong>the</strong> illuminated length (ℓ) of <strong>the</strong> optical<br />
element. For <strong>the</strong> X-ray optics c<strong>on</strong>sidered here this wavelength thus lies between λ<br />
<strong>and</strong> ℓ.<br />
The degradati<strong>on</strong> of transmissi<strong>on</strong> <strong>and</strong> image quality in <strong>the</strong> optical system due to<br />
mirror errors may be described by <strong>the</strong> deviati<strong>on</strong> from <strong>the</strong> ideal case, <strong>the</strong> so-called<br />
Strehl-factor:<br />
I(0) 8<br />
≈ 1−<br />
I0(0) Θ2δ2 �<br />
4π<br />
−<br />
λ cosϑi<br />
�2 σ 2<br />
with δ <strong>and</strong> σ are <strong>the</strong> rms values of <strong>the</strong> slope error <strong>and</strong> surface roughness within <strong>the</strong><br />
b<strong>and</strong>-pass of <strong>the</strong> optical comp<strong>on</strong>ent[91].<br />
Both<strong>the</strong>slopeerror<strong>and</strong><strong>the</strong>surface roughnessareintegral propertiesof<strong>the</strong>surface,<br />
i.e. <strong>the</strong> accumulated error is what affects <strong>the</strong> <strong>beam</strong>:<br />
δ 2 = 4π 2<br />
1/W �<br />
1/L<br />
dfxS1(fx)f 2 x; σ 2 =<br />
�<br />
1/λ<br />
1/W<br />
dfxS1(fx)<br />
Owing to this property of <strong>the</strong> imaging system <strong>on</strong>e is faced with an array of different<br />
problems when it comes to manufacturing <strong>and</strong> commissi<strong>on</strong>ing a device with such<br />
stringent dem<strong>and</strong>s <strong>on</strong> surface quality:<br />
• Manufacturing<br />
<strong>–</strong> Polishing a surface down to a few nanometers peak-to-peak roughness over<br />
a large area (typically <strong>the</strong> mirrors are above 25 cm l<strong>on</strong>g)<br />
<strong>–</strong> Process such a large substrate to a determined shape.<br />
• Metrology of <strong>the</strong> manufactured surface with high (sub-nm) accuracy[92, 93]. A<br />
detailed account of techniques <strong>and</strong> metrology methods for <strong>the</strong> manufacturing<br />
of X-ray optical elements is given in <strong>the</strong> book ”Modern developments in X-ray<br />
<strong>and</strong> Neutr<strong>on</strong> Optics” edited by A. Erko et al.[94].
4.2. Focussing mirrors <strong>–</strong> back-reflecting geometry example 65<br />
• Moving <strong>and</strong> mounting <strong>the</strong> finished element into its positi<strong>on</strong> in <strong>the</strong> optical system<br />
of <strong>the</strong> facility without degrading <strong>the</strong> surface. One way to circumvent this<br />
problem is to make mirrors that have an mount where <strong>the</strong> surface can be mechanically<br />
distorted to compensate for <strong>the</strong> errors <strong>–</strong> so called adaptive optics (see<br />
e.g. Ref. [95]).<br />
As an example we here take <strong>the</strong> offset mirrors at <strong>the</strong> Lcls, <strong>the</strong>y have figure errors<br />
<strong>on</strong> <strong>the</strong> order of 2 nm (rms)[96] <strong>and</strong> because of <strong>the</strong> reflectivity c<strong>on</strong>diti<strong>on</strong> <strong>on</strong> <strong>the</strong> grazing<br />
incidence <strong>the</strong>y need to be of different lengths for <strong>the</strong> soft <strong>and</strong> hard X-ray regi<strong>on</strong>s:<br />
• soft X-rays, 25 cm l<strong>on</strong>g, bor<strong>on</strong>-carbide-coated a total of four.<br />
• hard X-rays, pair of 45 cm l<strong>on</strong>g mirrors with SiC-coating <strong>and</strong> 25 keV cut-off.<br />
Allows <strong>the</strong> throughput of <strong>the</strong> 3 rd harm<strong>on</strong>ic of <strong>the</strong> 8.3 keV fundamental.<br />
4.2 Focussing mirrors <strong>–</strong> back-reflecting geometry example<br />
So far we have <strong>on</strong>ly discussed plane mirrors, <strong>the</strong>re is naturally a dem<strong>and</strong> for focussing<br />
mirrors for experiments that utilize high phot<strong>on</strong>-density. Figure 4.1 shows a princi-<br />
Figure 4.1: Spherical/Parabolic mirror used to focus <strong>the</strong> free electr<strong>on</strong> laser <strong>beam</strong>. <strong>the</strong> focuspoint do not overlap<br />
with <strong>the</strong> incoming <strong>beam</strong> because of <strong>the</strong> <strong>beam</strong>stopper (black).<br />
ple for an experiment that uses a backscattering geometry with a focussing mirror<br />
that focus <strong>the</strong> phot<strong>on</strong><strong>beam</strong> to a point. Such set-ups are utilized, for instance, when<br />
investigating multiphot<strong>on</strong> i<strong>on</strong>izati<strong>on</strong> of gases. One such experiment utilized a Mo-Si<br />
multilayer spherical mirror with 68% reflectance (this number is made possible by<br />
progress in EUV-litography[97]) <strong>–</strong> which could <strong>the</strong>n be focussed down to 3 to 5 µm<br />
focus diameters[98].<br />
4.3 Damage<br />
Because of <strong>the</strong> high peak powers <strong>and</strong> short pulses routinely achieved at free electr<strong>on</strong><br />
laser it is entirely possible that new kinds of damage mechanisms that degrade optical<br />
comp<strong>on</strong>ents in X-ray <strong>beam</strong>lines have to be c<strong>on</strong>sidered. Often our knowledge for such<br />
mechanisms emanate from <strong>the</strong> world of storage ring synchrotr<strong>on</strong>s where ra<strong>the</strong>r a high<br />
average power load provides <strong>the</strong> source for potential damage to optical elements <strong>and</strong><br />
coatings.<br />
At a free electr<strong>on</strong> laser <strong>the</strong> high peak power could potentially render an (costly)<br />
optical comp<strong>on</strong>ent useless within fracti<strong>on</strong>s of a sec<strong>on</strong>d[99]. The research of various<br />
damagemechanismscausedbythiskindofsources is<strong>the</strong>reforeanactivefield[100,101].<br />
The empirical data for damage thresholds that exist are often very specific to a certain<br />
(synchrotr<strong>on</strong>) <strong>beam</strong>line <strong>and</strong> are thus unique to <strong>the</strong> flux <strong>and</strong> operating wavelength
66 4. X-ray optics<br />
under c<strong>on</strong>siderati<strong>on</strong>. Recently materials for optics <strong>and</strong> <strong>the</strong>ir coatings employed at Xray<br />
free electr<strong>on</strong> laser around <strong>the</strong> world have begun to be studied in a more systematic<br />
fashi<strong>on</strong>[101, 102], notably <strong>the</strong> low Z materials B4C <strong>and</strong> SiC[103].<br />
Damage to opical elements at a free electr<strong>on</strong> laser can be thought of as direct <strong>and</strong><br />
in-direct: direct damage could be ablati<strong>on</strong> cratering of <strong>the</strong> surface, distorti<strong>on</strong> due to<br />
<strong>the</strong> heat-load caused by <strong>the</strong> pulse, etc. In-direct damage mechanisms are more subtle<br />
<strong>and</strong> include damage to multilayers by diffusi<strong>on</strong> or chemical modificati<strong>on</strong> of surfaces<br />
<strong>and</strong> layers, changes to <strong>the</strong> refractive index.<br />
Careful m<strong>on</strong>itoringof<strong>the</strong><strong>beam</strong>line performance is thusimportant<strong>and</strong><strong>the</strong>methods<br />
described in <strong>the</strong> sec<strong>on</strong>d part of this book inherently give informati<strong>on</strong> that can be used<br />
to diagnose <strong>the</strong> optics.<br />
4.4 Diffracti<strong>on</strong> gratings<br />
A diffracti<strong>on</strong> grating (henceforth taken to be syn<strong>on</strong>ymous to ’grating’ <strong>on</strong>ly) is a periodically<br />
structuredsurface thatdivides <strong>and</strong>diffracts alight<strong>beam</strong> intoseveral <strong>beam</strong>lets<br />
propagating in different directi<strong>on</strong>s depending <strong>on</strong> <strong>the</strong>ir wavelength. This can readily<br />
be understood from <strong>the</strong> Huygens-Fresnel principle <strong>–</strong> stating that each point <strong>on</strong> a<br />
wavefr<strong>on</strong>t act as an independent source <strong>and</strong> that by adding up <strong>the</strong> c<strong>on</strong>tributi<strong>on</strong> from<br />
such pointsources <strong>the</strong> properties of any subsequent point can be found.<br />
Light reflected from an an ideal grating can be c<strong>on</strong>sideredt to equal to that from<br />
emitted from a set of infinitely l<strong>on</strong>g narrow slits spaced with distance d from each<br />
o<strong>the</strong>r. If we add up <strong>the</strong> <strong>beam</strong>s from each slit at some point (far) away from <strong>the</strong><br />
grating <strong>the</strong> optical path difference between <strong>the</strong> <strong>beam</strong>s will casue positive <strong>and</strong> negative<br />
interference owing to <strong>the</strong> phase difference between <strong>the</strong> waves. If <strong>the</strong> path difference<br />
between <strong>the</strong> slits are some multiple of <strong>the</strong> wavelength d = n·λ positive interference<br />
occur <strong>–</strong> for a given wavelength this c<strong>on</strong>diti<strong>on</strong> will be fulfilled at some angle ϑ away<br />
from <strong>the</strong> normal (taken to be perpendicular to <strong>the</strong> surface)<br />
dsinϑ = n·λ<br />
Ifweallow for <strong>the</strong>incominglight’s (c<strong>on</strong>sidered tobeaplanewave)angle tobedifferent<br />
from that of <strong>the</strong> outgoing we get a generalizati<strong>on</strong> of <strong>the</strong> equati<strong>on</strong> above:<br />
d(sinϑout −sinϑin) = n·λ (4.1)<br />
This equati<strong>on</strong> is comm<strong>on</strong>ly referred to as <strong>the</strong> grating equati<strong>on</strong>. Since <strong>the</strong> result was<br />
obtained using <strong>the</strong> phase differences this holds for regular structures, i.e. wavefr<strong>on</strong>t<br />
distorti<strong>on</strong>s occur through <strong>the</strong> irregularities of <strong>the</strong> grating.<br />
The soluti<strong>on</strong> corresp<strong>on</strong>ding to n = 0 is <strong>the</strong> zeroth order comp<strong>on</strong>ent menti<strong>on</strong>ed<br />
before (thisisakintospecular reflecti<strong>on</strong>atamirror); <strong>the</strong>n<strong>on</strong>zerosoluti<strong>on</strong> corresp<strong>on</strong>ds<br />
to different diffracti<strong>on</strong> orders.<br />
A grating is thus a dispersive optical comp<strong>on</strong>ent that can be used in at normal or<br />
grazing incidence todeflect a certain wavelength part of <strong>the</strong> <strong>beam</strong> intoadefinedangle.<br />
At short wavelengths (in <strong>the</strong> EUV/soft X-ray regi<strong>on</strong>s) it is necessary to operate with<br />
grazing incidences since <strong>the</strong> reflectivity materials increase with decreasing angles.<br />
The zeroth order diffracti<strong>on</strong> have <strong>the</strong> same diffracti<strong>on</strong> angle as <strong>the</strong> incoming angle<br />
whereas <strong>the</strong> diffracted orders have a different angle as compared to <strong>the</strong> incoming light<br />
(angles α <strong>and</strong> β in Figure 4.3). Since <strong>the</strong> grating splits <strong>the</strong> <strong>beam</strong>, ei<strong>the</strong>r <strong>the</strong> diffracted
4.5. M<strong>on</strong>ochromators 67<br />
ordersor<strong>the</strong>zerothordercanbeusedfor<strong>beam</strong>diagnostic purposeswithoutdisturbing<br />
<strong>the</strong> user’s experimental stati<strong>on</strong>s downstream <strong>–</strong> this aspect is fur<strong>the</strong>r discussed below<br />
in chapter 5 (see page 73),<br />
Because of <strong>the</strong>ir dispersive nature gratings act as b<strong>and</strong>pass filters <strong>on</strong> <strong>the</strong> radiati<strong>on</strong><br />
<strong>and</strong> can thus be used to define <strong>the</strong> wavelength at <strong>the</strong> experimental stati<strong>on</strong>s (see<br />
below).<br />
Gratings that are blazed produce a maximum efficiency vis-à-vis reflectivity into<br />
a certain order (o<strong>the</strong>r than <strong>the</strong> zeroth) for <strong>the</strong> light that hit <strong>the</strong> grating. The higher<br />
reflectivity decreases <strong>the</strong> potential for radiati<strong>on</strong> damage to <strong>the</strong> grating.<br />
4.5 M<strong>on</strong>ochromators<br />
Although <strong>the</strong> b<strong>and</strong>width of <strong>the</strong> radiati<strong>on</strong> from free electr<strong>on</strong> laser can be very small,<br />
e.g. at Flash it is about 1%[104], many experiments <strong>–</strong> especially spectroscopic dittos<br />
<strong>–</strong> have a more stringent dem<strong>and</strong> <strong>on</strong> <strong>the</strong> spectral purity of <strong>the</strong> light. This is <strong>on</strong>e reas<strong>on</strong><br />
why m<strong>on</strong>ochromators are present at some free electr<strong>on</strong> laser<strong>–</strong> o<strong>the</strong>r reas<strong>on</strong>s include<br />
<strong>the</strong> increase of stability of <strong>the</strong> central wavelength as discussed below.<br />
Some experimental cevats c<strong>on</strong>cerning free electr<strong>on</strong> laser radiati<strong>on</strong><br />
A Sase pulse from a free electr<strong>on</strong> laser can be c<strong>on</strong>sidered as being built up from a<br />
series of spikes arising from <strong>the</strong> radiating l<strong>on</strong>gitudinal modes that happended to be<br />
amplified as that pulse passed through <strong>the</strong> undulator structure. Each spike in <strong>the</strong><br />
spectrum is transform limited 1 whereas <strong>the</strong> spectral distributi<strong>on</strong> in<strong>the</strong> pulseis chaotic<br />
in <strong>the</strong> sense that each pulse have a unique spectral compositi<strong>on</strong>. Thus a Sase pulse<br />
c<strong>on</strong>sists of many independently radiating modes whose intensity varies from pulse to<br />
pulse <strong>–</strong> hence <strong>the</strong> median wavelength of <strong>the</strong> pulses change, as well as <strong>the</strong> spectral<br />
intensity distributi<strong>on</strong>, <strong>on</strong> a pulse to pulse basis. Additi<strong>on</strong>ally, as seen in Figure 1.10,<br />
<strong>the</strong> radiati<strong>on</strong> emitted in <strong>the</strong> Sase part of <strong>the</strong> spectrum sits <strong>on</strong> top of a large broad<br />
background of sp<strong>on</strong>taneous undulator radiati<strong>on</strong>.<br />
If <strong>the</strong> undulators are not perfectly helical (that is <strong>the</strong> electr<strong>on</strong>s emits n<strong>on</strong>-circularly<br />
polarized radiati<strong>on</strong>) <strong>the</strong> spectrum will c<strong>on</strong>tain harm<strong>on</strong>ics of <strong>the</strong> fundamental wavelength<br />
emitted. In certain instances this can be viewed as fortuitous since <strong>the</strong> harm<strong>on</strong>ics<br />
will have shorter wavelengths (but <strong>the</strong>n <strong>the</strong> intense fundamental becomes a<br />
problem at <strong>the</strong> experiment) or as a serious drawback if it is <strong>the</strong> fundamental wavelength<br />
that is to be used <strong>–</strong> <strong>and</strong> <strong>the</strong> harm<strong>on</strong>ics becomes a problem at <strong>the</strong> experiment<br />
side.<br />
Seeded free electr<strong>on</strong> laser schemes (secti<strong>on</strong> 1.5, see page 15) improves up<strong>on</strong> <strong>the</strong><br />
basic Sase scheme in various ways <strong>–</strong> all striving to improve <strong>the</strong> quality of <strong>the</strong> emitted<br />
radiati<strong>on</strong> by enhancing <strong>the</strong> microbunching of <strong>the</strong> electr<strong>on</strong>s in various ways. To avoid<br />
timing errors between <strong>the</strong> seed pulse(s) <strong>and</strong> <strong>the</strong> electr<strong>on</strong> bunch (timing jitter) <strong>the</strong><br />
seed pulse is often significantly shorter than <strong>the</strong> electr<strong>on</strong> bunch. Hence, <strong>on</strong>ly a part<br />
of <strong>the</strong> electr<strong>on</strong>s experiences <strong>the</strong> additi<strong>on</strong>al density modulati<strong>on</strong> owing to <strong>the</strong> seeding<br />
process, in additi<strong>on</strong> to <strong>the</strong> seeded free electr<strong>on</strong> laser radiati<strong>on</strong> <strong>on</strong>e thus obtains a<br />
Sase background from <strong>the</strong> rest of <strong>the</strong> electr<strong>on</strong> bunch (as well as <strong>the</strong> background from<br />
sp<strong>on</strong>taneous undulator radiati<strong>on</strong> menti<strong>on</strong>ed before). Eventhough <strong>the</strong> Sase part of<br />
1 i.e. <strong>the</strong> spectral width is minimal for a given pulse-length. For a Gaussian pulse this implies<br />
that <strong>the</strong> time-b<strong>and</strong>width product is 0.44.
68 4. X-ray optics<br />
<strong>the</strong> <strong>beam</strong> do not reach saturati<strong>on</strong> it can still carry significant power. The unseeded<br />
part of <strong>the</strong> <strong>beam</strong> can thus disturb downstream experiments both with <strong>the</strong> background<br />
itself <strong>and</strong> that it arrives before, <strong>and</strong> extends after, <strong>the</strong> main pulse.<br />
Benefits <strong>and</strong> drawbacks of from a m<strong>on</strong>ochromator<br />
A m<strong>on</strong>ochromator is a device that filters a phot<strong>on</strong> <strong>beam</strong> with regard to wavelength<br />
<strong>–</strong> acting essentially as a wavelength b<strong>and</strong>-pass filter. C<strong>on</strong>sidering <strong>on</strong>ly <strong>the</strong> wavelength<br />
variati<strong>on</strong> issue first, it is obviously beneficial to filter <strong>the</strong> phot<strong>on</strong> <strong>beam</strong> with a<br />
m<strong>on</strong>ochromator since it resolves many of <strong>the</strong> issues menti<strong>on</strong>ed above. A m<strong>on</strong>ochromator<br />
provides:<br />
• Suppressi<strong>on</strong> of <strong>the</strong> sp<strong>on</strong>taneous emissi<strong>on</strong> background.<br />
• Selecti<strong>on</strong>ofanarrow(er)wavelengthrange <strong>–</strong>essentially translatingcentralwavelength<br />
jitter to intensity jitter. The latter is significantly easier to measure <strong>on</strong><br />
a pulse by pulse basis 2 to be used in <strong>the</strong> analysis of o<strong>the</strong>r experimental data.<br />
• Selecti<strong>on</strong> of a single harm<strong>on</strong>ic. Ei<strong>the</strong>r filtering away <strong>the</strong> fundamental if higher<br />
harm<strong>on</strong>ics <strong>and</strong> thus shorter wavelengths are desired, or suppressing <strong>the</strong> c<strong>on</strong>tributi<strong>on</strong><br />
from higher orders if <strong>the</strong> fundamental wavelength is to be used.<br />
• Selecting <strong>the</strong>seeded part of <strong>the</strong>spectrum <strong>–</strong>suppressing <strong>the</strong>sp<strong>on</strong>taneous undulator<br />
emissi<strong>on</strong> <strong>and</strong> <strong>the</strong> Sase background. The sp<strong>on</strong>taneous <strong>and</strong> Sase background<br />
which lies directly underneath <strong>the</strong> seeded part will not be filtered away <strong>and</strong> thus<br />
c<strong>on</strong>tribute to a intensity jitter of <strong>the</strong> m<strong>on</strong>ochromatized pulse.<br />
From a wavelength stability aspect it is thus very advantageous to insert a m<strong>on</strong>ochromator<br />
before <strong>the</strong>experiments. This is providedthat<strong>the</strong>intensityjitter betweenpulses<br />
can be measured <strong>on</strong> a pulse by pulse basis which can be included in <strong>the</strong> data analysis<br />
of <strong>the</strong> experiments. Ways of measuring <strong>the</strong> intensity are discussed in chapter 7 (see<br />
page 99).<br />
The price to pay for <strong>the</strong> wavelength stability is that <strong>the</strong> transmitted power through<br />
<strong>the</strong> optical system gets smaller (per each new optical element) <strong>and</strong> that <strong>the</strong> pulses<br />
get temporally stretched. The time-stretch can be c<strong>on</strong>trolled or compensated at <strong>the</strong><br />
cost of transmissi<strong>on</strong> as will be seen below.<br />
For high energy phot<strong>on</strong>s (larger than about 2 keV) it is not possible to use gratings<br />
because <strong>the</strong>ir cut-off energy prohibits transmissi<strong>on</strong>. Instead crystal m<strong>on</strong>ochromators<br />
can be employed which is c<strong>on</strong>structed from channel cut crystals (often Si) optimized<br />
to transmit <strong>on</strong>e phot<strong>on</strong> energy optimally. At Lcls <strong>on</strong>e such m<strong>on</strong>ochromator is built<br />
into <strong>the</strong> <strong>beam</strong> <strong>transport</strong> system that is optimized for 8.3 keV[96].<br />
Time-stretching<br />
In <strong>the</strong> soft X-ray ranges <strong>the</strong> incidence angle <strong>on</strong> any optical element needs to be small<br />
(i.e. <strong>the</strong> <strong>beam</strong> impinges at <strong>the</strong> optic at grazing incidence). Thus <strong>the</strong>re will be a time<br />
difference between <strong>the</strong> parts of <strong>the</strong> <strong>beam</strong> that hits <strong>the</strong> surface first <strong>and</strong> <strong>the</strong> parts<br />
2 O<strong>the</strong>rwise <strong>the</strong> full spectrum of <strong>the</strong> pulse (i.e. both wavelength <strong>and</strong> intensity distributi<strong>on</strong>)<br />
needs to be measured <strong>on</strong> a pulse by pulse basis. This is slightly more involved than measuring <strong>the</strong><br />
intensity in this manner, as discussed in chapter 7 (see page 99).
4.6. Beam attenuators 69<br />
that hit at a later time, as illustrated in Figure 4.2. The time-stretching can be<br />
reversed by letting <strong>the</strong> <strong>beam</strong> bounce off a sec<strong>on</strong>d surface <strong>–</strong> at <strong>the</strong> cost of reduced<br />
transmissi<strong>on</strong>, it can also be c<strong>on</strong>trolled as it is proporti<strong>on</strong>al to <strong>the</strong> number of grooves<br />
that are illuminated by <strong>the</strong> <strong>beam</strong>[105]. By illuminating <strong>the</strong> grating parallel to <strong>the</strong><br />
grooves (off-plane mounting) <strong>the</strong> time-stretching can be reduced also[106, 107].<br />
Figure 4.2: Time stretching of a pulse arising from <strong>the</strong> grazing incidence.<br />
α<br />
β<br />
α<br />
β 0 th order<br />
Figure 4.3: A time-stretch compensating double grating setup. The <strong>beam</strong> moves from left to right in a Z-shaped<br />
path <strong>and</strong> <strong>the</strong> outgoing <strong>beam</strong> is parallel to <strong>the</strong> incoming.<br />
4.6 Beam attenuators<br />
Although not a proper optical element per se, gas attenuators are a integral comp<strong>on</strong>ent<br />
of <strong>the</strong> <strong>beam</strong> <strong>transport</strong> system of free electr<strong>on</strong> laser providing a robust mean of<br />
c<strong>on</strong>trolling <strong>the</strong> intensity of <strong>the</strong> radiati<strong>on</strong> at <strong>the</strong> experiments. The intensity can be<br />
c<strong>on</strong>trolled in a c<strong>on</strong>tinuous manner over several orders of magnitude with <strong>the</strong> limit set<br />
essentially by vacuum c<strong>on</strong>siderati<strong>on</strong>s, i.e. how good <strong>the</strong> differential pumping is.<br />
Beam attenuators <strong>and</strong> filters based <strong>on</strong> metal foils <strong>and</strong> metal/ceramic windows free<br />
electr<strong>on</strong> laser <strong>beam</strong> can be used at higher energies provided that <strong>the</strong>y can withst<strong>and</strong><br />
<strong>the</strong> fluence of <strong>the</strong> X.rays.<br />
There is str<strong>on</strong>g indicati<strong>on</strong>s that, at least, gas attenuators do not distort <strong>the</strong> wavefr<strong>on</strong>t<br />
[104] thus c<strong>on</strong>serving <strong>the</strong> coherence properties of <strong>the</strong> x-ray <strong>beam</strong>.<br />
Figure 4.4 describes a generic attenuator, at <strong>the</strong> Lcls <strong>the</strong>re are solid attenuators<br />
included whereas at Flash <strong>and</strong> Scss <strong>on</strong>ly <strong>the</strong> gas attenuator is needed (owing to
70 4. X-ray optics<br />
Intensity detector<br />
Pumping<br />
Solid attenuators<br />
Gas input<br />
Intensity detector<br />
Pumping<br />
Figure 4.4: Schematic of a gas attenuator with intensity m<strong>on</strong>itors before <strong>and</strong> after.<br />
<strong>the</strong>ir wavelength ranges). Intensity m<strong>on</strong>itors are usually put before <strong>and</strong> after <strong>the</strong><br />
attenuators 3 .<br />
The gas attenuator at Flash is 15 m l<strong>on</strong>g <strong>and</strong> s<strong>and</strong>wiched between intensity m<strong>on</strong>itors.<br />
It is operated ei<strong>the</strong>r with nitrogen for <strong>the</strong> wavelength ranges 60-19 nm, <strong>and</strong><br />
for smaller wavelengths xen<strong>on</strong> or krypt<strong>on</strong> can be employed. The differential pumping<br />
system is fast <strong>and</strong> changes of transmissi<strong>on</strong> of up to four orders of magnitude can be<br />
provided by <strong>the</strong> attenuator within minutes[104, 108].<br />
At <strong>the</strong> Scss a smaller gas-cell is used with arg<strong>on</strong> as attenuator gas[109, 110].<br />
Lclsemploysa4.5metersl<strong>on</strong>ggas attenuatorusingnitrogenfor operati<strong>on</strong>between<br />
800 <strong>and</strong> 2000 eV phot<strong>on</strong> energies. The pressure range is up to about 10 mbar <strong>and</strong><br />
thus provide an attenuati<strong>on</strong> span of four orders of magnitude. A set of solid beryllium<br />
attenuators (0.1 to 32 mm thickness) provide <strong>the</strong> attenuati<strong>on</strong> for <strong>the</strong> harder X-rays<br />
up to 8 keV.<br />
3 Intensity diagnostic devices will be discussed fur<strong>the</strong>r in secti<strong>on</strong> 7.2 (see page 100).
4.6. Beam attenuators 71<br />
Summary<br />
• The dem<strong>and</strong>s <strong>on</strong> X-rayoptical elements for free electr<strong>on</strong> lasers<br />
are more stringent than those utilized for e.g. storage ring<br />
lightsources <strong>–</strong> owing to <strong>the</strong>, in most instances, higher peak<br />
power of free electr<strong>on</strong> lasers compared to <strong>the</strong> high average<br />
power exerted from storage ring synchrotr<strong>on</strong>s.<br />
• Damage<strong>on</strong>opticalelementschanges<strong>the</strong>propertiesof<strong>the</strong>radiati<strong>on</strong><br />
at <strong>the</strong> user stati<strong>on</strong>s vis-á-vis spectral c<strong>on</strong>tent, intensity,<br />
coherence <strong>and</strong> temporal structure.<br />
• Optical elements used at free electr<strong>on</strong> lasers generally suffers<br />
damage primarily from ablati<strong>on</strong> caused by <strong>the</strong> high peak brilliance<br />
of <strong>the</strong> source.<br />
• In<strong>the</strong>VUV<strong>and</strong> soft X-rayregi<strong>on</strong>s diffracti<strong>on</strong> gratings areuniversally<br />
adopted as <strong>the</strong> dispersive optic necessary to provide<br />
wavelength selecti<strong>on</strong> in m<strong>on</strong>ochromators.<br />
• Simulati<strong>on</strong> codes: Shadow[111], Xtrace[112], Spectra.
5. Beam-splitting methods<br />
The material presented here in this chapter is partly adapted from ”Survey of<br />
<strong>beam</strong> splitters” by M. A. Bowler, A. J. Glees<strong>on</strong>, D Laundy, <strong>and</strong> M. D. Roper.<br />
Iruvx WP7, 2010 by A. Lindblad.<br />
5.1 Introducti<strong>on</strong><br />
The number of <strong>beam</strong>lines, where experiments can be carried out, at Free Electr<strong>on</strong><br />
Laser (FEL) facilities is much less than <strong>on</strong> synchrotr<strong>on</strong>s, <strong>and</strong> may not be enough to<br />
meet user dem<strong>and</strong>. One possibility of increasing <strong>the</strong> number of users being able to<br />
carry out experiments <strong>on</strong> free electr<strong>on</strong> lasers is to split <strong>the</strong> radiati<strong>on</strong> in a <strong>beam</strong>line<br />
into two or more separate paths allowing more than <strong>on</strong>e experiment to be carried out<br />
simultaneously. This could be achieved by splitting <strong>the</strong> phot<strong>on</strong> <strong>beam</strong>, or if <strong>the</strong> pulse<br />
repetiti<strong>on</strong> rate is slow enough, by kicking <strong>the</strong> electr<strong>on</strong> bunches into different paths.<br />
This chapter is mainly c<strong>on</strong>cerned with <strong>the</strong> former technique, <strong>and</strong> gives a survey of<br />
techniques for splitting a phot<strong>on</strong> <strong>beam</strong>.<br />
The type of <strong>beam</strong> splitter used will depend <strong>on</strong> <strong>the</strong> wavelength range over which it<br />
is required to operate. This chapter c<strong>on</strong>centrates <strong>on</strong> <strong>the</strong> wavelengths from <strong>the</strong> vacuum<br />
ultra-violet (VUV) to <strong>the</strong> soft X-ray (SXR) regi<strong>on</strong>s. However, menti<strong>on</strong> will be made<br />
of techniques employed at o<strong>the</strong>r wavelengths, at harder X-ray energies of relevance for<br />
example to XFEL, <strong>and</strong> at much l<strong>on</strong>ger wavelengths in <strong>the</strong> infrared regime of relevance<br />
to existing free electr<strong>on</strong> lasers <strong>and</strong> possible future far infrared (FIR) sources.<br />
Beam splitters are also usedtopartiti<strong>on</strong> <strong>the</strong>radiati<strong>on</strong> for pump-probeexperiments,<br />
for sending a small fracti<strong>on</strong> of <strong>the</strong> radiati<strong>on</strong> for diagnostic purposes, <strong>and</strong> for input to<br />
interferometers. Beam splitters designed for <strong>the</strong>se <strong>and</strong> o<strong>the</strong>r uses have been included<br />
as <strong>the</strong>y may be able to be adapted to fullfil <strong>the</strong> requirements for allowing multiple<br />
end-stati<strong>on</strong>s to be used simultaneously.<br />
Beam splitters can be divided into two main categories. Firstly, <strong>the</strong>re are those<br />
that divide <strong>the</strong> amplitude of <strong>the</strong> radiati<strong>on</strong>, such as:<br />
• partiallytransmittingmirrors -metallic foils, multilayers, pellicles, <strong>beam</strong>splitter<br />
plates<br />
• <strong>beam</strong> splitter cubes<br />
• thin crystals<br />
73
74 5. Beam-splitting methods<br />
• diffracti<strong>on</strong> gratings<br />
• wire grids<br />
Sec<strong>on</strong>dly, <strong>the</strong>re are those that divide <strong>the</strong> wavefr<strong>on</strong>t, such as<br />
• knife edge mirrors or crystals<br />
• Fresnel bi-mirror<br />
• slotted or perforated mirrors<br />
• structured arrays<br />
In <strong>the</strong> case of a pulsed source, it is also possible to divide <strong>the</strong> <strong>beam</strong> in time by<br />
using moving mirrors (translating, rotating, vibrating) to deflect pulses in different<br />
directi<strong>on</strong>s.<br />
Each type of <strong>beam</strong> splitter is discussed in turn, <strong>and</strong> in secti<strong>on</strong> 5.6 a list is drawn up<br />
of those which may be suitable c<strong>and</strong>idates for splitting a main free electr<strong>on</strong> laser <strong>beam</strong><br />
for multiple experiments for different wavelength regimes. General points for <strong>the</strong><br />
specificati<strong>on</strong> of a <strong>beam</strong> splitter are given in secti<strong>on</strong> 2 before <strong>the</strong> survey of <strong>the</strong> different<br />
types.<br />
5.2 Beam-splitter specificati<strong>on</strong><br />
A sample specificati<strong>on</strong> is given in Table 5.1 for a <strong>beam</strong> splitter <strong>on</strong> an XUV-FEL.<br />
The full specificati<strong>on</strong> of a <strong>beam</strong> splitter will include <strong>the</strong> maximum power loading,<br />
overall efficiency, relative intensity of <strong>the</strong> split <strong>beam</strong>s, minimum angular separati<strong>on</strong>,<br />
polarisati<strong>on</strong> <strong>and</strong> wavefr<strong>on</strong>t preservati<strong>on</strong>. The required power h<strong>and</strong>ling <strong>and</strong> efficiency<br />
to a large extent will determine <strong>the</strong> incident angle <strong>and</strong> <strong>the</strong> material(s) used. The<br />
incidence angle will have a large impact <strong>on</strong> <strong>the</strong> size of <strong>the</strong> optic. Cost <strong>and</strong> ease of<br />
manufacture of <strong>the</strong> comp<strong>on</strong>ent are also important c<strong>on</strong>siderati<strong>on</strong>s.<br />
FEL radiati<strong>on</strong> has a high degree of polarisati<strong>on</strong> <strong>and</strong> coherence. In c<strong>on</strong>sidering<br />
<strong>the</strong> suitability of different types of <strong>beam</strong> splitter, <strong>the</strong> starting assumpti<strong>on</strong> is that <strong>the</strong><br />
quality of <strong>the</strong> incident <strong>beam</strong> is to be preserved in <strong>the</strong> split <strong>beam</strong>s, i.e. polarisati<strong>on</strong>,<br />
wavefr<strong>on</strong>t shape <strong>and</strong> pulse durati<strong>on</strong> are preserved as far as possible. However, it may<br />
be that in order to increase <strong>the</strong> efficiency <strong>the</strong>se assumpti<strong>on</strong>s have to be relaxed, at<br />
least in <strong>on</strong>e if not both of <strong>the</strong> <strong>beam</strong>s. Obviously <strong>the</strong> exact <strong>beam</strong> qualities required<br />
will depend <strong>on</strong> <strong>the</strong> experiment <strong>and</strong> preserving all properties may not be important<br />
in all cases <strong>and</strong> such a relaxati<strong>on</strong> may not matter. Different splitting techniques will<br />
compromise different aspects of <strong>the</strong> <strong>beam</strong> <strong>and</strong> <strong>the</strong> correct choice will depend <strong>on</strong> <strong>the</strong><br />
experiment; <strong>the</strong>re is unlikely to be a universal <strong>beam</strong> splitter.<br />
The minimum required efficiency will be set by <strong>the</strong> ability of <strong>the</strong> optics to h<strong>and</strong>le<br />
<strong>the</strong> power load or <strong>beam</strong> fluence. The efficiency requirement as determined by <strong>the</strong> flux<br />
needs of <strong>the</strong> experiments falls outside <strong>the</strong> scope of this survey. It is however assumed<br />
that <strong>the</strong> experiments <strong>on</strong> each branch will be equally dem<strong>and</strong>ing of phot<strong>on</strong> flux <strong>and</strong><br />
so <strong>the</strong> <strong>beam</strong> should be split roughly into equal parts. It is however noted that for<br />
some applicati<strong>on</strong>s <strong>the</strong> free electr<strong>on</strong> laser be may be too powerful, <strong>and</strong> it may be that<br />
a <strong>beam</strong> splitter could be used as an attenuator <strong>on</strong> <strong>on</strong>e <strong>beam</strong> path.<br />
A fur<strong>the</strong>r point to note is that he space available for <strong>the</strong> <strong>beam</strong>lines may well also<br />
limit <strong>the</strong> maximum angular separati<strong>on</strong> <strong>and</strong> in general it may not be practical to have<br />
very large angular separati<strong>on</strong>s between <strong>the</strong> <strong>beam</strong>s.
5.2. Beam-splitter specificati<strong>on</strong> 75<br />
Parameter Value Comments<br />
Phot<strong>on</strong> energy 8-100 eV<br />
Average power 10-100 W Depends <strong>on</strong> rep. rate<br />
Beam fluence ≤ 50 mJ/cm 2<br />
Value at 100 eV, normal incidence<br />
Grazing angle < 5 ◦ , preferable ∼ 3 ◦<br />
Determined by reflectivity<br />
requirements <strong>and</strong> ablati<strong>on</strong><br />
threshold<br />
Size 100-200 mm by 50 mm Depends <strong>on</strong> grazing angle<br />
Overall efficeny > 50% This may increase if power<br />
loading becomes problematic<br />
Intensity split Roughly equal in each<br />
branch<br />
Polarisati<strong>on</strong> Ideally small/negligable This will be difficult for<br />
lower energies<br />
Wavefr<strong>on</strong>t distorti<strong>on</strong> Ideally <strong>the</strong> modal structure<br />
of <strong>the</strong> <strong>beam</strong> should be preserved<br />
Minimum angular 5 mrad (0.3<br />
separati<strong>on</strong> of <strong>beam</strong>s<br />
◦ )<br />
Vacuum compatibil- UVH bakable hydrocarb<strong>on</strong> free for operaityti<strong>on</strong><br />
near <strong>the</strong> carb<strong>on</strong> edge<br />
Table 5.1: Sample specificati<strong>on</strong> for a <strong>beam</strong>-splitter for XUV radiati<strong>on</strong>.
76 5. Beam-splitting methods<br />
5.3 Amplitude divisi<strong>on</strong> <strong>beam</strong> splitters<br />
Partially transmitting materials<br />
Partially transmitting mirrors can be made from metallic foils or multilayers. When<br />
<strong>the</strong>se are deposited <strong>on</strong> glass <strong>the</strong>y are termed plate <strong>beam</strong> splitters, or <strong>on</strong> a thin (of<br />
<strong>the</strong> order of µm thickness) stretched polymer membranes, <strong>the</strong>y are termed pellicles.<br />
Thin crystals are also used as <strong>beam</strong> splitters in <strong>the</strong> harder X-ray regime.<br />
Plate <strong>beam</strong> splitters, by <strong>the</strong>ir nature of being deposited <strong>on</strong> glass, operate mainly<br />
<strong>the</strong> visible <strong>and</strong> near infrared (NIR) but <strong>the</strong>ir range can be extended to 200 nm using<br />
UV grade fused silica as <strong>the</strong> substrate. They will normally have <strong>the</strong> <strong>beam</strong> splitter<br />
coating <strong>on</strong> <strong>the</strong> fr<strong>on</strong>t face of <strong>the</strong> plate <strong>and</strong> an anti-reflecti<strong>on</strong> coating <strong>on</strong> <strong>the</strong> back to<br />
prevent ghosting <strong>and</strong> <strong>the</strong> substrate will be slightly wedged to eliminate interference<br />
fringes. They can be ei<strong>the</strong>r polarising or n<strong>on</strong>-polarising. Polarising <strong>beam</strong> splitters<br />
use bi-refringent materials <strong>and</strong>/or are operated near <strong>the</strong> Brewster Angle. Plate <strong>beam</strong><br />
splitters can be made for high power applicati<strong>on</strong>s, but those that are readily available<br />
are mainly single wavelength, single angle devices, made for specific laser lines. As an<br />
example, ESCO[113] make a range of <strong>beam</strong> splitters with a 10% b<strong>and</strong>pass, damage<br />
threshold 300 - 500 W/cm 2 , designed to work at 45 ◦ incidence for a range of laser<br />
lines from <strong>the</strong> UV to IR.<br />
Broadb<strong>and</strong> dielectric plate <strong>beam</strong> splitters are available in <strong>the</strong> visible <strong>and</strong> NIR, e.g.<br />
Newport[114] provide <strong>beam</strong> splitters covering <strong>the</strong> wavelength ranges 480 - 700 nm,<br />
700 - 950 nm, 1290 - 1500 nm. These operate at 45 ◦ angle of incidence <strong>and</strong> all are<br />
slightly polarising. The damage threshold is quoted as typically 500 W/cm 2 CW, 0.5<br />
J/cm 2 with 10 ns pulses.<br />
C<strong>on</strong>venti<strong>on</strong>al plate <strong>beam</strong> splitters may not be applicable for ultra-fast use due to<br />
dispersi<strong>on</strong> in <strong>the</strong> transmitted <strong>beam</strong>s. Newport provide thin (3mm) ”ultra-fast” plate<br />
splitters made from UV quality fused-silica operating over 700 - 950 nm for s-polarised<br />
light <strong>and</strong> 680 - 1060 nm for p-polarised light. Again <strong>the</strong>se operate at 45 ◦ angle of<br />
incidence <strong>and</strong> split <strong>the</strong> radiati<strong>on</strong> nearly 50:50 <strong>and</strong> are usable for pulses in <strong>the</strong> 100’s<br />
of fs regime.<br />
Pellicles<br />
Pellicles operate in <strong>the</strong> wavelength range 400 - 2500 nm. They have <strong>the</strong> advantage<br />
over plates in that <strong>the</strong>re is no ghost image due to <strong>the</strong>ir extreme thinness (except for<br />
extremely short pulses which would <strong>on</strong>ly be a few cycles l<strong>on</strong>g at <strong>the</strong>se wavelengths).<br />
For uncoated pellicles <strong>the</strong> reflectivity is about 10%, transmissi<strong>on</strong> about 90%, but<br />
coatings have been made which increase <strong>the</strong> reflectance up to <strong>the</strong> order of 50 %.<br />
Typical damage thresholds are 2 W/cm 2 CW <strong>and</strong> 1 J/cm 2 with 10 ns pulses for<br />
uncoated membranes, which makes <strong>the</strong>m unsuitable for free electr<strong>on</strong> laser <strong>beam</strong>lines.<br />
The thin membranes are also susceptible to vibrati<strong>on</strong> <strong>and</strong> interference fringes. For<br />
fur<strong>the</strong>r details see for example: [114, 115].<br />
As an extensi<strong>on</strong> to what is normally c<strong>on</strong>sidered to be a pellicle, a <strong>beam</strong> splitter for<br />
an FTIR spectrometer has been made for <strong>the</strong> THz free electr<strong>on</strong> laser at KAERI by<br />
coating a polyester film with silver [116]. At 3 THz, <strong>the</strong> absorpti<strong>on</strong> of <strong>the</strong> polyester<br />
film is about 2%, <strong>and</strong><strong>the</strong> balance between reflecti<strong>on</strong> <strong>and</strong>transmissi<strong>on</strong> was obtained by<br />
coating <strong>the</strong> film with several tens of nanometers of silver to create <strong>the</strong> <strong>beam</strong> splitter.
5.3. Amplitude divisi<strong>on</strong> <strong>beam</strong> splitters 77<br />
In an analogous manner, thin foils of a low-Z material might be used at soft x-ray<br />
<strong>and</strong> shorter wavelengths.<br />
For example, Lcls propose to use 30 µm thick polished beryllium foils at a grazing<br />
angle (∼ 1 ◦ for energies around 8 keV) above <strong>the</strong> critical angle to reflect a small<br />
( 0.01%) part of <strong>the</strong> <strong>beam</strong> to a diagnostic instrument, while transmitting 99% of <strong>the</strong><br />
radiati<strong>on</strong>[117]. Because low-Z materials give a sharp reflecti<strong>on</strong> cut-off, achieving a<br />
more balanced split will require <strong>the</strong> grazing angle to be adjusted to suit <strong>the</strong> phot<strong>on</strong><br />
energy <strong>and</strong> hence <strong>the</strong> angle of <strong>beam</strong> separati<strong>on</strong> would be a functi<strong>on</strong> of phot<strong>on</strong> energy.<br />
At lower phot<strong>on</strong> energies high transmissi<strong>on</strong> will not be possible e.g. it is effectively<br />
zero below 1 keV for a 30 µm Be foil.<br />
Extensi<strong>on</strong> of this technique into <strong>the</strong> XUV would require excepti<strong>on</strong>ally thin foils<br />
where <strong>the</strong> challenge of manufacturing <strong>and</strong> supporting a surface of sufficient quality<br />
for good reflecti<strong>on</strong> would be very severe indeed. Where absorpti<strong>on</strong> is high, <strong>the</strong>re is<br />
also <strong>the</strong> c<strong>on</strong>cern of radiati<strong>on</strong> damage.<br />
Multi-layer <strong>beam</strong> splitters<br />
Multi-layer <strong>beam</strong>splitters canbemade for <strong>the</strong>XUV<strong>and</strong>shorter wavelengths, however<br />
in general <strong>the</strong>y <strong>on</strong>ly operate for a given wavelength <strong>and</strong> incident angle. Multi-layers<br />
are usually formed <strong>on</strong>SiC, SiNor Si3N4 membranes butobviously for <strong>the</strong>transmissi<strong>on</strong><br />
multi-layers required for <strong>beam</strong> splitters, absorpti<strong>on</strong> in <strong>the</strong> membrane is a problem at<br />
XUV wavelengths. Much work has been d<strong>on</strong>e in <strong>the</strong> 13<strong>–</strong>16 nm wavelength range<br />
for applicati<strong>on</strong>s in lithography using multi-layers <strong>on</strong> Si3N4 membranes, however in<br />
general <strong>the</strong> overall efficiencies are not very high. Some examples found <strong>on</strong> <strong>the</strong> web<br />
with overall efficiency greater than 20% include:<br />
• Near-normal incidence (10 ◦ ) Mo/Si multilayer - reflectivity 28%, transmissi<strong>on</strong><br />
32% [118]<br />
• Ru/SiNbilayeroperatingat17.5 ◦ incidence -reflectivity<strong>and</strong>transmissi<strong>on</strong> about<br />
11% [118]<br />
• Mo/Si multilayer <strong>on</strong> silic<strong>on</strong> nitride at 7.2 ◦ incidence - reflectivity 20%, transmissi<strong>on</strong><br />
22% [119]<br />
Some work has been d<strong>on</strong>e <strong>on</strong> manufacturing free-st<strong>and</strong>ing multi-layers. For example,<br />
Haga, et al. [120] report <strong>the</strong> manufacture of a 10 by 10 mm 2 Mo/Si multilayer<br />
where <strong>the</strong> silic<strong>on</strong> nitride membrane is etched away. The outer Mo layers were replaced<br />
by Ru which was much more resistant to <strong>the</strong> etching process. They also investigated<br />
<strong>the</strong> effect of <strong>the</strong> substrate smoothness <strong>on</strong> <strong>the</strong> efficiency of <strong>the</strong> multi-layer. Measurements<br />
using synchrotr<strong>on</strong> radiati<strong>on</strong> revealed that <strong>the</strong> multilayer worked as a <strong>on</strong>e-to-<strong>on</strong>e<br />
<strong>beam</strong> splitter whose reflectivity<strong>and</strong> transmittance for s-polarised radiati<strong>on</strong> at 13.4 nm<br />
are both 27% at an angle of incidence of 45 ◦ , i.e. <strong>the</strong> efficiency is similar to supported<br />
multilayers. More recent work <strong>on</strong> free-st<strong>and</strong>ing multilayers has not been identified.<br />
By varying <strong>the</strong> thickness of <strong>the</strong> multi-layers with depth, <strong>the</strong> wavelength <strong>and</strong>/or<br />
angle range can be increased, e.g. for reflecting multi-layers a reflectivity of larger<br />
than 40% is expected over <strong>the</strong> energy range 4 - 9 keV using 20 Mo/Si bi-layers with<br />
five different spacings <strong>on</strong> an SiO2 substrate[94]. If <strong>the</strong>se multi-layers could be made<br />
<strong>on</strong> transparent substrates, <strong>the</strong>ir use as <strong>beam</strong>-splitters could be investigated. Note<br />
again <strong>the</strong>re may be a problem of dispersi<strong>on</strong> which may preclude <strong>the</strong>ir use for very<br />
high time resoluti<strong>on</strong> applicati<strong>on</strong>[121].
78 5. Beam-splitting methods<br />
Radiati<strong>on</strong> damage is an area for c<strong>on</strong>cern for <strong>the</strong> use of multilayers in free electr<strong>on</strong><br />
laser <strong>beam</strong>lines. Recently Bajt, et al. [122] reported that a normal incidence parabolic<br />
Mo/Si multilayer mirror with a reflectivity of about 60%, used to focus 13.5 nm<br />
radiati<strong>on</strong> at Flash did not show signs of damage. This efficiency is similar to <strong>the</strong><br />
overall efficiency of some of <strong>the</strong> <strong>beam</strong> splitters menti<strong>on</strong>ed above. Obviously more<br />
work needs to be d<strong>on</strong>e in this area. However, it is unlikely that a multilayer <strong>beam</strong><br />
splitter would be used for <strong>the</strong> current applicati<strong>on</strong> due to <strong>the</strong> wavelength specificity as<br />
well as possible power h<strong>and</strong>ling issues.<br />
Beam splitter cubes<br />
Beam splitter cubes <strong>on</strong>sist of 2 right-angled prisms, made of fused silica for UV<br />
applicati<strong>on</strong>s, normally cemented toge<strong>the</strong>r with an epoxy. Broadb<strong>and</strong> cubes, with<br />
b<strong>and</strong>widths of 300 - 400 nm, are available over <strong>the</strong> wavelength range 400 - 1600 nm,<br />
<strong>and</strong> may alter <strong>the</strong> polarizati<strong>on</strong> of <strong>the</strong> light by about 10%. There are n<strong>on</strong>polarizing<br />
cubes designed for specific laser lines in <strong>the</strong> UV, for moderate power laser operati<strong>on</strong>.<br />
The epoxy absorbs radiati<strong>on</strong> <strong>and</strong> hence cannot be used in high power applicati<strong>on</strong>s.<br />
However, cubes which do not use adhesives to cement <strong>the</strong> prisms toge<strong>the</strong>r have been<br />
recently designed for high power laser applicati<strong>on</strong>s, e.g. Showa Optr<strong>on</strong>ics[123] market<br />
a cube for <strong>the</strong> UV over <strong>the</strong> range 193nm - 355 nm with a damage threshold at 248<br />
nm of 1 J/cm 2 <strong>and</strong> Precisi<strong>on</strong> Phot<strong>on</strong>ics Corporati<strong>on</strong>[124] make cubes for high power<br />
applicati<strong>on</strong>s (damage threshold of 10 J/cm 2 at 1100 nm) in <strong>the</strong> visible <strong>and</strong> IR.<br />
Crystal diffracti<strong>on</strong> <strong>beam</strong> splitters<br />
Perfect crystals are comm<strong>on</strong>ly used as m<strong>on</strong>ochromating elements for hard X-rays<br />
(working at X-ray energies above about 2 keV). An X-ray entering a perfect crystal<br />
scatters from <strong>the</strong> regularly space atomic planes - a process known as dynamical<br />
diffracti<strong>on</strong>[125]. This leads to a very sharp reflectivity curve with a b<strong>and</strong>pass (∆E/E)<br />
for a given angle of incidence (Bragg angle) that is typically less than 10 −4 . The b<strong>and</strong>pass<br />
depends <strong>on</strong> <strong>the</strong> crystal material (diam<strong>on</strong>d is narrower than silic<strong>on</strong> which in turn<br />
is narrower than germanium), <strong>on</strong> <strong>the</strong> crystal planes used (planes with lower order<br />
indices generally give narrower reflecti<strong>on</strong>s) <strong>and</strong> <strong>on</strong> whe<strong>the</strong>r Bragg or Laue geometry<br />
is employed. In Bragg reflecting geometry, <strong>the</strong> X-rays enter <strong>and</strong> exit from <strong>the</strong> same<br />
surface of <strong>the</strong> crystal while in Laue geometry, <strong>the</strong> X-rays enter <strong>and</strong> exit from different<br />
surfaces. In Bragg geometry, <strong>the</strong> X-rays penetrate a short distance into <strong>the</strong> crystal<br />
<strong>and</strong> <strong>the</strong> reflectivity curve is given by a Darwin curve, which approximates to <strong>the</strong><br />
ideal top hat shape. A general c<strong>on</strong>sequence of <strong>the</strong> narrow b<strong>and</strong>pass associated with<br />
dynamical diffracti<strong>on</strong> is that <strong>the</strong> temporal profile of a short X-ray pulse is affected.<br />
When <strong>the</strong> radiati<strong>on</strong> source b<strong>and</strong>pass is larger than <strong>the</strong> crystal reflecti<strong>on</strong> b<strong>and</strong>pass,<br />
as is <strong>the</strong> case with X-ray FEL radiati<strong>on</strong>, a crystal m<strong>on</strong>ochromator can be used as a<br />
<strong>beam</strong> splitter. This method uses a crystal to deflect a small energy b<strong>and</strong> from <strong>the</strong><br />
broader b<strong>and</strong> source to <strong>on</strong>e experiment while <strong>the</strong> remaining transmitted radiati<strong>on</strong><br />
is passed <strong>on</strong>to a sec<strong>on</strong>d experiment. Thin crystals are normally used to minimise<br />
absorpti<strong>on</strong>. Crystal reflecti<strong>on</strong>s are sensitive to heating from <strong>the</strong> radiati<strong>on</strong> which can<br />
result in changes in lattice parameter <strong>and</strong> lattice orientati<strong>on</strong> which may degrade <strong>the</strong><br />
deflected <strong>beam</strong>. The ideal <strong>beam</strong> splitter crystal should have low X-ray absorpti<strong>on</strong> to<br />
minimise losses to <strong>the</strong> X-ray <strong>beam</strong> <strong>and</strong> to reduce X-ray <strong>beam</strong> power absorbed inside<br />
<strong>the</strong> crystal.
5.3. Amplitude divisi<strong>on</strong> <strong>beam</strong> splitters 79<br />
This method of splitting <strong>beam</strong>s for multiple experiments is used <strong>on</strong> some undulator<br />
<strong>and</strong> high-energy wiggler X-ray <strong>beam</strong>s at synchrotr<strong>on</strong> radiati<strong>on</strong> sources. In <strong>the</strong> lower<br />
X-ray energy range, diam<strong>on</strong>d is often used as <strong>the</strong> <strong>beam</strong> splitter as it has low Xray<br />
absorpti<strong>on</strong> <strong>and</strong> also good <strong>the</strong>rmal c<strong>on</strong>ductivity that allows <strong>the</strong> heat to dissipate<br />
efficiently, reducing <strong>the</strong>rmal distorti<strong>on</strong> of <strong>the</strong> crystal. The difficulty of obtaining<br />
diam<strong>on</strong>d crystals with high enough perfecti<strong>on</strong> for use as m<strong>on</strong>ochromators is a problem<br />
that has been recognised[126]. A sec<strong>on</strong>d m<strong>on</strong>ochromator crystal may be used to<br />
deflect <strong>the</strong> <strong>beam</strong> back into <strong>the</strong> incident <strong>beam</strong> directi<strong>on</strong> <strong>and</strong> if <strong>the</strong> first reflecti<strong>on</strong> is<br />
a diam<strong>on</strong>d (111) reflecti<strong>on</strong> it is possible to use a germanium (220) reflecti<strong>on</strong> as <strong>the</strong><br />
sec<strong>on</strong>d reflecti<strong>on</strong> as <strong>the</strong> d-spacings of <strong>the</strong> two reflecti<strong>on</strong>s are very similar. Using a<br />
germanium reflecti<strong>on</strong> for <strong>the</strong> sec<strong>on</strong>d crystal has <strong>the</strong> advantage that <strong>the</strong> reflecti<strong>on</strong><br />
has a broad width making alignment easier <strong>and</strong> reducing loss of X-ray flux caused<br />
by strain within <strong>the</strong> diam<strong>on</strong>d crystal. The additi<strong>on</strong> of a sec<strong>on</strong>d crystal may also<br />
allow <strong>the</strong> X-ray energy to be changed while maintaining almost c<strong>on</strong>stant X-ray <strong>beam</strong><br />
directi<strong>on</strong>. This method of X-ray <strong>beam</strong> splitting is used at <strong>the</strong> ESRF <strong>on</strong> <strong>the</strong> Troika<br />
<strong>beam</strong>line ID10, which has three undulator segments <strong>and</strong> has available a selecti<strong>on</strong> of<br />
m<strong>on</strong>ochromator crystals - diam<strong>on</strong>d (111), diam<strong>on</strong>d (220), <strong>and</strong> silic<strong>on</strong> (111) - allowing<br />
a variati<strong>on</strong> in b<strong>and</strong>width <strong>on</strong> two side stati<strong>on</strong>s. Ano<strong>the</strong>r example at <strong>the</strong> ESRF is <strong>the</strong><br />
macromolecular crystallography <strong>beam</strong>line ID14 which has three diam<strong>on</strong>d (111) <strong>and</strong><br />
germanium (220) m<strong>on</strong>ochromator pairs, in line, to give three 13.3 keV fixed energy<br />
stati<strong>on</strong>s <strong>and</strong> a single variable energy stati<strong>on</strong> using <strong>the</strong> straight through transmitted<br />
<strong>beam</strong>.<br />
In <strong>the</strong> higher X-ray energy range, X-ray absorpti<strong>on</strong> is lower <strong>and</strong> silic<strong>on</strong> or germanium<br />
may be used as <strong>the</strong> <strong>beam</strong> splitting crystal. This allows <strong>the</strong> b<strong>and</strong>pass of <strong>the</strong><br />
reflecti<strong>on</strong> to be varied by applying a bend to <strong>the</strong> crystal. An example of this applicati<strong>on</strong><br />
at <strong>the</strong> ESRF is <strong>the</strong> high-energy <strong>beam</strong>line ID15 which can use two bent crystals<br />
to deflect <strong>beam</strong> from <strong>the</strong> wiggler source to two side stati<strong>on</strong>s at X-ray energies from<br />
30 keV up to 300 keV.<br />
Where <strong>beam</strong> splitting is required for X-ray interferometry, perfect crystals are<br />
used. Laue interferometers[127] use <strong>the</strong> forward transmitted <strong>and</strong> reflected <strong>beam</strong>s at<br />
<strong>the</strong>crystalexitsurface tosplit<strong>the</strong><strong>beam</strong>. Interferometric <strong>beam</strong>splitters usingmultiple<br />
reflecti<strong>on</strong>s[128] or <strong>the</strong> <strong>beam</strong>s reflected from <strong>and</strong> transmitted through a crystal whose<br />
thickness is less than <strong>the</strong> extincti<strong>on</strong> depth can also be used. These techniques might<br />
be useful where multiple low-b<strong>and</strong>pass (∆E/E ∼ 10 −5 ) <strong>beam</strong>s are required, though<br />
<strong>the</strong>re could be <strong>the</strong>rmal problems since <strong>the</strong> radiati<strong>on</strong> out of this b<strong>and</strong>pass will be<br />
absorbed in <strong>the</strong> crystal.<br />
A similar applicati<strong>on</strong> to that of X-ray interferometry is <strong>the</strong> use of crystal <strong>beam</strong><br />
splitters in optical delay lines. A splitter/delay line at 8 keV has been designed<br />
for <strong>the</strong> Lcls using Si (400) crystals[129]. A 10 µm thick Si (400) crystal has 80%<br />
reflectivity in a b<strong>and</strong>pass of ∆E/E ∼ 1.4·10 −5 with a transmissi<strong>on</strong> outside this regi<strong>on</strong><br />
of 75%. The reflected <strong>and</strong> transmitted <strong>beam</strong>s are sent via different sets of crystals<br />
to be ultimately recombined <strong>on</strong> a comm<strong>on</strong> path but with a variable delay created<br />
by translating <strong>on</strong>e set of crystals. Two pulses are created by tuning <strong>the</strong> crystal sets<br />
to wavelengths that differ by more than <strong>the</strong> b<strong>and</strong>pass of <strong>the</strong> crystal reflecti<strong>on</strong> but<br />
with both c<strong>on</strong>tained within <strong>the</strong> b<strong>and</strong>width of <strong>the</strong> free electr<strong>on</strong> laser pulse. A similar<br />
device working at 8.39 keV with Si (511) crystals <strong>and</strong> 12.4 keV with Si (553) has been<br />
c<strong>on</strong>structed at HASYLAB<strong>and</strong> tested <strong>on</strong> <strong>beam</strong>lines at DORIS-III, PETRA-II <strong>and</strong> <strong>the</strong><br />
ESRF[130, 131].
80 5. Beam-splitting methods<br />
Gratings<br />
Gratings provide a very simple way of splitting a <strong>beam</strong>, though <strong>the</strong>re are a number<br />
of practical limitati<strong>on</strong>s <strong>and</strong> c<strong>on</strong>sequences. A grating divides an incoming <strong>beam</strong> of a<br />
given wavelength into a series of orders spaced around <strong>the</strong> ”zeroth” order <strong>beam</strong>, which<br />
has a diffracti<strong>on</strong> angle equal to <strong>the</strong> incidence angle. Inside orders have a diffracti<strong>on</strong><br />
angle (measured from <strong>the</strong> grating normal) smaller in magnitude than <strong>the</strong> incidence<br />
angle <strong>and</strong> outside orders have a diffracti<strong>on</strong> angle that is larger in magnitude than <strong>the</strong><br />
incidence angle. By c<strong>on</strong>venti<strong>on</strong>, diffracti<strong>on</strong> angles that are <strong>on</strong> <strong>the</strong> opposite side of <strong>the</strong><br />
normal are negative.<br />
For a <strong>beam</strong> splitter, <strong>on</strong>e could choose to use ei<strong>the</strong>r <strong>on</strong>e of <strong>the</strong> first order <strong>and</strong> <strong>the</strong><br />
zeroth order <strong>beam</strong>s, or <strong>the</strong> first inside <strong>and</strong> <strong>the</strong> first outside order <strong>beam</strong>s. Higher<br />
diffracti<strong>on</strong> orders are unlikely to be used as <strong>the</strong>y have lower efficiency.<br />
A possible advantage of using <strong>the</strong> first inside <strong>and</strong> outside orders is that <strong>the</strong> grating<br />
acts as a m<strong>on</strong>ochromator for both. C<strong>on</strong>versely, <strong>the</strong> zeroth order c<strong>on</strong>tains all <strong>the</strong><br />
spectral c<strong>on</strong>tentof<strong>the</strong>incident<strong>beam</strong>upto<strong>the</strong>cut-offdeterminedby<strong>the</strong>reflectivityof<br />
<strong>the</strong> grating coating <strong>and</strong> so a sec<strong>on</strong>d grating would be needed to give a m<strong>on</strong>ochromatic<br />
<strong>beam</strong>. However, this would allow independent choice of wavelengths for <strong>the</strong> two<br />
<strong>beam</strong>s. The relative intensity of <strong>the</strong> first diffracted to <strong>the</strong> zeroth order depends <strong>on</strong><br />
<strong>the</strong> shape of <strong>the</strong> diffracti<strong>on</strong> grating grooves. A careful choice of <strong>the</strong> groove profile<br />
based <strong>on</strong> modelling <strong>the</strong> efficiency with a code such as Gradif 1 can give a certain<br />
degree of tuning of <strong>the</strong> relative intensity, but <strong>on</strong>e cannot expect perfect c<strong>on</strong>trol if <strong>the</strong><br />
grating is to operate over a wide range of wavelengths.<br />
One should also remember that <strong>the</strong> required zero order efficiency could be, <strong>and</strong><br />
probably will be, at a wavelength that is unrelated to <strong>the</strong> first order wavelength.<br />
Therefore, a comprehensive set of calculati<strong>on</strong>s would have to be performed to give<br />
not <strong>on</strong>ly <strong>the</strong> first order efficiency as a functi<strong>on</strong> of wavelength, but also <strong>the</strong> zeroth<br />
order efficiency as a functi<strong>on</strong> of both wavelength <strong>and</strong> incidence angle. There is thus<br />
no uniquevalue to <strong>the</strong> efficiency at a particular wavelength into <strong>the</strong> zeroth order <strong>beam</strong><br />
as it depends <strong>on</strong> wavelength of <strong>the</strong> first order <strong>beam</strong> <strong>and</strong> hence angle of <strong>the</strong> grating.<br />
Anyrequirement totune <strong>the</strong>grating leads to <strong>the</strong> most significant practical problem<br />
with using a grating as a <strong>beam</strong> splitter. As <strong>the</strong> grating is rotated to select a different<br />
wavelength, <strong>the</strong> angle between <strong>the</strong> first <strong>and</strong> zeroth orders will change. Similarly, <strong>the</strong><br />
angle between <strong>the</strong> first inside <strong>and</strong> first outside orders that have <strong>the</strong> same wavelength<br />
will also change. (C<strong>on</strong>versely, <strong>the</strong> wavelength into a fixed outside order directi<strong>on</strong> will<br />
change in <strong>the</strong> opposite directi<strong>on</strong> <strong>and</strong> at a different rate to <strong>the</strong> wavelength in a fixed<br />
inside order directi<strong>on</strong>). This is very inc<strong>on</strong>venient for a <strong>beam</strong> splitter that is to feed<br />
fixed end stati<strong>on</strong>s from a fixed source. One soluti<strong>on</strong> is to place a plane mirror, which<br />
can both translate <strong>and</strong> rotate, after <strong>the</strong> grating. This mirror intercepts <strong>the</strong> zeroth<br />
order <strong>beam</strong> <strong>and</strong> steers it always to a fixed output path. The disadvantages of this are<br />
that <strong>the</strong> path length will change (so changing <strong>the</strong> overall <strong>beam</strong> timing) <strong>and</strong> that <strong>the</strong><br />
mechanism is complicated <strong>and</strong> so pr<strong>on</strong>e to introducing small errors giving temporal<br />
<strong>and</strong> spatial jitter to <strong>the</strong> <strong>beam</strong>.<br />
An alternative approach is to use <strong>the</strong> SX700 type of variable included angle grating<br />
mount. In this, a plane mirror rotates about an axis not in <strong>the</strong> mirror surface <strong>and</strong><br />
allows <strong>the</strong> included angle at <strong>the</strong> grating to be varied by just a single rotati<strong>on</strong>. The<br />
1 Gradif is an update of <strong>the</strong> LUMNAB code of M. Nevière, et al. [132]
5.3. Amplitude divisi<strong>on</strong> <strong>beam</strong> splitters 81<br />
mechanically simpler mount will work with less mechanical error, but <strong>the</strong>re is still a<br />
path length change, <strong>and</strong> so <strong>the</strong> overall <strong>beam</strong> timing is a functi<strong>on</strong> of wavelength.<br />
Providing <strong>the</strong> grating is working in collimated light, <strong>the</strong>re can a free choice of<br />
included angle without changing <strong>the</strong> focusing properties of <strong>the</strong> m<strong>on</strong>ochromator. This<br />
free choice of included angle can be used to ei<strong>the</strong>r keep a fixed angle between <strong>the</strong><br />
first diffracted order <strong>and</strong> <strong>the</strong> zeroth order, or to keep <strong>the</strong> first inside <strong>and</strong> first outside<br />
orders at a <strong>the</strong> same wavelength with a fixed angle between <strong>the</strong>m.<br />
In <strong>the</strong> case where <strong>the</strong> angle between <strong>the</strong> first <strong>and</strong> zeroth order is to be fixed, <strong>on</strong>e<br />
also finds that this is <strong>the</strong> same c<strong>on</strong>straint for scanning a blazed grating ’<strong>on</strong>-blaze’ <strong>and</strong><br />
thus has a potential advantage in optimising <strong>the</strong> first order efficiency. This would<br />
naturally be at <strong>the</strong> expense of <strong>the</strong> zeroth order efficiency at that wavelength, but this<br />
will not be a problem if <strong>the</strong> two branches are to operate at different wavelengths.<br />
If <strong>the</strong> angle between <strong>the</strong> first inside <strong>and</strong> zeroth order <strong>beam</strong> is ψ, <strong>the</strong>n <strong>the</strong> grating<br />
equati<strong>on</strong> under <strong>the</strong> c<strong>on</strong>straint that ψ is fixed becomes<br />
Nmλ = 2sin<br />
� ψ<br />
2<br />
�<br />
cos<br />
� ψ<br />
2 −β<br />
�<br />
(5.1)<br />
where β is <strong>the</strong> diffracti<strong>on</strong> angle. For a blazed grating operating <strong>on</strong>-blaze, <strong>the</strong> blaze<br />
angle should be ψ/2.<br />
A similar expressi<strong>on</strong> is obtained if <strong>the</strong> angle between <strong>the</strong> first inside <strong>and</strong> outside<br />
orders is to be kept c<strong>on</strong>stant <strong>and</strong> both orders are to pass <strong>the</strong> same wavelength. If<br />
β + is <strong>the</strong> diffracti<strong>on</strong> angle of <strong>the</strong> first inside order <strong>and</strong> β − <strong>the</strong> diffracti<strong>on</strong> angle of <strong>the</strong><br />
first outside order, <strong>the</strong>n <strong>the</strong> angle between <strong>the</strong>m is<br />
ξ = β + −β −<br />
<strong>and</strong> <strong>the</strong> grating equati<strong>on</strong> for c<strong>on</strong>stant ξ becomes<br />
Nλ = 2sin<br />
� ξ<br />
2<br />
�<br />
cos<br />
� ξ<br />
2 −β+<br />
�<br />
(5.2)<br />
(5.3)<br />
which gives <strong>the</strong> diffracti<strong>on</strong> angle of <strong>the</strong> inside order for agiven wavelength, from which<br />
<strong>the</strong> incidence angle <strong>and</strong> diffracti<strong>on</strong> angle of <strong>the</strong> outside order can be calculated.<br />
In both <strong>the</strong>se modes of operati<strong>on</strong>, <strong>the</strong> tuning range will be limited if <strong>the</strong> grazing<br />
angles at <strong>the</strong> grating are not to become large (<strong>and</strong> hence <strong>the</strong> efficiencies low). In<br />
general, <strong>the</strong> angles between <strong>the</strong> orders (ψ or ξ) will have to be
82 5. Beam-splitting methods<br />
for <strong>the</strong> sec<strong>on</strong>d grating with c<strong>on</strong>sequent impact <strong>on</strong> <strong>the</strong> cost <strong>and</strong> fur<strong>the</strong>r path length<br />
variati<strong>on</strong>s. The system with a translating <strong>and</strong> rotating plane mirror that intercepts<br />
with just <strong>the</strong> zeroth order <strong>beam</strong> after <strong>the</strong> grating would be simpler in this respect as<br />
both <strong>the</strong> grating mounts could simply be fixed included angle type.<br />
Alternatively, c<strong>on</strong>ical diffracti<strong>on</strong> mounting can be used to reduce <strong>the</strong> pulse stretch<br />
(since <strong>the</strong> effective number of illuminated groves is reduced when compared with <strong>the</strong><br />
classical mount). The fur<strong>the</strong>r advantage of <strong>the</strong> c<strong>on</strong>ical mount is that <strong>the</strong> diffracti<strong>on</strong><br />
efficiency should be much higher. However, in <strong>the</strong> c<strong>on</strong>text of a <strong>beam</strong> splitter, <strong>the</strong><br />
c<strong>on</strong>ical mounting leads to difficulties. It is normal to operate <strong>the</strong> grating in fixed<br />
altitude mode as this allows <strong>the</strong> grating to be tuned with just a simple rotati<strong>on</strong><br />
(about an axis parallel to <strong>the</strong> grooves). Unfortunately, in this mode, <strong>the</strong> zeroth order<br />
(for example) changes directi<strong>on</strong> in both <strong>the</strong> horiz<strong>on</strong>tal <strong>and</strong> vertical planes. Capturing<br />
<strong>and</strong> steering <strong>the</strong> zeroth order <strong>beam</strong> into a fixed directi<strong>on</strong> will be very difficult. Fixed<br />
azimuth mode would make capturing <strong>the</strong> zeroth order <strong>beam</strong> easier, but scanning <strong>the</strong><br />
grating requires translating <strong>and</strong> rotating mirrors.<br />
A scheme for using diffracti<strong>on</strong> gratings as a <strong>beam</strong> splitter has been proposed for<br />
FERMI@Elettra for wavelengths around 40 nm. Light from <strong>the</strong> 0 <strong>and</strong> +1 orders<br />
is used. For <strong>the</strong> 1st order radiati<strong>on</strong>, a sec<strong>on</strong>d grating followed by a translatable<br />
plane mirror allows <strong>the</strong> pulse stretch to be compensated <strong>and</strong> gives a fixed positi<strong>on</strong><br />
for <strong>the</strong> output <strong>beam</strong>[133]. An efficiency of about 30% has been estimated for both<br />
<strong>the</strong> zero <strong>and</strong> first orders using at 100 lines/mm grating, 84 ◦ incidence angle, over <strong>the</strong><br />
wavelength range of 34 - 46 nm. This design requires <strong>the</strong> manufacture of a l<strong>on</strong>g (60<br />
mm) grating to a very high specificati<strong>on</strong>, as well as a translating mirror hence it is<br />
technically challenging.<br />
The above applicati<strong>on</strong>s are all for reflecti<strong>on</strong> gratings. Transmissi<strong>on</strong> gratings can<br />
also be used to split <strong>the</strong> <strong>beam</strong> with <strong>the</strong> advantage that, since <strong>the</strong> gratings are used<br />
at (or near) normal incidence, <strong>the</strong> geometry of <strong>the</strong> split <strong>beam</strong>s is much simpler.<br />
Manufacturing transmissi<strong>on</strong> gratings that can work in <strong>the</strong> XUV to x-ray regi<strong>on</strong> is of<br />
course a major technical challenge. Achieving adequate dispersi<strong>on</strong> (<strong>and</strong> hence <strong>beam</strong><br />
separati<strong>on</strong>) at short wavelengths requires <strong>the</strong> grating period to very small. The aspect<br />
ratio (depth/width) of <strong>the</strong> grating bars is inevitably quite high if <strong>the</strong> gratings are to<br />
be robust <strong>and</strong> <strong>the</strong>y are <strong>the</strong>refore not suitable for str<strong>on</strong>gly divergent light. The risk of<br />
ablati<strong>on</strong> of <strong>the</strong> grating in a free electr<strong>on</strong> laser pulse is also a major c<strong>on</strong>cern.<br />
In <strong>the</strong> XUV, a transmissi<strong>on</strong> grating will almost certainly behave as an amplitude<br />
grating, since it will be difficult to make <strong>the</strong> grating bars anything o<strong>the</strong>r than 100%<br />
absorbing. Str<strong>on</strong>g absorpti<strong>on</strong> means <strong>the</strong> grating must also be made unsupported,<br />
which is very difficult. Assuming a perfect amplitude grating can be made, <strong>the</strong> maximum<br />
first order efficiency occurs when <strong>the</strong> groove width is half <strong>the</strong> grating period<br />
<strong>and</strong> is just 10% <strong>and</strong> <strong>the</strong> zeroth order efficiency is 25%.<br />
C<strong>on</strong>versely, for hard x-rays, it is difficult to make <strong>the</strong> aspect ratio of <strong>the</strong> grating<br />
bars high enough to be perfectly absorbing <strong>and</strong> <strong>the</strong> grating will functi<strong>on</strong> as a phase<br />
grating. The efficiency depends <strong>on</strong> <strong>the</strong> grating material <strong>and</strong> bar profile, <strong>and</strong> this offers<br />
scope for tuning <strong>the</strong> grating performance.<br />
Weitkamp, et al. [134] used a R<strong>on</strong>chi phase grating to make an x-ray shearing<br />
interferometer. The grating is made by electr<strong>on</strong>-<strong>beam</strong> lithography from silic<strong>on</strong> <strong>and</strong><br />
has a groove period of 2 µm <strong>and</strong> depth of 9 µm. They operated <strong>the</strong> grating at 12.4<br />
keV (1 ˚A), but were <strong>on</strong>ly producing a small shear in <strong>the</strong> <strong>beam</strong>. The phase shift of <strong>the</strong><br />
grating was tuned by tilting <strong>the</strong> grating about an axis perpendicular to <strong>the</strong> grooves<br />
<strong>and</strong> <strong>the</strong> <strong>beam</strong> axis so as to vary <strong>the</strong> effective thickness of <strong>the</strong> grating. This allowed
5.4. Wavefr<strong>on</strong>t divisi<strong>on</strong> <strong>beam</strong>splitters 83<br />
<strong>the</strong> phase shift to be increased to π <strong>and</strong> hence <strong>the</strong> zeroth diffracti<strong>on</strong> order eliminated<br />
<strong>and</strong> first order efficiencies maximised. Naturally, this technique can <strong>on</strong>ly be employed<br />
when <strong>the</strong> grating bars have sufficient transmissi<strong>on</strong>, <strong>and</strong> is thus <strong>on</strong>ly applicable for<br />
harder x-rays due to <strong>the</strong> difficulty in manufacturing very thin gratings with such a<br />
fine structure.<br />
Gratings can also be used to send a small part of <strong>the</strong> <strong>beam</strong> (in first order) to a<br />
spectrometer for measuring <strong>the</strong> spectral c<strong>on</strong>tent of <strong>the</strong> <strong>beam</strong>, while most of <strong>the</strong> <strong>beam</strong><br />
is in <strong>the</strong> zeroth order <strong>and</strong> is passed down <strong>the</strong> <strong>beam</strong>line to <strong>the</strong> experiments. The groove<br />
profile of <strong>the</strong> grating is tuned to give just sufficient intensity in <strong>the</strong> diffracted order<br />
for <strong>the</strong> spectrometer to work (thus maximising <strong>the</strong> <strong>beam</strong> intensity to <strong>the</strong> experiment)<br />
<strong>and</strong> <strong>the</strong> line spacing is varied to give a flat field for <strong>the</strong> dispersed spectrum <strong>on</strong> <strong>the</strong><br />
detector. Such an instrument is being installed at Flash [135].<br />
A point of c<strong>on</strong>cern for operating gratings in free electr<strong>on</strong> laser <strong>beam</strong>s is <strong>the</strong> effect<br />
of <strong>the</strong> structured surface <strong>on</strong> <strong>the</strong> likelihood of ablati<strong>on</strong> since parts of <strong>the</strong> surface may<br />
make very steep angles to <strong>the</strong> incoming <strong>beam</strong>. The effect of <strong>the</strong> groove shape <strong>on</strong><br />
<strong>the</strong> ablati<strong>on</strong> threshold is not understood. If this were to be a problem it would be<br />
exacerbated with classical grating mounts where <strong>the</strong> grating is likely to operate at<br />
quite a steep angle to <strong>the</strong> <strong>beam</strong> at l<strong>on</strong>g wavelength part of <strong>the</strong> spectrum. In this<br />
regard, c<strong>on</strong>ical diffracti<strong>on</strong> in c<strong>on</strong>stant altitude mode has an advantage as <strong>the</strong> <strong>beam</strong><br />
strikes <strong>the</strong> grating at effectively <strong>the</strong> same grazing angle even as <strong>the</strong> grating is tuned.<br />
Grids<br />
Wire grids can be used as polarising <strong>beam</strong> splitters for FIR radiati<strong>on</strong> <strong>and</strong> are used<br />
in Fourier Transform Infra-Red (FTIR) spectrometers. Radiati<strong>on</strong> with polarisati<strong>on</strong><br />
parallel to <strong>the</strong> wires is reflected, whereas <strong>the</strong> comp<strong>on</strong>ent polarised perpendicular to<br />
<strong>the</strong> wires is transmitted. As an example, <strong>the</strong> Millimetre-Wave Technology group[136]<br />
in <strong>the</strong> Space Science <strong>and</strong> Technology Department of <strong>the</strong> UK Science <strong>and</strong> Technology<br />
Facilities Council (STFC) has manufactured wire grids for a FTIR spectrometer to be<br />
used <strong>on</strong> <strong>the</strong> THz <strong>beam</strong>line <strong>on</strong> ALICE, <strong>the</strong> energy-recovery-linac-based developmental<br />
light source at Daresbury Laboratory.<br />
5.4 Wavefr<strong>on</strong>t divisi<strong>on</strong> <strong>beam</strong>splitters<br />
Beamline apertures<br />
The simplest method of splitting a <strong>beam</strong> by wavefr<strong>on</strong>t divisi<strong>on</strong> is to use apertures to<br />
divide <strong>the</strong> <strong>beam</strong> into two spatially separated parts, as is often d<strong>on</strong>e <strong>on</strong> synchrotr<strong>on</strong><br />
sourceswhere<strong>the</strong>reisalarge fanofradiati<strong>on</strong>(e.g.fromdipolesorwavelengthshifters).<br />
The disadvantage ofthis is that <strong>the</strong> angular separati<strong>on</strong> of<strong>the</strong> two <strong>beam</strong>s is determined<br />
by <strong>the</strong> natural divergence of <strong>the</strong> source, which will be ra<strong>the</strong>r small for a free electr<strong>on</strong><br />
laser. Never<strong>the</strong>less, <strong>the</strong> technique might be suitable for separating off a small part<br />
from <strong>the</strong> extremity of <strong>the</strong> <strong>beam</strong> to pass to a <strong>beam</strong> m<strong>on</strong>itor or some <strong>beam</strong> diagnostics,<br />
or for coherent scattering experiments from small samples. If greater separati<strong>on</strong> is<br />
required, a mirror could be used to deflect <strong>on</strong>e <strong>beam</strong> downstream of <strong>the</strong> aperture,<br />
though this is effectively <strong>the</strong> same situati<strong>on</strong> as <strong>the</strong> knife-edge mirror described below.<br />
As with o<strong>the</strong>r methods that divide <strong>the</strong> wavefr<strong>on</strong>t, edge diffracti<strong>on</strong> effects are likely to
84 5. Beam-splitting methods<br />
be significant. The design of <strong>the</strong> aperture would have to eliminate <strong>the</strong> risk of radiati<strong>on</strong><br />
damage.<br />
Knife-edge mirrors<br />
The radiati<strong>on</strong> can be split by inserting a mirror part way into <strong>the</strong> <strong>beam</strong> to deflect a<br />
porti<strong>on</strong> of it. As an example, a grazing incidence (3 ◦ ) knife-edge mirror is used as<br />
part of an autocorrelator system designed at BESSY for use in soft X-ray pump-probe<br />
experiments at Flash[137]. The autocorrelator was designed to work up to 200 eV,<br />
<strong>and</strong> <strong>the</strong> slope error <strong>on</strong> <strong>the</strong> mirror is required to be less than 0.5 mikro-rad. This slope<br />
error must be maintained up to <strong>the</strong> cutting edge of <strong>the</strong> mirror <strong>and</strong> this is very difficult<br />
to achieve with c<strong>on</strong>venti<strong>on</strong>al polishing techniques as <strong>the</strong>re is always some ”roll-off”<br />
at <strong>the</strong> mirror edges. The required quality was achieved by cutting away <strong>the</strong> end of<br />
<strong>the</strong> mirror after polishing to remove <strong>the</strong> roll-off regi<strong>on</strong>. Alternatively, <strong>the</strong> edge of <strong>the</strong><br />
mirror could be masked with an aperture (see above).<br />
Beam splitter 3°<br />
Figure 5.1: Schematic of knife-edge grazing incidence mirror <strong>beam</strong> splitter for soft X-rays.<br />
For harder X-rays, <strong>the</strong> grazing angle needs to be smaller to maintain a high reflectivity.<br />
The required minimum <strong>beam</strong> separati<strong>on</strong> of 0.3 ◦ in <strong>the</strong> sample specificati<strong>on</strong><br />
above means that <strong>the</strong> grazing angle must be greater than 0.15 ◦ . For carb<strong>on</strong>, <strong>the</strong><br />
reflectivity is greater than 98% for energies from 1 keV to 10 keV at this incidence<br />
angle, but <strong>the</strong> mirror could become very l<strong>on</strong>g. For slightly larger angles <strong>the</strong> cut-off in<br />
reflectivity with increasing energy will be <strong>the</strong> main limiting factor in <strong>the</strong> usable wavelength<br />
range, e.g. <strong>the</strong> reflectivity of carb<strong>on</strong> decreases rapidly above about 3 keV for a<br />
grazing angle of 0.5 ◦ . Using a coating with higher atomic number (nickel, rhodium)<br />
will give a reflectivity cut-off at higher energy for a given angle, but such materials<br />
do not have as high a damage threshold as carb<strong>on</strong>. The main c<strong>on</strong>cern about using<br />
a mirror as a <strong>beam</strong> splitter is that edge diffracti<strong>on</strong> could have a significant effect <strong>on</strong><br />
<strong>the</strong> wavefr<strong>on</strong>t, especially as <strong>the</strong> <strong>beam</strong> is being cut in <strong>the</strong> middle where <strong>the</strong> amplitude<br />
is likely to be highest. This type of <strong>beam</strong> splitter cannot <strong>the</strong>refore be expected to<br />
produce two <strong>beam</strong>s that are lower intensity replicas of <strong>the</strong> original <strong>beam</strong>.<br />
Knife-edge crystals<br />
To achieve higher angular separati<strong>on</strong> at shorter wavelengths, <strong>the</strong> knife-edge mirror<br />
could be replaced by a knife-edge crystal. For example, <strong>the</strong> Bragg angle of <strong>the</strong> silic<strong>on</strong><br />
(111) reflecti<strong>on</strong>at8keVis14.3 ◦ , whichgivesa<strong>beam</strong>deflecti<strong>on</strong>angle of28.6 ◦ . Doublecrystal<br />
arrangements could be used to give a deflected <strong>beam</strong> with a fixedexit directi<strong>on</strong><br />
as <strong>the</strong> crystal is rotated to tune <strong>the</strong> phot<strong>on</strong> energy. The splitting crystal would have<br />
6°
5.4. Wavefr<strong>on</strong>t divisi<strong>on</strong> <strong>beam</strong>splitters 85<br />
to be translated orthog<strong>on</strong>ally to <strong>the</strong> <strong>beam</strong> directi<strong>on</strong> or rotated about its cutting edge<br />
if <strong>the</strong> fracti<strong>on</strong> of <strong>the</strong> <strong>beam</strong> it intercepts is to remain c<strong>on</strong>stant. Edge diffracti<strong>on</strong> <strong>and</strong><br />
<strong>the</strong> impact <strong>on</strong> <strong>the</strong> wavefr<strong>on</strong>t would still be an issue, especially as it may be difficult<br />
to maintain a perfect crystalline structure to its edge. There would also be a change<br />
in <strong>the</strong> pulse length of <strong>the</strong> <strong>beam</strong> deflected by <strong>the</strong> crystal due to <strong>the</strong> m<strong>on</strong>ochromating<br />
acti<strong>on</strong> of <strong>the</strong> crystal, <strong>and</strong> <strong>the</strong> reduced b<strong>and</strong>width will also limit <strong>the</strong> overall efficiency<br />
for <strong>the</strong> reflected <strong>beam</strong>.<br />
Fresnel bi-mirror<br />
Fresnel bi-mirrors c<strong>on</strong>sist of two flat mirrors, normally joined al<strong>on</strong>g <strong>on</strong>e edge <strong>and</strong><br />
inclined at an angle to each o<strong>the</strong>r <strong>–</strong> see Figure 5.2. In general <strong>the</strong>y are used in<br />
interferometers where <strong>the</strong> radiati<strong>on</strong> reflected from <strong>the</strong> two parts of <strong>the</strong> mirror is<br />
inclined towards each o<strong>the</strong>r, resulting in interference. An example is <strong>the</strong>ir use in an<br />
interferometer <strong>on</strong> SU7 at SUPERACO[138], where silica mirrors at a grazing angle of<br />
3−6 ◦ were used for 4.4 nm. While bi-mirrors could be used to cross <strong>the</strong> <strong>beam</strong>s over<br />
each o<strong>the</strong>r <strong>and</strong> separate <strong>the</strong>m, it is hard to see any advantage over <strong>the</strong> use of a single<br />
grazing incidence knife-edge mirror<br />
a<br />
a’<br />
Fresnel’s bi-mirror<br />
Figure 5.2: Basic design of <strong>the</strong> Fresnel mirror interferometer. Rays a <strong>and</strong> a ′ create an interference pattern<br />
when <strong>the</strong>y add up.<br />
Slotted or perforated mirrors<br />
In this method, <strong>the</strong> incident wavefr<strong>on</strong>t is coherently split <strong>on</strong> a microscopic scale with<br />
<strong>the</strong> use of holes or slots cut in a mirror. This method is easier for l<strong>on</strong>ger wavelengths,<br />
but has been realised in <strong>the</strong> XUV regime, e.g. a slotted mirror has been used in an<br />
interferometer <strong>on</strong> <strong>beam</strong>line 9.3.2 <strong>on</strong> <strong>the</strong> ALS[139]. This is similar to <strong>the</strong> proposal<br />
for a prototype <strong>beam</strong> splitter to be made for <strong>IRUVX</strong> by AZM at BESSY[140], in<br />
which arrays of small holes will be machined in a grazing incidence mirror. An area<br />
of c<strong>on</strong>cern is <strong>the</strong> ability to manufacture high aspect ratio holes to a great enough<br />
precisi<strong>on</strong> <strong>and</strong> surface quality. The effect <strong>on</strong> <strong>the</strong> coherence of <strong>the</strong> radiati<strong>on</strong> must also<br />
be c<strong>on</strong>sidered.<br />
p
86 5. Beam-splitting methods<br />
Losses in reflecti<strong>on</strong> due to diffracti<strong>on</strong> as well as filling factor have to be taken<br />
into account for mirrors with holes in <strong>the</strong>m. One such example in <strong>the</strong> field of microelectromechanical<br />
systems (MEMS), an area of c<strong>on</strong>siderable research effort, has been<br />
found. A key comp<strong>on</strong>ent for future nanoscale optical devises is <strong>the</strong> freest<strong>and</strong>ing<br />
micro-machined mirror <strong>–</strong> as shown in Figure 5.3.<br />
Figure 5.3: A MEMS free-space optical reflector. Taken from Zou, et al. [141] .Note <strong>the</strong> scale at <strong>the</strong> top of<br />
<strong>the</strong> figure <strong>–</strong> <strong>the</strong> line is 200 µm l<strong>on</strong>g.<br />
The holes in <strong>the</strong> mirror surface serve no useful purpose regarding <strong>the</strong> functi<strong>on</strong><br />
of <strong>the</strong> reflective surface. They are comm<strong>on</strong>ly referred to as release holes <strong>and</strong> allow<br />
release etchant to flow behind <strong>the</strong> mirror <strong>on</strong>ce <strong>the</strong> micromachining process is finished,<br />
releasing <strong>the</strong> comp<strong>on</strong>ent from <strong>the</strong> bulk material. In[141], <strong>the</strong> losses in <strong>the</strong> reflectivity<br />
due to <strong>the</strong> filling factor <strong>and</strong> diffracti<strong>on</strong> are calculated for light of wavelength 632.8<br />
nm as a functi<strong>on</strong> of hole size from 5 - 23 µm <strong>and</strong> spacings of 10 - 30 µm. For <strong>the</strong><br />
case of 21 µm square holes spaced at 30 µm, <strong>the</strong> filling factor is 50%, <strong>and</strong> <strong>the</strong> loss in<br />
reflected light due to diffracti<strong>on</strong> was estimated to be 14%. For <strong>the</strong> same spacing, as
5.4. Wavefr<strong>on</strong>t divisi<strong>on</strong> <strong>beam</strong>splitters 87<br />
<strong>the</strong> hole size decreases, <strong>the</strong> diffracti<strong>on</strong> loss increases, so that for a 10 µm hole size <strong>the</strong><br />
filling factor loss is 11%, <strong>and</strong> <strong>the</strong> diffracti<strong>on</strong> loss 15%.<br />
Much bigger holes relative to <strong>the</strong> wavelength were used in <strong>the</strong> <strong>beam</strong> splitter for<br />
<strong>the</strong> ALS interferometer, designed to operate between 60 eV <strong>and</strong> 100 eV. Slots were<br />
cut in a highly polished (rms roughness ∼ 3 ˚A) single crystal silic<strong>on</strong> wafer. Based <strong>on</strong><br />
<strong>the</strong> coherence properties of <strong>the</strong> incident X-ray <strong>beam</strong>, <strong>the</strong> width <strong>and</strong> spacing of <strong>the</strong><br />
slots were set to 50 µm <strong>and</strong> 100 µm respectively. The slots were 15 mm in length<br />
<strong>and</strong> created by chemical etching. The completed assembly was <strong>the</strong>n coated with<br />
molybdenum. A major c<strong>on</strong>cern in <strong>the</strong> manufacturing was to keep <strong>the</strong> mirror flat to<br />
within 1 µrad, <strong>and</strong> to maintain <strong>the</strong> surface smoothness.<br />
Structured arrays<br />
A ’1-D capillary <strong>beam</strong> splitter’ has been designed to work around 13.9 nm (89 eV) <strong>on</strong><br />
a plasma-based XUV source[142]. It c<strong>on</strong>sists of a stack of 20 µm thick plates, 7.9 mm<br />
l<strong>on</strong>g <strong>and</strong> separated by 130 µm. The plates are tilted at a small angle (grazing angle<br />
of 0−0.8 ◦ ) with respect to <strong>the</strong> incoming radiati<strong>on</strong>. Light can ei<strong>the</strong>r pass unhindered<br />
between <strong>the</strong> plates, or else undergo a single reflecti<strong>on</strong>, causing two <strong>beam</strong>s to emerge<br />
at different angles. At 0.8 ◦ angle of incidence, all <strong>the</strong> light has to be reflected to get<br />
through <strong>the</strong> device. The transmittance (efficiency of <strong>the</strong> direct path) varies from 85%<br />
to 0% depending <strong>on</strong> <strong>the</strong> angle of incidence. The efficiency of <strong>the</strong> reflected light varies<br />
from 0% to 75% <strong>and</strong> 15% of <strong>the</strong> light is lost by absorpti<strong>on</strong> <strong>on</strong> <strong>the</strong> fr<strong>on</strong>t edges of <strong>the</strong><br />
plates. If a similar design were to be used for splitting free electr<strong>on</strong> laser <strong>beam</strong>s, <strong>the</strong><br />
stack would need to be designed to absorb a smaller fracti<strong>on</strong> of <strong>the</strong> radiati<strong>on</strong>. The<br />
effect <strong>on</strong> <strong>the</strong> wavefr<strong>on</strong>t would also need to be investigated.<br />
Capillary arrays have been used in <strong>the</strong> keV regime to suppress higher order harm<strong>on</strong>ics<br />
passed by a m<strong>on</strong>ochromator <strong>on</strong> a bending magnet <strong>beam</strong>line at BESSY[143].<br />
This device uses a double reflecti<strong>on</strong> in <strong>the</strong> array, <strong>the</strong> grazing angle of 3.6 mrad giving<br />
an 89% efficiency at each reflecti<strong>on</strong>, so <strong>the</strong> reflected light is in <strong>the</strong> same directi<strong>on</strong> as<br />
<strong>the</strong> incident; however this example shows that single reflecti<strong>on</strong> capillary plates could<br />
be used at this wavelength.<br />
An alternative c<strong>on</strong>structi<strong>on</strong> scheme could be to adopt <strong>the</strong> same technology used to<br />
form Multilayer Laue Lenses (MLLs)[144]. The x-ray lens technology developed by<br />
Arg<strong>on</strong>ne Nati<strong>on</strong>al Laboratory c<strong>on</strong>sists of many individual layers precisely sputtered<br />
<strong>on</strong>to a silic<strong>on</strong> wafer. The multilayer stack is <strong>the</strong>n ”sliced” to form a thin transmissi<strong>on</strong><br />
element in which <strong>the</strong> stacked diffracting surfaces are oriented almost parallel with <strong>the</strong><br />
optical axis. Although developed as a Fresnel lens structure for micro-focus applicati<strong>on</strong>s,<br />
it is foreseeable that <strong>the</strong> same technology could be used to create a <strong>beam</strong><br />
splitter, ei<strong>the</strong>r by employing a similar geometry to that used in <strong>the</strong> capillary <strong>beam</strong><br />
splitter stack or as a knife edge diffractive element redirecting a proporti<strong>on</strong> of <strong>the</strong><br />
<strong>beam</strong>.<br />
Possible drawbacks for this unproven technology include radiati<strong>on</strong> damage to <strong>the</strong><br />
multilayer structure <strong>and</strong> achieving <strong>the</strong> necessary manufacturing tolerances for both<br />
<strong>the</strong> microstructure fabricati<strong>on</strong> <strong>and</strong> material slicing.
88 5. Beam-splitting methods<br />
5.5 Time-based splitting<br />
An alternative to splitting <strong>the</strong> wavefr<strong>on</strong>t in space is to send alternate pulses or trains<br />
of pulses to different <strong>beam</strong>lines. One scenario is to send hours/minutes worth of<br />
pulses to <strong>on</strong>e experiment while <strong>the</strong> o<strong>the</strong>r endstati<strong>on</strong> is changing samples, checking<br />
data, etc. This could be d<strong>on</strong>e simply using a switching mirror. At <strong>the</strong> o<strong>the</strong>r end of<br />
<strong>the</strong> time scale, is may be possible to use vibrating mirrors or alternating mirrors <strong>and</strong><br />
slots <strong>on</strong> a rotating disc to send alternate pulses to two end-stati<strong>on</strong>s. The feasibility<br />
of this will depend <strong>on</strong> <strong>the</strong> repetiti<strong>on</strong> rate of <strong>the</strong> free electr<strong>on</strong> laser.<br />
An early example utilising a disc rotating at 25 Hz was designed <strong>and</strong> used at<br />
<strong>on</strong> a synchrotr<strong>on</strong> radiati<strong>on</strong> source at DESY. A grazing incidence mirror occupied a<br />
segment of roughly a quarter of <strong>the</strong> disc area, with an equally sized slot occupying<br />
about ano<strong>the</strong>r quarter. The system operated for wavelengths 20 - 280 eV, <strong>the</strong> grazing<br />
angle of <strong>the</strong> mirror being 4 ◦ [145].<br />
In order to increase <strong>the</strong> repetiti<strong>on</strong> rate, <strong>on</strong>e could use <strong>the</strong> fact that <strong>the</strong> free electr<strong>on</strong><br />
laser <strong>beam</strong> is much smaller than those from a synchrotr<strong>on</strong> radiati<strong>on</strong> source <strong>and</strong><br />
c<strong>on</strong>sider a system of several mirrors <strong>and</strong> slots <strong>on</strong> a disc, <strong>and</strong> also increase <strong>the</strong> rotati<strong>on</strong>al<br />
speed of <strong>the</strong> disc. High-speed slotted discs have been designed for use as <strong>beam</strong><br />
choppers. For example, a <strong>beam</strong> chopper for operati<strong>on</strong> at phot<strong>on</strong> energies below 50<br />
eV has been built by Forschungszentrum Jülich GmbH for use <strong>on</strong> <strong>the</strong> synchrotr<strong>on</strong><br />
radiati<strong>on</strong> source at BESSY. The disc is aluminium alloy with a diameter of 338 mm<br />
<strong>and</strong> has 1252 slots cut in <strong>the</strong> edge. It uses magnetic bearings <strong>and</strong> is designed to spin<br />
at about 1 kHz. It was reported at <strong>the</strong> SRI meeting in 2008 that <strong>the</strong> chopper had<br />
been successfully tested at 1 kHz <strong>and</strong> will be commissi<strong>on</strong>ed with phot<strong>on</strong> pulses in <strong>the</strong><br />
autumn of 2008[146].<br />
Asec<strong>on</strong>dexample, inthiscaseusingairbearings, is<strong>the</strong>chopperwhichwasdesigned<br />
to chop <strong>the</strong> 4.3 MHz pulsed <strong>beam</strong> from <strong>the</strong> VUV-FEL <strong>on</strong> proposed 4GLS facility to<br />
100 kHz. The disc would have to have withstood a high heat load from <strong>the</strong> 400<br />
W of <strong>beam</strong> power as well as high mechanical stresses from <strong>the</strong> high speed rotati<strong>on</strong>.<br />
C<strong>on</strong>sequently, martensitic stainless steel was chosen for <strong>the</strong> disk material. The disc<br />
had a polished chamfered edge to reflect <strong>the</strong> unwanted light at 2.5 ◦ grazing angle. A<br />
prototype chopper with just 2 slots has been built <strong>and</strong> tested by Fluid Film Devices<br />
Ltd[147]. The disc has a diameter of 134 mm <strong>and</strong> was tested up to 500 Hz, half <strong>the</strong><br />
design frequency, before <strong>the</strong> project was disc<strong>on</strong>tinued due to 4GLS being replaced by<br />
<strong>the</strong> NLS project.<br />
If <strong>on</strong>e wanted to use <strong>the</strong> chamfered edge to reflect <strong>the</strong> light into a <strong>beam</strong>line for<br />
use by an experiment, <strong>the</strong> edge would need to be polished to an optical quality<br />
surface. An alternative would be to attach mirrors to <strong>the</strong> disc. Both opti<strong>on</strong>s require<br />
fur<strong>the</strong>r feasibility studies. For <strong>the</strong> martensitic steel prototype described above, <strong>the</strong><br />
manufacturer was not able to polish to <strong>the</strong> edge to optical quality, though <strong>the</strong> main<br />
aim was simply to reflect as much of <strong>the</strong> incident power as possible to prevent it<br />
from being absorbed in <strong>the</strong> disc. Distorti<strong>on</strong>s at <strong>the</strong> edge of <strong>the</strong> disc could also be<br />
a problem. For <strong>the</strong> sec<strong>on</strong>d opti<strong>on</strong>, <strong>the</strong> feasibility of having mirrors b<strong>on</strong>ded <strong>on</strong>to a<br />
high-speed rotating disc would need to be investigated. Fur<strong>the</strong>rmore, this technique<br />
would be difficult to apply to X-rays since <strong>the</strong> very grazing angle required for good<br />
reflectivity would lead to a thick disc <strong>and</strong> very high mechanical loads.<br />
At Flash <strong>the</strong> X-ray <strong>beam</strong> can be switched between two user experiments by a mechanically<br />
switching mirror. This reduces <strong>the</strong> repetiti<strong>on</strong> rate at <strong>the</strong> user experiments
5.6. Summary 89<br />
to 2.5 Hz (with maximal switching frequency). The stated accuracy of <strong>the</strong> movement<br />
back <strong>and</strong> forth is a few µ m in <strong>the</strong> positi<strong>on</strong> <strong>and</strong> about 1 arcsec<strong>on</strong>d in <strong>the</strong> angle[148].<br />
5.6 Summary<br />
As <strong>the</strong> preceding secti<strong>on</strong>s have shown, <strong>the</strong>re is a wide variety of techniques that can<br />
be used divide a phot<strong>on</strong> <strong>beam</strong>. Some of <strong>the</strong>se techniques are very well established,<br />
whilst some are more developmental. A key issue for free electr<strong>on</strong> laser sources is that<br />
<strong>the</strong> properties of <strong>the</strong> radiati<strong>on</strong> produced extend into new ground when compared<br />
with c<strong>on</strong>venti<strong>on</strong>al laboratory or synchrotr<strong>on</strong> sources. The short wavelengths, high<br />
transverse coherence, short pulse durati<strong>on</strong> <strong>and</strong> high pulse energy all mean that <strong>the</strong>re<br />
is some element of development required for any splitting technique.<br />
Two lists of techniques are presented for fur<strong>the</strong>r c<strong>on</strong>siderati<strong>on</strong> for use mainly in <strong>the</strong><br />
soft x-ray regime. The first list gives those techniques that would seem amenable to<br />
rapid development into practical <strong>beam</strong> splitters. The sec<strong>on</strong>d list gives <strong>the</strong> techniques<br />
that show potential but will require more extensive development to over come <strong>the</strong><br />
technical challenges. In all cases, <strong>the</strong> properties of a <strong>beam</strong> splitter derived from a<br />
particular technique will be somewhat specialised <strong>and</strong> so <strong>the</strong>re will be no ”universal”<br />
<strong>beam</strong> splitter. The technique chosen will depend <strong>on</strong> <strong>the</strong> nature of <strong>the</strong> phot<strong>on</strong> <strong>beam</strong><br />
being split <strong>and</strong> <strong>the</strong> particular needs of <strong>the</strong> experiment.<br />
Techniques requiring <strong>the</strong> least development<br />
Diffracti<strong>on</strong> gratings<br />
Reflecti<strong>on</strong> gratings give amplitude divisi<strong>on</strong> <strong>and</strong> since <strong>the</strong>y can be made to very high<br />
tolerances, splitting with good wavefr<strong>on</strong>t c<strong>on</strong>trol should be possible. Polarizati<strong>on</strong><br />
effects will be present but should <strong>on</strong>ly be significant at VUV <strong>and</strong> XUV wavelengths.<br />
At least <strong>on</strong>e of <strong>the</strong> <strong>beam</strong>s will be m<strong>on</strong>ochromatic. Additi<strong>on</strong>al optics are required to<br />
keep <strong>the</strong> output <strong>beam</strong> directi<strong>on</strong>s c<strong>on</strong>stant if tuning of <strong>the</strong> phot<strong>on</strong> energy is required.<br />
Pulse stretch is inevitable for ultra-short pulses, but can be corrected with a sec<strong>on</strong>d<br />
grating. In general, flexibility is high, but <strong>the</strong> systems are likely to be complex <strong>and</strong><br />
optimizati<strong>on</strong>s will give a more restricted operating envelope. The likely operating<br />
range is from <strong>the</strong> VUV to <strong>the</strong> soft X-rays. Infrared gratings are also feasible, though<br />
<strong>the</strong>re are arguably easier splitting techniques for this part of <strong>the</strong> spectrum.<br />
Knife-edge mirrors<br />
A knife-edge mirror is <strong>on</strong>e of <strong>the</strong> simplest techniques <strong>and</strong> also offers a very flexible<br />
splitting with minimal c<strong>on</strong>straints. Both <strong>beam</strong>s are essentially spectrally unmodified,<br />
though <strong>the</strong> reflected <strong>beam</strong> will be filtered at wavelengths shorter than <strong>the</strong> mirror<br />
reflecti<strong>on</strong> cut-off. Very low grazing angles will thus be required for hard X-ray operati<strong>on</strong>,<br />
<strong>and</strong> so <strong>the</strong> splitting angle will become very small. (Bragg reflecti<strong>on</strong> from a<br />
crystal will give larger angles but with <strong>the</strong> disadvantages of reduced b<strong>and</strong>width <strong>and</strong><br />
<strong>the</strong> need to rotate <strong>the</strong> crystal for wavelength tuning). The splitting is achieved by<br />
wavefr<strong>on</strong>t divisi<strong>on</strong> <strong>and</strong> so <strong>the</strong> main disadvantage is that nei<strong>the</strong>r <strong>beam</strong> is a replica at<br />
reduced intensity <strong>the</strong> incident <strong>beam</strong> since diffracti<strong>on</strong> effects at <strong>the</strong> edge will distort<br />
<strong>the</strong> wavefr<strong>on</strong>t. However, pulse lengths should be preserved. A key technical challenge
90 5. Beam-splitting methods<br />
is achieving a mirror with an edge that does not badly degrade <strong>the</strong> <strong>beam</strong> at <strong>the</strong> divisi<strong>on</strong><br />
regi<strong>on</strong>. Knife-edged mirrors could be designed to operate over <strong>the</strong> entire spectral<br />
range from infrared to X-ray wavelengths (though not necessarily in <strong>on</strong>e device).<br />
Slotted mirrors<br />
A slotted (or perforated) mirror may overcome <strong>the</strong> key disadvantage of <strong>the</strong> knifeedge<br />
mirror by dividing <strong>the</strong> wavefr<strong>on</strong>t periodically in space (thus making each <strong>beam</strong><br />
closer to aless intense replica of <strong>the</strong> incident <strong>beam</strong>) whilst maintaining <strong>the</strong> advantages<br />
of transparency (to <strong>the</strong> pulse properties) <strong>and</strong> flexibility. The technical challenge of<br />
making <strong>the</strong> mirror is however much more severe. There is no inherent restricti<strong>on</strong> <strong>on</strong><br />
spectral range, though <strong>the</strong> technical challenges will become more severe at shorter<br />
wavelengths <strong>and</strong> <strong>the</strong> devices may be limited to <strong>the</strong> soft X-ray regime <strong>and</strong> below.<br />
Crystal diffracti<strong>on</strong> <strong>beam</strong> splitters<br />
These are mainly applicable to use at shorter wavelengths (< 6 ˚A), but have <strong>the</strong><br />
advantage in this range over mirror type splitters of allowing much greater angular<br />
separati<strong>on</strong>s. Wavelengthtuningrequires arotati<strong>on</strong> of <strong>the</strong>crystal <strong>and</strong> henceadditi<strong>on</strong>al<br />
optics to maintain a c<strong>on</strong>stant output <strong>beam</strong> positi<strong>on</strong>. Laue <strong>and</strong> Bragg reflecti<strong>on</strong>s<br />
are always highly m<strong>on</strong>ochromatic (unless <strong>on</strong>e distorts <strong>the</strong> crystal lattice) <strong>and</strong> so <strong>the</strong><br />
full b<strong>and</strong>width of <strong>the</strong> free electr<strong>on</strong> laser is not preserved. Accompanying this is<br />
a stretching in <strong>the</strong> pulse length <strong>and</strong> whilst this stretching should be small (a few<br />
femtosec<strong>on</strong>ds), it cannot be reversed as is <strong>the</strong> case with a grating. Only in <strong>the</strong> case<br />
of very thin crystals can a broadb<strong>and</strong> transmissi<strong>on</strong> be achieved, though <strong>the</strong>re will be<br />
a missing comp<strong>on</strong>ent matching <strong>the</strong> b<strong>and</strong>width of Laue/Bragg reflecti<strong>on</strong> of <strong>the</strong> split<br />
<strong>beam</strong>. The most important area for technical development is in achieving higher<br />
quality diam<strong>on</strong>d crystals, which are attractive due to <strong>the</strong>ir high <strong>the</strong>rmal c<strong>on</strong>ductivity<br />
<strong>and</strong> resistance to radiati<strong>on</strong> damage.<br />
Techniques requiring more development<br />
Multilayers<br />
A transmissi<strong>on</strong> multilayer is <strong>the</strong> most likely way that a plate <strong>beam</strong> splitter can be<br />
realized at short wavelengths. In fact, <strong>the</strong> multilayer <strong>beam</strong> splitter will be more akin<br />
to a pellicle. The technical challenges are thus making a membrane that is robust<br />
<strong>and</strong> flat but has adequate transmissi<strong>on</strong>. If <strong>the</strong> membrane is small, this will be easier<br />
but <strong>the</strong>n <strong>the</strong> <strong>beam</strong> fluence will be high if <strong>the</strong> <strong>beam</strong> must be focussed <strong>on</strong>to it in order<br />
to fit through it. A larger membrane would allow operati<strong>on</strong> in <strong>the</strong> diverged light but<br />
may be challenging to keep flat <strong>and</strong> vibrati<strong>on</strong> free.<br />
Structured arrays<br />
These devices have similar properties to slotted mirrors but differ in <strong>the</strong> approach<br />
to fabricati<strong>on</strong>. Operati<strong>on</strong>al range will depend <strong>on</strong> <strong>the</strong> fabricati<strong>on</strong> technique (e.g. <strong>the</strong><br />
overall thickness of <strong>the</strong> structure is linked to <strong>the</strong> angular acceptance). Wavefr<strong>on</strong>t<br />
qualitywill beverydependent<strong>on</strong><strong>the</strong>manufacturing<strong>and</strong>thusdevelopmentisrequired.
5.6. Summary 91<br />
Time-based splitters<br />
Mechanical switching to direct alternate pulses (or trains of pulses) to different <strong>beam</strong>lines<br />
is a logical approach for an inherently pulsed source. The potential advantage to<br />
<strong>the</strong> experimentis that all received pulses c<strong>on</strong>tain <strong>the</strong> full free electr<strong>on</strong> laser output<strong>and</strong><br />
can (in principle) be unchanged in all o<strong>the</strong>r properties. The difference is a lowering of<br />
<strong>the</strong> repetiti<strong>on</strong> rate or pulse structure (e.g. <strong>the</strong> change from a uniform pulse train to a<br />
macropulsed train). For some experiments this may offset <strong>the</strong> advantage of <strong>the</strong> intact<br />
pulse single pulse energy. In any case, <strong>the</strong>re is a c<strong>on</strong>siderable engineering challenge<br />
of achieving a mechanical based system that can deflect alternating pulses or pulse<br />
trains at rates of <strong>the</strong> order of a kHz or higher. High speed operati<strong>on</strong> will probably<br />
be restricted to <strong>the</strong> VUV/XUV to ease <strong>the</strong> challenge of making a fast moving mirror<br />
that can deflect a complete pulse.
92 5. Beam-splitting methods<br />
Summary<br />
• Splitting <strong>the</strong> phot<strong>on</strong> <strong>beam</strong> can be d<strong>on</strong>e to serve several experiments<br />
in parallel, it also enables <strong>the</strong> use of part of <strong>the</strong> <strong>beam</strong><br />
for diagnostic purposes. The trade off is that less (in some<br />
sense) of <strong>the</strong> <strong>beam</strong> gets h<strong>and</strong>ed out for <strong>the</strong> various purposes.<br />
• A <strong>beam</strong> can be split in <strong>the</strong> amplitude (using e.g. a semitransparent<br />
mirror), frequency (a dispersive optic is needed)<br />
<strong>and</strong> temporal (using for instance a moving mirror) domains.<br />
• Of <strong>the</strong> techniques listed in this chapter not all are suitable<br />
for <strong>the</strong> use at free electr<strong>on</strong> laser. Often <strong>the</strong> limiting factor is<br />
<strong>the</strong> intended splitting techniques robustness when it comes to<br />
withst<strong>and</strong>ing <strong>the</strong> high peak power at X-ray wavelengths.<br />
• In some instances <strong>the</strong> following techniques are already in use<br />
at free electr<strong>on</strong> laser whereas some need some kind of adaptati<strong>on</strong><br />
for <strong>the</strong> purpouse:<br />
<strong>–</strong> Diffracti<strong>on</strong> gratings (dispersive). Induces a pulsestretching<br />
whose length depends <strong>on</strong> how many grooves<br />
are illuminated. Pulse-stretch gets reversed if two gratings<br />
are used, at <strong>the</strong> expense of lower transmissi<strong>on</strong>.<br />
<strong>–</strong> Crystal diffracti<strong>on</strong> splitter <strong>–</strong> effective below ∼ 6˚A wavelengths.<br />
An attractive material is diam<strong>on</strong>d crystals, owing<br />
to <strong>the</strong>ir high <strong>the</strong>rmal c<strong>on</strong>ductivity combined with<br />
good radiati<strong>on</strong> hardness[149]. Thediffracti<strong>on</strong> in<strong>the</strong>crystalcausesan<strong>on</strong>-reversiblepulsestretchofafewfemtosec<strong>on</strong>ds.<br />
<strong>–</strong> Knife-edge mirrors<br />
<strong>–</strong> Slotted mirrors<br />
• O<strong>the</strong>r techniques have been employed for specific purposes<br />
<strong>and</strong> proven to be applicable in <strong>the</strong> free electr<strong>on</strong> laser regime<br />
of experimental c<strong>on</strong>diti<strong>on</strong>s. Introducing <strong>the</strong>m for general utilizati<strong>on</strong><br />
require fur<strong>the</strong>r development <strong>and</strong> research:<br />
<strong>–</strong> Multilayers<br />
<strong>–</strong> Structured arrays<br />
<strong>–</strong> Time-based splitters
Part II<br />
Beam diagnostics
6. Introducti<strong>on</strong><br />
Written by: A. Lindblad<br />
Since <strong>the</strong> Sase-process starts up from white noise <strong>–</strong> i.e. <strong>the</strong> initial shot-noise in <strong>the</strong><br />
<strong>beam</strong> is uniformly distributed, each light-pulse will have different temporal, spatial<br />
<strong>and</strong>spectral properties. Over<strong>the</strong>course ofmanyshots saidproperties average out<strong>and</strong><br />
<strong>the</strong> machine attains its ”average” properties in terms of intensity, pulse-length <strong>and</strong><br />
spectral purity; it is <strong>the</strong>refore natural that <strong>beam</strong> diagnostic methods are an integral<br />
part of any free electr<strong>on</strong> laser-project (see, for instance Ref. [89]).<br />
Diagnostics of <strong>the</strong> phot<strong>on</strong>s (<strong>and</strong> electr<strong>on</strong>s) also provide valuable feedback to <strong>the</strong><br />
accelerator part of <strong>the</strong> machine. This feedback is essential to ensure stable operati<strong>on</strong><br />
<strong>and</strong> l<strong>on</strong>g up-time for <strong>the</strong> users.<br />
The various schemes that exist to enhance <strong>the</strong> overall shot-to-shot repeatability,<br />
e.g. HGHG, EEHG 1 , may seem to loosen <strong>the</strong> dem<strong>and</strong> <strong>on</strong> diagnostics <strong>–</strong> however <strong>the</strong><br />
delicate problem of overlapping a laser pulse (which can be of HHG type <strong>–</strong> also requiring<br />
its own diagnostics) with <strong>the</strong> electr<strong>on</strong> <strong>beam</strong> still requires a strict characterizati<strong>on</strong><br />
of <strong>the</strong> light as in <strong>the</strong> Sase case.<br />
In this chapter <strong>the</strong> various categories of diagnostics are presented, as well as <strong>the</strong><br />
different subcategories that we can sort <strong>the</strong>m into.<br />
6.1 Diagnostics categorizati<strong>on</strong><br />
Figure 6.1 gives an indicati<strong>on</strong> of how we can categorize <strong>the</strong> different diagnostic methods<br />
that needs to be employed to characterize <strong>the</strong> free electr<strong>on</strong> laser phot<strong>on</strong> <strong>beam</strong>.<br />
• Beam cross-secti<strong>on</strong><br />
<strong>–</strong> Transverse (also al<strong>on</strong>g <strong>the</strong> <strong>beam</strong> path to discern <strong>the</strong> focus-size)<br />
<strong>–</strong> L<strong>on</strong>gitudinal<br />
• Pulse arrival time<br />
• The jitter between pulses<br />
• Intensity / Pulse energy<br />
1 Secti<strong>on</strong>s 1.5, see page 17 <strong>and</strong> 1.5, see page 18.<br />
95
96 6. Introducti<strong>on</strong><br />
y<br />
x<br />
z<br />
I<br />
Figure 6.1: Phot<strong>on</strong> pulses needs to be diagnosed vis-à-vis spatial <strong>and</strong> temporal extents. Spectral properties<br />
can be inferred from <strong>the</strong> temporal distributi<strong>on</strong>.<br />
• Spectral c<strong>on</strong>tent<br />
• Median energy<br />
The <strong>beam</strong>’s size in space, <strong>and</strong> how it varies al<strong>on</strong>g <strong>the</strong> optical system is important<br />
to characterize since those properties needs to be known to know <strong>the</strong> focus points<br />
al<strong>on</strong>g <strong>the</strong> <strong>beam</strong> <strong>–</strong> both for simulati<strong>on</strong> purposes <strong>and</strong> experiments.<br />
The l<strong>on</strong>gitudinal cross-secti<strong>on</strong> of <strong>the</strong> <strong>beam</strong> gives <strong>the</strong> pulse length <strong>and</strong> shape. This<br />
is c<strong>on</strong>nected both to <strong>the</strong> spectral c<strong>on</strong>tent <strong>and</strong> <strong>the</strong> pulse to pulse arrival time jitter.<br />
Forexperimentsthatare c<strong>on</strong>sideringtemporal propertiesofmatter (pump-<strong>and</strong>-probe)<br />
this is crucial informati<strong>on</strong>.<br />
The pulse energy (or intensity) follows a gamma-distributi<strong>on</strong> depending <strong>on</strong> how<br />
many radiating modes that are present[104] <strong>–</strong> hence a shot-to-shot measurement of<br />
<strong>the</strong> intensity is necessary to have at a free electr<strong>on</strong> laser facility.<br />
The centroid of <strong>the</strong> phot<strong>on</strong> energy fluctuates about 0.5% at Flash[150], obviously<br />
a shot-to-shot measurement of this needs to be provided, both to <strong>the</strong> users <strong>and</strong> to <strong>the</strong><br />
staff h<strong>and</strong>ling <strong>the</strong> accelerator itself.<br />
Spectral diagnostics (Intensity <strong>and</strong> energy) are discussed in chapter 7 below.<br />
Various methods c<strong>on</strong>cerning <strong>the</strong> measurements of <strong>the</strong> transverse spatial extent of<br />
<strong>the</strong> phot<strong>on</strong> <strong>beam</strong> are described in chapter 8 (see page 109).<br />
A survey of pulse length, profile <strong>and</strong> jitter diagnostics can be found in chapter 9<br />
(see page 151).<br />
Subcategorizati<strong>on</strong>s<br />
Shot-to-shot / Average<br />
Many properties of <strong>the</strong> free electr<strong>on</strong> laser phot<strong>on</strong> <strong>beam</strong> needs to be known at a shotto-shot<br />
basis. A spectroscopic experiment, for instance, needs to know <strong>the</strong> incoming<br />
phot<strong>on</strong>s’ energy <strong>and</strong> intensity per pulse as to allow sorting of <strong>the</strong> experimental<br />
data. Knowing just <strong>the</strong> average intensity <strong>and</strong> phot<strong>on</strong> energy does not allow this<br />
post-experiment analysis of <strong>the</strong> data.<br />
Average properties, <strong>on</strong> <strong>the</strong> o<strong>the</strong>r h<strong>and</strong> says a lot about <strong>the</strong> l<strong>on</strong>g term stability<br />
of <strong>the</strong> free electr<strong>on</strong> laser <strong>and</strong> may also serve as a measurement of <strong>the</strong> c<strong>on</strong>diti<strong>on</strong> of<br />
<strong>transport</strong> optics. Averaging measurements are usually more stable than <strong>the</strong>ir shotto-shot<br />
counterparts <strong>–</strong> <strong>and</strong> can thus be used to calibrate o<strong>the</strong>r diagnostics.<br />
t
6.2. C<strong>on</strong>clusi<strong>on</strong> 97<br />
Transparent/Opaque/Blocking<br />
A diagnostic can be, more or less, invasive, i.e. how much it affects <strong>the</strong> phot<strong>on</strong> <strong>beam</strong>’s<br />
properties for experiments <strong>and</strong> o<strong>the</strong>r diagnostics downstream. An positi<strong>on</strong> measurement<br />
based <strong>on</strong> <strong>the</strong> photo-current generated <strong>on</strong> a slit will cut away parts of <strong>the</strong> <strong>beam</strong>,<br />
thus reducing <strong>the</strong> available intensity downstream from <strong>the</strong> diagnostic.<br />
As can be inferred from <strong>the</strong> title, we can divide <strong>the</strong> degree of invasiveness of a<br />
diagnostic tool into transparent, opaque <strong>and</strong> blocking. As <strong>on</strong>-line diagnostics it is<br />
preferable to have transparent diagnostics since <strong>the</strong>y have least effect <strong>on</strong> <strong>the</strong> <strong>beam</strong>.<br />
For commissi<strong>on</strong>ing of diagnostics, <strong>beam</strong>-<strong>transport</strong> elements, calibrating of diagnostics<br />
<strong>and</strong> accelerator c<strong>on</strong>diti<strong>on</strong>ing opaque <strong>and</strong> blocking diagnostics can be used.<br />
As discussed previously (chapter 5) it is possible to split off part of <strong>the</strong> <strong>beam</strong><br />
to be diagnosed in parallel to <strong>the</strong> downstream experiments/diagnostics. Hence even<br />
a blocking diagnostic that o<strong>the</strong>rwise have <strong>the</strong> needed specificati<strong>on</strong>s can be used to<br />
provide informati<strong>on</strong> to <strong>the</strong> downstream activities.<br />
Phot<strong>on</strong>-energy range<br />
Physical processes that may be used as basis for a diagnostic can be challenging to<br />
find. For infrared <strong>and</strong> THz <strong>beam</strong>s it is not possible to photo-i<strong>on</strong>ize a gas, whereas for<br />
UV <strong>and</strong> soft X-rays <strong>the</strong> cross-secti<strong>on</strong> for this processes is very large <strong>–</strong> <strong>and</strong> in turn, for<br />
hard X-rays <strong>the</strong> cross-secti<strong>on</strong>s for photo-i<strong>on</strong>izati<strong>on</strong> become very small.<br />
Hence, <strong>the</strong> phot<strong>on</strong>-energy range(s) of interest needs to be taken into account in<br />
designing <strong>the</strong> diagnostic array for a facility.<br />
6.2 C<strong>on</strong>clusi<strong>on</strong><br />
There is no such thing as an perfect diagnostic, i.e. a device that measure a property<br />
<strong>on</strong> a shot-to-shot basis in a transparent manner for any phot<strong>on</strong>-energy with negligible<br />
error. Thus we have torely <strong>on</strong> acombinati<strong>on</strong> of diagnostics tomeasure <strong>the</strong>desired unknowns<br />
of <strong>the</strong> phot<strong>on</strong> <strong>beam</strong>. To ensure <strong>the</strong> integrity of <strong>the</strong> resulting diagnostics array<br />
<strong>on</strong>e needs to calibrate <strong>the</strong>m against each o<strong>the</strong>r (<strong>and</strong> possibly additi<strong>on</strong>al diagnostics).
98 6. Introducti<strong>on</strong><br />
Summary<br />
• A diagnostic needs to be more robust <strong>and</strong> more user friendly<br />
than an experiment, as <strong>the</strong> informati<strong>on</strong> provided is used to<br />
analyze experimental data <strong>–</strong> for users, as feedback to <strong>the</strong> running<br />
of <strong>the</strong> accelerator <strong>and</strong> for commissi<strong>on</strong>ing of <strong>the</strong> <strong>transport</strong><br />
optics.<br />
• Diagnostics can be divided into:<br />
<strong>–</strong> Beam cross-secti<strong>on</strong> <strong>–</strong> transverse <strong>and</strong> l<strong>on</strong>gitudinal<br />
<strong>–</strong> Arrival time, jitter<br />
<strong>–</strong> Intensity <strong>and</strong> Pulse energy<br />
<strong>–</strong> Spectral c<strong>on</strong>tent<br />
<strong>–</strong> Median energy<br />
• Any diagnostic method can also be fur<strong>the</strong>r characterized by:<br />
<strong>–</strong> its ability to measure <strong>on</strong> a shot-to-shot basis or if it provides<br />
an average measurement of <strong>the</strong> property.<br />
<strong>–</strong> if it is transparent, opaque or <strong>beam</strong> stopping/blocking for<br />
a downstream experiment.<br />
<strong>–</strong> what phot<strong>on</strong>-energy range it can be used in, i.e. infrared/THz,<br />
UV, soft X-ray <strong>and</strong> hard X-rays.<br />
• No perfect diagnostic exists (nei<strong>the</strong>r an universal that measures<br />
everything, nor optimal for all phot<strong>on</strong> ranges). Thus<br />
a judicious combinati<strong>on</strong> of diagnostics needs to be composed<br />
into a diagnostics array distributed al<strong>on</strong>g <strong>the</strong> <strong>beam</strong>-path that<br />
can be used to<br />
<strong>–</strong> Measure <strong>–</strong> during <strong>the</strong> course of o<strong>the</strong>r experiments<br />
<strong>–</strong> Calibrate <strong>–</strong> o<strong>the</strong>r diagnostics during commissi<strong>on</strong>ing<br />
<strong>–</strong> Cross-check <strong>–</strong> <strong>the</strong> integrity of <strong>the</strong> diagnostics array<br />
• Beam-splitters allows <strong>the</strong> use of opaque/blocking diagnostics<br />
in parallel to o<strong>the</strong>r experiments <strong>and</strong> diagnostics.
7. Spectral diagnostics: Intensity & Energy<br />
Written by: A. Lindblad<br />
In this chapter some ways to infer <strong>the</strong> spectral properties (or some spectral property)<br />
of <strong>the</strong> free electr<strong>on</strong> laser light. During <strong>the</strong> course of Part I of <strong>the</strong> book we have<br />
gotten <strong>the</strong> indicati<strong>on</strong> that both seeded <strong>and</strong> Sase free electr<strong>on</strong> laser provide light that<br />
need to be diagnosed <strong>on</strong> a shot to shot basis.<br />
The Sase process start up from current shot noise in <strong>the</strong> <strong>beam</strong> that is subsequently<br />
amplified with a few radiati<strong>on</strong> modes c<strong>on</strong>tributing to <strong>the</strong> final spectrum at/after<br />
saturati<strong>on</strong>. Each pulse is <strong>the</strong>refore unique <strong>and</strong> for an experiment to be meaningful<br />
<strong>the</strong> mean intensity <strong>and</strong> mean-energy of <strong>the</strong> pulses can be c<strong>on</strong>sidered tobe <strong>the</strong> minimal<br />
informati<strong>on</strong> to be provided to <strong>the</strong> user. In various seeding schemes <strong>the</strong> quality of <strong>the</strong><br />
pulses needs to be m<strong>on</strong>itored to ensure stability. The harm<strong>on</strong>ic c<strong>on</strong>tent of <strong>the</strong> pulses<br />
<strong>and</strong> <strong>the</strong> sp<strong>on</strong>taneous emissi<strong>on</strong> background levels needs to be diagnosed as well.<br />
Ideally <strong>the</strong> full spectrum of <strong>the</strong> pulse should be measured <strong>on</strong> a pulse to pulse basis<br />
in a manner that is transparent to <strong>the</strong> users of <strong>the</strong> <strong>beam</strong>. This is often not practically<br />
possible, as will be seen in <strong>the</strong> following, but this can be overcome by dividing <strong>the</strong><br />
<strong>beam</strong>between<strong>the</strong>experiment<strong>and</strong><strong>the</strong>diagnostics utilizing, e.g.a<strong>beam</strong>splittingdevice<br />
as discussed above in chapter 5.<br />
7.1 X-ray spectrometry<br />
The obvious spectral diagnostic of <strong>the</strong> fel <strong>beam</strong> is to measure it, or parts of it directly<br />
with an X-ray spectrometer. With <strong>on</strong>e or more gratings it is possible to disperse <strong>the</strong><br />
phot<strong>on</strong> <strong>beam</strong> c<strong>on</strong>verting energy spread into a spatial distributi<strong>on</strong>. In most instances<br />
variable line spacing gratings is used to focus a higher order diffracted <strong>beam</strong> <strong>on</strong>to a<br />
focal plane, passing <strong>the</strong> 0 th order reflected <strong>beam</strong> for <strong>the</strong> experiment (Figure 7.1).<br />
Rewriting <strong>the</strong> grating equati<strong>on</strong> (Equati<strong>on</strong> 4.1) in terms of line density<br />
sinα−sinβ = n·λσ0<br />
<strong>on</strong>e can vary <strong>the</strong> groove depth according to a third degree polynomial (with x al<strong>on</strong>g<br />
<strong>the</strong> grating) as:<br />
σ(x) = σ0 +σ1x+σ2x 2 +σ3x 3<br />
99
100 7. Spectral diagnostics: Intensity & Energy<br />
Incoming FEL pulse<br />
α<br />
β<br />
focal plane<br />
O th order<br />
Figure 7.1: A variable line space grating disperses different wavelengths al<strong>on</strong>g <strong>the</strong> same focal plane.<br />
λ range 6-40 nm 20-60 nm<br />
central line spacing 900 l/mm 300 l/mm<br />
fracti<strong>on</strong> in 1 st order 8-0.5% 11-1.5%<br />
diffracti<strong>on</strong> angle 83.8-74.5 ◦<br />
83.5-79 ◦<br />
Res. power (CCD) > 7000 > 4000<br />
incident angle 88 ◦<br />
88 ◦<br />
coating C, Ni C<br />
Table 7.1: Design parameters of <strong>the</strong> flash VLS grating spectrometer <strong>–</strong> as given in Ref. [104].<br />
Then <strong>on</strong>e can choose σ(x) so that <strong>the</strong> abberati<strong>on</strong> <strong>and</strong> spectral defocusing effects are<br />
minimized. With proper materials chosen between <strong>on</strong>e <strong>and</strong> ten percent of <strong>the</strong> radiati<strong>on</strong><br />
is dispersed <strong>on</strong>to <strong>the</strong> focal plane (this percentage also depend <strong>on</strong> <strong>the</strong> wavelength).<br />
This kind of spectrometers provide <strong>the</strong> full spectrum around a certain phot<strong>on</strong><br />
energy <strong>–</strong> harm<strong>on</strong>ics are usually filtered away by <strong>the</strong> grating. The detecti<strong>on</strong> can be<br />
d<strong>on</strong>e ei<strong>the</strong>r by CCD camera or strip detectors. At Flash <strong>the</strong> spectrum is recorded<br />
by a Ce:YAG screen imaged by a CCD camera. The camera can record images at a<br />
rate of 5 Hz[104].<br />
Similar set-ups are used at Lcls[151] <strong>and</strong> at Fermi@Elettra[152].<br />
7.2 Intensity/Beam energy<br />
Earlier we discussed <strong>the</strong> use of m<strong>on</strong>ochromators in combinati<strong>on</strong> with <strong>the</strong> free electr<strong>on</strong><br />
laser<strong>beam</strong> <strong>–</strong> in secti<strong>on</strong> 4.5 (see page 67) <strong>–</strong> as a means to c<strong>on</strong>vert <strong>the</strong> spectral jitter<br />
(wavelength <strong>and</strong> intensity fluctuati<strong>on</strong>s per pulse) into intensity jitter.<br />
Intensitycan be measured <strong>on</strong> a per pulse basis or as an average property over many<br />
pulses, of course a fast enough detecti<strong>on</strong> scheme can be made to integrate over many<br />
pulses if <strong>on</strong>e needs to measure <strong>the</strong> average intensity. As free electr<strong>on</strong> laser pulses are<br />
often in <strong>the</strong> order of tenths of femtosec<strong>on</strong>ds (or shorter) a measuring <strong>on</strong> a pulse by<br />
pulse basis poses quite a challenge as will be seen below.<br />
As for most diagnostics we can roughly divide intensity measurements into opaque<br />
<strong>and</strong>transparent <strong>–</strong>as seenfrom animagined experimentalstati<strong>on</strong> downstream from <strong>the</strong><br />
diagnostic. Diagnostics which are, more or less, transparent are possible to distribute<br />
al<strong>on</strong>g a <strong>beam</strong> path leading up to an experimental stati<strong>on</strong>, whereas opaque diagnostics
7.2. Intensity/Beam energy 101<br />
needs to use ei<strong>the</strong>r a part of <strong>the</strong> free electr<strong>on</strong> laser <strong>beam</strong> using a <strong>beam</strong>splitter, or be<br />
placed after <strong>the</strong> experiment (provided that <strong>the</strong> experiment is somewhat transparent).<br />
Besides <strong>the</strong> gas m<strong>on</strong>itor detectors <strong>and</strong> solid state devices described below a way of<br />
discerning <strong>the</strong> average energy of <strong>the</strong> free electr<strong>on</strong> laser <strong>beam</strong> have been invented at<br />
<strong>the</strong> Lcls[96]. By determining <strong>the</strong> energy loss for different trajectories of <strong>the</strong> electr<strong>on</strong><br />
<strong>beam</strong> through<strong>the</strong>undulatorsameasure of<strong>the</strong>average pulseenergycan bedetermined<br />
within 1 <strong>and</strong> 5%.<br />
Gas m<strong>on</strong>itor detectors<br />
I<strong>on</strong>/electr<strong>on</strong> detecti<strong>on</strong><br />
To provide a transparent diagnostic of <strong>the</strong> intensity at <strong>the</strong> Flash free electr<strong>on</strong> laser a<br />
an intensity m<strong>on</strong>itor based <strong>on</strong> photoi<strong>on</strong>izati<strong>on</strong> of gases <strong>and</strong> detecti<strong>on</strong> of i<strong>on</strong>s <strong>and</strong><br />
electr<strong>on</strong>s have been developed [153] at Flash. These detectors are placed before <strong>and</strong><br />
after <strong>the</strong> gas attenuator[104]. The latter is places immediately before entering <strong>the</strong><br />
experimental hall.<br />
By measuring <strong>the</strong> yield (electr<strong>on</strong> or i<strong>on</strong>) from a known density of a gas it is possible<br />
to c<strong>on</strong>clude <strong>the</strong> intensity of <strong>the</strong> phot<strong>on</strong> <strong>beam</strong> via:<br />
N = Nγ ·ρ·σ(E)·ℓ (7.1)<br />
relates <strong>the</strong> number of particles i<strong>on</strong>ized (N) with <strong>the</strong> number of phot<strong>on</strong>s Nγ; <strong>the</strong> target<br />
density (ρ); <strong>the</strong> photoi<strong>on</strong>izati<strong>on</strong> cross-secti<strong>on</strong> at <strong>the</strong> phot<strong>on</strong> energy in questi<strong>on</strong> σ(E)<br />
<strong>and</strong> <strong>the</strong> length of <strong>the</strong> interacti<strong>on</strong> volume ℓ.<br />
-V<br />
+V<br />
Figure 7.2: A Faraday cup counts <strong>the</strong> i<strong>on</strong>s <strong>and</strong> electr<strong>on</strong>s produced by photoi<strong>on</strong>izati<strong>on</strong> of a target gas to produce<br />
a measure of <strong>the</strong> intensity of <strong>the</strong> FEL phot<strong>on</strong> <strong>beam</strong> via Equati<strong>on</strong> 7.1.<br />
The gas m<strong>on</strong>itor detector scheme is shown in Figure 7.2. The charged particles<br />
(electr<strong>on</strong>s <strong>and</strong> i<strong>on</strong>s) created by <strong>the</strong> i<strong>on</strong>izati<strong>on</strong> of <strong>the</strong> gas is separated <strong>and</strong> accelerated<br />
byahomogeneous electric field, <strong>and</strong> can thus be detected separately. The gas pressure<br />
is typically held at 10 -6 mbar, as to disturb <strong>the</strong> downstream experiments minimally.<br />
The charged particles are detected by Faraday cups.<br />
With this type of detector it is possible to measure <strong>the</strong> pulse intensity with an<br />
error less than 10% with a jitter between pulses of 1%. The latter is dominated by<br />
<strong>the</strong> signal statistics <strong>and</strong> holds for more than 10 10 phot<strong>on</strong>s per pulse.<br />
+
102 7. Spectral diagnostics: Intensity & Energy<br />
It is important to note that, since <strong>the</strong> detected intensity depends <strong>on</strong> <strong>the</strong> crosssecti<strong>on</strong><br />
1 for photo-i<strong>on</strong>izati<strong>on</strong> <strong>the</strong> sensitivity of <strong>the</strong> detecti<strong>on</strong> scheme varies str<strong>on</strong>gly<br />
with phot<strong>on</strong> energy. This is an issue to c<strong>on</strong>sider when this type of detector is to<br />
be used for hard X-rays, where cross-secti<strong>on</strong>s are several orders of magnitude lower<br />
than in <strong>the</strong> VUV/soft X-ray regi<strong>on</strong>. The sensitivity of <strong>the</strong> scheme when it comes to<br />
<strong>the</strong> detecti<strong>on</strong> of intensities of higher harm<strong>on</strong>ics in <strong>the</strong> free electr<strong>on</strong> laser pulses are<br />
<strong>the</strong>refore also impaired.<br />
Photoluminescence detecti<strong>on</strong><br />
At <strong>the</strong> Lcls a gas m<strong>on</strong>itor detector have been developed that detects <strong>the</strong> fluorescence<br />
of nitrogen with two photomultiplier tubes[96, 154].<br />
Magnetic coils around a 30 cm l<strong>on</strong>g <strong>and</strong> 8 cm wide pressure chamber (with 0.015-<br />
0.9 mbar of gas pressure) c<strong>on</strong>fine <strong>the</strong> photoelectr<strong>on</strong>s produced by <strong>the</strong> free electr<strong>on</strong><br />
laser <strong>beam</strong>, <strong>the</strong>se electr<strong>on</strong>s excite <strong>the</strong> surrounding nitrogen gas. The de-excitati<strong>on</strong> of<br />
<strong>the</strong> molecules occur by <strong>the</strong> emissi<strong>on</strong> of phot<strong>on</strong>s in <strong>the</strong> UV range between 300 to 400<br />
nm. During <strong>the</strong> course of detecti<strong>on</strong> of cosmic rays it have been c<strong>on</strong>cluded that <strong>the</strong><br />
yield in this spectrum depends weakly <strong>on</strong> <strong>the</strong> exciting electr<strong>on</strong> energy.<br />
Calorimeters<br />
A calorimeter (also called radiometer in <strong>the</strong> present c<strong>on</strong>text <strong>and</strong> will henceforth be<br />
denoted thusly) measure, in principle, <strong>the</strong> integral spectral power impinging <strong>on</strong> it.<br />
Hence, <strong>the</strong> sensitivity is equal for <strong>the</strong> harm<strong>on</strong>ic c<strong>on</strong>tent in <strong>the</strong> pulses. St<strong>and</strong>ard<br />
for measuring radiated power from UV/X-ray lightsources around <strong>the</strong> world (i.e. at<br />
PTB[155] in Germany, NIST[156] in <strong>the</strong> USA, <strong>and</strong> NMIJ[157, 158] in Japan).<br />
The device c<strong>on</strong>sists of a cryogenically cooled temperature sensor in fr<strong>on</strong>t of a target<br />
up<strong>on</strong> which <strong>the</strong> radiati<strong>on</strong> impinges <strong>on</strong> (Figure 7.3). The pulse energy is given by:<br />
E = ∆T<br />
s·f<br />
(7.2)<br />
where <strong>the</strong> temperature difference (∆T) is <strong>the</strong> temperature raise in <strong>the</strong> absorbing<br />
cavity, f is <strong>the</strong> repetiti<strong>on</strong> rate of <strong>the</strong> source <strong>and</strong> s is <strong>the</strong> <strong>the</strong>rmal resp<strong>on</strong>se of <strong>the</strong><br />
system. The radiated power is <strong>the</strong>n simply P = E ·f.<br />
The <strong>the</strong>rmal resp<strong>on</strong>se of <strong>the</strong> system can have more or less inertia, but <strong>the</strong> time<br />
c<strong>on</strong>stant for transiti<strong>on</strong> from <strong>on</strong>e equilibrium of <strong>the</strong> system to ano<strong>the</strong>r up<strong>on</strong> changing<br />
absorbed power is measured in minutes. Hence, average energies per pulse can be obtained,<br />
however with small systematic errors (dominated by <strong>the</strong> intensity fluctuati<strong>on</strong>s<br />
of <strong>the</strong> radiati<strong>on</strong>).<br />
A radiometer of this kind is also effectively a <strong>beam</strong> stopper <strong>and</strong> needs to be placed<br />
at <strong>the</strong> very end of <strong>the</strong> <strong>beam</strong> <strong>transport</strong> system, i.e. after <strong>the</strong> experiment(s) or operate<br />
at a split of branch of <strong>the</strong> <strong>beam</strong>. This type of diagnostic can <strong>the</strong>refore be used as a<br />
st<strong>and</strong>ard which to calibrate o<strong>the</strong>r intensity diagnostics against, for instance <strong>the</strong> gas<br />
m<strong>on</strong>itor detectors menti<strong>on</strong>ed above, or during commissi<strong>on</strong>ing runs <strong>and</strong> as a machine<br />
diagnostic.<br />
1 Cross-secti<strong>on</strong>s for <strong>the</strong> noble gases have been tabulated by K. Tiedtke <strong>and</strong> co-workers for <strong>the</strong><br />
noble gases up to 300 eV phot<strong>on</strong> energy[153].
7.2. Intensity/Beam energy 103<br />
Solid state devices<br />
Photodiodes<br />
Temp. sensor<br />
Liquid He<br />
Liquid N2<br />
Heater<br />
Figure 7.3: Illustrati<strong>on</strong> of a cryogenic calorimeter setup.<br />
Phot<strong>on</strong> <strong>beam</strong><br />
Photodiodes, comm<strong>on</strong>ly employed at synchrotr<strong>on</strong> laboratories for intensity diagnostic<br />
purposes have shown to exhibit quite large errors when employed at free electr<strong>on</strong><br />
laser, at Scss in Japan <strong>on</strong>e such measurements yielded an error of about 30% of <strong>the</strong><br />
intensity.<br />
Bolometers<br />
A solid state bolometric sensor that can withst<strong>and</strong> <strong>the</strong> power from a free electr<strong>on</strong><br />
laser laser <strong>beam</strong> can be realized from a device where <strong>the</strong> resistance change of a colossal<br />
magneto-resistance <strong>the</strong>rmistor film up<strong>on</strong> absorpti<strong>on</strong> of electromagnetic radiati<strong>on</strong>.<br />
With a sufficiently efficient coupling to a cooling substrate <strong>the</strong> operati<strong>on</strong> can be fast<br />
enough to allow very precise measurement of <strong>the</strong> <strong>beam</strong> energy <strong>on</strong> a pulse to pulse<br />
basis <strong>–</strong> since <strong>the</strong>y can be operated close to <strong>the</strong>ir metal-insulator transiti<strong>on</strong> where <strong>the</strong><br />
resistance changes are verylarge. At low temperatures <strong>the</strong>c<strong>on</strong>tributi<strong>on</strong>s from <strong>the</strong>rmal<br />
noise in <strong>the</strong> circuit is also lower.<br />
The resistivity <strong>and</strong> <strong>the</strong> temperature of such <strong>the</strong>rmistor films can be varied depending<br />
<strong>on</strong> <strong>the</strong>ir compositi<strong>on</strong>[159]. The sensitivity of <strong>the</strong> resistance up<strong>on</strong> temperature<br />
changes (understood as 1<br />
∂R<br />
R ∂T<br />
) can be as large as 10%/K.<br />
Assuming that <strong>the</strong> sensor is efficiently coupled to <strong>the</strong> cooling substrate <strong>the</strong>n <strong>the</strong><br />
current signal S from a voltage biased sensor is proporti<strong>on</strong>al to <strong>the</strong> total X-ray energy<br />
<strong>and</strong> inversely proporti<strong>on</strong>al to <strong>the</strong> heat capacity of <strong>the</strong> substrate C:<br />
∆T ∝ Efel<br />
C<br />
(7.3)
104 7. Spectral diagnostics: Intensity & Energy<br />
Assuming that <strong>the</strong> noise in <strong>the</strong> circuit mainly arises from <strong>the</strong>rmal noise (i.e. Johns<strong>on</strong><br />
noise) of <strong>the</strong> sensor <strong>and</strong> <strong>the</strong> readout (in,en) we can write <strong>the</strong> signal to noise ratio<br />
(S/N) during an integrati<strong>on</strong> time τ[159]:<br />
S √ Vbias<br />
τ =<br />
N R2 ∂R<br />
∂T �<br />
4kBT/R+i 2<br />
n +(en/R) 2∆(t)√ τ (7.4)<br />
For low resistances <strong>and</strong> low temperatures this expressi<strong>on</strong> is maximized. Low noise<br />
operati<strong>on</strong>al amplifers have en as low as 1 nV/ √ Hz <strong>and</strong> in in <strong>the</strong> orders of pA/ √ Hz.<br />
Signal to noise ratios of 100 000 can be obtained for integrati<strong>on</strong> times of millisec<strong>on</strong>ds.<br />
Neodynium str<strong>on</strong>tium manganese oxide (NSMO) sensors grown <strong>on</strong> a silic<strong>on</strong>e substrate<br />
can be used to measure <strong>the</strong> total energy <strong>on</strong> a pulse to pulse basis with very<br />
small errors[96, 160].<br />
Even-though this diagnostic interrupts <strong>the</strong> <strong>beam</strong> (which can be worked around as<br />
seen earlier) <strong>the</strong> devices can be absolutely calibrated with an ordinary pulsed laser.<br />
Lastly this kind of detectors have a sensitivity that is linear over three orders of<br />
magnitude of incoming <strong>beam</strong> energy. This kind of detectors are currently in use (<strong>and</strong><br />
being fur<strong>the</strong>r developed) at <strong>the</strong> Lcls free electr<strong>on</strong> laserwhere <strong>the</strong>y also serve as to<br />
calibrate <strong>the</strong> photoluminescence detectors described above.<br />
At 8.3 keV <strong>the</strong> average energy is determined with a pulse to pulse jitter of about<br />
8%[96].<br />
7.3 Phot<strong>on</strong>-energy<br />
Measuring <strong>the</strong> phot<strong>on</strong>-pulse directly, as outlined above in secti<strong>on</strong> 7.1, needs <strong>the</strong> <strong>beam</strong><br />
to be split (in amplitude or in frequency) or to be placed at <strong>the</strong> very end after an<br />
experiment <strong>–</strong> that, in turn, needs to be transparent to <strong>the</strong> diagnostic. In various<br />
circumstances this is not desirable or even possible <strong>–</strong> ei<strong>the</strong>r because <strong>the</strong> experiment<br />
is phot<strong>on</strong>-hungry <strong>and</strong> can not afford to use <strong>the</strong> loss of transmissi<strong>on</strong> from a <strong>beam</strong><br />
splitting device, <strong>and</strong>/or <strong>the</strong> experiment is opaque (i.e. effectively a <strong>beam</strong>-stopper).<br />
One way to circumvent this is to measure <strong>the</strong> time-of-flight of <strong>the</strong> i<strong>on</strong>s <strong>and</strong>/or electr<strong>on</strong>s<br />
in amannersimilar to<strong>the</strong>intensitymeasurement with <strong>the</strong> gas-m<strong>on</strong>itor detectors<br />
described above (secti<strong>on</strong> 7.2). Since <strong>the</strong> arrival time of <strong>the</strong> pulses at <strong>the</strong> diagnostic is<br />
known (or can be inferred from o<strong>the</strong>r diagnostics) we can measure different aspects<br />
of <strong>the</strong> i<strong>on</strong>izati<strong>on</strong> processes occurring in, for instance, a rare gas via <strong>the</strong> time-of-flight<br />
of <strong>the</strong> produced charged particles in a homogeneous electric (<strong>and</strong>/or magnetic) field.<br />
I<strong>on</strong> time-of-flight<br />
The time of flight of i<strong>on</strong>s through an electric field is proporti<strong>on</strong>al to <strong>the</strong>ir mass <strong>and</strong><br />
charge <strong>–</strong> for a small source regi<strong>on</strong> <strong>the</strong> flight times for different charge to mass ratios<br />
are deterministic <strong>and</strong> depends <strong>on</strong>ly <strong>on</strong> electric field strengths <strong>and</strong> <strong>the</strong> geometry of <strong>the</strong><br />
apparatus, usually referred to as a Wiley-MacLaren spectrometer[161]. I<strong>on</strong> time-offlight<br />
is thus a mass-spectroscopic measurement, in essence.<br />
The resoluti<strong>on</strong> of a Wiley-Maclaren setup (spatial <strong>and</strong> temporal) can be analyzed,<br />
let us spell it out in detail: define<br />
qsEs +dEd<br />
Ut = , k =<br />
sEs<br />
Ut<br />
qsEs
7.3. Phot<strong>on</strong>-energy 105<br />
s<br />
d0,E1 d1,E2 D<br />
Figure 7.4: The field in <strong>the</strong> drift tube is zero. The ratio between <strong>the</strong> fields is uniquely determined by <strong>the</strong><br />
geometry given by s,d1 <strong>and</strong> D.<br />
With T as <strong>the</strong> total flight time, zero initial kinetic energy <strong>and</strong> starting positi<strong>on</strong> s,<br />
<strong>the</strong> positi<strong>on</strong> where i<strong>on</strong>s having s± 1<br />
δs pass each o<strong>the</strong>r can be found where<br />
2<br />
�<br />
dT �<br />
� = 0 ⇒ D = 2sk<br />
ds<br />
3/2<br />
�<br />
1<br />
1−<br />
k + √ �<br />
d<br />
k s<br />
� 0,s<br />
This focus c<strong>on</strong>diti<strong>on</strong> is <strong>the</strong> same for all i<strong>on</strong>s <strong>and</strong> is independent of <strong>the</strong> systems total<br />
energy. Hence, if s, d, <strong>and</strong> D is given, <strong>the</strong> ratio Ed/Es since k can <strong>on</strong>ly have <strong>on</strong>e<br />
physically reas<strong>on</strong>able value.<br />
T(U,s) has ei<strong>the</strong>r a maximum, minimum, or an inflecti<strong>on</strong> point where dT<br />
�<br />
� = 0, ds 0,s<br />
<strong>the</strong> latter can be found with:<br />
d 2 T<br />
ds2 �<br />
�<br />
� = 0,⇒ d<br />
s =<br />
� �<br />
k −3 D<br />
k 2s<br />
� 0,s<br />
For <strong>the</strong> parameter values chosen for best resoluti<strong>on</strong>, two-field systems are operated<br />
smaller than <strong>the</strong> righth<strong>and</strong>-side.<br />
at <strong>the</strong> maxiumum, i.e. with <strong>the</strong> d<br />
s<br />
Spatial resoluti<strong>on</strong><br />
Let Ms be <strong>the</strong> largest mass for which <strong>the</strong> flight times are discernibly different,<br />
Tm+1 −Tm = τ ≈ Tm<br />
�<br />
s<br />
�2 ⇒ Ms ≈ 16k<br />
2m ∆s<br />
The latter is true whenever k ≫ 1 <strong>and</strong> k ≫ d/s.<br />
This shows that <strong>the</strong> distance to <strong>the</strong> sourcepoint s must be larger than <strong>the</strong> spread<br />
∆s for space resoluti<strong>on</strong> to be made adequate <strong>–</strong> this, in turn, is dependent <strong>on</strong> D<br />
being large since D/s determines k. Increasing d (thus increasing k) improves space<br />
resoluti<strong>on</strong>.
106 7. Spectral diagnostics: Intensity & Energy<br />
Energy resoluti<strong>on</strong><br />
C<strong>on</strong>sider two i<strong>on</strong>s at <strong>the</strong> same initial positi<strong>on</strong> s but with opposite velocities al<strong>on</strong>g <strong>the</strong><br />
spectrometer axis, equal in magnitude, <strong>the</strong>n <strong>the</strong> turn-around time is<br />
∆T = 1.02 2√ 2mU0<br />
qEs<br />
Then <strong>the</strong> maximum resolvable mass becomes, with D/s given by <strong>the</strong> focusing c<strong>on</strong>diti<strong>on</strong>:<br />
ME = 1<br />
� � √<br />
Ut k +1 k +1<br />
√ −<br />
4 U0 k k + √ �<br />
d<br />
k s<br />
To find <strong>the</strong> overall resoluti<strong>on</strong> a compromise between Ms <strong>and</strong> ME has to be found.<br />
Higherorderfocussingcanbeachievedbyhavingadditi<strong>on</strong>aldrift-secti<strong>on</strong>s<strong>and</strong>fields[162]<br />
<strong>–</strong> for those <strong>the</strong> flight times, etc. can still be calculated analytically[163].<br />
I<strong>on</strong> time-of-flight as a diagnostic<br />
A precise way of determining <strong>the</strong> charge to mass ratio of photo-i<strong>on</strong>s allows us to<br />
measure <strong>the</strong> phot<strong>on</strong>-energy. The photoi<strong>on</strong>izati<strong>on</strong> cross-secti<strong>on</strong> depends <strong>on</strong> phot<strong>on</strong><br />
energy, i.e. <strong>on</strong>e can measure it directly via <strong>the</strong> intensity of <strong>on</strong>e charged state; a much<br />
more stable measurement of<strong>the</strong>phot<strong>on</strong>energyis obtained via<strong>the</strong>ratiobetween singly<br />
<strong>and</strong> doubly charged i<strong>on</strong>s (or higher charge states). All this assumes that <strong>the</strong> crosssecti<strong>on</strong>s<br />
as functi<strong>on</strong>s of energy <strong>and</strong> charge state are known beforeh<strong>and</strong>. Moreover, <strong>the</strong><br />
phot<strong>on</strong>-density must be low enough to ensure that <strong>on</strong>ly single-phot<strong>on</strong> events occur <strong>–</strong><br />
something which is usually fulfilled for an unfocussed free electr<strong>on</strong> laser <strong>beam</strong>[153].<br />
Juranić et al. have used a Wiley-MacLaren spectrometer to measure <strong>the</strong> phot<strong>on</strong><br />
energyatFlashwithuncertaintiesstayingbelow1%upto150eVphot<strong>on</strong>energy[164].<br />
I<strong>on</strong> time-of-flight measurements can be shielded from perturbing magnetic fields<br />
easier, <strong>and</strong> provides higher countrates than <strong>the</strong> electr<strong>on</strong> measurements described below.<br />
The time-of-flight times are also l<strong>on</strong>ger since <strong>the</strong> particles have higher mass<br />
which makes <strong>the</strong> measurement less dem<strong>and</strong>ing with respect to <strong>the</strong> data-acquisiti<strong>on</strong>.<br />
Electr<strong>on</strong> time-of-flight<br />
The time-of-flight for <strong>the</strong> electr<strong>on</strong>s can be c<strong>on</strong>verted into kinetic energy with <strong>the</strong> aid<br />
of known i<strong>on</strong>izati<strong>on</strong> energies of atomic states <strong>–</strong> hence this is a spectroscopic measurement.<br />
If performed at high enough resoluti<strong>on</strong> electr<strong>on</strong> time-of-flight can thus give<br />
informati<strong>on</strong> <strong>on</strong> <strong>the</strong> spectral c<strong>on</strong>tent of <strong>the</strong> pulse as well as <strong>the</strong> mean energy. Potentially<br />
this spectrum also give access to <strong>the</strong> pulse length[165] as discussed in chapter 9.<br />
This allows for measurement of <strong>the</strong> phot<strong>on</strong>-energy <strong>and</strong> <strong>the</strong> fluctuati<strong>on</strong>s of it, as<br />
have been d<strong>on</strong>e near 93 eV at Flash[150]. The resoluti<strong>on</strong> in <strong>the</strong> spectra for <strong>the</strong> He<br />
1s photoelectr<strong>on</strong> line was about 100 meV.<br />
The limitati<strong>on</strong> of this photo-electr<strong>on</strong> spectroscopic measurement is <strong>the</strong> relatively<br />
low countrate (in <strong>the</strong> order of thous<strong>and</strong>s of electr<strong>on</strong>s per pulse). The kinetic energy<br />
of <strong>the</strong> electr<strong>on</strong>s is also not invariant with changing intensity of <strong>the</strong> free electr<strong>on</strong><br />
laser <strong>beam</strong>, where <strong>the</strong> attractive forced from <strong>the</strong> positively charged i<strong>on</strong>s cases <strong>the</strong><br />
kinetic energy to be lowered for <strong>the</strong> electr<strong>on</strong>s <strong>–</strong> which, if not accounted for, induces<br />
an apparent decrease in phot<strong>on</strong>-energy with increasing phot<strong>on</strong>-densities.
7.3. Phot<strong>on</strong>-energy 107<br />
However, <strong>the</strong> lower cross-secti<strong>on</strong> at higher energies lowers <strong>the</strong> Coulomb attracti<strong>on</strong><br />
betweeni<strong>on</strong>s<strong>and</strong>electr<strong>on</strong>s, since<strong>the</strong>numberofelectr<strong>on</strong>-i<strong>on</strong>pairs(forsingle-i<strong>on</strong>ziati<strong>on</strong><br />
events) is:<br />
Nparis = Nphot<strong>on</strong>s ·ngas ·σgas ·ℓ (7.5)<br />
where ℓ is <strong>the</strong> length of <strong>the</strong> interacti<strong>on</strong> regi<strong>on</strong> <strong>and</strong> n = p/kBT for an ideal gas. The<br />
n<strong>on</strong>-ideality of <strong>the</strong> gas can be accounted for via a correcti<strong>on</strong> using <strong>the</strong> mean-free<br />
path[150].<br />
For higher phot<strong>on</strong>-energies thus, electr<strong>on</strong> time-of-flight measurements can be a<br />
viable opti<strong>on</strong> for determining <strong>the</strong> phot<strong>on</strong>-energy <strong>and</strong> its fluctuati<strong>on</strong>s.
108 7. Spectral diagnostics: Intensity & Energy<br />
Summary<br />
• The <strong>beam</strong> energy (or intensity) is a critical parameter for user<br />
experiments <strong>and</strong> o<strong>the</strong>r diagnostics.<br />
• Gas m<strong>on</strong>itor detectors analyze <strong>the</strong> total yield occurring from<br />
photoi<strong>on</strong>izati<strong>on</strong> (which is proporti<strong>on</strong>al to <strong>the</strong> <strong>beam</strong> energy) of<br />
a target gas by accelerating <strong>the</strong>m in an electric (<strong>and</strong> possibly<br />
an magnetic field). This is a diagnostic that is transparent.<br />
• Ano<strong>the</strong>r transparent diagnostic is photoluminescence measurements<br />
of, for instance, nitrogen gas.<br />
• Calorimeters (Radiometers) is a measurement that gives <strong>the</strong><br />
average intensity of <strong>the</strong> pulses in a very exact manner. This<br />
is an opaque diagnostic which can also be used to calibrate<br />
o<strong>the</strong>r intensity diagnostics.<br />
• Bolometers provides a measurement of <strong>the</strong> <strong>beam</strong> energy over<br />
a large phot<strong>on</strong> range <strong>–</strong> for instance with 8% error at 8.3 keV<br />
phot<strong>on</strong> energy at <strong>the</strong> Lcls.<br />
• Diodes have shown to have ra<strong>the</strong>r large errors when used at<br />
free electr<strong>on</strong> laser, e.g. 30% at <strong>the</strong> Scss.<br />
• Bolometers <strong>and</strong> diodes are opaque diagnostics <strong>and</strong> thus require<br />
splitting or a transparent user experiment.<br />
• X-ray spectrometry measures <strong>the</strong> dispersed fel <strong>beam</strong> from a<br />
(VLS) diffractive grating. Thus obtaining <strong>the</strong> full spectrum<br />
of <strong>the</strong> free electr<strong>on</strong> laser <strong>beam</strong> <strong>on</strong> a shot to shot basis.<br />
• I<strong>on</strong> time-of-flight measurements diagnoses <strong>the</strong> phot<strong>on</strong>-energy<br />
of <strong>the</strong> <strong>beam</strong> with relatively small errors <strong>–</strong> assuming that <strong>the</strong><br />
cross-secti<strong>on</strong>s for <strong>the</strong> i<strong>on</strong>ized gas is known as a functi<strong>on</strong> of<br />
energy <strong>and</strong> <strong>the</strong> various charged states.<br />
• Electr<strong>on</strong> time-of-flight can provide a measurement of <strong>the</strong> spectrum<br />
of <strong>the</strong> pulse <strong>and</strong> provides a way of discerning <strong>the</strong> fluctuati<strong>on</strong>s<br />
in phot<strong>on</strong>-energy.<br />
• Electr<strong>on</strong> <strong>and</strong> i<strong>on</strong> time-of-flight measurements that are transparent<br />
to <strong>the</strong> user’s experiments.<br />
• Time-of-flight measurements utilize photoi<strong>on</strong>izati<strong>on</strong> for which<br />
<strong>the</strong> cross-secti<strong>on</strong>s drops fast after 100-200 eV <strong>–</strong> i.e. for higher<br />
phot<strong>on</strong>-energies <strong>the</strong>y may be impractical due to low countrates.
8. Beam cross-secti<strong>on</strong> diagnostics<br />
The material presented here in this chapter is adapted from ”Survey of diagnostic<br />
techniques for measuring <strong>the</strong> <strong>beam</strong> cross-secti<strong>on</strong> of ultra-short phot<strong>on</strong><br />
pulses” by M. A. Bowler, A. J. Glees<strong>on</strong> <strong>and</strong> M. D. Roper. Iruvx WP7, 2010<br />
by A. Lindblad.<br />
8.1 Introducti<strong>on</strong><br />
By measuring <strong>the</strong> profile of <strong>the</strong> generated phot<strong>on</strong>-<strong>beam</strong> many important parameters<br />
important for <strong>the</strong> <strong>beam</strong> <strong>transport</strong> towards <strong>the</strong> experiments can be learned. The<br />
<strong>beam</strong>-profile is also an important diagnostic for <strong>the</strong> machine <strong>and</strong> as an parameter for<br />
experiments (e.g. <strong>the</strong> spot-size determines <strong>the</strong> energy density at <strong>the</strong> experiment).<br />
The specific informati<strong>on</strong> that is required is:<br />
• The transverse intensity distributi<strong>on</strong> of <strong>the</strong> pulse <strong>–</strong> allowing <strong>the</strong> source size,<br />
positi<strong>on</strong> <strong>and</strong> quality factor (M 2 ) to be calculated from <strong>the</strong> sec<strong>on</strong>d moment 1 .<br />
• The centroid (first moment) of <strong>the</strong> transverse pulse profile <strong>–</strong> giving <strong>beam</strong> positi<strong>on</strong><br />
<strong>and</strong> (in combinati<strong>on</strong> with a sec<strong>on</strong>d measurement of <strong>the</strong> same pulse at<br />
different l<strong>on</strong>gitudinal distance) <strong>the</strong> <strong>beam</strong> angle.<br />
• The pulse wavefr<strong>on</strong>t <strong>–</strong> giving a complete descripti<strong>on</strong> of <strong>the</strong> spatial properties of<br />
<strong>the</strong> <strong>beam</strong>.<br />
• The focused spot size of <strong>the</strong> <strong>beam</strong> <strong>–</strong> critical for optimizing adaptive mirrors to<br />
give <strong>the</strong> best focus<strong>and</strong> for achieving high fluences for n<strong>on</strong>-linear studies.<br />
The ideal cross-secti<strong>on</strong> diagnostic<br />
Any measurement that gives a full <strong>beam</strong> profile can be used to calculate <strong>the</strong> <strong>beam</strong><br />
centroid but a measurement that gives <strong>on</strong>ly centroid informati<strong>on</strong> gives no profile<br />
informati<strong>on</strong>. Centroiding measurementsare never<strong>the</strong>less useful where <strong>the</strong>y are less<br />
1 The quality factor for a diffracti<strong>on</strong> limited gaussian phot<strong>on</strong> <strong>beam</strong> at wavelength lambda is<br />
λ/π. For a real <strong>beam</strong> <strong>the</strong> product of <strong>the</strong> minimum waist-size of <strong>the</strong> <strong>beam</strong> with <strong>the</strong> divergence of<br />
<strong>the</strong> <strong>beam</strong> in <strong>the</strong> far field is called <strong>the</strong> <strong>beam</strong> parameter product (B<strong>PP</strong>). The ratio between <strong>the</strong> B<strong>PP</strong><br />
<strong>and</strong> λ/π is <strong>the</strong> quality measure M 2 . For a diffracti<strong>on</strong> limited <strong>beam</strong> this ratio is unity; for real<br />
<strong>beam</strong>s this measure is larger than unity.<br />
109
110 8. Beam cross-secti<strong>on</strong> diagnostics<br />
invasive or can give pulse by pulse informati<strong>on</strong>. For a free electr<strong>on</strong> laser source, <strong>the</strong><br />
ideal diagnostic would have <strong>the</strong> following properties:<br />
• A sub-µm spatial resoluti<strong>on</strong> to allow <strong>the</strong> focused <strong>beam</strong> to be measured.<br />
• A field of view of ∼ 1 cm to allow <strong>the</strong> unfocused <strong>beam</strong> to be measured.<br />
• N<strong>on</strong>-invasive <strong>–</strong> give negligible disrupti<strong>on</strong> to <strong>the</strong> <strong>beam</strong>.<br />
• Sensitive <strong>–</strong> to allow a single pulse to be measured.<br />
• Wide dynamic range with linear resp<strong>on</strong>se <strong>–</strong> to measure attenuated <strong>and</strong> fullpower<br />
<strong>beam</strong>s, focused <strong>and</strong> unfocused, fundamental <strong>and</strong> harm<strong>on</strong>ics without damage,<br />
or excessive noise.<br />
• Large b<strong>and</strong>width <strong>–</strong> to measure every pulse up to MHz repetiti<strong>on</strong> rates in real<br />
time.<br />
• Broadb<strong>and</strong> <strong>–</strong> work at THz/IR or from <strong>the</strong> VUV to hard X-rays.<br />
• Spectrally discriminating <strong>–</strong> to separate signals from e.g. fundamental <strong>and</strong> harm<strong>on</strong>ics.<br />
The numberof <strong>the</strong>seproperties thatagiven practical m<strong>on</strong>itor will needwill depend<br />
<strong>on</strong> <strong>the</strong>particular applicati<strong>on</strong> or locati<strong>on</strong> in <strong>the</strong>phot<strong>on</strong> <strong>transport</strong> system. For example,<br />
sub-µm resoluti<strong>on</strong> is <strong>on</strong>ly required to measure <strong>the</strong> size of <strong>the</strong> <strong>beam</strong> at a focus, it will<br />
not be necessary for a m<strong>on</strong>itor to be able to wavelength-discriminate if it is situated<br />
after a m<strong>on</strong>ochromator, <strong>and</strong> diagnostics situated after <strong>the</strong> experiment do not need to<br />
be n<strong>on</strong>-invasive.<br />
Distributi<strong>on</strong> of diagnostics al<strong>on</strong>g <strong>the</strong> <strong>beam</strong><br />
feedback<br />
to source<br />
Source<br />
On-line centroid m<strong>on</strong>itors for<br />
<strong>beam</strong> positi<strong>on</strong> <strong>and</strong> angle<br />
Pro�lin m<strong>on</strong>itors for<br />
quality factor analysis<br />
Centroid m<strong>on</strong>itors for<br />
mirror alignment<br />
Beamline optics<br />
Pro�ling m<strong>on</strong>itor for<br />
commisi<strong>on</strong>ing<br />
Focus spot-size<br />
m<strong>on</strong>itor<br />
Wavefr<strong>on</strong>t<br />
sensor<br />
Figure 8.1: A schematic <strong>on</strong> how to distribute various diagnostics to determin transverse <strong>beam</strong> properties.<br />
Figure 8.1 shows schematically how <strong>the</strong> various diagnostics might be distributed<br />
al<strong>on</strong>g a <strong>beam</strong>line. Before any optics it will be necessary to have n<strong>on</strong>-invasive (or<br />
minimally invasive) ”<strong>on</strong>-line” diagnostics that give at least <strong>beam</strong> positi<strong>on</strong> <strong>and</strong> angle<br />
informati<strong>on</strong> c<strong>on</strong>tinuously <strong>and</strong> individually for every pulse. These m<strong>on</strong>itors could<br />
be used in feedback c<strong>on</strong>trol of <strong>the</strong> machine to ensure <strong>the</strong> phot<strong>on</strong> <strong>beam</strong> is stable in<br />
positi<strong>on</strong> <strong>and</strong> angle. There should also be diagnostics that can give a full pulse profile<br />
at three or more positi<strong>on</strong>s such that <strong>the</strong> source positi<strong>on</strong> <strong>and</strong> size <strong>and</strong> <strong>beam</strong> quality<br />
factor M 2 <strong>and</strong> can be determined[166]. The main applicati<strong>on</strong> here would be during<br />
commissi<strong>on</strong>ing <strong>and</strong> so <strong>the</strong> m<strong>on</strong>itors could be invasive, though if that were case it
8.1. Introducti<strong>on</strong> 111<br />
would not be possible to calculate <strong>the</strong> quality factor for a single pulse. Therefore a<br />
n<strong>on</strong>-invasive measurement is preferred, but it need not work at <strong>the</strong> full rep rate of<br />
<strong>the</strong> free electr<strong>on</strong> laser since statistical methods can be used to infer <strong>the</strong> overall <strong>beam</strong><br />
quality.<br />
After each optical element a <strong>beam</strong> positi<strong>on</strong> m<strong>on</strong>itor is required to ensure <strong>the</strong> <strong>beam</strong><br />
alignment is correct. These might just give centroid informati<strong>on</strong> <strong>and</strong> may average<br />
over a number of pulses. Ideally, <strong>the</strong>y would be <strong>on</strong>-line so <strong>the</strong> <strong>beam</strong> stability can be<br />
c<strong>on</strong>stantly m<strong>on</strong>itored, though this may be unnecessary. Additi<strong>on</strong>al profiling m<strong>on</strong>itors<br />
will also be available specifically for commissi<strong>on</strong>ing <strong>and</strong> diagnosing problems; <strong>the</strong>se<br />
can be invasive.<br />
At <strong>the</strong> experiment it is necessary to determine <strong>the</strong> positi<strong>on</strong> <strong>and</strong> quality of <strong>the</strong> <strong>beam</strong><br />
focus to:<br />
• Ensure multiple <strong>beam</strong>s can be overlapped spatially<br />
• Optimise adaptive mirrors<br />
• Achieve <strong>the</strong> highest <strong>beam</strong> fluence<br />
• Positi<strong>on</strong> <strong>the</strong> sample at <strong>the</strong> focus<br />
It would generally be acceptable for <strong>the</strong>se measurements to be invasive since, with<br />
a stable source, <strong>the</strong>y would normally <strong>on</strong>ly be needed during commissi<strong>on</strong>ing <strong>and</strong> experimental<br />
set-up. Depending <strong>on</strong> need, <strong>the</strong> measurements could ei<strong>the</strong>r be averaged<br />
over many pulses (e.g. for positi<strong>on</strong>ing) or measure just a single pulse (e.g. focus quality).<br />
If a measure of every pulse is needed outside <strong>the</strong> realm of commissi<strong>on</strong>ing <strong>the</strong>n<br />
a n<strong>on</strong>invasive detector or a detector remote from <strong>the</strong> sample positi<strong>on</strong> is needed. The<br />
latter is quite easy with gas-phase experiments (which are almost transparent to <strong>the</strong><br />
<strong>beam</strong>) since <strong>the</strong> detector can be placed after <strong>the</strong> experiment. It would not be possible<br />
to measure <strong>the</strong> focus directly, so <strong>the</strong> wavefr<strong>on</strong>t would have to be measured <strong>and</strong><br />
reverse-propagated to rec<strong>on</strong>struct <strong>the</strong> <strong>beam</strong> focus.<br />
Direct measurement of <strong>the</strong> wavefr<strong>on</strong>t would be <strong>the</strong> optimal way to measure <strong>the</strong><br />
<strong>beam</strong> as it allows for simulated propagati<strong>on</strong> to arbitrary positi<strong>on</strong>s al<strong>on</strong>g <strong>the</strong> <strong>transport</strong><br />
path, e.g. back to <strong>the</strong> source. However, wavefr<strong>on</strong>t measurement is invasive <strong>and</strong> so<br />
cannot be a general ”<strong>on</strong>-line” diagnostic. Fur<strong>the</strong>rmore, accurate propagati<strong>on</strong> across<br />
an optical element requires detailed informati<strong>on</strong> <strong>on</strong> <strong>the</strong> element surface shape at a<br />
large range of spatial frequencies <strong>and</strong> thus <strong>the</strong> accuracy of any predicti<strong>on</strong> will fall as<br />
<strong>the</strong> simulati<strong>on</strong> traverses more optical elements.<br />
C<strong>on</strong>tent of this chapter<br />
In this chapter, a broad survey of <strong>the</strong> range of techniques that have been used to<br />
profile n<strong>on</strong>-visible phot<strong>on</strong> <strong>beam</strong>s is presented. In <strong>the</strong> VUV to X-ray range, most<br />
existing diagnostics have been developed for use <strong>on</strong> synchrotr<strong>on</strong> radiati<strong>on</strong> sources.<br />
The challenges <strong>the</strong>re tend to be ra<strong>the</strong>r different, <strong>and</strong> <strong>the</strong> techniques may not be easy<br />
to modify for free electr<strong>on</strong> laser use. Specific problems for FEL <strong>beam</strong>s include:<br />
• Damage from ablati<strong>on</strong> ra<strong>the</strong>r than high average power.<br />
• The need for pulse resolved ra<strong>the</strong>r than time averaged measurements.<br />
• The need to avoid <strong>beam</strong> disrupti<strong>on</strong> through coherent diffracti<strong>on</strong> effects.
112 8. Beam cross-secti<strong>on</strong> diagnostics<br />
It is worthwhile to describe briefly several comm<strong>on</strong> techniques that are used in <strong>the</strong><br />
diagnostics as follows:<br />
• Scanning <strong>–</strong> in which a scan through <strong>the</strong> <strong>beam</strong> secti<strong>on</strong> is made, recording <strong>the</strong><br />
intensity in a step-wise manner to build up <strong>the</strong> profile<br />
• Imaging <strong>–</strong> in which <strong>the</strong> entire intensity profile, in <strong>on</strong>e or two dimensi<strong>on</strong>s, is<br />
measured in <strong>on</strong>e shot<br />
• Sampling <strong>–</strong> in which a small part of <strong>the</strong> <strong>beam</strong> is extracted <strong>and</strong> <strong>the</strong> required<br />
informati<strong>on</strong> deduced from this whilst <strong>the</strong> bulk of <strong>the</strong> <strong>beam</strong> passes <strong>on</strong> to <strong>the</strong><br />
experiment<br />
• Replicating <strong>–</strong> in which <strong>the</strong> <strong>beam</strong> profile informati<strong>on</strong> is transferred to ano<strong>the</strong>r<br />
medium <strong>and</strong> that measured to give <strong>the</strong> actual profile.<br />
In some cases a mixture of <strong>the</strong>se techniques is used, for example in imaging a<br />
replica of <strong>the</strong> <strong>beam</strong>.<br />
In <strong>the</strong> THz <strong>and</strong> IR ranges, diagnostics at existing free electr<strong>on</strong> laser sources tend to<br />
belimitedtocharacterizing<strong>the</strong><strong>beam</strong>at<strong>the</strong>experimentra<strong>the</strong>rthanhavingdistributed<br />
diagnostics al<strong>on</strong>g <strong>the</strong> <strong>transport</strong> system. The available means of detecting IR <strong>and</strong> THz<br />
radiati<strong>on</strong> restrict <strong>the</strong> range of diagnostic techniques that can be applied, in particular<br />
because <strong>the</strong> l<strong>on</strong>g wavelength radiati<strong>on</strong> cannot directly i<strong>on</strong>ize materials. For <strong>the</strong> near<br />
<strong>and</strong> mid-IR, techniques can be adapted from <strong>the</strong> visible regime.<br />
In secti<strong>on</strong> 8.4 will be described those techniques that can give a profile of <strong>the</strong><br />
<strong>beam</strong> intensity. In some cases this will be al<strong>on</strong>g a single axis (or two axes with two<br />
instruments situated orthog<strong>on</strong>ally), <strong>and</strong> in o<strong>the</strong>rs a complete 2-dimensi<strong>on</strong>al map of<br />
<strong>the</strong> <strong>beam</strong> intensity will be recorded. Secti<strong>on</strong> 8.10 will describe those techniques that<br />
give <strong>on</strong>ly informati<strong>on</strong> about <strong>the</strong> positi<strong>on</strong> of <strong>the</strong> <strong>beam</strong> centroid (”centre of gravity”,<br />
or first moment, of <strong>the</strong> intensity). How <strong>the</strong> complete wavefr<strong>on</strong>t can be measured is<br />
described in secti<strong>on</strong> 8.11 <strong>and</strong> specific applicati<strong>on</strong>s of <strong>beam</strong> profiling to determine <strong>the</strong><br />
size <strong>and</strong> quality of <strong>the</strong> focused <strong>beam</strong> are described in secti<strong>on</strong> 8.8. Diagnostics for IR<br />
<strong>and</strong> THz wavelengths will be described collectively in secti<strong>on</strong> 8.12.<br />
8.2 Definiti<strong>on</strong>s<br />
In this chapter we will look into various schemes as how to determine <strong>the</strong> transverse<br />
(x,y) distributi<strong>on</strong> of phot<strong>on</strong>s in <strong>the</strong> <strong>beam</strong> 2 . Most of <strong>the</strong> methods also carry over to<br />
more applicati<strong>on</strong>s of particle <strong>beam</strong>s in general.<br />
Let us define <strong>the</strong> problem more specifically, c<strong>on</strong>sider <strong>the</strong> particle <strong>beam</strong> to have a<br />
Gaussian distributi<strong>on</strong> in <strong>the</strong> x,y plane orthog<strong>on</strong>al to <strong>the</strong> directi<strong>on</strong> of <strong>the</strong> <strong>beam</strong> (<strong>the</strong><br />
s directi<strong>on</strong>)<br />
N(x,y) ∝ 1<br />
e<br />
σxσy<br />
−1 2(x 2 /σx+y 2 /σy)<br />
Al<strong>on</strong>g <strong>the</strong> s-axis <strong>the</strong> distributi<strong>on</strong> is ideally a step functi<strong>on</strong>. The measurement of this<br />
profile will be covered more specifically in chapter 9.<br />
Various schemes can be envisi<strong>on</strong>ed <strong>on</strong> how to measure <strong>the</strong> profiles c<strong>on</strong>cerned, each<br />
with its own merits <strong>–</strong> as a first rough divisi<strong>on</strong> we can divide <strong>the</strong>m into invasive <strong>and</strong><br />
n<strong>on</strong>-invasive methods:<br />
2 Diagnostics c<strong>on</strong>cerning <strong>the</strong> l<strong>on</strong>gitudinal (s) extent of <strong>the</strong> pulses will be covered in chapter 9.
8.3. Direct imaging of <strong>the</strong> <strong>beam</strong> 113<br />
y<br />
x<br />
Figure 8.2: Projecti<strong>on</strong> of <strong>the</strong> spatial density distributi<strong>on</strong> in <strong>the</strong> x.y plane (left) <strong>and</strong> <strong>on</strong>to individual coordinateaxes<br />
(right).<br />
invasive <strong>–</strong> or direct measurements<br />
Direct imaging of <strong>the</strong> <strong>beam</strong><br />
Wire grids<br />
Scanning wires, slits, knife-edges, pin-holes<br />
n<strong>on</strong>-invasive <strong>–</strong> or in-direct measurements<br />
rest gas i<strong>on</strong>izati<strong>on</strong><br />
photo dissociati<strong>on</strong><br />
synchrotr<strong>on</strong> light<br />
Compt<strong>on</strong> scattering<br />
8.3 Direct imaging of <strong>the</strong> <strong>beam</strong><br />
The simplest way to image <strong>the</strong> transverse footprint of a phot<strong>on</strong> <strong>beam</strong> is to directly<br />
illuminate an array detector such as a CCD with <strong>the</strong> <strong>beam</strong>[167, 168]. Providing <strong>the</strong><br />
detector is sensitive to <strong>the</strong> phot<strong>on</strong> wavelength, a direct readout of <strong>the</strong> <strong>beam</strong> profile is<br />
achieved.<br />
If <strong>the</strong> array is two-dimensi<strong>on</strong>al, <strong>the</strong>n a complete transverse map of <strong>the</strong> <strong>beam</strong> can<br />
be recorded. The spatial resoluti<strong>on</strong> of a CCD detector is determined, in principle,<br />
by <strong>the</strong> photo-site size <strong>and</strong> spacing in <strong>the</strong> detector array. In practice this limit cannot<br />
be achieved due to diffusi<strong>on</strong>, where electr<strong>on</strong>s created in <strong>on</strong>e pixel are collected in an<br />
adjacent pixel.<br />
To record an image of every free electr<strong>on</strong> laser pulse individually, <strong>the</strong> frame rate<br />
of <strong>the</strong> camera must of course match <strong>the</strong> pulse repetiti<strong>on</strong> rate. Extremely high-speed<br />
cameras are available for optical imaging (e.g. 600,000 fps with <strong>the</strong> NAC Memrecam<br />
GX-8 3 ) <strong>and</strong> commercial high-speed X-ray imaging services are available (e.g. Speed<br />
Visi<strong>on</strong> Technologies Inc. offer frame rates of 1000 fps 4 ). Speeds for scientific applicati<strong>on</strong>s<br />
are typically much lower.<br />
3 www.nacinc.com<br />
4 www.speedvisi<strong>on</strong>tech.com/speedvisi<strong>on</strong>-x-ray.php<br />
s<br />
I<br />
I<br />
x<br />
y
114 8. Beam cross-secti<strong>on</strong> diagnostics<br />
For example, Princet<strong>on</strong> Instruments 5 manufacture<br />
CCD cameras for both direct <strong>and</strong> indirect (q.v.) X-ray<br />
imaging that have readout rates of 2 MHz or 100 kHz<br />
depending <strong>on</strong> <strong>the</strong> sensitivity <strong>and</strong> signal to noise ratio.<br />
This rate equates to roughly <strong>the</strong> rate at which a single<br />
pixel can be read out since all <strong>the</strong> data passes through<br />
a single serial register. Thus <strong>the</strong> frame rate depends<br />
<strong>on</strong> <strong>the</strong> number of pixels. They offer a 512 x 512 pixel<br />
camera (with 13 µm pixel spacing) which could thus<br />
be read out at <strong>on</strong>ly ∼ 7.5 fps.<br />
Never<strong>the</strong>less, it is clear that higher speeds are<br />
achievable, though <strong>the</strong> balance of sensitivity <strong>and</strong> noise<br />
needs to be c<strong>on</strong>sidered. We might <strong>the</strong>refore reas<strong>on</strong>ably<br />
expect to be able to record every pulse at repetiti<strong>on</strong><br />
rates of about 1 kHz. For single pulse imaging at repetiti<strong>on</strong><br />
rates above <strong>the</strong> detector frame rate, <strong>the</strong> camera<br />
would need to be gated to record just <strong>on</strong>e pulse in <strong>the</strong><br />
Figure 8.3: A typical scintillator<br />
screen setup.<br />
frame cycle. Gating at <strong>the</strong> nanosec<strong>on</strong>d level is available with optical cameras, but is<br />
presumably achieved using electro-optical shutters which are not available for X-rays.<br />
A mechanical shutter would be needed to pick just <strong>on</strong>e pulse <strong>and</strong> this would be also<br />
be challenging to design <strong>and</strong> synchr<strong>on</strong>ize.<br />
The high fluence of a free electr<strong>on</strong> laser pulse also raises significant c<strong>on</strong>cerns over<br />
ablati<strong>on</strong>, radiati<strong>on</strong> damage, <strong>and</strong> linearity / saturati<strong>on</strong> effects. The saturati<strong>on</strong> level<br />
is a compromise with spatial resoluti<strong>on</strong> since if <strong>the</strong> pixels are made smaller <strong>the</strong>n<br />
<strong>the</strong>y can hold less charge <strong>and</strong> will saturate earlier. In fact, CCD detectors are not<br />
often used to measure <strong>the</strong> direct <strong>beam</strong> <strong>on</strong> synchrotr<strong>on</strong> sources because <strong>the</strong>y saturate<br />
too easily. Fedotov in 2000[169] reported that an ”old” 1200LC1 type CCD would<br />
saturate with 500 phot<strong>on</strong>s at 10 keV compared with 5-50 phot<strong>on</strong>s for ”more modern”<br />
CCDs. Therefore, a c<strong>on</strong>venti<strong>on</strong>al CCD is limited to <strong>the</strong> direct measurement of <strong>on</strong>ly<br />
attenuatedorspatiallydilute<strong>beam</strong>s. Directdetecti<strong>on</strong>withsolid-state arraysoffers<strong>the</strong><br />
potential of energy discriminati<strong>on</strong>, which might allow <strong>the</strong> fundamental <strong>and</strong> harm<strong>on</strong>ics<br />
to be distinguished. However, this may <strong>on</strong>ly be possible if each pixel collects no more<br />
than <strong>on</strong>e phot<strong>on</strong>[167].<br />
Ano<strong>the</strong>r factor to c<strong>on</strong>sider is <strong>the</strong> wavelength sensitivity of <strong>the</strong> CCD. A st<strong>and</strong>ard<br />
fr<strong>on</strong>t illuminated CCD detector will be insensitive to VUV phot<strong>on</strong>s as <strong>the</strong>y cannot<br />
penetrate through <strong>the</strong> inactive layer <strong>on</strong> <strong>the</strong> detector surface. C<strong>on</strong>versely, <strong>the</strong> sensitivity<br />
can drop with harder x-rays as <strong>the</strong>y can pass straight through <strong>the</strong> depleti<strong>on</strong><br />
layer of <strong>the</strong> detector. Different types of CCD are thus needed for different parts of <strong>the</strong><br />
spectrum,for example ’back thinned’ for soft X-rays less than 2 keV, ordinary ’fr<strong>on</strong>t<br />
illuminated’ from 2 to 10 keV, <strong>and</strong> ’deep depleti<strong>on</strong>’ type for X-rays above 10 keV.<br />
Imaging a replica of <strong>the</strong> <strong>beam</strong><br />
A comm<strong>on</strong> approach for imaging techniques is to measure indirectly via <strong>the</strong> producti<strong>on</strong><br />
of a replica of <strong>the</strong> <strong>beam</strong>. One way of achieving this is by illuminating a luminescent<br />
screen with <strong>the</strong> <strong>beam</strong> <strong>and</strong> <strong>the</strong>n imaging <strong>the</strong> luminescence through a viewport<br />
<strong>on</strong> <strong>the</strong> vacuum vessel with an optical camera[170]. This allows for higher ultimate<br />
5 www.princet<strong>on</strong>instruments.com/products/xraycam/
8.3. Direct imaging of <strong>the</strong> <strong>beam</strong> 115<br />
Source<br />
pinhole array<br />
YAG<br />
Viewport<br />
Mirror<br />
Camera<br />
Beam profile<br />
Figure 8.4: The use of a YAG screen toge<strong>the</strong>r with a pinhole array for X-ray <strong>beam</strong> profiling as described by<br />
Bol<strong>and</strong> <strong>and</strong> co-workers.<br />
spatial resoluti<strong>on</strong> than with direct CCD imaging. The resoluti<strong>on</strong> is determined by <strong>the</strong><br />
quality <strong>and</strong> thickness of <strong>the</strong> screen, <strong>the</strong> magnificati<strong>on</strong> <strong>and</strong> aberrati<strong>on</strong>s of <strong>the</strong> camera<br />
optics, <strong>and</strong> <strong>the</strong> camera sensor resoluti<strong>on</strong>. The ultimate limit is set by diffracti<strong>on</strong> of<br />
<strong>the</strong> visible light through <strong>the</strong> camera optics, <strong>and</strong> is thus ∼ 0.5 µm. The viewport must<br />
be of high optical quality if it is not to degrade <strong>the</strong> image. On <strong>the</strong> Australian Light<br />
Source diagnostic <strong>beam</strong>line, Bol<strong>and</strong> et al. [170] placed a pinhole array before a YAG<br />
screen (Figure 8.4) so that several fully resolved images are recorded <strong>and</strong> this allows<br />
<strong>the</strong> <strong>beam</strong> divergence as well as <strong>the</strong> profile to be measured. This approach could be<br />
useful with a free electr<strong>on</strong> laser since it would simplify single-pulse measurement of<br />
<strong>the</strong> <strong>beam</strong> divergence.<br />
With traditi<strong>on</strong>al powder phosphors a grain size of c. 1 µm is available <strong>and</strong> <strong>the</strong> resoluti<strong>on</strong><br />
as defined by <strong>the</strong> line-spread functi<strong>on</strong> is approximately equal to <strong>the</strong> thickness<br />
of <strong>the</strong> phosphor layer[171]. But if <strong>the</strong> phosphor layer is made too thin (less than a<br />
few µm) <strong>the</strong>n <strong>the</strong> light yield decreases dramatically <strong>and</strong> performance is compromised.<br />
Optically transparent luminescent screens, or scintillators, are a better choice for<br />
achieving high spatial resoluti<strong>on</strong>. Since <strong>the</strong> camera is now focussed <strong>on</strong> a transparent<br />
screen, <strong>the</strong> screen thickness <strong>and</strong> depth of field of <strong>the</strong> camera optics play an important<br />
part in <strong>the</strong> resoluti<strong>on</strong>. The scintillators must <strong>the</strong>refore be thin, have a surface of high<br />
optical quality, <strong>and</strong> c<strong>on</strong>tain high Z elements to increase absorpti<strong>on</strong>. Cerium doped<br />
aluminum garnets are most often used. Koch et al. [171] used 5 µm YAG:Ce <strong>on</strong> 170<br />
µm undoped YAG crystal in combinati<strong>on</strong> with diffracti<strong>on</strong>-limited microscope objectives<br />
<strong>and</strong> achieved spatial resoluti<strong>on</strong>s of less than 1 µm in micro-imaging experiments<br />
at <strong>the</strong> ESRF. Tous et al. [172] achieved resoluti<strong>on</strong> of about 1 µm with an anode X-ray<br />
source using YAG:Ce <strong>and</strong> LuAG:Ce, both of 20 µm thickness.<br />
The b<strong>and</strong>width of such a system will be limited by <strong>the</strong> camera read-out rate <strong>and</strong><br />
ultimately by <strong>the</strong> decay time of <strong>the</strong> luminescent material. The decay time of some<br />
luminescent materials can be roughly 1 µs, but <strong>the</strong> visible luminescence from YAG:Ce<br />
is very fast at ∼ 70 ns[173] <strong>and</strong> is thus fast enough to resolve single pulses at even 1<br />
MHz. As discussed above, cameras with frame rates up to 600,000 Hz are available,<br />
though not with c<strong>on</strong>tinuous output at that rate. It would need to be checked that<br />
<strong>the</strong>y would have <strong>the</strong> sensitivity to record <strong>the</strong> luminescence from a single free electr<strong>on</strong><br />
laser pulse (<strong>the</strong> m<strong>on</strong>ochrome sensitivity of <strong>the</strong> Memrecam GX-8 referred to is 20,000<br />
ISO). With slower frame rates, it should be possible to select just <strong>on</strong>e pulse in <strong>the</strong><br />
frame cycle by gating <strong>the</strong> luminescence with a high-speed electro-optical shutter such<br />
as a Pockels cell. Clearly, <strong>the</strong> total number of phot<strong>on</strong>s collected from <strong>the</strong> screen in<br />
this mode will be low <strong>and</strong> so an image intensified camera may be required. These are
116 8. Beam cross-secti<strong>on</strong> diagnostics<br />
available commercially, for example <strong>the</strong> Lambert Instruments LI2CAM 6 ,which has a<br />
frame rate of just 15 fps but can be gated down to 2 ns.<br />
Itis also possible tocreate anelectr<strong>on</strong> replicaof<strong>the</strong>phot<strong>on</strong><strong>beam</strong> profilebydirectly<br />
illuminating a multichannel plate with <strong>the</strong> free electr<strong>on</strong> laser <strong>beam</strong>. A phosphor<br />
screen placed near <strong>the</strong> plate c<strong>on</strong>verts <strong>the</strong> electr<strong>on</strong>s to visible light whilst preserving<br />
<strong>the</strong> spatial origin of <strong>the</strong> electr<strong>on</strong>s, <strong>and</strong> <strong>the</strong> luminescence from <strong>the</strong> screen is imaged<br />
by a CCD camera. This approach was used by Yang et al. to image <strong>the</strong> profile of<br />
<strong>the</strong> X-ray pulses from a Compt<strong>on</strong> back-scattering source[174] (though <strong>the</strong> image was<br />
integrated over many pulses due to <strong>the</strong> very low intensity). The spatial resoluti<strong>on</strong><br />
will be determined by <strong>the</strong> channel pore size, which at 10 µm would give a similar<br />
resoluti<strong>on</strong> to direct CCD imaging. The sensitivity would be determined by <strong>the</strong> photoemissivity<br />
of <strong>the</strong> channel plate, which is dependent <strong>on</strong> wavelength. Coatings can be<br />
added to enhance <strong>the</strong> photoemissi<strong>on</strong> at l<strong>on</strong>g wavelengths. At shorter wavelengths,<br />
<strong>the</strong> efficiency drops as <strong>the</strong> X-rays are absorbed more in <strong>the</strong> bulk of <strong>the</strong> channel plate<br />
material. At very short wavelengths, <strong>the</strong> X-rays may penetrate through <strong>the</strong> pore walls<br />
<strong>and</strong> this will reduce <strong>the</strong> spatial resoluti<strong>on</strong>.<br />
The b<strong>and</strong>width will still be limited by <strong>the</strong> camera frame rate, but <strong>the</strong> ultimate<br />
limit will also be influenced by <strong>the</strong> time of <strong>the</strong> avalanching process in <strong>the</strong> pores,<br />
as well as <strong>the</strong> luminescence decay. The b<strong>and</strong>width could be greatly increased by<br />
replacing <strong>the</strong> phosphor screen <strong>and</strong> camera with an anode array. Assuming parallel<br />
readout of each anode, <strong>the</strong> detector resp<strong>on</strong>se could be reduced to <strong>the</strong> multichannel<br />
plate resp<strong>on</strong>se time, which could be in <strong>the</strong> nanosec<strong>on</strong>d regi<strong>on</strong>. This would allow every<br />
pulse to be measured, but <strong>the</strong> spatial resoluti<strong>on</strong> would be limited by <strong>the</strong> anode array<br />
size. Alternatively, <strong>the</strong> charge pulse from <strong>the</strong> multichannel plate as <strong>the</strong> phot<strong>on</strong> pulse<br />
strikes it could be used to trigger <strong>the</strong> gating of <strong>the</strong> camera to select a single pulse.<br />
This would obviate <strong>the</strong> need for synchr<strong>on</strong>izati<strong>on</strong> to <strong>the</strong> X-ray <strong>beam</strong> itself. If this is<br />
not possible, <strong>the</strong> timing trigger from <strong>the</strong> free electr<strong>on</strong> laser pulse could be used to<br />
gate <strong>the</strong> multichannel plate.<br />
A refinement of this approach would be to illuminate a photo-emissive material<br />
(e.g. a metal foil) <strong>and</strong> image <strong>the</strong> emitted photoelectr<strong>on</strong>s. A key requirement for this<br />
to work is preserving <strong>the</strong> spatial informati<strong>on</strong> encoded into <strong>the</strong> photoelectr<strong>on</strong>s whilst<br />
<strong>the</strong>y <strong>transport</strong>ed to <strong>the</strong> multichannel plate. Similar problems face <strong>the</strong> techniques<br />
described in secti<strong>on</strong>s 8.6 <strong>and</strong> 8.7.<br />
An imaging detector based <strong>on</strong> <strong>the</strong> photoc<strong>on</strong>ductive effect in Type IIa CVD diam<strong>on</strong>d<br />
has been developed at <strong>the</strong> APS byShu et al. [175]. This detector is an extensi<strong>on</strong><br />
of work d<strong>on</strong>e <strong>on</strong> quadrant detectors (q.v.). A 127 µm thick diam<strong>on</strong>d disc was patterned<br />
<strong>on</strong> both sides with sixteen 0.2 µm thick <strong>and</strong> 175 µm wide aluminum strips.<br />
The patterns <strong>on</strong> <strong>the</strong> two sides are orthog<strong>on</strong>al such that a 16 by 16 pixel array is<br />
created with 175 µm by 175 µm pixel size. The strips <strong>on</strong> <strong>on</strong>e side are c<strong>on</strong>nected to a<br />
bias supply via a 16-channel switch, whilst those <strong>on</strong> <strong>the</strong> o<strong>the</strong>r side are c<strong>on</strong>nected to<br />
sixteen discrete current amplifiers.<br />
The disc has a high transmissi<strong>on</strong> for hard X-rays (around 10 keV) <strong>and</strong> thus <strong>the</strong><br />
m<strong>on</strong>itor can be used <strong>on</strong>-line for c<strong>on</strong>stant <strong>beam</strong> m<strong>on</strong>itoring. When <strong>the</strong> X-ray <strong>beam</strong><br />
passes through <strong>the</strong> diam<strong>on</strong>d, <strong>the</strong> localized c<strong>on</strong>ductivity rises in proporti<strong>on</strong> to <strong>the</strong><br />
absorbed X-ray power. Thus, <strong>the</strong> current passing through <strong>the</strong> diam<strong>on</strong>d when <strong>the</strong> bias<br />
is applied is highest where <strong>the</strong> incident X-ray <strong>beam</strong> is most intense. In order to build<br />
up a two dimensi<strong>on</strong>al picture of <strong>the</strong> <strong>beam</strong> intensity profile, <strong>the</strong> bias is applied to each<br />
6 www.lambert-instruments.com
8.4. Scanning techniques 117<br />
strip <strong>on</strong> <strong>on</strong>e side in turn <strong>and</strong> <strong>the</strong> current from <strong>the</strong> sixteen strips <strong>on</strong> <strong>the</strong> o<strong>the</strong>r side<br />
recorded.<br />
The spatial resoluti<strong>on</strong> is naturally fairly low, but sufficient to give a true <strong>beam</strong><br />
profile assuming <strong>the</strong> <strong>beam</strong> is not highly structured <strong>and</strong> overlaps with enough of <strong>the</strong><br />
electrode strips. The b<strong>and</strong>width is limited by <strong>the</strong> need to apply <strong>the</strong> bias voltage to<br />
each strip in turn. Never<strong>the</strong>less, <strong>the</strong> data acquisiti<strong>on</strong> system was able to scan at 300<br />
to 3000 columns per sec<strong>on</strong>d (from 19 to 190 Hz). Of course, this still means that<br />
<strong>the</strong> system will give <strong>on</strong>ly aline profile <strong>and</strong> not a full image of a single free electr<strong>on</strong><br />
laser pulse; <strong>the</strong> electrode structure would have to be modified to give simultaneous<br />
readout of all 256 channels for single pulse image.<br />
Summary of imaging techniques<br />
All <strong>the</strong> imaging techniques described above are invasive. Direct imaging with a CCD<br />
<strong>and</strong> direct illuminati<strong>on</strong> of a micro-channel plate will stop <strong>the</strong> entire <strong>beam</strong> <strong>and</strong> so<br />
could <strong>on</strong>ly be used during commissi<strong>on</strong>ing or if <strong>the</strong> experiment is transparent (e.g. gas<br />
phase) so that <strong>the</strong> detector can be placed after <strong>the</strong> experiment. The o<strong>the</strong>r techniques<br />
could be made partially transparent. For example, hard X-rays could pass through a<br />
sufficiently thin luminescent screen without excessive loss. The luminescent intensity<br />
is proporti<strong>on</strong>al to <strong>the</strong> number of phot<strong>on</strong>s absorbed <strong>and</strong> so some losses are required for<br />
<strong>the</strong> detector to work. On <strong>the</strong> o<strong>the</strong>r h<strong>and</strong>, since photoemissi<strong>on</strong> is essentially a surface<br />
phenomen<strong>on</strong>, a very thin <strong>and</strong> thus highly transmitting foil would give <strong>the</strong> same signal<br />
as a thick <strong>on</strong>e. In any case, <strong>the</strong> disrupti<strong>on</strong> to a coherent free electr<strong>on</strong> laser <strong>beam</strong><br />
as it passes through a screen or foil would probably be unacceptable. There are also<br />
c<strong>on</strong>cerns over radiati<strong>on</strong> damage, ablati<strong>on</strong>,linearity <strong>and</strong> saturati<strong>on</strong> with high-fluence,<br />
ultra-short free electr<strong>on</strong> laser pulses. The risk of ablati<strong>on</strong> would need to be c<strong>on</strong>trolled<br />
by using <strong>the</strong>se techniques <strong>on</strong>ly where <strong>the</strong> <strong>beam</strong> is spatially dilute, <strong>and</strong> this might also<br />
be sufficient to prevent saturati<strong>on</strong> <strong>and</strong> n<strong>on</strong>-linear effects.<br />
The wavelength resp<strong>on</strong>se of <strong>the</strong> detectors needs to be c<strong>on</strong>sidered. It is obviously<br />
desirable for <strong>the</strong> detector to work over as wide a range of phot<strong>on</strong> energies as possible.<br />
However, a broad-b<strong>and</strong> resp<strong>on</strong>se can cause problems if it is very n<strong>on</strong>-linear. For<br />
example, photo-emissi<strong>on</strong> yield is much greater at VUV than X-ray wavelengths <strong>and</strong><br />
this can distort an X-ray <strong>beam</strong> profile if <strong>the</strong>re is low level VUV light with a different<br />
spatial pattern to <strong>the</strong> X-ray profile.<br />
8.4 Scanning techniques<br />
Scanning wire<br />
This is perhaps, at a glance, <strong>the</strong> simplest soluti<strong>on</strong> to <strong>the</strong> present problem: scan a<br />
wire through <strong>the</strong> <strong>beam</strong>. A thin metal wire (such as tungsten) is step-scanned through<br />
<strong>the</strong> <strong>beam</strong> <strong>and</strong> <strong>the</strong> <strong>beam</strong> intensity deduced from, for example, <strong>the</strong> drain current in<br />
<strong>the</strong> wire[176], <strong>the</strong> intensity of electr<strong>on</strong>s emitted from <strong>the</strong> wire, or <strong>the</strong> intensity of<br />
scattered or fluorescent light from <strong>the</strong> wire, all of which should be proporti<strong>on</strong>al to <strong>the</strong><br />
<strong>beam</strong> intensity hitting <strong>the</strong> wire. The signal at each positi<strong>on</strong> in <strong>the</strong> scan is <strong>the</strong> result<br />
of an integrati<strong>on</strong> of <strong>the</strong> <strong>beam</strong> intensity al<strong>on</strong>g <strong>the</strong> illuminated length of <strong>the</strong> wire, i.e.<br />
in <strong>the</strong> directi<strong>on</strong> orthog<strong>on</strong>al to <strong>the</strong> scan. The measured profile is thus a c<strong>on</strong>voluti<strong>on</strong><br />
of <strong>the</strong> actual <strong>beam</strong> profile <strong>and</strong> <strong>the</strong> illuminated length of <strong>the</strong> wire. This means <strong>the</strong>
118 8. Beam cross-secti<strong>on</strong> diagnostics<br />
scanningxwires.eps<br />
Figure 8.5: Working principle of a scanning crossed-wire m<strong>on</strong>itor, after Ref. [178].<br />
measured profile will be distorted when <strong>the</strong> orthog<strong>on</strong>al <strong>beam</strong> secti<strong>on</strong> is not uniform<br />
such that <strong>the</strong> illuminated length varies through <strong>the</strong> scan[177]. This will occur, for<br />
example when <strong>the</strong> wire is tilted relative to an elliptical <strong>beam</strong>.<br />
The resoluti<strong>on</strong> of <strong>the</strong> wire type m<strong>on</strong>itor depends <strong>on</strong> <strong>the</strong> step resoluti<strong>on</strong> of <strong>the</strong><br />
scanning mechanism, <strong>the</strong> diameter of <strong>the</strong> wire relative to <strong>the</strong> <strong>beam</strong> width, <strong>and</strong> <strong>the</strong><br />
straightness <strong>and</strong> uniformity of <strong>the</strong> wire. Radiati<strong>on</strong> scattering from <strong>the</strong> edges of <strong>the</strong><br />
wire will degrade <strong>the</strong> resoluti<strong>on</strong>. Thin wires give higher resoluti<strong>on</strong>, but are harder to<br />
cool. If a wire gets too hot, <strong>the</strong>rmi<strong>on</strong>ic emissi<strong>on</strong> can occur even before melting <strong>and</strong><br />
this will distort <strong>the</strong> profile when electr<strong>on</strong> detecti<strong>on</strong> is used to infer <strong>the</strong> <strong>beam</strong> intensity.<br />
Scanning crossed wires<br />
Two wires are crossed at 90 ◦ <strong>and</strong> scanned through <strong>the</strong> <strong>beam</strong> al<strong>on</strong>g a directi<strong>on</strong> at 45 ◦<br />
to each wire <strong>–</strong> see Figure 8.5. In this way, two orthog<strong>on</strong>al profiles can be derived in<br />
<strong>on</strong>e scan, but detecti<strong>on</strong> is limited to drain current to allow <strong>the</strong> signals to be distinguished.<br />
Each profile is still an integrati<strong>on</strong> in <strong>the</strong> orthog<strong>on</strong>al directi<strong>on</strong>.The instrument<br />
developed by Fajardo <strong>and</strong> Ferrer[178] has a reported resoluti<strong>on</strong> of better than 5 µm,<br />
limited by mechanical reproducibility <strong>and</strong> vibrati<strong>on</strong> in <strong>the</strong> scanning mechanism. The<br />
finite resp<strong>on</strong>se time of <strong>the</strong> amplifiers results in a difference in apparent positi<strong>on</strong> <strong>on</strong><br />
forward <strong>and</strong> backward scans if <strong>the</strong> scan speed is too high; this effect was not observed<br />
at a speed below ∼ 1 mm/sec.<br />
Scanning slit<br />
A fine slit is scanned through <strong>the</strong> <strong>beam</strong> <strong>and</strong> <strong>the</strong> transmitted intensity measured by<br />
a detector (e.g. a photodiode, a micro channel plate, or a luminescent screen <strong>and</strong><br />
video camera combinati<strong>on</strong>)[179].Again, <strong>the</strong> intensity in <strong>the</strong> orthog<strong>on</strong>al directi<strong>on</strong> is<br />
integrated by <strong>the</strong> length of <strong>the</strong> slit. The result is analogous to <strong>the</strong> scanning wire<br />
but <strong>the</strong> technique is more invasive, though easier to cool. Scanning slits are however
8.4. Scanning techniques 119<br />
useful for probing aperture related aberrati<strong>on</strong>s in optical systems, though <strong>the</strong> <strong>beam</strong><br />
spread after <strong>the</strong> slit caused by diffracti<strong>on</strong> can c<strong>on</strong>fuse <strong>the</strong> results.<br />
Scanning pinhole<br />
A refinement of <strong>the</strong> scanning slit in which <strong>the</strong> <strong>beam</strong> profile is not integrated al<strong>on</strong>g <strong>the</strong><br />
directi<strong>on</strong> orthog<strong>on</strong>al to <strong>the</strong> scan directi<strong>on</strong> <strong>and</strong> so true line profiles through <strong>the</strong> <strong>beam</strong><br />
can be made. With two-axis c<strong>on</strong>trol of <strong>the</strong> pin-hole moti<strong>on</strong>, line profiles in arbitrary<br />
directi<strong>on</strong>s through <strong>the</strong> <strong>beam</strong> can be made. The pin-hole is comm<strong>on</strong>ly achieved by<br />
using ei<strong>the</strong>r two slits crossed at 90 ◦ to make a rectangular pinhole or with four jaws<br />
making <strong>the</strong> two orthog<strong>on</strong>al slits. The advantage of <strong>the</strong> latter is that <strong>the</strong> size of <strong>the</strong><br />
pin-hole can be easily changed, though a4-axis driveis needed<strong>and</strong> verysmall pinholes<br />
are not realizable because of diffracti<strong>on</strong> at each jaw <strong>and</strong> <strong>the</strong> necessary l<strong>on</strong>gitudinal<br />
separati<strong>on</strong> between <strong>the</strong>m.<br />
Scanning knife-edge<br />
A blade is scanned through <strong>the</strong> <strong>beam</strong> such that it successively obscures (or reveals)<br />
more <strong>and</strong> more of <strong>the</strong> <strong>beam</strong>. The intensity passing <strong>the</strong> blade is recorded by a detector<br />
such as a photodiode or mictro-channel plate[180]. The recorded signal is <strong>the</strong> integral<br />
of <strong>the</strong> profile in <strong>the</strong> scan directi<strong>on</strong> <strong>and</strong> <strong>the</strong> deduced profile is integrated in <strong>the</strong> orthog<strong>on</strong>al<br />
directi<strong>on</strong>. If <strong>the</strong> profile is being measured at a focus, a wire of diameter greater<br />
than <strong>the</strong> <strong>beam</strong> size can be used instead of an edge[181]. This has <strong>the</strong> advantage that<br />
it is easy to achieve a smooth edge with a wire than with a blade.<br />
Summary of scanning techniques<br />
The most important drawback when applying <strong>the</strong>se techniques to a free electr<strong>on</strong><br />
lasersource is that <strong>the</strong>y cannot be used to measure a single pulse due to <strong>the</strong> step-wise<br />
nature of <strong>the</strong> measurement. In additi<strong>on</strong>, <strong>the</strong> techniques are invasive (i.e. disruptive<br />
to <strong>the</strong> <strong>beam</strong>), especially as <strong>the</strong> coherent nature of <strong>the</strong> phot<strong>on</strong> <strong>beam</strong> will mean <strong>the</strong><br />
disrupti<strong>on</strong> will be enhanced due to diffracti<strong>on</strong> effects. Therefore, in <strong>the</strong> c<strong>on</strong>text of a<br />
free electr<strong>on</strong> laser source, <strong>the</strong>se techniques are useful nei<strong>the</strong>r during commissi<strong>on</strong>ing<br />
(when <strong>the</strong> invasive nature would not be an issue but <strong>the</strong> inability to resolve single<br />
pulses is), nor during operati<strong>on</strong> (as <strong>the</strong> invasive nature makes <strong>the</strong>m unsuitable as <strong>on</strong>line<br />
m<strong>on</strong>itors). In additi<strong>on</strong>, <strong>the</strong> high pulse intensity of an unattenuated free electr<strong>on</strong><br />
laser fundamental gives serious c<strong>on</strong>cern over <strong>the</strong> damage to <strong>the</strong> scanning elements.<br />
With a free electr<strong>on</strong> laser source, <strong>the</strong>re are two modes of damage, viz. melting <strong>and</strong><br />
ablati<strong>on</strong>. At low repetiti<strong>on</strong> rates (less than 1 kHz) melting is unlikely as <strong>the</strong> average<br />
power is less than in a synchrotr<strong>on</strong> <strong>beam</strong>, but ablati<strong>on</strong> is likely unless <strong>the</strong> pulses<br />
are attenuated (for example with a gas absorber, as discussed above in chapter 4 see<br />
page 69). Without attenuati<strong>on</strong>, <strong>the</strong>re is also <strong>the</strong> possibility of reaching n<strong>on</strong>-linear<br />
regimes where <strong>the</strong> measured signal is no l<strong>on</strong>ger proporti<strong>on</strong>al to <strong>the</strong> incident intensity,<br />
e.g. through space charge effects.
120 8. Beam cross-secti<strong>on</strong> diagnostics<br />
8.5 I<strong>on</strong>izati<strong>on</strong> <strong>beam</strong>profile detectors<br />
The <strong>beam</strong>-profile from a high-energy <strong>beam</strong> of particles (phot<strong>on</strong>s, electr<strong>on</strong>s, neutr<strong>on</strong>s...)<br />
can be measured by detecting <strong>the</strong> i<strong>on</strong>s (or electr<strong>on</strong>s) resultant from i<strong>on</strong>izati<strong>on</strong><br />
events occurring in a residual gas intersecting <strong>the</strong> <strong>beam</strong>. By accelerating <strong>the</strong><br />
i<strong>on</strong>s in a homogeneous electric field towards a multichannel plate detector (see Figure<br />
8.6) combined with a positi<strong>on</strong> sensitive read-out anode an image of <strong>the</strong> <strong>beam</strong> can<br />
be recorded.<br />
From Equati<strong>on</strong> 2.5 <strong>on</strong>e would expect <strong>the</strong> i<strong>on</strong>s to get accelerated in straight lines<br />
towards <strong>the</strong> detector since <strong>the</strong> force <strong>on</strong> <strong>the</strong> charged particle is directly proporti<strong>on</strong>al<br />
to <strong>the</strong> electric field strength; <strong>the</strong> i<strong>on</strong>ized particles, however, will have velocity comp<strong>on</strong>ents<br />
in o<strong>the</strong>r directi<strong>on</strong>s besides normal to <strong>the</strong> detector <strong>–</strong> this will give rise to a<br />
broadening of <strong>the</strong> profile which can be minimized by applying a str<strong>on</strong>ger electric field.<br />
Amicrochannel plate detector also haveafiniteresoluti<strong>on</strong> since <strong>the</strong>actual channels<br />
are in <strong>the</strong> order of 10 µm in diameter. There is also a possibility that several channels<br />
detect a single event which will blur <strong>the</strong> image fur<strong>the</strong>r.<br />
Anode<br />
I<strong>on</strong><br />
MCP 1<br />
MCP 2<br />
Output signal<br />
Figure 8.6: Microchannel plates mounted in a chevr<strong>on</strong> geometry with voltages coupled to detect i<strong>on</strong>s. When an<br />
i<strong>on</strong> hit a microchannel plate it gives rise to several sec<strong>on</strong>dary i<strong>on</strong>izati<strong>on</strong>s <strong>–</strong> <strong>the</strong> electr<strong>on</strong>s from those i<strong>on</strong>izati<strong>on</strong>s,<br />
in turn, gives rise to o<strong>the</strong>r sec<strong>on</strong>dary electr<strong>on</strong>s, thus an amplificati<strong>on</strong> occurs. The resulting charge cloud hits<br />
<strong>the</strong> anode <strong>and</strong> gives rise to an electric current which can be read out. An alternative to this scheme exist where<br />
a phosphor plate is mounted behind <strong>the</strong> anode which can be read out optically with, for instance, an CCD<br />
camera.<br />
At Flash this type of <strong>beam</strong> positi<strong>on</strong> m<strong>on</strong>itor, using a phosphor screen toge<strong>the</strong>r<br />
with a camera, gives a reported spatial resoluti<strong>on</strong> of c. 50 µm[182]. Obviously this<br />
type of detector also gives <strong>the</strong> positi<strong>on</strong> of <strong>the</strong> <strong>beam</strong>.<br />
8.6 Imaging i<strong>on</strong> chambers<br />
An established technique for profiling particle <strong>beam</strong>s in high-energy accelerators is to<br />
image <strong>the</strong> <strong>beam</strong> path through <strong>the</strong> residual gas (or gas added at a very low pressure<br />
gas, i.e. less than 10 -5 mbar) in <strong>the</strong> <strong>beam</strong> <strong>transport</strong> system. As <strong>the</strong> <strong>beam</strong> passes<br />
through <strong>the</strong> gas, it will i<strong>on</strong>ize it <strong>and</strong> <strong>the</strong> i<strong>on</strong> density is proporti<strong>on</strong>al to <strong>the</strong> particle<br />
density in <strong>the</strong> <strong>beam</strong>. Thus, if <strong>the</strong> i<strong>on</strong>s can be channelled linearly to a luminescent<br />
screen with a uniform electric field, <strong>the</strong> intensity of luminescence is also proporti<strong>on</strong>al<br />
to particle density <strong>and</strong> <strong>the</strong> <strong>beam</strong> profile can be recorded with a video camera. The i<strong>on</strong>
8.6. Imaging i<strong>on</strong> chambers 121<br />
signal is usually amplified by generating multiple electr<strong>on</strong>s for each incident i<strong>on</strong> with<br />
a micro-channel plate placed in fr<strong>on</strong>t of <strong>the</strong> screen. The benefit of this system is that,<br />
when using just <strong>the</strong> residual gas, <strong>the</strong> m<strong>on</strong>itor is completely n<strong>on</strong>-invasive. However,<br />
<strong>the</strong> achievable resoluti<strong>on</strong> has tended to be ra<strong>the</strong>r poor, of <strong>the</strong> 1 mm. This is mainly<br />
due toperturbati<strong>on</strong> of <strong>the</strong> drifting i<strong>on</strong>s by<strong>the</strong> electric field of <strong>the</strong> particle <strong>beam</strong>, which<br />
causes <strong>the</strong>mtospread awayfrom <strong>the</strong>regi<strong>on</strong>s ofhighi<strong>on</strong> density,<strong>and</strong>sobroadening<strong>the</strong><br />
recorded image. I<strong>on</strong>s, ra<strong>the</strong>r than electr<strong>on</strong>s, are usually detected since <strong>the</strong>ir greater<br />
mass means <strong>the</strong>y are less susceptible to <strong>the</strong>se perturbati<strong>on</strong>s. Never<strong>the</strong>less, Fischer<br />
<strong>and</strong> Koopman were able to improve <strong>the</strong> resoluti<strong>on</strong> by measuring <strong>the</strong> electr<strong>on</strong>s[183].<br />
They achieved this by placing <strong>the</strong> i<strong>on</strong> chamber in a uniform magnetic field parallel to<br />
<strong>the</strong> electr<strong>on</strong> trajectories. The emitted electr<strong>on</strong>s will precess about <strong>the</strong> field <strong>and</strong> so can<br />
be channelled more linearly. The resoluti<strong>on</strong> was improved such that an actual <strong>beam</strong><br />
width of 1 mm RMS could be measured without instrumental broadening (implying<br />
a resoluti<strong>on</strong> not worse than a few hundred µm).<br />
The same measurement principle can be applied to an X-ray <strong>beam</strong>, with which<br />
<strong>the</strong>re is <strong>the</strong> advantage that <strong>the</strong> <strong>beam</strong> will not perturb <strong>the</strong> electr<strong>on</strong>s <strong>and</strong> i<strong>on</strong>s directly<br />
<strong>on</strong>ce created. However, preserving accurately <strong>the</strong>ir spatial point of origin is still<br />
difficult. The approach used by Ioudin et al. [184] is to encode <strong>the</strong> point of <strong>the</strong> spatial<br />
origin of <strong>the</strong> i<strong>on</strong>s <strong>on</strong>to <strong>the</strong>ir kinetic energy by accelerating <strong>the</strong>m with an extracti<strong>on</strong><br />
field <strong>–</strong> see Figure 8.7.<br />
The fur<strong>the</strong>r <strong>the</strong> i<strong>on</strong>s are from <strong>the</strong> cathode when created, <strong>the</strong> greater <strong>the</strong> kinetic energy<br />
<strong>the</strong>y gain during <strong>the</strong> accelerati<strong>on</strong>. The i<strong>on</strong>s are accelerated towards <strong>the</strong> entrance<br />
slit of an electrostatic energy analyzer, which disperses <strong>the</strong>m in kinetic energy <strong>on</strong>to a<br />
micro-channel plate. Thus positi<strong>on</strong> al<strong>on</strong>g <strong>the</strong> plate corresp<strong>on</strong>ds to spatial coordinate<br />
of i<strong>on</strong> generati<strong>on</strong>. The multi-channel plate amplifies <strong>the</strong> i<strong>on</strong> signal, which is imaged<br />
using a phosphor screen <strong>and</strong> video camera.<br />
This instrument, called <strong>the</strong> Beam Cross-secti<strong>on</strong> Image Detector (BCID), gives a<br />
profile of <strong>the</strong> <strong>beam</strong> in two axes <strong>–</strong> <strong>the</strong> secti<strong>on</strong> al<strong>on</strong>g x is mapped al<strong>on</strong>g <strong>the</strong> microchannel<br />
plate as shown in <strong>the</strong> figure, X1 = 2XEe/Ea, whilst <strong>the</strong> secti<strong>on</strong> al<strong>on</strong>g y is<br />
mapped in <strong>the</strong> orthog<strong>on</strong>al directi<strong>on</strong> <strong>on</strong> <strong>the</strong> plate. The spatial resoluti<strong>on</strong> is determined<br />
by a number of factors.I<strong>on</strong>s generated at l<strong>on</strong>gitudinally adjacent positi<strong>on</strong>s a <strong>and</strong> b to<br />
q2 in Figure 8.7 are mapped to different positi<strong>on</strong>s <strong>on</strong> <strong>the</strong> channel plate despite having<br />
<strong>the</strong> same kinetic energy. The slit width determines <strong>the</strong> l<strong>on</strong>gitudinal acceptance <strong>and</strong><br />
hence <strong>the</strong> positi<strong>on</strong>al spread <strong>on</strong> <strong>the</strong> plate <strong>and</strong> must thus be kept small to c<strong>on</strong>trol<br />
this blurring. The analyzer resoluti<strong>on</strong> is determined by <strong>the</strong> energy dispersi<strong>on</strong> <strong>and</strong><br />
<strong>the</strong> camera spatial resoluti<strong>on</strong>. Aberrati<strong>on</strong>s in <strong>the</strong> analyzer will distort <strong>the</strong> measured<br />
profile. The accuracy in <strong>the</strong> y-directi<strong>on</strong> is determined by how linearly <strong>the</strong> i<strong>on</strong> chamber<br />
/ encoder can preserve <strong>the</strong> transverse positi<strong>on</strong> al<strong>on</strong>g <strong>the</strong> length of <strong>the</strong> slit <strong>and</strong> <strong>the</strong><br />
linearity of <strong>the</strong> analyzer resp<strong>on</strong>se in <strong>the</strong> plane orthog<strong>on</strong>al to <strong>the</strong> dispersi<strong>on</strong> plane. The<br />
ultimate resoluti<strong>on</strong> is limited by<strong>the</strong> extent towhich <strong>the</strong> i<strong>on</strong>s acquire extra momentum<br />
in <strong>the</strong> y- <strong>and</strong> z-directi<strong>on</strong>s as <strong>the</strong> result of inter-i<strong>on</strong> scattering <strong>and</strong> <strong>the</strong> influence of stray<br />
external (especially magnetic) fields. These effects will be reduced by increasing <strong>the</strong><br />
gradient of <strong>the</strong> extracting field to increase <strong>the</strong> kinetic energy of <strong>the</strong> i<strong>on</strong>s. But, if <strong>the</strong><br />
kinetic energy is too high, <strong>the</strong>n <strong>the</strong> analyzer performance will be degraded.<br />
The sensitivity of <strong>the</strong> technique is limited by <strong>the</strong> number of i<strong>on</strong>s generated in <strong>the</strong><br />
residual gas <strong>and</strong> <strong>the</strong> detecti<strong>on</strong> efficiency. I<strong>on</strong> generati<strong>on</strong> is more likely at VUVthan Xray<br />
wavelengths <strong>and</strong> thus <strong>the</strong> spectral c<strong>on</strong>tent of <strong>the</strong> <strong>beam</strong> will influence <strong>the</strong> recorded<br />
profile. To measure <strong>the</strong> X-ray profile in, for example, <strong>the</strong> <strong>beam</strong> from a synchrotr<strong>on</strong><br />
dipole source would require <strong>the</strong> l<strong>on</strong>g wavelength comp<strong>on</strong>ents to be removed by a filter
122 8. Beam cross-secti<strong>on</strong> diagnostics<br />
X<br />
Extracti<strong>on</strong> field Ee<br />
+<br />
-<br />
X1<br />
q1<br />
q2<br />
X-ray <strong>beam</strong><br />
+<br />
Phosphor screen<br />
MCP<br />
-<br />
y<br />
x<br />
z<br />
Analyzer field Ea<br />
Figure 8.7: The <strong>beam</strong> cross-secti<strong>on</strong> image detector (BCID) as described by Ioudin et al. [184].<br />
such as a beryllium window[185]. This would however facilitate <strong>the</strong> additi<strong>on</strong> of a gas<br />
such as arg<strong>on</strong> or xen<strong>on</strong> at a low pressure to improve <strong>the</strong> i<strong>on</strong> count. In all cases,<br />
<strong>the</strong> necessity for a small analyzer slit limits <strong>the</strong> total count rate <strong>and</strong> all reported<br />
measurements of X-ray <strong>beam</strong>s have been d<strong>on</strong>e with a gas pressure of 10 -5 to 10 -3<br />
mbar <strong>and</strong> by integrating up to 256 frames with frame rate of 12.5 Hz [185, 186]. It<br />
is thus debatable whe<strong>the</strong>r <strong>the</strong> technique could have sufficient efficiency to record a<br />
single shot of a free electr<strong>on</strong> laser <strong>beam</strong>. There is little informati<strong>on</strong> in <strong>the</strong> references<br />
<strong>on</strong> <strong>the</strong> spatial resoluti<strong>on</strong> achieved with <strong>the</strong> BCID.<br />
A residual gas <strong>beam</strong> positi<strong>on</strong> m<strong>on</strong>itor is also being developed for use as an X-ray<br />
<strong>beam</strong> positi<strong>on</strong> m<strong>on</strong>itor at PETRA III at HASYLAB. The RGBPM as described by<br />
Ilinski et al. [187] uses a layout similar to <strong>the</strong> original particle <strong>beam</strong> m<strong>on</strong>itors, i.e. <strong>the</strong><br />
kinetic energy encoding approach of Ioudin is not used <strong>and</strong> <strong>the</strong> spatial coordinate of<br />
<strong>the</strong> <strong>beam</strong> is mapped directly <strong>on</strong>to <strong>the</strong> detector. The generated i<strong>on</strong>s or electr<strong>on</strong>s are<br />
drifted in an applied electric field to a micro-channel plate (MCP) which produces<br />
an intensified image <strong>on</strong> a phosphor screen <strong>–</strong> Figure 8.8. The <strong>beam</strong> profile is recorded<br />
in <strong>on</strong>e axis <strong>on</strong>ly, this being in <strong>the</strong> directi<strong>on</strong> perpendicular to both <strong>the</strong> drift field <strong>and</strong><br />
<strong>beam</strong> directi<strong>on</strong>. The profile is recorded for a finite length in <strong>the</strong> propagati<strong>on</strong> directi<strong>on</strong>
8.6. Imaging i<strong>on</strong> chambers 123<br />
X-ray <strong>beam</strong><br />
Phosphor<br />
MCP<br />
Guide electrode<br />
Guide electrode<br />
Repeller electrode<br />
Field axis<br />
Profile axis<br />
Propagati<strong>on</strong> axis<br />
Figure 8.8: Schematic of PETRA-III RGBPM; a vertical profile of <strong>the</strong> <strong>beam</strong> is measured.<br />
of <strong>the</strong> <strong>beam</strong> determined by <strong>the</strong> l<strong>on</strong>gitudinal aperture of <strong>the</strong> detecti<strong>on</strong> system.<br />
Improvements in <strong>the</strong> resoluti<strong>on</strong> come from close attenti<strong>on</strong> to <strong>the</strong> quality of <strong>the</strong><br />
electric field, initial kinetic energy of <strong>the</strong> i<strong>on</strong>s or electr<strong>on</strong>s, resoluti<strong>on</strong> of <strong>the</strong> detector<br />
system, <strong>and</strong> data processing. To quote: ”The electrical field has to be uniform in<br />
order to provide aberrati<strong>on</strong> free <strong>beam</strong> profile. Broadening of <strong>the</strong> <strong>beam</strong> profile occurs<br />
due to electrical field n<strong>on</strong>-uniformity <strong>and</strong> presence of <strong>the</strong> transverse comp<strong>on</strong>ent of <strong>the</strong><br />
electrical field. This broadening should not exceed <strong>the</strong> broadening of <strong>the</strong> <strong>beam</strong> profile<br />
which is caused by <strong>the</strong> initial transverse kinetic energy of <strong>the</strong> i<strong>on</strong>s or electr<strong>on</strong>s. The<br />
resoluti<strong>on</strong> of detecti<strong>on</strong> system is defined by <strong>the</strong> MCP, <strong>the</strong> phosphor screen, optical<br />
coupling <strong>and</strong> signal background ratio. A proper data processing allows for sub-pixel<br />
resoluti<strong>on</strong>.” The guide electrodes shown in Figure 8.8 are designed to improve <strong>the</strong><br />
repeller field uniformity.<br />
A prototype RGXBPM was tested <strong>on</strong> ID6 at <strong>the</strong> ESRF at 29 m from <strong>the</strong> centre<br />
of a straight c<strong>on</strong>taining three undulators. The m<strong>on</strong>itor was located after a diam<strong>on</strong>d<br />
window of 300 µm thickness. Two readout systems were tried, viz. optical by imaging<br />
<strong>the</strong> phosphor screen with a CCD camera, <strong>and</strong> current by using a multi-channel plate<br />
with a split saw-tooth electrode. The channel plate had a channel diameter of 12 µm<br />
<strong>and</strong> <strong>the</strong> CCD camera had a resoluti<strong>on</strong> of 15 µm/pixel. With <strong>the</strong> optical readout, each<br />
CCD frame had an integrati<strong>on</strong> period of 300 ms <strong>and</strong> <strong>the</strong> <strong>beam</strong> centre of gravity could<br />
be calculated for each frame with a ring current of 68 mA <strong>and</strong> a residual gas pressure<br />
of ∼10 -7 mbar. A 5 µm step in <strong>the</strong> RGBPM positi<strong>on</strong> could clearly be resolved. The<br />
noise was not quoted, but looked to be 2 to 3 µm. The resoluti<strong>on</strong> with <strong>the</strong> splitelectrode<br />
detecti<strong>on</strong> was about twice that with <strong>the</strong> optical detecti<strong>on</strong>, with a 10 µm
124 8. Beam cross-secti<strong>on</strong> diagnostics<br />
step being resolved.<br />
An important limitati<strong>on</strong> of <strong>the</strong>se devices for measuring X-ray <strong>beam</strong>s is that <strong>the</strong><br />
cross-secti<strong>on</strong> for creating i<strong>on</strong>s is much greater at VUV than at X-ray wavelengths <strong>and</strong><br />
thus <strong>the</strong> sensitivity of m<strong>on</strong>itor is str<strong>on</strong>gly dependent <strong>on</strong> <strong>the</strong> <strong>beam</strong> spectral c<strong>on</strong>tent.<br />
This is a real issue <strong>on</strong> synchrotr<strong>on</strong> sources where <strong>the</strong> l<strong>on</strong>g wavelength halo around an<br />
undulator <strong>beam</strong> will give a false broadening of <strong>the</strong> measured profile even thoughit is<br />
at a low intensity compared to <strong>the</strong> <strong>on</strong>-axis X-rays[187]. In both <strong>the</strong> measurements<br />
of Ioudin <strong>and</strong> Ilinski, windows in <strong>the</strong> X-ray <strong>beam</strong> acted as high-pass filters. Such<br />
filtering is unlikely to be possible <strong>on</strong> a free electr<strong>on</strong> laser source (because of <strong>the</strong><br />
ablati<strong>on</strong> risk <strong>and</strong> <strong>beam</strong> disrupti<strong>on</strong>) but <strong>the</strong> spectral c<strong>on</strong>tent in such a source should<br />
not c<strong>on</strong>tain <strong>the</strong> l<strong>on</strong>g wavelength comp<strong>on</strong>ents anyway. Never<strong>the</strong>less, it is important to<br />
c<strong>on</strong>sider any possible sources of stray light (from dipoles, steering magnets etc <strong>and</strong><br />
<strong>the</strong> sp<strong>on</strong>taneous radiati<strong>on</strong> from <strong>the</strong> undulators) that might propagate with <strong>the</strong> free<br />
electr<strong>on</strong> laser <strong>beam</strong>.<br />
It should also be noted that <strong>the</strong> RGBPM is principally being designed to measure<br />
<strong>the</strong> centroid of <strong>the</strong> <strong>beam</strong>, this being achieved through measuring <strong>and</strong> analyzing <strong>the</strong><br />
<strong>beam</strong> profile. Thus, a small amount of profile broadening can be accounted for. Of<br />
course, bi-axial profiling requires a sec<strong>on</strong>d m<strong>on</strong>itor. There is also <strong>the</strong> need to fur<strong>the</strong>r<br />
improve <strong>the</strong> resoluti<strong>on</strong> <strong>and</strong> speed of <strong>the</strong> m<strong>on</strong>itor if it is to meet <strong>the</strong> requirements of<br />
a free electr<strong>on</strong> laser <strong>beam</strong> positi<strong>on</strong> m<strong>on</strong>itor.<br />
Fluorescence detecti<strong>on</strong> in residual gas m<strong>on</strong>itors<br />
When atoms in a gas are excited or i<strong>on</strong>ized by VUV to soft X-ray phot<strong>on</strong>s, <strong>the</strong><br />
dominant decay process is Auger emissi<strong>on</strong>. However, at hard X-ray wavelengths,<br />
decay by fluorescence becomes a significant process.There is <strong>the</strong>refore <strong>the</strong> opti<strong>on</strong> of<br />
recording <strong>the</strong> <strong>beam</strong> profile by imaging <strong>the</strong> fluorescent light. The principle is <strong>the</strong> same<br />
as with imaging <strong>the</strong> i<strong>on</strong> or electr<strong>on</strong> emissi<strong>on</strong>. The density of fluorescent phot<strong>on</strong>s is<br />
proporti<strong>on</strong>al to <strong>the</strong> density in X-rays in <strong>the</strong> <strong>beam</strong>. With fluorescence, <strong>the</strong>re is <strong>the</strong><br />
advantage that <strong>the</strong> phot<strong>on</strong>s will not be perturbed <strong>on</strong>ce emitted since <strong>the</strong> probability<br />
of scatter in a low-pressure gas will be negligible. However, <strong>the</strong> phot<strong>on</strong> emissi<strong>on</strong> is<br />
not instantaneous with <strong>the</strong> atom being excited by <strong>the</strong> x-ray. Thus, by <strong>the</strong> time <strong>the</strong><br />
atom emits, it will have moved under <strong>the</strong> influence of <strong>the</strong> space charge of all <strong>the</strong> i<strong>on</strong>s.<br />
The average moti<strong>on</strong> will <strong>the</strong>refore be away from <strong>the</strong> <strong>beam</strong> centre <strong>and</strong> this will result<br />
in a broadening of <strong>the</strong> fluorescence profile.<br />
This broadening effect is much more significant when measuring charged particle<br />
<strong>beam</strong> profiles since <strong>the</strong> i<strong>on</strong>s are also under <strong>the</strong> influence of <strong>the</strong> <strong>beam</strong> space charge.<br />
This effect has been observed when measuring <strong>the</strong> profile of prot<strong>on</strong> <strong>beam</strong>s[188]. When<br />
measuring an X-ray <strong>beam</strong> in a low pressure gas, <strong>the</strong> effect of inter-i<strong>on</strong> repulsi<strong>on</strong> is<br />
probably negligible. The i<strong>on</strong>s will still move r<strong>and</strong>omly before emitting <strong>the</strong> phot<strong>on</strong>s,<br />
<strong>and</strong> statistically more will move away from <strong>the</strong> <strong>beam</strong> centre than towards it. Thus,<br />
<strong>the</strong>re can still be some broadening effect that will depend <strong>on</strong> <strong>the</strong> lifetime of <strong>the</strong> excited<br />
state, which will in turn depend <strong>on</strong> <strong>the</strong> gas being i<strong>on</strong>ized.<br />
This type of m<strong>on</strong>itor is in use at <strong>the</strong> Cornell synchrotr<strong>on</strong> CHESS, where <strong>the</strong> m<strong>on</strong>itors<br />
are called video <strong>beam</strong> positi<strong>on</strong> m<strong>on</strong>itors (VBPM). The layout is shown schematically<br />
in Figure 8.9. The <strong>beam</strong> tube is filled with helium at atmospheric pressure.<br />
Whilst this undoubtedly increases <strong>the</strong> fluorescence intensity, it would seem <strong>the</strong> main<br />
reas<strong>on</strong> for this is that <strong>the</strong> entire <strong>beam</strong>line is gas filled after a window of unspecified<br />
material which isolates it from <strong>the</strong> machine vacuum. (These are of course hard X-ray
8.6. Imaging i<strong>on</strong> chambers 125<br />
Vert. profile camera<br />
He gas<br />
Horiz. profile camera<br />
Figure 8.9: Schema of <strong>the</strong> CHESS VBPM system.<br />
X-ray <strong>beam</strong><br />
<strong>beam</strong>lines). The video cameras image <strong>the</strong> fluorescence via plane mirrors to prevent<br />
<strong>the</strong>m being damaged by scattered radiati<strong>on</strong> coming through <strong>the</strong> viewports.<br />
One issue that affects <strong>the</strong> resoluti<strong>on</strong> of <strong>the</strong> VBPM is <strong>the</strong> depth of field of <strong>the</strong><br />
video camera lens. The depth of field of <strong>the</strong> vertical profile camera is smaller than<br />
<strong>the</strong> horiz<strong>on</strong>tal <strong>beam</strong> size <strong>and</strong> so edges of <strong>the</strong> <strong>beam</strong> are not in focus. The blurring of<br />
<strong>the</strong> image leads to a broadening of <strong>the</strong> recorded <strong>beam</strong> profile. This is not an issue<br />
when <strong>the</strong> main purpose of <strong>the</strong> m<strong>on</strong>itor is to determine <strong>the</strong> <strong>beam</strong> centroid, as in this<br />
applicati<strong>on</strong>, but would be if accurate profiling were required. The spatial resoluti<strong>on</strong><br />
is also dependent of <strong>the</strong> lens magnificati<strong>on</strong> <strong>and</strong> camera CCD pixel size, which need<br />
to be chosen with <strong>the</strong> size of <strong>the</strong> <strong>beam</strong> to be measured in mind, <strong>and</strong> <strong>the</strong> number of<br />
digitizati<strong>on</strong> levels <strong>and</strong> overall signal to noise ratio. The camera system was tested to<br />
have an accuracy of 0.4 µm fwhm.<br />
The imaging system of <strong>the</strong> VBPM runs at 15 frames per sec<strong>on</strong>d <strong>and</strong> <strong>the</strong> intensity<br />
map is usually averaged over 10 frames. This low data rate is not an issue with an<br />
essentially c<strong>on</strong>tinuous source like a synchrotr<strong>on</strong>, but would be unacceptable for a free<br />
electr<strong>on</strong> laser source. A faster camera could of course be used; <strong>the</strong> main c<strong>on</strong>cern is<br />
whe<strong>the</strong>r enough fluorescence can be generated with a single free electr<strong>on</strong> laser pulse to<br />
be measurable. Enhancement of <strong>the</strong> signal byadding agas at a low pressure should be<br />
feasible; most X-ray free electr<strong>on</strong> lasers have a windowless gas attenuator anyway (c.f.<br />
chapter 4, p. 69). But <strong>the</strong> pressure limit will be determined by absorpti<strong>on</strong>, vacuum
126 8. Beam cross-secti<strong>on</strong> diagnostics<br />
c<strong>on</strong>taminati<strong>on</strong> (<strong>the</strong> gas cell cannot be isolated with windows) <strong>and</strong> self-modulati<strong>on</strong> of<br />
<strong>the</strong> intense phot<strong>on</strong> pulse as it passes through <strong>the</strong> gas.<br />
8.7 Sampling techniques<br />
The ideal sampling process would be to extract a time slice from <strong>the</strong> <strong>beam</strong> so that<br />
<strong>the</strong> full spatial profile can be measured of <strong>the</strong> slice whilst allowing <strong>the</strong> majority of<br />
<strong>the</strong> <strong>beam</strong> to pass <strong>on</strong>to <strong>the</strong> experiment. Unfortunately, extracting a time slice of a<br />
femtosec<strong>on</strong>d durati<strong>on</strong> X-ray pulse is not practical. Therefore,sampling in <strong>the</strong> spatial<br />
domain has to be used, for which <strong>the</strong>re are two approaches. One can remove just a<br />
small part of <strong>the</strong> spatial extent of <strong>the</strong> <strong>beam</strong>, which leads to <strong>on</strong>ly centroid informati<strong>on</strong><br />
(see secti<strong>on</strong> 8.10), or <strong>the</strong> <strong>beam</strong> can be sampled by uniformly removing part of <strong>the</strong><br />
overall intensity, which allows a profile to be measured. Clearly, <strong>the</strong> main objective is<br />
to remove as little of <strong>the</strong> overall <strong>beam</strong> intensity as possible to maximize <strong>the</strong> intensity<br />
reaching <strong>the</strong> experiment. Profiling by sampling requires an intensity <strong>beam</strong> splitter,<br />
whichisdifficulttoachievein<strong>the</strong>VUVtosoftX-rayrange. Thusmostdem<strong>on</strong>strati<strong>on</strong>s<br />
of this approach have been at shorter wavelengths.<br />
In an effort to make an effectively n<strong>on</strong>-invasive profiling measurement, van Silfhout<br />
developed a replicating technique in which <strong>the</strong> bulk of <strong>the</strong> X-ray <strong>beam</strong> passes through<br />
a thin ”featureless” foil angled in <strong>on</strong>e plane to <strong>the</strong> <strong>beam</strong> whilst a small fracti<strong>on</strong> of<br />
<strong>the</strong> X-rays are scattered from <strong>the</strong> foil <strong>and</strong> are imaged by a linear photodiode array<br />
to give line profile of <strong>the</strong> <strong>beam</strong>[189]. Because <strong>the</strong> x-rays are scattered ra<strong>the</strong>r than<br />
reflected, a Soller slit is used to give accurate mapping of each scattering point <strong>on</strong><br />
<strong>the</strong> foil to a single diode in <strong>the</strong> array -see Figure 8.10. Never<strong>the</strong>less, <strong>the</strong> measured<br />
profile must be dec<strong>on</strong>voluted from an instrumental functi<strong>on</strong> determined from <strong>the</strong><br />
profile measured with a very small <strong>beam</strong> footprint <strong>on</strong> <strong>the</strong> foil. The limiting spatial<br />
resoluti<strong>on</strong> is determined by <strong>the</strong> spatial sampling of <strong>the</strong> projected <strong>beam</strong> footprint <strong>on</strong><br />
<strong>the</strong> foil <strong>and</strong> can thus be improved by angling <strong>the</strong> foil at a more grazing angle to<br />
<strong>the</strong> <strong>beam</strong>. A <strong>beam</strong> positi<strong>on</strong> accuracy of 1 µm was claimed. The technique can be<br />
extended to 3-D imaging by tilting <strong>the</strong> foil in two planes <strong>and</strong> using a crossed-Soller slit<br />
<strong>and</strong> diode array. A more recent paper[190] shows how <strong>the</strong> technique can give a fast<br />
output of <strong>the</strong> <strong>beam</strong> profile (still at in <strong>on</strong>e dimensi<strong>on</strong>). The ultimate limit was 10 kHz,<br />
determined by <strong>the</strong> readout speed of <strong>the</strong> electr<strong>on</strong>ics, though <strong>the</strong> actual measurements<br />
were performed at 2400 Hz. The obvious c<strong>on</strong>cerns for free electr<strong>on</strong> laser use are: 1)<br />
ablati<strong>on</strong> damage to <strong>the</strong> foil, 2) disrupti<strong>on</strong> to <strong>the</strong> <strong>beam</strong> through coherent diffracti<strong>on</strong><br />
if <strong>the</strong> foil is not perfectly featureless <strong>and</strong> 3) <strong>the</strong> limitati<strong>on</strong> to hard x-rays to get high<br />
transmissi<strong>on</strong> through <strong>the</strong> foil.<br />
Ano<strong>the</strong>r approach, tested <strong>on</strong> an undulator <strong>beam</strong>line at SPring-8, is described in<br />
Kudo et al. [191]. A 30 µm thick CVD diam<strong>on</strong>d film was grown <strong>on</strong> a silic<strong>on</strong> substrate<br />
<strong>and</strong><strong>the</strong>silic<strong>on</strong> was etchedaway from acentralregi<strong>on</strong> of10mmdiameter. Theexposed<br />
diam<strong>on</strong>d has silic<strong>on</strong> doping from <strong>the</strong> substrate that causes it to photo-luminesce<br />
at 739 nm when exposed to an X-ray <strong>beam</strong>. The luminescence was imaged by a<br />
CCD camera giving a 2-D picture of <strong>the</strong> <strong>beam</strong> profile. The diam<strong>on</strong>d film is almost<br />
transparent to hard X-rays (50% transmissi<strong>on</strong> at 3300 eV, 90% at 6200 eV, for a<br />
density of 3.5 g/cm 3 ) <strong>and</strong> so most of <strong>the</strong> <strong>beam</strong> passes through it to <strong>the</strong> experiment.<br />
The luminescence resp<strong>on</strong>se to <strong>beam</strong> intensity was shown to be linear over at least<br />
four orders of magnitude. However, <strong>the</strong> luminescence is stimulated by a wide range<br />
of X-ray wavelengths <strong>and</strong> so <strong>the</strong> method is unable to distinguish between <strong>the</strong> <strong>on</strong> axis
8.7. Sampling techniques 127<br />
X-ray <strong>beam</strong><br />
Diode array<br />
Scattered X-rays<br />
Thin foil<br />
Soller slit<br />
Figure 8.10: The profiling system of van Silfhout, based <strong>on</strong> a Soller slit collimating <strong>the</strong> scattered X-rays from<br />
a thin foil.<br />
emissi<strong>on</strong> at <strong>the</strong>res<strong>on</strong>ant wavelength <strong>and</strong><strong>the</strong> lower energy radiati<strong>on</strong> outside <strong>the</strong>central<br />
emissi<strong>on</strong> c<strong>on</strong>e of <strong>the</strong> undulator, leading to an artificially broadened <strong>beam</strong> profile.<br />
However, this should not be an issue with a free electr<strong>on</strong> laser <strong>beam</strong>. No specific<br />
data for spatial resoluti<strong>on</strong> is given, but this will be determined by <strong>the</strong> combinati<strong>on</strong><br />
of <strong>the</strong> camera resoluti<strong>on</strong> <strong>and</strong> <strong>the</strong> <strong>beam</strong> footprint <strong>on</strong> <strong>the</strong> diam<strong>on</strong>d. B<strong>and</strong>width will be<br />
determined by <strong>the</strong> readout rate of <strong>the</strong> camera <strong>and</strong> <strong>the</strong> persistence of <strong>the</strong> luminescence<br />
in <strong>the</strong> diam<strong>on</strong>d. Diam<strong>on</strong>d has high <strong>the</strong>rmal c<strong>on</strong>ductivity <strong>and</strong> <strong>the</strong> film, mounted in<br />
a water-cooled assembly, was able to withst<strong>and</strong> <strong>the</strong> full pink <strong>beam</strong> <strong>on</strong> BL46XU at<br />
Spring-8. Power loading is less of an issue with a free electr<strong>on</strong> laser <strong>beam</strong> but <strong>the</strong>re<br />
is a significant risk of ablati<strong>on</strong> if <strong>the</strong> diam<strong>on</strong>d is exposed to <strong>the</strong> full intensity of <strong>the</strong><br />
fundamental. A fur<strong>the</strong>r c<strong>on</strong>cern is that <strong>the</strong> CVD diam<strong>on</strong>d is polycrystalline <strong>and</strong> thus<br />
<strong>the</strong>re may be significant disrupti<strong>on</strong> to a coherent X-ray <strong>beam</strong> <strong>on</strong> passing through <strong>the</strong><br />
film.<br />
An alternative approach to intensity sampling is to Bragg reflect part of <strong>the</strong> <strong>beam</strong><br />
from a thin crystal <strong>on</strong>to a 2-D CCD detector whilst most of <strong>the</strong> <strong>beam</strong> intensity passes<br />
through <strong>the</strong> crystal. This also allows <strong>the</strong> <strong>beam</strong> to be fully imaged <strong>and</strong> so profile<br />
informati<strong>on</strong> to be extracted, Fajardo <strong>and</strong> Ferrer used a 500 µm thickberyllium crystal<br />
in a white <strong>beam</strong> from an undulator at <strong>the</strong> ESRF[192]. The crystal was set a 45 ◦ <strong>and</strong><br />
so measured X-rays at 4.45 keV. The quality of <strong>the</strong> image is degraded by <strong>the</strong> effects<br />
of mosaic spread <strong>and</strong> <strong>the</strong> finite extincti<strong>on</strong> depth of <strong>the</strong> crystal. This does not affect
128 8. Beam cross-secti<strong>on</strong> diagnostics<br />
centroiding resoluti<strong>on</strong> but does affect any profile measurement.<br />
Themajor disadvantage is <strong>the</strong>spectral dependenceof <strong>the</strong>reflected<strong>and</strong>transmitted<br />
<strong>beam</strong>s.Varying <strong>the</strong> Bragg angle to work at different wavelengths would make a very<br />
complicated system. Fur<strong>the</strong>rmore, in <strong>the</strong> c<strong>on</strong>text of a narrow-b<strong>and</strong>width free electr<strong>on</strong><br />
laser source, <strong>the</strong> impact <strong>on</strong> <strong>the</strong> transmitted <strong>beam</strong> will be significant. The crystal acts<br />
as a b<strong>and</strong>-cut filter <strong>and</strong>, because a significant fracti<strong>on</strong> of <strong>the</strong> radiati<strong>on</strong> could lie inside<br />
<strong>the</strong>crystal rocking curvewidth, <strong>the</strong>notchin <strong>the</strong>transmitted spectrumwould be large.<br />
The mosaic spread of <strong>the</strong> crystal is also likely to cause str<strong>on</strong>g diffractive disrupti<strong>on</strong> to<br />
<strong>the</strong> transmitted <strong>beam</strong>. Finally, <strong>the</strong> technique is <strong>on</strong>ly applicable to hard X-rays where<br />
adequate transmissi<strong>on</strong> through <strong>the</strong> crystal is possible.<br />
At lower phot<strong>on</strong> energies, a diffracti<strong>on</strong> grating can be used to split <strong>the</strong> <strong>beam</strong> in<br />
intensity (as discussed previously in chapter 5). This can be utilized in <strong>on</strong>e of two<br />
ways; ei<strong>the</strong>r <strong>the</strong> first-order diffracted <strong>beam</strong> is sent to <strong>the</strong> diagnostic <strong>and</strong> <strong>the</strong> zeroth<br />
order to <strong>the</strong> experiment or vice versa.<br />
For a <strong>beam</strong>line that requires a m<strong>on</strong>ochromator, it makes sense to use <strong>the</strong> zeroth<br />
order <strong>beam</strong> for <strong>the</strong> diagnostic. In such a case, it is necessary to ensure <strong>the</strong> zeroth<br />
order<strong>beam</strong> directi<strong>on</strong> isfixedas <strong>the</strong>gratingis turnedtotune<strong>the</strong>wavelength, o<strong>the</strong>rwise<br />
<strong>the</strong> diagnostic system will have to move c<strong>on</strong>siderably to follow it.In a normal fixed<br />
included angle m<strong>on</strong>ochromator, this can <strong>on</strong>ly be achieved by using additi<strong>on</strong>al steering<br />
mirror(s) to catch <strong>the</strong> zeroth order <strong>beam</strong> <strong>and</strong> redirect it to <strong>the</strong> diagnostic. Such a<br />
mechanism could be both large <strong>and</strong>complicated since translati<strong>on</strong> as well as rotati<strong>on</strong> of<br />
<strong>the</strong> steering mirrors is likely to be necessary. An alternative approach is possible with<br />
a variable included angle m<strong>on</strong>ochromator such as <strong>the</strong> SX700 mount when operated in<br />
collimated light. In this m<strong>on</strong>ochromator it is possible to operate in <strong>the</strong> so-called ’<strong>on</strong>blaze’<br />
mode <strong>and</strong> this maintains a fixed angle between zeroth <strong>and</strong> first order <strong>beam</strong>s.<br />
In this mode, when <strong>the</strong> angle between <strong>the</strong> first <strong>and</strong> zeroth order <strong>beam</strong>s is ψ, <strong>the</strong><br />
wavelength λ is related to <strong>the</strong> diffracti<strong>on</strong> angle β by<br />
N ·n·λ = 2·sin<br />
� ψ<br />
2<br />
�<br />
cos<br />
� ψ<br />
2 −β<br />
�<br />
(8.1)<br />
Whilst this mode also c<strong>on</strong>veniently maximizes <strong>the</strong> first order efficiency when a blazed<br />
grating with a blaze angle of ψ/2 is used, <strong>the</strong>re is a significant reducti<strong>on</strong> in tuning<br />
range for a grating of a given line density <strong>and</strong> thus more gratings are required to cover<br />
a wide phot<strong>on</strong> energy range.<br />
In <strong>the</strong> alternative approach when <strong>the</strong> zeroth order is sent to <strong>the</strong> experiment, <strong>the</strong><br />
grating should ideally be kept at a fixed angle to minimize <strong>the</strong> reflecti<strong>on</strong>s in <strong>the</strong><br />
main <strong>beam</strong> path. The diffracted order will thus be reflected at a different angle<br />
as <strong>the</strong> free electr<strong>on</strong> laser wavelength is tuned <strong>and</strong> <strong>the</strong> profile m<strong>on</strong>itor will need to<br />
follow it. This will be easier than in <strong>the</strong> case where <strong>the</strong> grating is turned since<br />
<strong>the</strong> angular range over which <strong>the</strong> diffracted order moves will be smaller. Thus it<br />
should be possible to arrange <strong>the</strong> imaging detector to move <strong>on</strong> a rail to follow <strong>the</strong><br />
<strong>beam</strong>. It must be remembered that <strong>the</strong> diffracted order will need to be imaged<br />
<strong>on</strong>to <strong>the</strong> detector. This is best achieved by using a varied-line-spacing grating that<br />
also allows aberrati<strong>on</strong>s to be corrected. This is basically <strong>the</strong> approach used in <strong>the</strong><br />
diagnostic spectrometer at Flash[193], discussed elsewhere. When applied to spatial<br />
imaging,<strong>the</strong>re are two important c<strong>on</strong>siderati<strong>on</strong>s when interpreting <strong>the</strong> measurement.<br />
Firstly, residual aberrati<strong>on</strong>s could still be present <strong>and</strong> sec<strong>on</strong>dly, <strong>the</strong> image will be<br />
blurred due to <strong>the</strong> dispersi<strong>on</strong> of <strong>the</strong> pulse spectrum. A detailed design study would
8.8. Spot size 129<br />
need to be performed to investigate whe<strong>the</strong>r this technique could give a useful pulse<br />
profile diagnostic.<br />
Ano<strong>the</strong>r factor that should be remembered is that <strong>the</strong> positi<strong>on</strong> of <strong>the</strong> <strong>beam</strong> at <strong>the</strong><br />
diagnostic will be dependent <strong>on</strong> <strong>the</strong> grating angle <strong>and</strong> thus <strong>the</strong> technique is not ideal<br />
for getting informati<strong>on</strong> <strong>on</strong> absolute positi<strong>on</strong>s <strong>and</strong> how <strong>the</strong> <strong>beam</strong> is moving.<br />
8.8 Spot size<br />
From <strong>the</strong> users’ perspective, <strong>on</strong>e of <strong>the</strong> critical factors determining <strong>the</strong> performance<br />
of a free electr<strong>on</strong> laser is <strong>the</strong> size <strong>and</strong> quality of <strong>the</strong> focused <strong>beam</strong> spot. For many<br />
experiments, <strong>the</strong> requirement is for as small a focused spot as possible to maximize<br />
<strong>the</strong> flux density or fluence <strong>and</strong> to restrict interacti<strong>on</strong> to a specific, targeted sample<br />
area.Transverse intensity profiling is also critical when aligning <strong>the</strong> focusing optics<br />
to optimize <strong>the</strong> spot shape by minimizing any asymmetry <strong>and</strong> eliminating tails <strong>and</strong><br />
flares. A precise measurement of <strong>the</strong> spot size is crucial to determining <strong>the</strong> absolute<br />
flux density, which must be known for some experiments.<br />
The most desirable soluti<strong>on</strong> for spot size determinati<strong>on</strong> would have <strong>the</strong> ability<br />
to directly image <strong>the</strong> spot with a suitable two-dimensi<strong>on</strong>al, high resoluti<strong>on</strong>, high<br />
repetiti<strong>on</strong> rate detector which is suitably robust to accept <strong>the</strong> unattenuated <strong>beam</strong>.<br />
However, extensive experience <strong>on</strong> synchrotr<strong>on</strong> sources has dem<strong>on</strong>strated that <strong>the</strong><br />
current generati<strong>on</strong> of CCD <strong>and</strong> proporti<strong>on</strong>al gas-filled detectors can be permanently<br />
damaged bymomentaryexposureto<strong>the</strong>unattenuatedX-ray<strong>beam</strong>ofarelatively large<br />
(several millimeters) diameter. Whilst such devices should not be excluded from a<br />
survey of possible techniques it is reas<strong>on</strong>able to suggest that <strong>the</strong> majority of 2-D<br />
imaging systems will require significant attenuati<strong>on</strong> <strong>and</strong> shielding to provide a usable<br />
service life <strong>on</strong> a free electr<strong>on</strong> laser source. It should be noted that attenuating <strong>the</strong><br />
<strong>beam</strong> using solid filters or foils has been dem<strong>on</strong>strated to affect <strong>the</strong> <strong>beam</strong> wavefr<strong>on</strong>t<br />
at Flash although <strong>the</strong> effect of using a gas attenuators is negligible 7 .<br />
The remainder of this secti<strong>on</strong> is <strong>the</strong>refore subdivided into two secti<strong>on</strong>s covering<br />
those techniques that can be used with <strong>the</strong> unattenuated <strong>beam</strong>, <strong>and</strong> those for which<br />
significant attenuati<strong>on</strong> will be required.<br />
Techniques useable with unattenuated <strong>beam</strong>s<br />
Ablati<strong>on</strong> crater analysis<br />
One of <strong>the</strong> most established methods of determining <strong>the</strong> <strong>beam</strong> cross secti<strong>on</strong> in c<strong>on</strong>venti<strong>on</strong>al<br />
high power UV-Vis-IRlasers is byanalysis of <strong>the</strong> laser ablati<strong>on</strong> crater imprinted<br />
into a well characterized sample, predominantly PMMA (polymethyl methacrylate).<br />
PMMA is used extensively because of its well characterized ablati<strong>on</strong> characteristics<br />
across a wide wavelength spectrum, its short heat diffusi<strong>on</strong> length <strong>and</strong> <strong>the</strong> predominance<br />
of n<strong>on</strong>-<strong>the</strong>rmal processes when exposed to ultra-short laser pulses. The low<br />
ablati<strong>on</strong> threshold of PMMA also allows characterizati<strong>on</strong> to be performed <strong>on</strong> less<br />
efficient or highly attenuated <strong>beam</strong>lines.<br />
Techniques exist to comprehensively rec<strong>on</strong>struct <strong>the</strong> <strong>beam</strong> profile from <strong>the</strong> ablative<br />
imprint[194]. The <strong>beam</strong> can be characterized at any point al<strong>on</strong>g <strong>the</strong> <strong>beam</strong>line or<br />
7 P. Juranić et al. Desy internal presentati<strong>on</strong>.
130 8. Beam cross-secti<strong>on</strong> diagnostics<br />
Open multiplier<br />
Diff. pumping<br />
TOF<br />
I<strong>on</strong>s I<strong>on</strong>s<br />
±2 cm<br />
-<br />
+<br />
-<br />
+<br />
GMD<br />
e -<br />
Faraday cup<br />
Faraday cup<br />
FEL <strong>beam</strong><br />
Figure 8.11: Setup for <strong>the</strong> i<strong>on</strong> yield saturati<strong>on</strong> measurement at a <strong>beam</strong> focus.<br />
end stati<strong>on</strong> where it is possible to place a sample of PMMA. The material is readily<br />
available, inexpensive <strong>and</strong> can be easily shaped. It is particularly suitable for<br />
characterizing <strong>the</strong> <strong>beam</strong> profile in user-supplied sample holders <strong>and</strong> envir<strong>on</strong>mental<br />
chambers.<br />
Despite all <strong>the</strong>se advantages, <strong>the</strong>re are very significant practical barriers to using<br />
crater analysis bey<strong>on</strong>d <strong>the</strong> initial commissi<strong>on</strong>ing stage. Measurements can <strong>on</strong>ly be<br />
taken of a single pulse (although some form of carousel or sample changer could<br />
<strong>the</strong>oretically be used for verylow repetiti<strong>on</strong> rates). The technique is clearly disruptive<br />
to any experimental data collecti<strong>on</strong> <strong>and</strong> requires significant time tomount <strong>and</strong> remove<br />
<strong>the</strong> ablati<strong>on</strong> sample. Although it may be possible to make a limited determinati<strong>on</strong><br />
of <strong>the</strong> <strong>beam</strong> cross-secti<strong>on</strong> using in-situ optical microscopy, detailed analysis of <strong>the</strong><br />
<strong>beam</strong> quality will be c<strong>on</strong>ducted offline. The measurements to determine <strong>the</strong> crater<br />
profile typically incorporate both optical <strong>and</strong> atomic force microscopy,so results are<br />
far from instantaneous. It is possible to envisage a certain degree of automati<strong>on</strong> being<br />
employed if <strong>the</strong> number of routine measurements justified <strong>the</strong> investment. Even so,<br />
it is difficult to imagine <strong>the</strong> time between sample exposure <strong>and</strong> accurate <strong>beam</strong> cross<br />
secti<strong>on</strong> determinati<strong>on</strong> being reduced below <strong>the</strong> level of ”several hours”.<br />
Photoi<strong>on</strong>isati<strong>on</strong> saturati<strong>on</strong> of rare gases<br />
An advanced, n<strong>on</strong>-disruptive technique for spot size minimizati<strong>on</strong> has been developed<br />
at Flash by A.A. Sorokin et al. [195]. This is based <strong>on</strong> <strong>the</strong> saturati<strong>on</strong> effect of <strong>the</strong><br />
photoi<strong>on</strong>isati<strong>on</strong> of rare gases. At lower irradiance levels <strong>the</strong>re exists a linear relati<strong>on</strong>ship<br />
between <strong>the</strong> number of incident phot<strong>on</strong>s <strong>and</strong> <strong>the</strong> number of i<strong>on</strong>s generated.<br />
However as <strong>the</strong> irradiance increases (e.g. due to <strong>the</strong> reducti<strong>on</strong> of <strong>the</strong> spot size at <strong>the</strong><br />
ideal focus positi<strong>on</strong>) <strong>the</strong> fracti<strong>on</strong> of <strong>the</strong> atoms in <strong>the</strong> interacti<strong>on</strong> regi<strong>on</strong> that are i<strong>on</strong>ized<br />
approaches unity. The i<strong>on</strong> yield thus diminishes with respect to <strong>the</strong> number of<br />
incident phot<strong>on</strong>s as <strong>the</strong> interacti<strong>on</strong> regi<strong>on</strong> <strong>and</strong> focus coincide. This saturati<strong>on</strong> effect<br />
can be measured with an apertured time-of-flight (TOF) spectrometer mounted perpendicular<br />
to <strong>the</strong> <strong>beam</strong> directi<strong>on</strong> (see secti<strong>on</strong> 7.3, see page 104), whilst measurement<br />
of <strong>the</strong> absolute number of phot<strong>on</strong>s per pulse is made using a gas m<strong>on</strong>itor detector<br />
(<strong>the</strong> GMD presented in secti<strong>on</strong> 7.2, see page 100) <strong>–</strong> Figure 8.11. Careful selecti<strong>on</strong> of<br />
<strong>the</strong> target gas type <strong>and</strong> pressure relative to <strong>the</strong> energy of <strong>the</strong> phot<strong>on</strong> <strong>beam</strong> is required<br />
to restrict <strong>the</strong> photoi<strong>on</strong>isati<strong>on</strong> process to <strong>on</strong>e-phot<strong>on</strong> single i<strong>on</strong>izati<strong>on</strong>[196].
8.9. Techniques requiring attenuated <strong>beam</strong>s 131<br />
The technique is not quantitative; ra<strong>the</strong>r <strong>the</strong> maximum level of saturati<strong>on</strong> of <strong>the</strong><br />
photoi<strong>on</strong>isati<strong>on</strong> signal indicates <strong>the</strong> optimum focus positi<strong>on</strong>. Fur<strong>the</strong>r diagnostics are<br />
requiredtoquantify<strong>the</strong>resultant<strong>beam</strong>size,although photoi<strong>on</strong>isati<strong>on</strong> saturati<strong>on</strong>could<br />
be calibrated using a quantitative process (e.g. ablati<strong>on</strong> crater analysis) for a given<br />
lateral positi<strong>on</strong> <strong>and</strong> gas pressure. One benefit of <strong>the</strong> technique is that it is n<strong>on</strong>disruptive,<br />
since both <strong>the</strong> TOF spectrometer <strong>and</strong> <strong>the</strong> GMD do not impinge directly<br />
<strong>on</strong> <strong>the</strong> incident phot<strong>on</strong>s.The system has currently been tested using macropulses of<br />
Flash free electr<strong>on</strong> laser at a phot<strong>on</strong> energy of 38 eV.<br />
8.9 Techniques requiring attenuated <strong>beam</strong>s<br />
Wire, knife-edge <strong>and</strong> slit scans<br />
For <strong>the</strong> majority of existing synchrotr<strong>on</strong>-based micro-focus experiments, slit scanning<br />
methods are usedtocharacterize <strong>the</strong> <strong>beam</strong> size <strong>and</strong> profile[197]. Ingeneral, diffracti<strong>on</strong><br />
or scattering effects from <strong>the</strong> scanning object are not taken into c<strong>on</strong>siderati<strong>on</strong> when<br />
calculating <strong>the</strong> <strong>beam</strong> size. These techniques are covered in more detail in relati<strong>on</strong> to<br />
general <strong>beam</strong> profiling in secti<strong>on</strong> 8.4. For synchrotr<strong>on</strong> radiati<strong>on</strong> sources, any <strong>the</strong>rmal<br />
loading issues are overcome by implementing water cooling to <strong>the</strong> slit jaws or apertures.<br />
However,<strong>the</strong> fluence levels at <strong>the</strong> focus of a pulsed free electr<strong>on</strong> laser source will<br />
accentuate <strong>the</strong> difficulties associated with ablati<strong>on</strong>, for which significant attenuati<strong>on</strong><br />
will be <strong>the</strong> <strong>on</strong>ly soluti<strong>on</strong>.<br />
Photographic film<br />
This is included for <strong>the</strong> sake of completeness, <strong>and</strong> as a dem<strong>on</strong>strati<strong>on</strong> that a relatively<br />
low technology soluti<strong>on</strong> can prove extremely useful. Film was used extensively <strong>on</strong><br />
sec<strong>on</strong>d-generati<strong>on</strong> synchrotr<strong>on</strong>s e.g. SRS, Daresbury UK, to produce a permanent<br />
record of <strong>the</strong> size <strong>and</strong> shape of <strong>the</strong> focused X-ray <strong>beam</strong>. In this example <strong>the</strong> film used<br />
was Polaroid 55 large-format self-developing film which was chosen for its ease of use,<br />
speed, limited cost (at <strong>the</strong> time) <strong>and</strong> small grain size which led to comparatively high<br />
resoluti<strong>on</strong> images.Its thinness also made it practical in an experimental set-up as it<br />
could be placed practically anywhere in <strong>the</strong> hard X-ray <strong>beam</strong> path without disrupti<strong>on</strong><br />
to user equipment.<br />
One could suggest that photographic film is still viable for free electr<strong>on</strong> laser applicati<strong>on</strong>s<br />
since <strong>the</strong> grain size of high quality film stock can be as small as 0.5 µm,<br />
which is far smaller than <strong>the</strong> photo site spacing of even <strong>the</strong> best CCD sensors. Some<br />
form of pulse selecti<strong>on</strong> would be required to give single-pulse imaging <strong>and</strong> high levels<br />
of attenuati<strong>on</strong> would be required to avoid ablati<strong>on</strong> damage <strong>and</strong> over-exposure of<br />
<strong>the</strong> film. Since <strong>the</strong> film is by its nature disposable, damage would at least not be a<br />
catastrophe. In practical terms though, this is of little relevance since suitable film<br />
is now difficult to obtain in appropriate quantities <strong>and</strong> requires lengthy processing,<br />
digitizati<strong>on</strong> <strong>and</strong> subsequent image analysis. Polaroid self-developing film is no l<strong>on</strong>ger<br />
in producti<strong>on</strong>.<br />
For informati<strong>on</strong>, <strong>the</strong>re is a closely related material which can also be used for <strong>beam</strong><br />
size determinati<strong>on</strong>; namely self-developing X-ray dosimetry film 8 . Similar products<br />
8 E. g. http://www.gafchromic.com.
132 8. Beam cross-secti<strong>on</strong> diagnostics<br />
have been used <strong>on</strong> synchrotr<strong>on</strong>s for <strong>beam</strong> profiling <strong>and</strong> have broadly similar advantages<br />
<strong>and</strong> drawbacks as self-developing photographic film. However, <strong>the</strong> resoluti<strong>on</strong><br />
of dosimetry film (ca. 100 µm) is significantly worse than that for high quality photographic<br />
film <strong>and</strong> will be too low for many focused <strong>beam</strong> measurements <strong>on</strong> a free<br />
electr<strong>on</strong> laser source.<br />
Gas-filled detectors<br />
Gas proporti<strong>on</strong>al detecti<strong>on</strong> systems for X-rays are comm<strong>on</strong>ly based <strong>on</strong> ei<strong>the</strong>r wire<br />
grids[198] or, more recently, <strong>on</strong> metal strips lithographically printed <strong>on</strong>to ei<strong>the</strong>r traditi<strong>on</strong>al<br />
circuitboards orglass substrates[199]. Existinglarge-field commercial detectors<br />
typically have pixel sizes of <strong>the</strong> order of tens of micr<strong>on</strong>s, although it should be possible<br />
to lithographically produce dedicated <strong>beam</strong> imaging detectors with smaller pixel<br />
sizes,<strong>and</strong> resoluti<strong>on</strong> could be fur<strong>the</strong>r improved using pixel interpolati<strong>on</strong> algorithms.<br />
However, although <strong>the</strong>se detectors are sought after for <strong>the</strong>ir potential for measuring<br />
high global count rates <strong>and</strong> energy discriminati<strong>on</strong>,<strong>the</strong>y suffer from severe n<strong>on</strong>-linearity<br />
due to space charge effects. Thus high count-rates that are very localized, as would<br />
be experienced with free electr<strong>on</strong> laser <strong>beam</strong> imaging, would cause problems. Additi<strong>on</strong>ally,<br />
at high count rates <strong>the</strong>re are also problems with rapid c<strong>on</strong>taminati<strong>on</strong> of<br />
<strong>the</strong> gas <strong>and</strong> detector wires/elements,requiring very high gas flow rates <strong>and</strong> <strong>the</strong>refore<br />
high maintenance costs. These issues make <strong>the</strong>m highly unsuitable for direct <strong>beam</strong><br />
imaging purposes.<br />
Charge coupled device (CCD)<br />
Direct-detecti<strong>on</strong> CCD cameras for X-ray energies are commercially available with<br />
pixel sizes down to 8 x 8 µm 9 . This is not sufficient for <strong>the</strong> str<strong>on</strong>gest focusing that<br />
will be used <strong>on</strong> free electr<strong>on</strong> laser, where spot sizes around 1 µm or less will achieved.<br />
Depending <strong>on</strong> <strong>the</strong> energy range to be covered, a selecti<strong>on</strong> can be made between back<br />
thinned, fr<strong>on</strong>t illuminated <strong>and</strong> deep depleti<strong>on</strong> CCD types. However, <strong>the</strong>se sensors are<br />
specifically not designed for high flux density applicati<strong>on</strong>s; saturati<strong>on</strong> <strong>and</strong> damage<br />
occur at low irradiance.<br />
Significant effort has been channelled intodevelopingradiati<strong>on</strong> hard CCD cameras,<br />
<strong>the</strong> initial driver coming from improving <strong>the</strong> l<strong>on</strong>gevity of space-borne astr<strong>on</strong>omical<br />
instruments <strong>and</strong> remote observati<strong>on</strong> systems in <strong>the</strong> nuclear industry. Defects can be<br />
generated in <strong>the</strong> bulksilic<strong>on</strong> through exposure toradiati<strong>on</strong>, <strong>and</strong><strong>the</strong>se defects can <strong>the</strong>n<br />
become electrically active, leading to fur<strong>the</strong>r space-charge, charge leakage <strong>and</strong> charge<br />
trapping issues in CCDs[200]. Three key approaches have been taken to minimize <strong>the</strong><br />
degradati<strong>on</strong> effects inCCDs; i) engineering soluti<strong>on</strong>s such as guard structures, voltage<br />
biasing <strong>and</strong> a reducti<strong>on</strong> in <strong>the</strong> thickness of charge channels, ii) material developments<br />
such as reducing <strong>the</strong> c<strong>on</strong>taminati<strong>on</strong> defects in silic<strong>on</strong> or replacement of silic<strong>on</strong> with<br />
alternative insulator materials <strong>and</strong> iii) alternative structures such as p-channel CCDs<br />
or charge injecti<strong>on</strong> devices (CIDs).<br />
CIDs individually address each pixel in <strong>the</strong> detector <strong>and</strong> do not suffer from leakage<br />
of stored charge from <strong>on</strong>e pixel to ano<strong>the</strong>r. Commercial nuclear inspecti<strong>on</strong> CID<br />
systems are available for X-rays, infrared <strong>and</strong> <strong>the</strong> ultra-violett with a stated pixel<br />
9 See, for example, www.hamamatsu.com.
8.10. Positi<strong>on</strong> <strong>and</strong> centroiding 133<br />
size of 11.5 x 11.5 µm <strong>and</strong> a frame rate of up to 25 Hz 10 . A Thermo Scientific CID<br />
camera has been employed as part of <strong>the</strong> transverse <strong>beam</strong> profiler for <strong>the</strong> IFMIF-<br />
EVEDA prototype deuter<strong>on</strong> accelerator[201].<br />
As discussed in secti<strong>on</strong> 8.3, luminescent screens in c<strong>on</strong>juncti<strong>on</strong> with CCD cameras<br />
can be used for indirect detecti<strong>on</strong>. Using a scintillati<strong>on</strong> screen, imaging of <strong>the</strong> Xray<br />
<strong>beam</strong> from SRS dipole <strong>beam</strong>line 8.2 has been dem<strong>on</strong>strated using an attenuated<br />
Phot<strong>on</strong>ic Science CCD system. At <strong>the</strong> intensity levels experienced <strong>the</strong>re,<strong>the</strong> main<br />
risk of damage was assumed to be <strong>the</strong>rmal damage to <strong>the</strong> screen. For free electr<strong>on</strong><br />
laser <strong>the</strong> highest risk of damage will be ablati<strong>on</strong> of <strong>the</strong> screen, <strong>and</strong> hence attenuati<strong>on</strong><br />
of <strong>the</strong> <strong>beam</strong> will be essential.<br />
Multichannel plate (MCP)<br />
A number of commercially available <strong>beam</strong> imaging systems exist based <strong>on</strong> fibrecoupled<br />
MCP technology 11 <strong>and</strong> a large range of c<strong>on</strong>versi<strong>on</strong> media exist to enable<br />
<strong>the</strong> imaging of neutr<strong>on</strong> <strong>and</strong> electr<strong>on</strong> <strong>beam</strong>s in additi<strong>on</strong> to IR, UV <strong>and</strong> X-ray radiati<strong>on</strong>.<br />
However, <strong>the</strong>se systems are of limited applicati<strong>on</strong> to free electr<strong>on</strong> laser <strong>beam</strong>s<br />
since <strong>the</strong> inherent amplificati<strong>on</strong> due to <strong>the</strong> MCP is at odds with <strong>the</strong> requirement to<br />
str<strong>on</strong>gly attenuate <strong>the</strong> <strong>beam</strong>.<br />
Solid State Detectors<br />
For many applicati<strong>on</strong>s <strong>on</strong> existing synchrotr<strong>on</strong> sources, silic<strong>on</strong> pixel detectors (often<br />
referred to as M<strong>on</strong>olithic Active Pixel Sensors, MAPS) or hybrid pixel detectors,<br />
typified by <strong>the</strong> PILATUS system[202], are seen as a significant emergent technology.<br />
They combine volume manufacture with small pixel sizes,large dynamic range, high<br />
count-rates <strong>and</strong> fast readout. However, in comm<strong>on</strong> with CCD-based systems <strong>the</strong><br />
irreliance <strong>on</strong> silic<strong>on</strong> based lithographic plates makes <strong>the</strong>m susceptible to radiati<strong>on</strong><br />
damage at modest <strong>beam</strong> intensities.<br />
8.10 Positi<strong>on</strong> <strong>and</strong> centroiding<br />
Sampling techniques<br />
Beam centroidingis typically performed bysamplingpart of<strong>the</strong> <strong>beam</strong>, ei<strong>the</strong>r spatially<br />
or in intensity. The basic objective in measuring <strong>the</strong> centroid is to measure <strong>the</strong> <strong>beam</strong><br />
positi<strong>on</strong> <strong>and</strong> angle mainly for <strong>the</strong> purposes of <strong>beam</strong> stabilizati<strong>on</strong> through feedback<br />
c<strong>on</strong>trol.<br />
Solid state photo-emissi<strong>on</strong> m<strong>on</strong>itors<br />
Blade m<strong>on</strong>itors are an example of spatial sampling <strong>and</strong> are widely used <strong>on</strong> synchrotr<strong>on</strong>s.<br />
Mortazavi et al. [203] describe an early implementati<strong>on</strong> at <strong>the</strong> NSLS<br />
(Brookhaven) giving a sensitivity of a few micr<strong>on</strong>s. Thin tungsten blades positi<strong>on</strong>ed<br />
edge-<strong>on</strong> to <strong>the</strong> <strong>beam</strong> intercept <strong>the</strong> periphery of <strong>the</strong> <strong>beam</strong> <strong>and</strong> <strong>the</strong> induced photocurrent<br />
is proporti<strong>on</strong>al to <strong>the</strong> amount of <strong>beam</strong> <strong>the</strong>y intercept. If two identical blades are<br />
10 www.<strong>the</strong>rmo.com/com/cda/product/.<br />
11 www.sciner.com/MCP/index.htm <strong>and</strong> www.<strong>beam</strong>imaging.com.
134 8. Beam cross-secti<strong>on</strong> diagnostics<br />
positi<strong>on</strong>ed ei<strong>the</strong>r side of <strong>the</strong> <strong>beam</strong>, <strong>the</strong>n <strong>the</strong> relative intensity <strong>the</strong>y see is a measure<br />
of <strong>the</strong> <strong>beam</strong> positi<strong>on</strong> relative to <strong>the</strong> centre of <strong>the</strong> gap between <strong>the</strong> blades. These<br />
devices are thus centroid m<strong>on</strong>itors giving <strong>beam</strong> positi<strong>on</strong> relative to <strong>the</strong> blade gap <strong>–</strong><br />
but <strong>the</strong>re is an underlying assumpti<strong>on</strong> that <strong>the</strong> <strong>beam</strong> intensity profile is symmetric.<br />
Johns<strong>on</strong> <strong>and</strong> Oversluizen[204] also assert that ”<strong>the</strong> apparent deviati<strong>on</strong> of <strong>the</strong> phot<strong>on</strong><br />
<strong>beam</strong> from <strong>the</strong> m<strong>on</strong>itor centroid depends <strong>on</strong> <strong>the</strong> <strong>on</strong> <strong>the</strong> size of <strong>the</strong> [...] <strong>beam</strong> relative<br />
to <strong>the</strong> blade gap”, though it is not clear why this should be if <strong>the</strong> detector <strong>and</strong><br />
phot<strong>on</strong> <strong>beam</strong> are symmetric (<strong>the</strong>re are however problems created by stray light from<br />
adjacent magnets, q.v.). It is however clearly important that <strong>the</strong> blades be identical<br />
both physically <strong>and</strong> also in terms of photoelectric yield. The latter is a c<strong>on</strong>diti<strong>on</strong><br />
that is hard to ensure given that photoemissi<strong>on</strong> is a predominantly surface effect <strong>and</strong><br />
so susceptible to c<strong>on</strong>taminati<strong>on</strong> from <strong>the</strong> residual vacuum. Aging of <strong>the</strong> blades in a<br />
white synchrotr<strong>on</strong> <strong>beam</strong> is likely <strong>and</strong> if <strong>the</strong> blades age differently <strong>the</strong>n this would lead<br />
to l<strong>on</strong>g-term change in <strong>the</strong> null positi<strong>on</strong> of <strong>the</strong> <strong>beam</strong> relative to <strong>the</strong> gap.<br />
A similar approach uses two parallel horiz<strong>on</strong>tal wires or rods with a fixed gap[205].<br />
The advantage of <strong>the</strong> blade approach is that blades are easier to cool than wires <strong>and</strong><br />
less invasive than rods. Alkire et al. [206] report a relative accuracy of ±5 µm for<br />
<strong>the</strong>ir m<strong>on</strong>itor which uses 1.5 mm diameter tungsten rods of 12 cm length <strong>and</strong> with a<br />
centre to centre spacing of 7.9 mm.<br />
Tungsten or molybdenum are often used as <strong>the</strong> blade material since <strong>the</strong>ir high<br />
melting point <strong>and</strong> hardness makes <strong>the</strong>m resistant to <strong>the</strong> high powers produced by<br />
3 rd generati<strong>on</strong> synchrotr<strong>on</strong> sources. However, when high-K undulators are used <strong>on</strong><br />
high-energy synchrotr<strong>on</strong>s <strong>the</strong> total power can be such that accidental exposure of<br />
such materials to <strong>the</strong> central part of <strong>the</strong> <strong>beam</strong> could be damaging. At <strong>the</strong> APS,<br />
CVD diam<strong>on</strong>d was chosen since it has 10 times higher <strong>the</strong>rmal c<strong>on</strong>ductivity than<br />
molybdenum, <strong>and</strong> lower <strong>the</strong>rmal expansi<strong>on</strong> allied to high strength <strong>and</strong> stiffness[207].<br />
These m<strong>on</strong>itors have sub-micr<strong>on</strong> sensitivity. For initial tests, <strong>the</strong> diam<strong>on</strong>d was coated<br />
with tungsten to give high photo-emissivity <strong>and</strong> electrical c<strong>on</strong>ductivity. Later, a 1<br />
µm gold coating <strong>on</strong> 150 µm diam<strong>on</strong>d blades was used[208]. This approach raises <strong>the</strong><br />
prospect that it may be possible to coat <strong>the</strong> blades with a low-Z material (e.g. carb<strong>on</strong><br />
or beryllium) that would resist ablati<strong>on</strong> from a free electr<strong>on</strong> laser <strong>beam</strong>, which would<br />
o<strong>the</strong>rwise be a major c<strong>on</strong>cern when using this type of m<strong>on</strong>itor <strong>on</strong> a such a <strong>beam</strong>.<br />
An advantage of <strong>the</strong> blade type m<strong>on</strong>itor is that extra blades can be added in<br />
various c<strong>on</strong>figurati<strong>on</strong>s such as a vertical cross[209], diag<strong>on</strong>al cross [210], etc. <strong>–</strong> see<br />
Figure 8.12. Thus, a single m<strong>on</strong>itor allows bi-axial positi<strong>on</strong>al informati<strong>on</strong> to be<br />
calculated. Two such m<strong>on</strong>itors l<strong>on</strong>gitudinally separated give <strong>beam</strong> angle informati<strong>on</strong>,though<br />
each should use a different blade arrangement to prevent <strong>the</strong> blades of<br />
<strong>the</strong> sec<strong>on</strong>d m<strong>on</strong>itor from lying in <strong>the</strong> shadow of <strong>the</strong> blades of <strong>the</strong> first m<strong>on</strong>itor[207].<br />
For <strong>the</strong> centroid measurement to give an absolute positi<strong>on</strong> <strong>and</strong> angle, <strong>the</strong> m<strong>on</strong>itors<br />
must be accurately mapped to an external reference frame. However, if <strong>the</strong>re is an<br />
asymmetry in <strong>the</strong> resp<strong>on</strong>se of <strong>the</strong> blades (e.g. due to surface c<strong>on</strong>taminati<strong>on</strong>) <strong>the</strong>n,<br />
when <strong>the</strong> m<strong>on</strong>itor is nulled, <strong>the</strong> <strong>beam</strong> centroid will not be centered <strong>on</strong> <strong>the</strong> gap. There<br />
is thus an error in <strong>the</strong> inferred absolute positi<strong>on</strong> relative to <strong>the</strong> external reference<br />
frame. Thus <strong>the</strong> absolute positi<strong>on</strong>al accuracy of a blade type m<strong>on</strong>itor is not always<br />
easy to define.<br />
In<strong>the</strong>caseofsynchrotr<strong>on</strong>lightfromdipoles, <strong>the</strong>sedetectorscanbemadeeffectively<br />
transparent to <strong>the</strong> X-ray <strong>beam</strong> by being designed to intercept <strong>on</strong>ly <strong>the</strong> UV light that<br />
hasamuchlarger openingangle than<strong>the</strong>X-rays, whichthuspassundisturbedthrough<br />
<strong>the</strong> blade gap (Figure 8.13). The same approach can also be used with undulator
8.10. Positi<strong>on</strong> <strong>and</strong> centroiding 135<br />
(a) (b) (c) (d)<br />
Figure 8.12: Possible arrangements for bi-axial blade m<strong>on</strong>itors. (a) simple vertical cross; (b) a diag<strong>on</strong>al cross<br />
allows better horiz<strong>on</strong>tal sensitivity when <strong>the</strong> horiz<strong>on</strong>tal opening angle changes c<strong>on</strong>siderably if an undulator is<br />
tuned from low to high K; (c) <strong>and</strong> (d) upstream <strong>and</strong> downstream arrangements used at <strong>the</strong> APS to prevent<br />
shadowing effects [40] (<strong>the</strong> tilted horiz<strong>on</strong>tal blades reduce <strong>the</strong> sensitivity to dipole radiati<strong>on</strong>).<br />
UV<br />
M<strong>on</strong>itor blades<br />
X-rays<br />
Figure 8.13: Figure 9 -A blade m<strong>on</strong>itor can be transparent at short wavelengths <strong>on</strong> a synchrotr<strong>on</strong> source due<br />
to <strong>the</strong> reducti<strong>on</strong> in opening angle as <strong>the</strong> wavelength decreases.<br />
sources since <strong>the</strong> emissi<strong>on</strong> outside <strong>the</strong> central c<strong>on</strong>e is at a l<strong>on</strong>ger wavelength than <strong>the</strong><br />
fundamental.However, free electr<strong>on</strong> laser radiati<strong>on</strong> does not have <strong>the</strong> same properties<br />
<strong>and</strong> so this approach cannot be used. There will be sp<strong>on</strong>taneous radiati<strong>on</strong> from <strong>the</strong><br />
undulator, but this will be at a low intensity due to <strong>the</strong> low average current <strong>and</strong> may<br />
notbeofsufficientintensitytomeasure. Fur<strong>the</strong>rmore, thisapproachhasitsdrawbacks<br />
since <strong>the</strong> phot<strong>on</strong>s being detected are not <strong>the</strong> <strong>on</strong>es being used in <strong>the</strong> experiment <strong>and</strong><br />
<strong>on</strong>e must assume <strong>the</strong>re is a unique <strong>and</strong> c<strong>on</strong>sistent spatial correlati<strong>on</strong> between <strong>the</strong><br />
spectral comp<strong>on</strong>ents in <strong>the</strong> <strong>beam</strong>.<br />
Whilst <strong>the</strong> range of wavelengths present in a synchrotr<strong>on</strong> <strong>beam</strong> can be used to advantage<br />
as described above, it can lead to problems when using photo-emissive type<br />
m<strong>on</strong>itors with inserti<strong>on</strong> devices <strong>on</strong> synchrotr<strong>on</strong> sources. The electr<strong>on</strong> yield is much<br />
greater at VUV wavelengths <strong>and</strong> thus <strong>the</strong>se m<strong>on</strong>itors are disproporti<strong>on</strong>ately sensitive<br />
to <strong>the</strong> low-level l<strong>on</strong>g-wavelength radiati<strong>on</strong> coming from <strong>the</strong> dipoles <strong>and</strong> steering magnets<br />
that surround <strong>the</strong> inserti<strong>on</strong> device. Extreme lengths have been used to overcome<br />
this problem at <strong>the</strong> APS where <strong>the</strong> machine lattice has been modified to separate <strong>the</strong><br />
inserti<strong>on</strong> device light from <strong>the</strong> stray light in order to facilitate sub-micr<strong>on</strong> level orbit
136 8. Beam cross-secti<strong>on</strong> diagnostics<br />
correcti<strong>on</strong>[211]. Galimberti et al. [212] describe a different approach that makes <strong>the</strong><br />
<strong>beam</strong> positi<strong>on</strong> m<strong>on</strong>itor <strong>on</strong>ly sensitive to <strong>the</strong> X-rays that are being used in <strong>the</strong> experiment.<br />
They have improved <strong>the</strong> blade m<strong>on</strong>itor by adding electr<strong>on</strong> energy analyzers<br />
to measure <strong>the</strong> blade signals. Thus <strong>the</strong>y can select <strong>on</strong>ly <strong>the</strong> electr<strong>on</strong>s emitted by <strong>the</strong><br />
fundamental radiati<strong>on</strong> <strong>and</strong> so isolate it from any low energy background <strong>and</strong> even<br />
electr<strong>on</strong>s emitted by higher harm<strong>on</strong>ics from <strong>the</strong> undulator. This is a much more sophisticated<br />
approach to that suggested by Warwick et al. [210] in which <strong>the</strong> blades are<br />
reverse-biased to prevent <strong>the</strong> low energy electr<strong>on</strong>s leaving <strong>the</strong> surface. Whe<strong>the</strong>r such<br />
precauti<strong>on</strong>s would be needed <strong>on</strong> a free electr<strong>on</strong> laser source would clearly depend <strong>on</strong><br />
<strong>the</strong> nature of <strong>the</strong> electr<strong>on</strong> <strong>beam</strong> <strong>transport</strong>, but it would be natural to assume <strong>the</strong> effect<br />
would be much reduced since <strong>the</strong> electr<strong>on</strong> path is straight <strong>and</strong> <strong>the</strong> l<strong>on</strong>g undulator<br />
length should limit <strong>the</strong> acceptance aperture of radiati<strong>on</strong> from o<strong>the</strong>r sources.<br />
In general, blade type m<strong>on</strong>itors when used <strong>on</strong> undulator sources are sensitive to<br />
<strong>the</strong> undulator tuning due to <strong>the</strong> changing radiati<strong>on</strong> pattern as <strong>the</strong> undulator K-value<br />
is changed. This makes positi<strong>on</strong> c<strong>on</strong>trol to sub-micr<strong>on</strong> levels difficult. A smart XBPM<br />
system (SBPM) has been developed at <strong>the</strong> APS in which <strong>the</strong> resp<strong>on</strong>se of <strong>the</strong> XPBM is<br />
automatically characterized under all possible operating c<strong>on</strong>diti<strong>on</strong>s of <strong>the</strong> undulator<br />
so that <strong>the</strong>se effects can be automatically corrected for[208].<br />
The effect of any change in <strong>beam</strong> footprint with wavelength must be c<strong>on</strong>sidered<br />
carefully for free electr<strong>on</strong> laser <strong>beam</strong>s.This source approximates to a coherent Gaussian<br />
source <strong>and</strong> thus <strong>the</strong> divergence will be roughly proporti<strong>on</strong>al to wavelength. We<br />
can <strong>the</strong>refore expect a c<strong>on</strong>siderable change in <strong>beam</strong> footprint at <strong>the</strong> m<strong>on</strong>itor as <strong>the</strong><br />
wavelength of it tuned. This will certainly change <strong>the</strong> sensitivity <strong>and</strong> resoluti<strong>on</strong> of <strong>the</strong><br />
m<strong>on</strong>itor at different wavelengths <strong>and</strong> <strong>the</strong>re is also <strong>the</strong> issue of <strong>the</strong> inferred positi<strong>on</strong><br />
being dependent <strong>on</strong> <strong>beam</strong>size. Possibly more important are <strong>the</strong> risk of ablati<strong>on</strong> <strong>and</strong><br />
<strong>the</strong> disrupti<strong>on</strong> to <strong>the</strong> <strong>beam</strong>. Providing <strong>the</strong> blades sit <strong>on</strong>ly in <strong>the</strong> wings of <strong>the</strong> <strong>beam</strong>,<br />
ablati<strong>on</strong> <strong>and</strong> diffractive disrupti<strong>on</strong> to <strong>the</strong> downstream <strong>beam</strong> may not be an issue.<br />
But if <strong>the</strong> exp<strong>and</strong>s significantly, <strong>the</strong> blades will cut <strong>the</strong> <strong>beam</strong> at a positi<strong>on</strong> of greater<br />
intensity <strong>and</strong> so both <strong>the</strong> risk of ablati<strong>on</strong> <strong>and</strong> diffractive disrupti<strong>on</strong> will increase. It<br />
may thus be necessary for a blade type m<strong>on</strong>itor to have blades that move depending<br />
<strong>on</strong> <strong>the</strong> source’s wavelength.<br />
In order to eliminate <strong>the</strong> sensitivity of a blade m<strong>on</strong>itor to <strong>beam</strong> size, schemes using<br />
two triangular wedge swith a gap between <strong>the</strong>m running at 45 ◦ to <strong>the</strong> horiz<strong>on</strong>tal have<br />
been developed[204] (see Figure 8.14(a)). The gap must be designed to intercept<br />
enough of <strong>the</strong> <strong>beam</strong> to get a decent signal with <strong>the</strong> smallest expected <strong>beam</strong>size (i.e. at<br />
<strong>the</strong> shortest wavelength). This means that any significant increase in <strong>beam</strong> size will<br />
resultinasignificantloss inthroughput. Avariablegapwill <strong>the</strong>refore beessential with<br />
a free electr<strong>on</strong> laser source. Even <strong>the</strong>n, this type of m<strong>on</strong>itor will be more disruptive to<br />
<strong>the</strong> <strong>beam</strong> <strong>and</strong> be at greater risk of ablati<strong>on</strong> <strong>the</strong>n blade m<strong>on</strong>itors <strong>and</strong> so is unlikely to<br />
be useful with a free electr<strong>on</strong> laser source. A refinement of this scheme was reported<br />
by Mitsuhashi <strong>and</strong> tested at Spring-8[213]. Here, two wedge m<strong>on</strong>itors are placed<br />
to just intercept <strong>the</strong> periphery of <strong>the</strong> <strong>beam</strong>, thus reducing <strong>the</strong> fracti<strong>on</strong> of <strong>the</strong> <strong>beam</strong><br />
intercepted <strong>and</strong> allowing bi-axial m<strong>on</strong>itoring. Initially, <strong>the</strong> m<strong>on</strong>itors were composed<br />
of triangular wedges but this design was found to be sensitive undulator gap. Thus a<br />
revised symmetrical scheme was developed <strong>and</strong> tested <strong>–</strong> see Figure 8.14(b) <strong>–</strong> <strong>and</strong> this<br />
reduced <strong>the</strong> sensitivity to <strong>the</strong> gap around ten times. Note <strong>the</strong> wedges are angled to<br />
<strong>the</strong> <strong>beam</strong> to reduce <strong>the</strong> power loading.<br />
The wedge type m<strong>on</strong>itor can be extended to give bi-axial positi<strong>on</strong> detecti<strong>on</strong> by<br />
using a classic quadrant detector. These can be made using metal-foil photodiodes
8.10. Positi<strong>on</strong> <strong>and</strong> centroiding 137<br />
X-ray <strong>beam</strong><br />
Wedge plates<br />
Signal out<br />
(a) (b)<br />
Upper electrodes<br />
Lower electrodes<br />
Figure 8.14: (a) The Wedge positi<strong>on</strong> m<strong>on</strong>itor eliminates <strong>the</strong> sensitivity to <strong>beam</strong> footprint of <strong>the</strong> blade counterpart<br />
but is more invasive; (b) <strong>the</strong> symmetric design of Mitsuhashi et al. reduces <strong>the</strong> <strong>beam</strong> loss <strong>and</strong> has low<br />
sensitivity to undulator tuning.<br />
but are also available commercially using semic<strong>on</strong>ductor juncti<strong>on</strong> photodiodes[214].<br />
One problem with using semi-c<strong>on</strong>ductor devices is that <strong>the</strong>y tend to be insensitive<br />
at <strong>the</strong> edges <strong>and</strong> thus <strong>the</strong> amount of <strong>beam</strong> overlap needed to give a signal is increased<br />
to <strong>the</strong> detriment of <strong>the</strong> transmitted <strong>beam</strong>. Kenney et al. [215] describe how activeedge<br />
silic<strong>on</strong> detectors, which are active to within a few micr<strong>on</strong>s of <strong>the</strong> detector edge,<br />
can be used in various geometries for positi<strong>on</strong>, profile <strong>and</strong> intensity m<strong>on</strong>itoring. For<br />
example, a quadrant detector with a small hole at <strong>the</strong> centre can be used to m<strong>on</strong>itor<br />
<strong>the</strong> stability of a tightly focused <strong>beam</strong>. The <strong>beam</strong> is focused through <strong>the</strong> hole <strong>and</strong><br />
<strong>on</strong>ly <strong>the</strong> periphery of <strong>the</strong> <strong>beam</strong> is stopped by <strong>the</strong> detector. The focus positi<strong>on</strong> is<br />
stabilized using feedback c<strong>on</strong>trol based <strong>on</strong> <strong>the</strong> quadrant signals. An example device<br />
with 100 µm diameter hole is pictured whilst test were made <strong>on</strong> a simpler single<br />
element torus with 200 µm hole. This device showed excellent resp<strong>on</strong>se uniformity<br />
to 12.5 keV X-rays. The effect of diffracti<strong>on</strong> at <strong>the</strong> hole with a coherent free electr<strong>on</strong><br />
laser <strong>beam</strong> is a potential problem with this approach, as is <strong>the</strong> high risk of damaging<br />
<strong>the</strong> detector if <strong>the</strong> central part of <strong>the</strong> <strong>beam</strong> is inadvertently steered <strong>on</strong>to it.<br />
A significant disadvantage of <strong>the</strong> classic quadrant detector is that <strong>the</strong> fracti<strong>on</strong> of<br />
<strong>the</strong> radiati<strong>on</strong> transmitted, i.e. that which can pass through <strong>the</strong> hole in <strong>the</strong> middle,<br />
may not be large enough. Shu et al. at <strong>the</strong> APS[216, 217] have developed a quadrant<br />
detector that has a high transmissi<strong>on</strong> to hard X-rays. The detector is based <strong>on</strong> a<br />
25 mm diameter CVD diam<strong>on</strong>d disc of 150 µm thickness. This has a transmissi<strong>on</strong><br />
of 78% at 10 keV. The quadrant pattern is formed with a 0.2 µm aluminum coating<br />
<strong>on</strong> <strong>the</strong> disc. In its simplest form, <strong>the</strong> photocurrent from <strong>the</strong> aluminum sectors is<br />
independently m<strong>on</strong>itored <strong>and</strong> gives <strong>the</strong> positi<strong>on</strong>al informati<strong>on</strong>.The diam<strong>on</strong>d in this<br />
scheme simply acts as a support for <strong>the</strong> aluminum electrodes that can withst<strong>and</strong> <strong>the</strong><br />
intense synchrotr<strong>on</strong> <strong>beam</strong>.<br />
A more sophisticated approach uses <strong>the</strong> photoc<strong>on</strong>ductive properties of insulatingtype<br />
(IIa) CVD diam<strong>on</strong>d in which <strong>the</strong> diam<strong>on</strong>d becomes c<strong>on</strong>ductive when exposed to<br />
<strong>the</strong>X-rays. Thealuminium patternis replicated <strong>on</strong>bothsidesof<strong>the</strong>diam<strong>on</strong>ddisc <strong>and</strong><br />
a bias applied across <strong>the</strong> fr<strong>on</strong>t <strong>and</strong> back electrodes <strong>–</strong> Figure 8.15. On exposure to Xrays,<br />
<strong>the</strong> diam<strong>on</strong>d becomes c<strong>on</strong>ductive <strong>and</strong> a current flows. Since <strong>the</strong> c<strong>on</strong>ductivity is<br />
dependent<strong>on</strong> <strong>the</strong> absorbed X-raypower, <strong>the</strong> current is proporti<strong>on</strong>al to<strong>the</strong> intercepted<br />
X-ray intensity. Also,<strong>the</strong> sensitivity increases with phot<strong>on</strong> energy <strong>and</strong> <strong>the</strong> detector
138 8. Beam cross-secti<strong>on</strong> diagnostics<br />
Bias<br />
Diam<strong>on</strong>d disc<br />
Al quadrant electrodes<br />
X-ray <strong>beam</strong><br />
Figure 8.15: Quadrant detector based <strong>on</strong> <strong>the</strong> photoc<strong>on</strong>ductivity of diam<strong>on</strong>d.<br />
Output signals<br />
less sensitive to stray light from bending magnets etc.<br />
There are o<strong>the</strong>r ways of spatially sampling <strong>the</strong> <strong>beam</strong> such as using a pin-hole<br />
array[218] but <strong>the</strong>se are significantly more invasive <strong>and</strong> ablati<strong>on</strong> damage is highly<br />
likely.<br />
Solid state fluorescence m<strong>on</strong>itors<br />
Measurement of <strong>the</strong> incident phot<strong>on</strong> intensity <strong>on</strong> <strong>the</strong> m<strong>on</strong>itor by recording <strong>the</strong> photoemissi<strong>on</strong><br />
in some way is widely used because <strong>the</strong> electr<strong>on</strong> yields are high <strong>and</strong> photoemissi<strong>on</strong><br />
is <strong>the</strong> dominant de-excitati<strong>on</strong> process until <strong>the</strong> Ga K-edge at ∼ 10 keV.<br />
Never<strong>the</strong>less, <strong>the</strong> radiative yield is appreciable above c. 5 keV <strong>and</strong> thus fluorescence<br />
presents an alternative detecti<strong>on</strong> route. Alkire et al. [219] describe a simple positi<strong>on</strong><br />
m<strong>on</strong>itor c<strong>on</strong>sisting of a 0.5 µm of Cr or Ti through which <strong>the</strong> <strong>beam</strong> (5 to 25 keV)<br />
passes with little attenuati<strong>on</strong>. An array of four PIN photodiodes surround <strong>the</strong> <strong>beam</strong><br />
axis in a vertical cross arrangement just upstream of <strong>the</strong> foil <strong>–</strong> Figure 8.16. The diodes<br />
record <strong>the</strong> fluorescence signal <strong>and</strong> give <strong>the</strong> same effect as <strong>the</strong> four blades of a normal<br />
bi-axial <strong>beam</strong> positi<strong>on</strong> m<strong>on</strong>itor. The advantage is that <strong>the</strong> <strong>beam</strong> is measured over its<br />
full cross-secti<strong>on</strong> <strong>and</strong> so <strong>the</strong> true centre of intensity of <strong>the</strong> <strong>beam</strong> is measured. The<br />
measured positi<strong>on</strong> sensitivity was 1 <strong>–</strong> 2 µm. As with o<strong>the</strong>r techniques that involve<br />
passing <strong>the</strong> <strong>beam</strong> through a foil, <strong>the</strong> c<strong>on</strong>cerns with a free electr<strong>on</strong> laser <strong>beam</strong> are<br />
ablati<strong>on</strong> of <strong>the</strong> foil a diffractive disrupti<strong>on</strong> to <strong>the</strong> transmitted <strong>beam</strong>.
8.10. Positi<strong>on</strong> <strong>and</strong> centroiding 139<br />
X-ray <strong>beam</strong><br />
Foil<br />
Photo-diodes<br />
Figure 8.16: Photodiode array BPM used to collect fluorescence from a thin foil.<br />
Gas phase photo-i<strong>on</strong>isati<strong>on</strong> m<strong>on</strong>itors<br />
Split-plate i<strong>on</strong> chambers are examples of intensity sampling. This approach is more<br />
sophisticated than blade m<strong>on</strong>itors as it samples <strong>the</strong> whole spatial extent of <strong>the</strong> <strong>beam</strong><br />
<strong>and</strong> should thus give a more reliable measure of <strong>the</strong> <strong>beam</strong> centre of intensity if <strong>the</strong><br />
<strong>beam</strong> is asymmetric or inhomogeneous. The <strong>beam</strong> passes through a gas at a low<br />
pressure between electrode plates with a high voltage bias between <strong>the</strong>m, <strong>and</strong> <strong>the</strong> i<strong>on</strong><br />
yield is recorded as a current from <strong>the</strong> plates. By splitting <strong>on</strong>e of <strong>the</strong> plates diag<strong>on</strong>ally<br />
(Figure 8.17), each half of <strong>the</strong> split plate receives a different signal depending <strong>on</strong> <strong>the</strong><br />
<strong>beam</strong> positi<strong>on</strong> relative to <strong>the</strong> middle of <strong>the</strong> slit <strong>and</strong> <strong>the</strong> i<strong>on</strong> chamber records positi<strong>on</strong><br />
parallel to <strong>the</strong> plane of <strong>the</strong> plates. The diag<strong>on</strong>al split improves <strong>the</strong> linearity of <strong>the</strong><br />
m<strong>on</strong>itor at <strong>the</strong> expense of sensitivity near <strong>the</strong> null positi<strong>on</strong>[220].<br />
A split i<strong>on</strong>-chamber that can measure <strong>the</strong> vertical positi<strong>on</strong> of two partially overlapping<br />
<strong>beam</strong>s simultaneously has been developed at <strong>the</strong> Cornell High Energy Synchrotr<strong>on</strong><br />
Source CHESS with a reported accuracy better than 10 µm <strong>and</strong> a b<strong>and</strong>width<br />
greater than100Hzoveralinear rangeof5mm[221]. Theaccuracywas limitedmainly<br />
by drift in <strong>the</strong> analogue signal electr<strong>on</strong>ics <strong>and</strong> <strong>the</strong> i<strong>on</strong> chamber was actually able to<br />
resolve movements at <strong>the</strong> micr<strong>on</strong> level. Differentiati<strong>on</strong> of <strong>the</strong> two <strong>beam</strong>s was achieved<br />
by designing <strong>the</strong> collecting field produced by <strong>the</strong> bias electrodes such that <strong>the</strong> col-
140 8. Beam cross-secti<strong>on</strong> diagnostics<br />
X-ray <strong>beam</strong><br />
+<br />
Bias plate<br />
Wedge plates<br />
Figure 8.17: Arrangement of <strong>beam</strong> <strong>and</strong> plates for a split plate i<strong>on</strong> chamber.<br />
Signal out<br />
lecting electrodes collect <strong>on</strong>ly i<strong>on</strong>s from <strong>the</strong> n<strong>on</strong>-overlapping edges of <strong>the</strong> two <strong>beam</strong>s.<br />
Thus, <strong>the</strong> i<strong>on</strong> path is short <strong>and</strong> this also improves linearity <strong>and</strong> b<strong>and</strong>width.<br />
Two make a bi-axial measurement, two i<strong>on</strong>-chambers are placed sequentially with<br />
<strong>the</strong>ir plate-pairs orthog<strong>on</strong>al. Schildkamp <strong>and</strong> Praderv<strong>and</strong>[222] describe a system<br />
tested at CHESS which achieved a resoluti<strong>on</strong> below 1 µm with a b<strong>and</strong>width of 1000<br />
Hz.<br />
Important c<strong>on</strong>siderati<strong>on</strong>s when using i<strong>on</strong> chambers are:<br />
• different gases may be needed to cover different phot<strong>on</strong> energy ranges;<br />
• <strong>the</strong> effect of saturati<strong>on</strong> <strong>and</strong> recombinati<strong>on</strong> <strong>on</strong> <strong>the</strong> measured current;<br />
• <strong>the</strong> transit time of <strong>the</strong> electr<strong>on</strong>s <strong>and</strong> i<strong>on</strong>s.<br />
A noble gas is preferred as it eliminates asymmetries that result when using polar<br />
molecules <strong>and</strong> lighter gases reduce <strong>the</strong> transit time of <strong>the</strong> i<strong>on</strong>s to <strong>the</strong> plates <strong>and</strong> so<br />
help reduce <strong>the</strong> build up of space charge in <strong>the</strong> chamber. Whilst <strong>the</strong> i<strong>on</strong> chamber<br />
cannot be damaged by high intensities, <strong>the</strong> probability of recombinati<strong>on</strong> before <strong>the</strong><br />
i<strong>on</strong>s reach <strong>the</strong> plates increases in proporti<strong>on</strong> to <strong>the</strong> <strong>beam</strong> intensity <strong>and</strong> <strong>the</strong> square of<br />
<strong>the</strong> distance travelled. If care is not taken, false positi<strong>on</strong> changes can be deduced as<br />
<strong>the</strong> <strong>beam</strong> intensity is changed. The upper limit <strong>on</strong> <strong>the</strong> detecti<strong>on</strong> b<strong>and</strong>width is set be<br />
<strong>the</strong> transit time of <strong>the</strong> i<strong>on</strong>s to <strong>the</strong> plates; increasing <strong>the</strong> b<strong>and</strong>width requires reducing<br />
<strong>the</strong> plate gap <strong>and</strong> increasing <strong>the</strong> bias potential[223].<br />
The o<strong>the</strong>r main limitati<strong>on</strong> is <strong>the</strong> need for a gas. With a transversely coherent<br />
<strong>beam</strong>, it is not desirable to use windows to isolate <strong>the</strong> gas <strong>and</strong> so <strong>the</strong> chamber must be<br />
isolated by means of differential pumping. In <strong>the</strong> c<strong>on</strong>text of a free electr<strong>on</strong> laser this is<br />
not such a major issue as gas attenuators will be a comm<strong>on</strong> feature <strong>and</strong> <strong>the</strong> significant
8.11. Wavefr<strong>on</strong>t measurements 141<br />
advantage of <strong>the</strong> i<strong>on</strong>izati<strong>on</strong> chamber is that it can be c<strong>on</strong>sidered n<strong>on</strong>-invasive if <strong>the</strong><br />
gas pressure is low enough. The i<strong>on</strong> chamber can thus be used as an <strong>on</strong>-line diagnostic<br />
giving pulse-by-pulse <strong>beam</strong> centroid positi<strong>on</strong>.<br />
8.11 Wavefr<strong>on</strong>t measurements<br />
A wavefr<strong>on</strong>t is defined by <strong>the</strong> surface <strong>on</strong> which <strong>the</strong> radiati<strong>on</strong> field has <strong>the</strong> same phase<br />
(assuming a m<strong>on</strong>ochromatic source). The directi<strong>on</strong> of propagati<strong>on</strong> of <strong>the</strong> radiati<strong>on</strong> is<br />
perpendicular to this surface, hence measurements of <strong>the</strong> propagati<strong>on</strong> directi<strong>on</strong> can<br />
be used to find <strong>the</strong> wavefr<strong>on</strong>t <strong>–</strong> this is <strong>the</strong> principle of <strong>the</strong> Hartmann sensor described<br />
below.<br />
A complete characterizati<strong>on</strong> of <strong>the</strong> radiati<strong>on</strong> field at a particular wavelength requires<br />
a measurement of <strong>the</strong> magnitude <strong>and</strong> relative phase of <strong>the</strong> field. These results<br />
could <strong>the</strong>n be input into simulati<strong>on</strong>s to deduce <strong>the</strong> radiati<strong>on</strong> field at o<strong>the</strong>r locati<strong>on</strong>s in<br />
<strong>the</strong> <strong>beam</strong>line. Such measurements could in principle be made using a Hartmann-type<br />
wavefr<strong>on</strong>t sensor for a m<strong>on</strong>ochromatic source. For narrow-b<strong>and</strong> sources such as free<br />
electr<strong>on</strong> lasers, <strong>the</strong> wavefr<strong>on</strong>t sensor can be used to measure <strong>the</strong> tilt of <strong>the</strong> wavefr<strong>on</strong>t<br />
<strong>and</strong> ray tracing used to find <strong>the</strong> shape of <strong>the</strong> <strong>beam</strong> at o<strong>the</strong>r locati<strong>on</strong>s, assuming that<br />
diffracti<strong>on</strong> effects are not important.<br />
The Hartmann sensor works by splitting <strong>the</strong> <strong>beam</strong> to be diagnosed into an array<br />
of ”mini-<strong>beam</strong>s” ei<strong>the</strong>r by passing <strong>the</strong> <strong>beam</strong> through grid of holes (Hartmann plate)<br />
or an array of lenslets (Shack-Hartmann array) <strong>and</strong> comparing <strong>the</strong> resultant pinhole<br />
images or microlens focal positi<strong>on</strong>s <strong>on</strong> a 2D detector with those from a reference<br />
wavefr<strong>on</strong>t. Variati<strong>on</strong>s in <strong>the</strong> positi<strong>on</strong> of each resultant spot can <strong>the</strong>n be used to<br />
determine <strong>the</strong> local slope in <strong>the</strong> wavefr<strong>on</strong>t. Let Sx ij denote <strong>the</strong> measured slope in <strong>the</strong><br />
x-directi<strong>on</strong> at <strong>the</strong> spot i,j <strong>on</strong> <strong>the</strong> detector, <strong>the</strong>n<br />
Sx ij = dWij<br />
dx<br />
λ dφ<br />
=<br />
2π dx<br />
(8.2)<br />
where W is <strong>the</strong> optical path difference <strong>and</strong> φ is <strong>the</strong> phase. A similar equati<strong>on</strong> can<br />
be written for <strong>the</strong> y-directi<strong>on</strong>. The field strength can be derived from <strong>the</strong> intensity<br />
of <strong>the</strong> spots. The actual wavefr<strong>on</strong>t W has to be rec<strong>on</strong>structed from <strong>the</strong> measured<br />
slopes <strong>–</strong> <strong>the</strong>re are two main methods of doing this, ei<strong>the</strong>r by assuming <strong>the</strong> wavefr<strong>on</strong>t<br />
can be written as a low (normally sec<strong>on</strong>d) order polynomial in <strong>the</strong> local co-ordinates<br />
(z<strong>on</strong>al method) or by exp<strong>and</strong>ing <strong>the</strong> wavefr<strong>on</strong>t in terms orthog<strong>on</strong>al functi<strong>on</strong>s, e.g. 2D<br />
Legendre polynomials (modal method)[224]. The modal rec<strong>on</strong>structi<strong>on</strong> is useful in<br />
being able to identify <strong>the</strong> c<strong>on</strong>tributi<strong>on</strong> of different aberrati<strong>on</strong>s to <strong>the</strong> wavefr<strong>on</strong>t shape.<br />
For X-rayapplicati<strong>on</strong>s a Hartmann plate is used due to <strong>the</strong> lack of microlens arrays<br />
capable of focussing <strong>the</strong> <strong>beam</strong>. For IR <strong>and</strong> UV energies suitable microlens arrays<br />
are available, <strong>the</strong>ir commercial design <strong>and</strong> manufacture having been stimulated by<br />
comm<strong>on</strong> use in ophthalmology <strong>and</strong> corrective laser eye surgery.<br />
The use of wavefr<strong>on</strong>t measurements in commissi<strong>on</strong>ing afree electr<strong>on</strong> laser <strong>beam</strong>line<br />
was dem<strong>on</strong>strated at Flash using a Hartmann sensor from Imagine Optics[225]. The<br />
sensor c<strong>on</strong>tained a Hartmann plate with a 51x51 pinhole array, each pinhole being a<br />
110 µm square tilted 25 ◦ to aid close packing <strong>and</strong> prevent interference with adjacent<br />
holes. A direct CCD camera was used as <strong>the</strong> detector. The reference spherical<br />
wavefr<strong>on</strong>t was generated by inserting a pinhole into <strong>the</strong> <strong>beam</strong>line.
142 8. Beam cross-secti<strong>on</strong> diagnostics<br />
From <strong>the</strong> wavefr<strong>on</strong>t measurements <strong>on</strong> <strong>beam</strong>line 2 (BL2) 12 , <strong>the</strong> depth of focus of<br />
<strong>the</strong> ellipsoidal mirror was calculated using ray tracing <strong>and</strong> a small astigmatism was<br />
found which was cured by remounting a switching mirror. The design focal spot size<br />
was still not obtained, but analysis of <strong>the</strong> wavefr<strong>on</strong>t measurements <strong>on</strong> BL2 <strong>and</strong> <strong>on</strong><br />
<strong>the</strong> unfocussed BL3 showed that this was not due to any remaining aberrati<strong>on</strong>s but<br />
to <strong>the</strong> source being larger than expected during that phase of operati<strong>on</strong>. The critical<br />
yaw angle of <strong>the</strong> toroidal mirror <strong>on</strong> BL1 was also set using <strong>the</strong> wavefr<strong>on</strong>t sensor.<br />
Based <strong>on</strong> this experience, an optimized wavefr<strong>on</strong>t measurement system, using a<br />
320 µm hole pitch, has subsequently been designed in c<strong>on</strong>juncti<strong>on</strong> with <strong>the</strong> Laser<br />
Laboratorium Göttingen for use as an end-stati<strong>on</strong> diagnostic <strong>on</strong> Flash. At <strong>beam</strong>line<br />
2 this wavefr<strong>on</strong>t sensor have been used to align a grazing incidence ellipsoidal mirror<br />
<strong>–</strong> decreasing <strong>the</strong> wavefr<strong>on</strong>t distorti<strong>on</strong> from 52.6 nm (peak-to-valley) <strong>and</strong> 9.2 nm (rms)<br />
to 12 nm <strong>and</strong> 2.6 nm respectively. This by correcting <strong>the</strong> mirror’s pitch -0.29 mrad<br />
<strong>and</strong> its yaw by -0.06 mrad[226]. At BL1 <strong>the</strong> focal spot size <strong>and</strong> <strong>the</strong> positi<strong>on</strong> of <strong>the</strong><br />
<strong>beam</strong>-waist (<strong>and</strong> its fluctuati<strong>on</strong> <strong>on</strong> a shot to shot basis) have been found with <strong>the</strong><br />
same sensor system[227].<br />
At <strong>the</strong> Scss a Hartman wavefr<strong>on</strong>t sensor have been used to do single-shot measurements<br />
to characterize <strong>the</strong> spatial propertis of <strong>the</strong> Sase radiati<strong>on</strong>[228].<br />
8.12 THz/IR techniques<br />
A major difficulty in IR <strong>and</strong> THz diagnostics is that of a suitable means of detecti<strong>on</strong><br />
of <strong>the</strong> l<strong>on</strong>g wavelength radiati<strong>on</strong>. The low quantum energy of IR <strong>and</strong> THz radiati<strong>on</strong><br />
means it is <strong>on</strong>ly able to stimulate vibrati<strong>on</strong>al <strong>and</strong> rotati<strong>on</strong>al modes in molecules <strong>and</strong><br />
cannot directly cause i<strong>on</strong>isati<strong>on</strong>. Therefore, measurement techniques that depend <strong>on</strong><br />
<strong>the</strong> measurement of emitted electr<strong>on</strong>s cannot be used in <strong>the</strong> IR <strong>and</strong> THz. There are<br />
two basic techniques for detecting IR <strong>and</strong> THz radiati<strong>on</strong> that are well established <strong>and</strong><br />
commercially available, namely:<br />
• Thermal<br />
• Phot<strong>on</strong>ic (quantum)<br />
The detectors can ei<strong>the</strong>r be photovoltaic (an induced voltage drives a current in <strong>the</strong><br />
detector circuit) or photoc<strong>on</strong>ductive (an induced resistivity change results in a voltage<br />
change in <strong>the</strong> detector circuit).<br />
In all cases, background radiati<strong>on</strong> is <strong>the</strong> ultimate limiting factor <strong>and</strong> detectors may<br />
require (cryogenic) cooling <strong>and</strong> / or <strong>the</strong>rmal shielding depending <strong>on</strong> <strong>the</strong> radiati<strong>on</strong><br />
levels <strong>and</strong> wavelengths to be measured <strong>and</strong> <strong>the</strong> required signal to noise ratio.<br />
Important factors to c<strong>on</strong>sider when selecting <strong>and</strong> IR detector are:<br />
• Photo-sensitivity (Resp<strong>on</strong>sivity) <strong>–</strong> The output voltage (or current) per watt<br />
of incident radiati<strong>on</strong> power. Units: A / W or V / W.<br />
• Noise equivalent power (NEP) <strong>–</strong> The amount of incident radiati<strong>on</strong> that gives<br />
a signal equal to <strong>the</strong> inherent noise level, i.e. that gives a signal to noise ratio<br />
of 1. Units: W / √ Hz.<br />
12 For a layout of <strong>the</strong> Flash <strong>beam</strong>lines, see Ref. [104]
8.12. THz/IR techniques 143<br />
• Detectivity D ∗ <strong>–</strong> The photo sensitivity per unit active area of <strong>the</strong> detector.<br />
The specific c<strong>on</strong>diti<strong>on</strong>s under which <strong>the</strong> detectivity was measured are usually<br />
given as a functi<strong>on</strong> of: temperature (K) or radiati<strong>on</strong> wavelength (µm), chopping<br />
frequency <strong>and</strong> b<strong>and</strong>width. Units: cm. √ Hz / W<br />
• Spectral resp<strong>on</strong>se <strong>–</strong> How <strong>the</strong> output varies with incident wavelength.<br />
• Resp<strong>on</strong>se time <strong>–</strong> How quickly <strong>the</strong> output rises <strong>and</strong> falls in resp<strong>on</strong>se to an<br />
input pulse. Gating may be needed to measure individual pulses if <strong>the</strong> resp<strong>on</strong>se<br />
is slow.<br />
• Background Limited Infrared Photodetecti<strong>on</strong> (BLIP) <strong>–</strong> The ultimate<br />
detecti<strong>on</strong> limit determined by fluctuati<strong>on</strong>s in <strong>the</strong> background radiati<strong>on</strong> flux in<br />
<strong>the</strong> ideal case of zero noise generated in <strong>the</strong> detector <strong>and</strong> processing circuits.<br />
This is inversely proporti<strong>on</strong>al to <strong>the</strong> square root of <strong>the</strong> background radiati<strong>on</strong><br />
flux.<br />
Thermal detecti<strong>on</strong><br />
Thermal detectors involve <strong>the</strong> measurement of a temperature dependent phenomen<strong>on</strong><br />
such as:<br />
• Temperature dependent resistance (bolometers),<br />
• Thermoelectric effect (<strong>the</strong>rmocouples <strong>and</strong> <strong>the</strong>rmopiles),<br />
• Thermal expansi<strong>on</strong> (Golay cells), <strong>and</strong><br />
• Pyroelectric effect (<strong>the</strong>rmally induced change in <strong>the</strong> surface charge of polarised<br />
crystals)<br />
Thermal detectors use <strong>the</strong> radiati<strong>on</strong> as heat <strong>and</strong> thus <strong>the</strong> photo-sensitivity is independent<br />
of wavelength. Of course, as <strong>the</strong> wavelength increases, more phot<strong>on</strong>s are<br />
needed to give <strong>the</strong> same incident power. Therefore <strong>the</strong> quantum yield is inversely<br />
proporti<strong>on</strong>al to wavelength. Since <strong>the</strong> envir<strong>on</strong>ment is a str<strong>on</strong>g source of l<strong>on</strong>g wavelength<br />
radiati<strong>on</strong>, achieving <strong>the</strong> required signal to noise at l<strong>on</strong>ger wavelengths becomes<br />
increasingly difficult.<br />
The spectral resp<strong>on</strong>se of <strong>the</strong>rmal detectors can be tailored by placing a window<br />
with a suitable transmissi<strong>on</strong> b<strong>and</strong> over <strong>the</strong> detector. It is also highly desirable to use<br />
windows that, as far as possible, block <strong>the</strong> parts of <strong>the</strong> black body spectrum from <strong>the</strong><br />
envir<strong>on</strong>ment that are outside <strong>the</strong> output spectrum of <strong>the</strong> free electr<strong>on</strong> laser source.<br />
Thermal detectors tend to have a slow resp<strong>on</strong>se <strong>and</strong> are more suitable for timeaveraged<br />
measurements or measurements <strong>on</strong> c<strong>on</strong>tinuous wave sources. For example,<br />
<strong>the</strong> resp<strong>on</strong>se of pyroelectric detectors is at <strong>the</strong> millisec<strong>on</strong>d level, though cryogenically<br />
cooled bolometers can resp<strong>on</strong>d much faster than this.<br />
Thepyroelectriceffectdoesnotproduceapermanentvoltage <strong>on</strong><strong>the</strong>crystalbecause<br />
<strong>the</strong> induced charge <strong>on</strong> <strong>the</strong> crystal surface dissipates through internal leakage <strong>and</strong> i<strong>on</strong>s<br />
in <strong>the</strong> air. Thus, pyroelectric detectors produce a signal <strong>on</strong>ly when <strong>the</strong> temperature<br />
of <strong>the</strong> crystal changes <strong>and</strong> <strong>the</strong>y <strong>on</strong>ly resp<strong>on</strong>d to pulsed sources. Use with a c<strong>on</strong>tinuous<br />
wave source requires <strong>the</strong> input light to be chopped, giving a signal of opposite sign at<br />
each opening <strong>and</strong> closing of <strong>the</strong> chopper.
144 8. Beam cross-secti<strong>on</strong> diagnostics<br />
Phot<strong>on</strong>ic detecti<strong>on</strong><br />
Phot<strong>on</strong>ic detectors are semic<strong>on</strong>ductors with b<strong>and</strong>-gaps that are narrow enough for<br />
<strong>the</strong> small energy quanta of IR phot<strong>on</strong>s to excite electr<strong>on</strong>s across it. They are more<br />
sensitive <strong>and</strong> have a higher resp<strong>on</strong>se b<strong>and</strong>width (i.e. are faster) than <strong>the</strong>rmal detectors.<br />
Background <strong>the</strong>rmal excitati<strong>on</strong> will result in a significant dark output <strong>and</strong> some<br />
sort of cooling is normally required.<br />
Phot<strong>on</strong>ic detectors operate over specific wavelength ranges determined by <strong>the</strong><br />
b<strong>and</strong>-gap. The b<strong>and</strong>-gap <strong>and</strong> resp<strong>on</strong>se time also tend to vary with temperature,<br />
so cooling a detector to a level at which <strong>the</strong> intrinsic noise is low enough may shift<br />
its spectral resp<strong>on</strong>se out of <strong>the</strong> required wavelength range.<br />
Most commercial phot<strong>on</strong>ic detectors work in <strong>the</strong> near to far-IR wavelength range<br />
from 0.75 to 15 µm (1.65 eV to 80 meV). Table 8.1 below 13 lists various phot<strong>on</strong>ic IR<br />
detectors.<br />
Detector Spectral<br />
resp<strong>on</strong>se [µm]<br />
Temp<br />
[K]<br />
D ∗ [cm, √ Hz/W] Type<br />
PbS 1 to 3.6 300 D ∗ (500,600,1) = 10 9<br />
PbSe 1.5 to 5.8 300 D ∗ (500,600,1) = 10 8<br />
InAs 2 to 5 213 D ∗ (500,1200,1) = 2·10 9<br />
InSb 2 to 16 77 D ∗ (500,1000,1) = 2·10 10<br />
Ge 0.8 to 1.8 300 D ∗ (λp) = 10 11<br />
InGaAs 0.7 to 1.7 300 D ∗ (λp) = 5·10 15<br />
InAs 1 to 3.1 77 D ∗ (500,1200,1) = 10 10<br />
InSb 1 to 5.5 77 D ∗ (500,1200,1) = 2·10 10<br />
HgCdTe 2 to 16 77 D ∗ (500,1000,1) = 10 10<br />
Ge:Au 1 to 10 77 D ∗ (500,900,1) = 10 11<br />
Ge:Hg 2 to 14 4.2 D ∗ (500,900,1) = 8·10 9<br />
Ge:Cu 2 to 30 4.2 D ∗ (500,900,1) = 5·10 9<br />
Ge:Zn 2 to 40 4.2 D ∗ (500,900,1) = 5·10 9<br />
Si:Ga 1 to 17 4.2 D ∗ (500,900,1) = 5·10 9<br />
Si:As 1 to 23 4.2 D ∗ (500,900,1) = 5·10 9<br />
Table 8.1: List of phot<strong>on</strong>ic IR detectors <strong>and</strong> operating ranges<br />
Intrinsic,<br />
Photoc<strong>on</strong>ductive<br />
Intrinsic,<br />
Photovoltaic<br />
Extrinsic<br />
A widely used phot<strong>on</strong>ic detector in existing IR-FEL facilities is <strong>the</strong> mercurycadmium-telluride<br />
or MCT detector. This is because <strong>the</strong> b<strong>and</strong>-gap <strong>and</strong> hence l<strong>on</strong>gwavelength<br />
cut-off can be tailored by adjusting <strong>the</strong> relative proporti<strong>on</strong>s of CdTe <strong>and</strong><br />
HgTe. The l<strong>on</strong>g wavelength limit of commercially available detectors is ∼ 24 µm 14 .<br />
13<br />
taken from Hamamatsu Technical Informati<strong>on</strong> SD-12 ”Characteristics an use of infrared detectors”.<br />
www.hamamatsu.com<br />
14<br />
InfraRed Associates Inc., www.irassociates.com
8.12. THz/IR techniques 145<br />
The website of <strong>the</strong> Felix IR Laser facility records that a Ge:Ga detector works<br />
from 10 to 200 µm 15 . Liquid helium cooling is of course essential at such a l<strong>on</strong>g<br />
wavelength.<br />
New detectors<br />
The increasing exploitati<strong>on</strong> of IR radiati<strong>on</strong> <strong>on</strong> synchrotr<strong>on</strong> radiati<strong>on</strong> sources has stimulated<br />
development into new types of IR <strong>and</strong> THz detectors that aim to give<br />
• Faster resp<strong>on</strong>se<br />
• Wider spectral resp<strong>on</strong>se<br />
• Higher quantum yield<br />
• Lower noise<br />
• Larger arrays<br />
• Faster array read-out<br />
• Higher spatial resoluti<strong>on</strong><br />
Developing <strong>and</strong> future technologies include:<br />
• Niobium nitride (NbN) superc<strong>on</strong>ducting bolometers (50 ps resp<strong>on</strong>se time, size<br />
0.1 x 1 µm)<br />
• Transiti<strong>on</strong> Edge Superc<strong>on</strong>ducting (TES) detectors (a superc<strong>on</strong>ductor is held<br />
near <strong>the</strong> transiti<strong>on</strong> temperature <strong>and</strong> thus a small amount of added heat gives<br />
an exaggerated c<strong>on</strong>ductivity change, improving sensitivity <strong>and</strong> resp<strong>on</strong>se time).<br />
• Quantum Well Infrared Photodetectors (QWIPs)<br />
• Zero-bias Schottky diodes<br />
Schottky diodes made at <strong>the</strong> Space Science Centre at Ru<strong>the</strong>rford Applet<strong>on</strong> Laboratory<br />
have been tested <strong>on</strong> <strong>the</strong> ALICE accelerator at Daresbury. The fastest has<br />
a measured resp<strong>on</strong>se time of 20 ns (1/e). They are able to distinguish (though not<br />
completely resolve) <strong>the</strong> individual THz pulses from <strong>the</strong> electr<strong>on</strong> bunch train with 81<br />
MHz repleti<strong>on</strong> rate (12 ns period).<br />
IR <strong>and</strong> THz <strong>beam</strong> profiling<br />
Scanning<br />
The simplest way to generate a profile in <strong>on</strong>e or two dimensi<strong>on</strong>s is to raster scan a<br />
detector element (<strong>the</strong>rmal or phot<strong>on</strong>ic) through <strong>the</strong> <strong>beam</strong>. The spatial resoluti<strong>on</strong> is<br />
limited by <strong>the</strong> size of <strong>the</strong> detector or <strong>the</strong> defining slit in fr<strong>on</strong>t of it. Diffracti<strong>on</strong> at a<br />
defining slit will limit <strong>the</strong> resoluti<strong>on</strong> if <strong>the</strong> slit size is comparable to <strong>the</strong> wavelength.<br />
Because IR <strong>beam</strong>s are relatively easy to manipulate, it is also possible to optically<br />
raster <strong>the</strong> <strong>beam</strong> over <strong>the</strong> fixed detector. This is likely to be faster than moving <strong>the</strong><br />
detector since <strong>the</strong> optical raster will use angular shifts of a lens or mirror whilst <strong>the</strong><br />
detector raster will use linear moti<strong>on</strong>s of <strong>the</strong> detector.<br />
15 Felix IR Laser facility: www.rijnhuizen.nl/en/felix/facilities
146 8. Beam cross-secti<strong>on</strong> diagnostics<br />
Scanning a linear array detector is more efficient, though <strong>the</strong> spatial sampling of<br />
<strong>the</strong> scan in <strong>the</strong> directi<strong>on</strong> al<strong>on</strong>g <strong>the</strong> array is fixed by <strong>the</strong> array spacing. The array<br />
must also be matched to <strong>the</strong> <strong>beam</strong> size, whilst a single element scan can used <strong>on</strong> an<br />
arbitrary <strong>beam</strong> size.<br />
imaging<br />
Infrared imaging is of course widespread. Even a st<strong>and</strong>ard CCD based digital camera<br />
can image in <strong>the</strong> near infrared, whilst security applicati<strong>on</strong>s have driven a huge development<br />
of sub-optical imaging systems. Here we will <strong>the</strong>refore c<strong>on</strong>sider <strong>the</strong> more<br />
challenging area of l<strong>on</strong>ger wavelength imaging <strong>and</strong> imaging which is tailored to <strong>the</strong><br />
nature of free electr<strong>on</strong> laser sources.<br />
It is c<strong>on</strong>ceivable that any of <strong>the</strong> basic types of single element IR detector can<br />
be built into an imaging array, ei<strong>the</strong>r 1-dimensi<strong>on</strong>al or 2-dimensi<strong>on</strong>al. The specific<br />
technical questi<strong>on</strong>s that need to be addressed are:<br />
• The size of <strong>the</strong> detector elements<br />
• The spacing of <strong>the</strong> detector elements<br />
• The read-out time<br />
• Sensitivity <strong>and</strong> spectral resp<strong>on</strong>se<br />
Achieving high spatial resoluti<strong>on</strong> requires small <strong>and</strong> closely spaced detector elements,<br />
but this can lead to problems with sensitivity at l<strong>on</strong>g wavelengths since <strong>the</strong><br />
low quantum efficiency means <strong>the</strong> signal generated in each element is too small to<br />
detect. For example, a commercial pyroelectric array detector was found to be unable<br />
to detect <strong>the</strong> THz output of <strong>the</strong> quantum cascade laser at Leeds University, UK.<br />
C<strong>on</strong>siderati<strong>on</strong> must also be given to diffractive effects at <strong>the</strong>se l<strong>on</strong>g wavelengths.<br />
Diffracti<strong>on</strong> at defining apertures could lead to a decrease <strong>the</strong> spatial resoluti<strong>on</strong>. Does<br />
a sensor element that is smaller than <strong>the</strong> wavelength of <strong>the</strong> radiati<strong>on</strong> accurately record<br />
<strong>the</strong> incident intensity?<br />
Beam splitters<br />
The detectors described in here are opaque to <strong>the</strong> <strong>beam</strong> <strong>and</strong> thus cannot be used as<br />
part of a n<strong>on</strong>invasive detector. However, it is relatively easy to split an IR <strong>and</strong> THz<br />
<strong>beam</strong> in amplitude such that <strong>on</strong>ly a small part of it passes to <strong>the</strong> detector <strong>and</strong> <strong>the</strong><br />
rest passes to <strong>the</strong> experiment 16 . The most suitable techniques for IR <strong>and</strong> THz are:<br />
• Plates <strong>and</strong> pellicles <strong>–</strong> can be made of various materials depending <strong>on</strong> <strong>the</strong><br />
transmissi<strong>on</strong> b<strong>and</strong> required. Pellicles can be coated to enhance <strong>the</strong> reflectivity<br />
at <strong>the</strong> expense of transmissi<strong>on</strong>.<br />
• Wire grids <strong>–</strong> <strong>the</strong>se are polarising <strong>beam</strong> splitters, suitable for <strong>the</strong> l<strong>on</strong>gest wavelengths<br />
<strong>on</strong>ly (determined by <strong>the</strong> wire spacing).<br />
16 See chapter 5 (see page 73).
8.12. THz/IR techniques 147<br />
Wavefr<strong>on</strong>t sensing<br />
The Shack-Hartmann sensor is a st<strong>and</strong>ard instrument for measuring wavefr<strong>on</strong>ts in<br />
<strong>the</strong> optical <strong>and</strong> IR regi<strong>on</strong>. Commercial instruments tend to be limited to operati<strong>on</strong><br />
in <strong>the</strong> near-IR (∼ 2 µm wavelength), probably because of <strong>the</strong> types of IR sensitive<br />
array detectors that are available with sufficient pixel count, density <strong>and</strong> sensitivity.<br />
CCD cameras would seem to be <strong>the</strong> st<strong>and</strong>ard detector, giving megapixel array size<br />
with spacing in <strong>the</strong> 20 µm range. High pixel count <strong>and</strong> small spatial separati<strong>on</strong> is<br />
required to allow accurate centroid determinati<strong>on</strong> of a large number of micro-<strong>beam</strong>s,<br />
both of which are necessary for accurate wavefr<strong>on</strong>t rec<strong>on</strong>structi<strong>on</strong>.<br />
Extending operati<strong>on</strong> to <strong>the</strong> far-infrared would require, for example, an MCT array<br />
detector. It is not clear that an MCT array with sufficient pixel count <strong>and</strong> density<br />
is technically feasible, let al<strong>on</strong>e cost effective. Alternatively, <strong>and</strong> for operati<strong>on</strong> in <strong>the</strong><br />
THz regi<strong>on</strong>, <strong>the</strong> array would have to be made of <strong>the</strong>rmal detectors. As menti<strong>on</strong>ed<br />
before, pyroelectric array detectors are commercially available. These currently have<br />
ra<strong>the</strong>r low pixel counts compared with CCD cameras <strong>and</strong> a detailed technical assessment<br />
would have to be made to decide <strong>on</strong> <strong>the</strong> minimum pixel count that would be<br />
required. This assessment would also need to c<strong>on</strong>sider <strong>the</strong> effects of <strong>the</strong> much str<strong>on</strong>ger<br />
diffracti<strong>on</strong> <strong>and</strong> <strong>the</strong> Hartmann plate of micro-lens array.<br />
Electro-Optical Imaging<br />
Electro-optical sampling of THz radiati<strong>on</strong> uses <strong>the</strong> Pockels effect in electro-optic crystals.<br />
A THz pulse acts like a transient bias that induces a transient polarisati<strong>on</strong> in<br />
<strong>the</strong> crystal. The polarisati<strong>on</strong> induces a birefringence in <strong>the</strong> crystal that is probed by<br />
a synchr<strong>on</strong>ous optical laser <strong>beam</strong>, <strong>the</strong> probe <strong>beam</strong> undergoing a polarisati<strong>on</strong> change<br />
as it passes through <strong>the</strong> crystal.<br />
Wu et al.[229] describe how to exploit <strong>the</strong> EO effect to produce a 2-dimensi<strong>on</strong>al<br />
image of <strong>the</strong> THz <strong>beam</strong> cross-secti<strong>on</strong>, see Figure 8.18. The THz <strong>beam</strong> was focused<br />
at a ZnTe EO crystal <strong>and</strong> was overlapped with a co-propagating optical laser <strong>beam</strong>.<br />
The optical field probes <strong>the</strong> spatial distributi<strong>on</strong> of <strong>the</strong> electric field in <strong>the</strong> crystal that<br />
<strong>the</strong> THz radiati<strong>on</strong> induces. Crossed-polarisers ei<strong>the</strong>r side of <strong>the</strong> EO crystal c<strong>on</strong>vert<br />
<strong>the</strong> resulting polarisati<strong>on</strong> modulati<strong>on</strong> of <strong>the</strong> optical <strong>beam</strong> as it passes through <strong>the</strong><br />
crystal into an intensity modulati<strong>on</strong> that is recorded by a CCD camera, which thus<br />
gives a 2-dimensi<strong>on</strong>al intensity image of <strong>the</strong> THz <strong>beam</strong>.<br />
This technique can be directly applied to determining <strong>the</strong> focus size of THz <strong>beam</strong>s.<br />
Obviously, a very fast optical laser that is synchr<strong>on</strong>ised to <strong>the</strong> THz pulse is also<br />
required. The Pockels effect is very fast <strong>and</strong> imaging rate is limited by <strong>the</strong> camera.<br />
Gating of <strong>the</strong> camera should allow single pulse measurement provided <strong>the</strong>re is enough<br />
modulati<strong>on</strong> in <strong>the</strong> optical <strong>beam</strong> to produce a measurable signal at <strong>the</strong> camera.<br />
Measurement of unfocussed <strong>beam</strong>s is likely to be limited by <strong>the</strong> phot<strong>on</strong> density of<br />
<strong>the</strong> THz <strong>and</strong> optical probe <strong>beam</strong>s, since <strong>the</strong> optical <strong>beam</strong> must spatially overlap <strong>the</strong><br />
THz <strong>beam</strong> for a complete 2-D image to be recorded in <strong>on</strong>e shot. The available size<br />
of EO crystals will be ano<strong>the</strong>r factor limiting <strong>the</strong> largest <strong>beam</strong> footprint that can be<br />
measured. These limitati<strong>on</strong>s could be overcome by using an optical system such as a<br />
telescope to compress <strong>the</strong> <strong>beam</strong> diameter without modifying <strong>the</strong> wavefr<strong>on</strong>t.
148 8. Beam cross-secti<strong>on</strong> diagnostics<br />
THz <strong>beam</strong><br />
8.13 Summary<br />
Pellicle<br />
Probe <strong>beam</strong><br />
Polariser<br />
ZnTe crystal<br />
Analyser<br />
Figure 8.18: Layout of <strong>the</strong> EO imaging system of Wu.<br />
CCD<br />
Camera<br />
The ideal or ”universal” diagnostic for a free electr<strong>on</strong> laser source would be able to:<br />
• Give a full spatial image of <strong>the</strong> phot<strong>on</strong> <strong>beam</strong>.<br />
• Do this for every pulse produced.<br />
• Not change <strong>the</strong> phot<strong>on</strong> pulse in any significant manner.<br />
• Operate over a wide spectral range (at least sufficient to cover <strong>the</strong> full output<br />
range of <strong>the</strong> source)<br />
At <strong>the</strong> moment, such a universal diagnostic is not possible.<br />
• Techniques that give full spatial profiles tend to be slow <strong>and</strong> invasive<br />
• Faster techniques often <strong>on</strong>ly give informati<strong>on</strong> such as <strong>beam</strong> centroid<br />
• N<strong>on</strong>-invasive techniques are too insensitive to measure a single pulse<br />
• Operating wavelength range is str<strong>on</strong>gly limited by <strong>the</strong> detecti<strong>on</strong> technique employed<br />
For radiati<strong>on</strong> with wavelengths from <strong>the</strong> VUV to X-rays, <strong>the</strong>re is a c<strong>on</strong>siderable<br />
range of diagnostics employed <strong>on</strong> synchrotr<strong>on</strong> radiati<strong>on</strong> sources that could be developed<br />
for use <strong>on</strong> free electr<strong>on</strong> laser sources. Many of <strong>the</strong>se techniques involve transferring<br />
<strong>the</strong> spatial informati<strong>on</strong> to electr<strong>on</strong>s that are detected <strong>and</strong> analysed to extract <strong>the</strong><br />
spatial informati<strong>on</strong>. Imaging detecti<strong>on</strong> is often achieved by c<strong>on</strong>verting <strong>the</strong> electr<strong>on</strong>s<br />
to visible phot<strong>on</strong>s with <strong>the</strong> aid of luminescent screens. For harder X-rays, fluorescence<br />
is <strong>the</strong> dominant process <strong>and</strong> detecti<strong>on</strong> of <strong>the</strong> fluorescent phot<strong>on</strong>s, probably indirectly<br />
by c<strong>on</strong>versi<strong>on</strong> to visible phot<strong>on</strong>s, is a better approach.<br />
For <strong>the</strong> IR <strong>and</strong> THz, <strong>the</strong>se approaches cannot be used <strong>and</strong> <strong>the</strong> choice of detecti<strong>on</strong><br />
method is much more limited. Phot<strong>on</strong>ic detectors are fast <strong>and</strong> efficient but are mainly<br />
limited to detecting in <strong>the</strong> near to far infrared, up to ∼ 24 µm with HgCdTe (though<br />
∼200 µm is possible with Ge:Ga). Thermal detectors must be used at frequencies<br />
below a few THz <strong>and</strong> <strong>the</strong>se tend to be slow. However, output at <strong>the</strong>se extremely l<strong>on</strong>g<br />
wavelengths is not generally in <strong>the</strong> realm of free electr<strong>on</strong> laser sources. Electro-optical<br />
techniques are probably a better soluti<strong>on</strong> for <strong>the</strong> very l<strong>on</strong>g wavelengths.<br />
It is thus inevitable that a range of diagnostics <strong>and</strong> detectors will be employed<br />
depending <strong>on</strong> <strong>the</strong> informati<strong>on</strong> required <strong>and</strong> <strong>the</strong> use to which it is to be put, for<br />
example:
8.13. Summary 149<br />
• Centroiding techniques for pulse by pulse <strong>beam</strong> positi<strong>on</strong> m<strong>on</strong>itoring <strong>and</strong> feedback<br />
• Invasive imaging for optimising <strong>the</strong> source <strong>and</strong> phot<strong>on</strong> <strong>transport</strong> during commissi<strong>on</strong>ing<br />
• Fast imaging arrays or wavefr<strong>on</strong>t sensors situated behind gas-phase experiments<br />
The use of <strong>beam</strong> splitters to separate a part of <strong>the</strong> <strong>beam</strong> for <strong>the</strong> more sophisticated<br />
diagnostics whilst <strong>the</strong> bulk of <strong>the</strong> <strong>beam</strong> is passed to <strong>the</strong> experiment are also likely to<br />
be a comm<strong>on</strong> feature of <strong>the</strong> phot<strong>on</strong> <strong>transport</strong> systems due to <strong>the</strong> lack of truly n<strong>on</strong>invasivediagnostics.<br />
These splitterscanberemovedfrom <strong>the</strong><strong>beam</strong>pathfor maximum<br />
throughput<strong>and</strong>/orif<strong>the</strong>diagnostic isnotrequired. Ideally, <strong>the</strong><strong>beam</strong>splittersshould<br />
divide <strong>the</strong> <strong>beam</strong> in amplitude so <strong>the</strong> diagnostic <strong>beam</strong> has <strong>the</strong> same <strong>beam</strong> profile as<br />
<strong>the</strong> measured <strong>beam</strong> (but at lower intensity). This should be straightforward in <strong>the</strong><br />
IR <strong>and</strong> THz, but more challenging in <strong>the</strong> VUV <strong>and</strong> Soft Xray, where knife-edged<br />
mirrors that divide <strong>the</strong> wavefr<strong>on</strong>t are <strong>the</strong> easiest splitter to implement. Multilayer<br />
<strong>and</strong> slotted-mirror type <strong>beam</strong> splitters would be required to give amplitude <strong>beam</strong><br />
divisi<strong>on</strong>.<br />
Despite <strong>the</strong> c<strong>on</strong>siderable challenges that must be faced when making good spatial<br />
diagnostics for free electr<strong>on</strong> laser <strong>beam</strong>s, <strong>the</strong>re are a wide range of techniques<br />
that can be employed. A judicious combinati<strong>on</strong> of techniques will allow <strong>the</strong> required<br />
informati<strong>on</strong> to be measured.
150 8. Beam cross-secti<strong>on</strong> diagnostics<br />
Summary<br />
• Cross-secti<strong>on</strong> diagnostics measures <strong>the</strong> transverse intensity<br />
distributi<strong>on</strong> of <strong>the</strong> <strong>beam</strong>. For both optimizati<strong>on</strong>, commissi<strong>on</strong>ing<br />
of experiments <strong>and</strong> instruments it is important to know<br />
where <strong>the</strong> <strong>beam</strong> is <strong>and</strong> how large it is.<br />
• Measuring <strong>the</strong> focus size can be d<strong>on</strong>e ei<strong>the</strong>r via ablati<strong>on</strong> crater<br />
analysis (<strong>the</strong> size of a hole in a thin film), by <strong>the</strong> saturati<strong>on</strong> of<br />
an i<strong>on</strong>izati<strong>on</strong> process in a gas or by using a wave-fr<strong>on</strong>t sensor.<br />
• Techniques developed for synchrotr<strong>on</strong> sources may not be immediately<br />
used at free electr<strong>on</strong> lasers or not at all.<br />
• Examples of invasive techniques are:<br />
<strong>–</strong> Direct imaging<br />
<strong>–</strong> Wire grids<br />
<strong>–</strong> Scanning wires, slits, knife-edges, pin-holes. All have <strong>the</strong><br />
drawback that <strong>the</strong>y are not single shot.<br />
• N<strong>on</strong>-invasive techniques can be used while o<strong>the</strong>r experiments<br />
are running.<br />
<strong>–</strong> Rest gas i<strong>on</strong>izati<strong>on</strong><br />
<strong>–</strong> Photo dissociati<strong>on</strong><br />
<strong>–</strong> Synchrotr<strong>on</strong> light<br />
<strong>–</strong> Compt<strong>on</strong> scattering<br />
• Acombinati<strong>on</strong>oftechniquesisneeded, inpractice, todiagnose<br />
<strong>the</strong> <strong>beam</strong>:<br />
<strong>–</strong> Centroiding techniques for pulse by pulse <strong>beam</strong> positi<strong>on</strong><br />
m<strong>on</strong>itoring<br />
<strong>–</strong> Invasive imaging for optimizing <strong>and</strong> commisi<strong>on</strong>ing<br />
<strong>–</strong> Fast imaging devices or wavefr<strong>on</strong>t sensors situated behind<br />
gas-phase experiments.<br />
• In <strong>the</strong> THz range photodiodes in <strong>the</strong> infrared or <strong>the</strong>rmal detectors<br />
for l<strong>on</strong>ger wavelengths can be used. The latter <strong>on</strong>ly<br />
for averaging measurements.<br />
• Beamsplitters offers <strong>the</strong> possibility to use invasive diagnostics<br />
in parallel to o<strong>the</strong>r experiments.
9. Pulse length, profile <strong>and</strong> jitter<br />
The material presented here in this chapter is partly adapted from ”Survey<br />
of diagnostics techniques for measuring <strong>the</strong> temporal properties of ultra-short<br />
phot<strong>on</strong> pulses” by M. A. Bowler, A. J. Glees<strong>on</strong> <strong>and</strong> M. D. Roper. Iruvx<br />
WP7, 2009 by A. Lindblad.<br />
9.1 Introducti<strong>on</strong><br />
In chapter 8 methods to discern <strong>the</strong> transverse extent of a phot<strong>on</strong>-<strong>beam</strong> were discussed.<br />
Here we will review methods as to determine <strong>the</strong> length <strong>and</strong> profile of a<br />
pulse; <strong>the</strong> jitter between <strong>the</strong> pulses is also an important temporal parameter which is<br />
necessary to measure.<br />
A key measure of <strong>the</strong> performance of a freeelectr<strong>on</strong><br />
laser is <strong>the</strong> temporal properties of <strong>the</strong><br />
phot<strong>on</strong>-<strong>beam</strong>. The pulse length is required for<br />
<strong>the</strong> integral pulse power at <strong>the</strong> experiment; <strong>the</strong><br />
pulse profile determines <strong>the</strong> ”quality” of <strong>the</strong><br />
pulse in terms of length <strong>and</strong> height of, <strong>and</strong> deviati<strong>on</strong><br />
from, <strong>the</strong> ideal pedestal shape in Figure<br />
9.1 (i.e. deviati<strong>on</strong> from <strong>the</strong> transform limit<br />
for <strong>the</strong> spectral c<strong>on</strong>tent of <strong>the</strong> pulse) <strong>–</strong> this is<br />
also related to <strong>the</strong> jitter, since if <strong>the</strong> pulse shape<br />
lacks repeating structure <strong>the</strong> centroid will be<br />
shifted <strong>on</strong> a pulse to pulse basis which is equivalent<br />
to a shift in relative occurrence times; <strong>the</strong><br />
pulse jitter is a r<strong>and</strong>om fluctuati<strong>on</strong> in <strong>the</strong> arrival<br />
time of a pulse, by necessity this needs<br />
to be correlated to ano<strong>the</strong>r timing event. For<br />
δt<br />
∆t<br />
Figure 9.1: Ideal pulses have square profiles of<br />
length δt, occurring with frequency ∆t −1 ; <strong>the</strong><br />
pulse shape can be significantly deviated from<br />
<strong>the</strong> ideal square <strong>and</strong> occur within a frequency<br />
envelope defined by a time-jitter.<br />
pump-probe experiments this is obviously a crucial parameter.<br />
The profile <strong>and</strong> timing of a free electr<strong>on</strong> laser pulse is certainly going to change <strong>on</strong><br />
a pulse by pulse basis by an amount that will cause difficulty to at least some experiments.<br />
This is especially true for Sase operati<strong>on</strong> because <strong>the</strong> pulses are generated<br />
from r<strong>and</strong>om noise. Therefore, <strong>the</strong>re is a general need for <strong>the</strong> temporal diagnostics to<br />
be permanently ”<strong>on</strong>-line” so that <strong>the</strong> profile <strong>and</strong> timing of every pulse can be measured.<br />
Such a diagnostic should obviously impose a negligible change <strong>on</strong> <strong>the</strong> pulse<br />
151
152 9. Pulse length, profile <strong>and</strong> jitter<br />
being measured. The diagnostic thus needs to be ei<strong>the</strong>r effectively transparent to <strong>the</strong><br />
pulse, or at <strong>the</strong> very least interrupt <strong>on</strong>ly a small part <strong>and</strong> pass <strong>the</strong> major part of <strong>the</strong><br />
pulse undisturbed to <strong>the</strong> experiment.<br />
Hence, <strong>the</strong>re is a very dem<strong>and</strong>ing specificati<strong>on</strong> <strong>on</strong> an ideal pulse timing diagnostic<br />
apparatus:<br />
• Measure all pulses at <strong>the</strong> repetiti<strong>on</strong> rate of <strong>the</strong> machine, i.e. in <strong>the</strong> kHz <strong>and</strong><br />
MHz regimes.<br />
• Meaure <strong>the</strong> intensity profiles of <strong>the</strong> pulses with a temporal resoluti<strong>on</strong> of about<br />
1 femtosec<strong>on</strong>d <strong>–</strong> carrying in mind that this resoluti<strong>on</strong> needs to be maintained<br />
over pulse lengths that can have a durati<strong>on</strong> of hundreds of femtosec<strong>on</strong>ds.<br />
• Measure <strong>the</strong> arrival time of <strong>the</strong> pulse with a resoluti<strong>on</strong> in <strong>the</strong> femtosec<strong>on</strong>d<br />
domain.<br />
• Be transparent to <strong>the</strong> pulse, or sample a minuscule part of <strong>the</strong> pulse.<br />
• Work in a spectral range from <strong>the</strong> VUV to <strong>the</strong> hard X-rays.<br />
A diagnostic tool that fulfils all of <strong>the</strong> above dem<strong>and</strong>s can not be found. Below<br />
we will survey <strong>the</strong> techniques available in <strong>the</strong> VUV <strong>and</strong> X-ray regime toge<strong>the</strong>r with<br />
<strong>the</strong>ir limitati<strong>on</strong>s vis-à-vis <strong>the</strong> ideal outlined above.<br />
Many of <strong>the</strong> techniques that are currently being used <strong>and</strong> developed are based<br />
around cross-correlati<strong>on</strong> with an external optical laser (a high-power IR Ti:Sapphire)<br />
<strong>and</strong> can give both pulse length <strong>and</strong> pulse jitter (relative to <strong>the</strong> optical laser). These<br />
techniques have started out as multi-shot measurements since <strong>the</strong>y initially required<br />
scanning <strong>the</strong> IR pulse delay. But <strong>the</strong>re is a lot of activity in developing <strong>the</strong> techniques<br />
for single-shot use <strong>and</strong> in improving<strong>the</strong> temporal resoluti<strong>on</strong> to<strong>the</strong>femtosec<strong>on</strong>d<br />
level (see page 153).<br />
Electro-optical sampling also uses cross-correlati<strong>on</strong> with an optical laser <strong>and</strong> is<br />
used mainly for electr<strong>on</strong> bunch measurements but can also be used for measuring <strong>the</strong><br />
lengths of THz pulses directly (see page 155). An alternative approach to pulse length<br />
measurement is auto-correlati<strong>on</strong>, (see page 155).<br />
Simple intensity autocorrelati<strong>on</strong> <strong>on</strong>ly gives a pulse length <strong>and</strong> not <strong>the</strong> profile. However,<br />
more sophisticated autocorrelati<strong>on</strong> techniques have been developed in <strong>the</strong> visible<br />
<strong>and</strong> UV that can give <strong>the</strong> full pulse profile of pulses as short as a few femtosec<strong>on</strong>ds.<br />
There is some possibility to extend <strong>the</strong>se techniques to shorter wavelengths, though<br />
<strong>the</strong> limit here is not clear.<br />
Reflectivity modulati<strong>on</strong> of a semic<strong>on</strong>ductor by a free electr<strong>on</strong> laser pulse has been<br />
used to give single shot measurements with a temporal resoluti<strong>on</strong> of 40 fs. Streak<br />
cameras areawell establishedtechnologyformeasuringpulseswithpicosec<strong>on</strong>dlengths<br />
<strong>and</strong> <strong>the</strong>y are being developed to achieve resoluti<strong>on</strong>s of a few hundred femtosec<strong>on</strong>ds.<br />
Streak cameras can give single pulse measurements but <strong>on</strong>ly at limited repetiti<strong>on</strong><br />
rates.<br />
Recently an elegant way of achieving few femtosec<strong>on</strong>ds resoluti<strong>on</strong> in <strong>the</strong> timedomain<br />
was dem<strong>on</strong>strated at Flash by Tavella <strong>and</strong> co-workers. Their technique<br />
utilized <strong>the</strong> terahertz radiati<strong>on</strong> generated in <strong>the</strong> undulator, which is <strong>the</strong>n phasecorrelated<br />
to <strong>the</strong> X-ray pulse. The optical laser system of <strong>the</strong> facility can <strong>the</strong>n be diagnosed<br />
toge<strong>the</strong>r with he terahertz radiati<strong>on</strong> without disturbing <strong>the</strong> X-ray pulse[230].
9.2. Cross-correlati<strong>on</strong> techniques 153<br />
9.2 Cross-correlati<strong>on</strong> techniques<br />
Cross-correlati<strong>on</strong> techniques are currently <strong>the</strong> most widely used techniques at XUV<br />
wavelengths as <strong>the</strong>y give pulse length <strong>and</strong> jitter informati<strong>on</strong>. A wide range of techniques<br />
based <strong>on</strong> <strong>the</strong> photo-i<strong>on</strong>isati<strong>on</strong> of gases are being developed as <strong>the</strong>y have <strong>the</strong><br />
potential to be transparent to <strong>the</strong> phot<strong>on</strong> <strong>beam</strong>.<br />
With a known reference laser pulse, cross-correlati<strong>on</strong> between this <strong>and</strong> a X-ray<br />
pulse can be used to measure <strong>the</strong> relative jitter of <strong>the</strong> free electr<strong>on</strong> laser pulse with<br />
respect to <strong>the</strong> laser pulse; in some circumstances said measurement can be used to<br />
estimate <strong>the</strong> length of <strong>the</strong> X-ray pulse.<br />
The p<strong>on</strong>dermotive energy is given by<br />
Up(t) = e 2 E 2 a(t)cos(ωℓt+φ)<br />
where Ea is <strong>the</strong> amplitude of <strong>the</strong> laser field, ωℓ <strong>the</strong> laser frequency <strong>and</strong> φ <strong>the</strong> phase<br />
respectively[231].<br />
In most experimental c<strong>on</strong>figurati<strong>on</strong>s, <strong>the</strong> presence of side-b<strong>and</strong>s would be <strong>the</strong> dominant<br />
effect, but this can be suppressed by measuring <strong>the</strong> photo-electr<strong>on</strong>s ejected in<br />
a directi<strong>on</strong> perpendicular to <strong>the</strong> polarisati<strong>on</strong> axis of <strong>the</strong> laser radiati<strong>on</strong>, allowing <strong>the</strong><br />
shift due to <strong>the</strong> p<strong>on</strong>deromotive energy to be observed.<br />
The intensity of <strong>the</strong> side-b<strong>and</strong>s is proporti<strong>on</strong>al to magnitude of <strong>the</strong> photoelectr<strong>on</strong><br />
wave-vector[232]<br />
k = 1<br />
�<br />
� 2m(�ωfel −Ip)<br />
Dec<strong>on</strong>voluti<strong>on</strong> of <strong>the</strong> side-b<strong>and</strong> intensity as a functi<strong>on</strong> of delay is obviously not a<br />
single shot measurement. In order to determine <strong>the</strong> pulse length, <strong>the</strong> jitter between<br />
<strong>the</strong> two pulses <strong>and</strong> <strong>the</strong> X-ray pulse length must be small enough not to dominate<br />
<strong>the</strong> cross-correlati<strong>on</strong> curve. Such a technique can be successfully applied to measure<br />
<strong>the</strong> pulse length of soft X-ray radiati<strong>on</strong> generated by HHG where <strong>the</strong> jitter between<br />
<strong>the</strong> generating infrared pulse <strong>and</strong> <strong>the</strong> resulting HHG radiati<strong>on</strong> is very small. In <strong>the</strong><br />
case of radiati<strong>on</strong> from a Sase free electr<strong>on</strong> laser, <strong>the</strong> cross-correlati<strong>on</strong> curve will most<br />
likely to be dominated by <strong>the</strong> jitter between <strong>the</strong> pulses, <strong>and</strong> can in fact be used to<br />
measure <strong>the</strong> distributi<strong>on</strong> of <strong>the</strong> jitter. It may be possible that this technique could<br />
be used for seeded free electr<strong>on</strong> lasers where <strong>the</strong> pulses will be more stable <strong>and</strong> <strong>the</strong><br />
jitter smaller.<br />
An example of being able to estimate <strong>the</strong> time delay from a single shot measurement<br />
is given in Radcliffe et al. [232], where <strong>the</strong>y used 13.8 nm pulses from Flash<br />
of about 20 fs l<strong>on</strong>g to i<strong>on</strong>ise Xe <strong>and</strong> measured <strong>the</strong> sideb<strong>and</strong> intensity in <strong>the</strong> presence<br />
of 120 fs pulses from a Ti:Sapphire laser. This case is favourable for <strong>the</strong> formati<strong>on</strong><br />
of side-b<strong>and</strong>s due to <strong>the</strong> relatively large photo-electr<strong>on</strong> wave-vector <strong>and</strong> up to four<br />
high energy side-b<strong>and</strong>s were obtained. From <strong>the</strong>oretical simulati<strong>on</strong>s of <strong>the</strong> side-b<strong>and</strong><br />
intensity, <strong>the</strong> number of side-b<strong>and</strong>s gives a measure of <strong>the</strong> laser field intensity during<br />
<strong>the</strong> FEL pulse, <strong>and</strong> hence <strong>the</strong> overlap of <strong>the</strong> pulses. In this experiment, a precisi<strong>on</strong><br />
of better than 50 fs was achieved for <strong>the</strong> relative delay, but note that <strong>the</strong> sign of<br />
<strong>the</strong> relative delay cannot be obtained. The cross-correlati<strong>on</strong> curve has a FWHM of<br />
about 600±50 fs, which is dominated by <strong>the</strong> jitter, <strong>and</strong> gives <strong>the</strong> FWHM of <strong>the</strong> jitter<br />
distributi<strong>on</strong> of 590 fs. It should be possible to determine <strong>the</strong> sign of <strong>the</strong> jitter by<br />
using a chirped laser pulse (as also suggested in <strong>the</strong> XFEL TDR [89] for <strong>the</strong> Auger<br />
electr<strong>on</strong> measurements menti<strong>on</strong>ed below) but this idea has yet to be tested.
154 9. Pulse length, profile <strong>and</strong> jitter<br />
Ifthis work were tobe extendedtoveryshort X-rayspulses, <strong>the</strong>nit would be found<br />
that<strong>the</strong>spectralwidthof<strong>the</strong>X-raypulsewouldsmear out<strong>the</strong>side-b<strong>and</strong>s. This canbe<br />
overcome by observing <strong>the</strong> photo-electr<strong>on</strong> spectra for electr<strong>on</strong>s ejected at right angles<br />
to <strong>the</strong> polarisati<strong>on</strong> of <strong>the</strong> laser. In this case, as noted above, sideb<strong>and</strong> formati<strong>on</strong> is<br />
suppressed, <strong>and</strong> <strong>on</strong>e can measure <strong>the</strong> red-shift in <strong>the</strong> energy of <strong>the</strong> electr<strong>on</strong>s due to <strong>the</strong><br />
p<strong>on</strong>deromotive force exerted by <strong>the</strong> laser field. This has been d<strong>on</strong>e successfully using<br />
an HHG source of SXR (90 eV) phot<strong>on</strong>s co-focussed with <strong>the</strong> generating 770 nm laser<br />
pulses [231]. A delay scan yielded an X-ray pulse width of <strong>the</strong> order of 2 fs FWHM;<br />
again, extending this to free electr<strong>on</strong> lasers would require <strong>the</strong> relative jitter to be of a<br />
similar size to <strong>the</strong> pulse width. For a seeded free electr<strong>on</strong> laser, this may be possible<br />
if <strong>the</strong> X-ray pulse timing is dictated by <strong>the</strong> laser seed. A significant disadvantage of<br />
<strong>the</strong>se techniques is <strong>the</strong> need to co-propagate <strong>the</strong> FEL <strong>and</strong> IR pulses to a comm<strong>on</strong><br />
focus. For <strong>on</strong>-line use, this requires a permanent extra focus to be included in <strong>the</strong><br />
<strong>beam</strong> <strong>transport</strong> system, which is not always c<strong>on</strong>venient or desirable. A perpendicular<br />
geometry would be more flexible - this has been used in <strong>the</strong> c<strong>on</strong>figurati<strong>on</strong> adapted by<br />
Cunovic et al. [233] where <strong>the</strong>y have used <strong>the</strong> sec<strong>on</strong>d method of obtaining <strong>the</strong> pulse<br />
lengthbymapping<strong>the</strong>temporalco-ordinateof<strong>the</strong>pulsetospatial co-ordinates. In<strong>the</strong><br />
proof of principle experiment, outlined below, 32 nm radiati<strong>on</strong> from Flash was used<br />
to photo-i<strong>on</strong>ize Kr in <strong>the</strong> presence of a pulse from a Ti:Sapphire laser. In principle<br />
this is a single shot technique, but for this first experiment <strong>the</strong> data were too noisy<br />
<strong>and</strong> had to be summed over several shots.<br />
The unfocussed free electr<strong>on</strong> laser <strong>beam</strong>, of FWHM 7 mm, entered <strong>the</strong> experimental<br />
chamber c<strong>on</strong>taining low pressure Kr through an aperture 500 µm wide. The FEL<br />
<strong>beam</strong> was crossed at right angles with a focussed <strong>beam</strong> from a short pulse Ti:Sapphire<br />
laser. The widthof <strong>the</strong>X-ray<strong>beam</strong> in<strong>the</strong>chamber is equivalentto1.7 ps, muchl<strong>on</strong>ger<br />
than <strong>the</strong> laser pulse length of 150 fs, <strong>and</strong> <strong>on</strong>e has to assume that <strong>the</strong> intensity variati<strong>on</strong><br />
over <strong>the</strong> width of <strong>the</strong> central part of <strong>the</strong> X-ray <strong>beam</strong> accepted by <strong>the</strong> aperture<br />
is not great. Hence as <strong>the</strong> laser <strong>beam</strong> traverses <strong>the</strong> pulse, <strong>the</strong> intensity of <strong>the</strong> side<br />
b<strong>and</strong>s in <strong>the</strong> photo-electr<strong>on</strong> spectra will map out <strong>the</strong> intensity of <strong>the</strong> free electr<strong>on</strong><br />
laser <strong>beam</strong> as a functi<strong>on</strong> of time. The interacti<strong>on</strong> regi<strong>on</strong> is imaged by an electr<strong>on</strong><br />
lens system c<strong>on</strong>taining a retarding grid which <strong>on</strong>ly allows <strong>the</strong> passage of electr<strong>on</strong>s<br />
whose energy has been upshifted by <strong>the</strong> laser <strong>beam</strong>. A line will be formed in <strong>the</strong> 2D<br />
electr<strong>on</strong> detector, corresp<strong>on</strong>ding to <strong>the</strong> different emissi<strong>on</strong> time of electr<strong>on</strong>s, which in<br />
turn yields informati<strong>on</strong> about <strong>the</strong> intensity variati<strong>on</strong> of <strong>the</strong> X-ray pulse.<br />
In order to be able to use this technique for single shot measurement, <strong>the</strong> signal<br />
would need to be increased by about two orders of magnitude from that obtained in<br />
[233]. This could be achieved by increasing <strong>the</strong> target gas density in c<strong>on</strong>juncti<strong>on</strong> with<br />
<strong>the</strong> free electr<strong>on</strong> laser pulse energy, but <strong>the</strong>re is a limit to <strong>the</strong> increase before space<br />
charge effects become important. In <strong>the</strong> measurement reported in [233] <strong>the</strong> total<br />
pulse energy was 2 - 15 µJ before <strong>the</strong> entrance aperture to <strong>the</strong> chamber. If photoelectr<strong>on</strong>s<br />
with higher energies were produced, <strong>the</strong> signal would also be increased as<br />
<strong>the</strong> side-b<strong>and</strong> producti<strong>on</strong> increases with increasing energy as noted above.<br />
For use as an <strong>on</strong>line diagnostic, <strong>the</strong> experimental set-up would need to be redesigned<br />
without <strong>the</strong> entrance aperture as this will disrupt <strong>the</strong> <strong>beam</strong> through edge<br />
diffracti<strong>on</strong> effects. There does not seem to be an intrinsic need for aperturing <strong>the</strong><br />
<strong>beam</strong> <strong>on</strong> entry to <strong>the</strong> experimental chamber.<br />
An alternative to detecting electr<strong>on</strong>s from direct i<strong>on</strong>isati<strong>on</strong> is to use electr<strong>on</strong>s<br />
generated by Auger decay of an inner shell hole. The energy of <strong>the</strong> electr<strong>on</strong>s can also<br />
be modified by <strong>the</strong> presence of a str<strong>on</strong>g laser field, creating side-b<strong>and</strong>s. An advantage
9.3. Electro-optic techniques 155<br />
of using Auger electr<strong>on</strong>s is that <strong>the</strong>ir energy spectrum is fixed <strong>and</strong> does not depend<br />
<strong>on</strong> <strong>the</strong> energy width of <strong>the</strong> exciting X-ray pulse, <strong>and</strong> <strong>the</strong> Auger decay times are short<br />
compared with <strong>the</strong> typical durati<strong>on</strong> of free electr<strong>on</strong> laser pulses. If <strong>the</strong> laser pulse were<br />
chirped so that <strong>the</strong> side b<strong>and</strong>s are broadened, <strong>the</strong>n some measure of <strong>the</strong> X-ray pulse<br />
length can be obtained as well as <strong>the</strong> jitter <strong>–</strong> e.g. in <strong>the</strong> European X-Fel technical<br />
design report it is said that a linear chirp of 1 eV in a laser pulse of width of 300 fs<br />
would lead to a broadening of 0.25 eV of <strong>the</strong> sideb<strong>and</strong> for an 80 fs X-ray pulse[89].<br />
9.3 Electro-optic techniques<br />
The electro-optic technique uses birefringence induced in an electro-optic crystal by<br />
<strong>the</strong>electricfieldofTHzpulsesorelectr<strong>on</strong>pulses. Theamountofbirefringencedepends<br />
<strong>on</strong> <strong>the</strong> electric field <strong>and</strong> is probed by m<strong>on</strong>itoring <strong>the</strong> change of polarizati<strong>on</strong> of a<br />
short optical laser pulse. The limitati<strong>on</strong> to <strong>the</strong> THz regime for direct phot<strong>on</strong> pulse<br />
measurements is due <strong>the</strong> availability of crystals with a suitable electro-optic resp<strong>on</strong>se<br />
functi<strong>on</strong>.<br />
For electr<strong>on</strong> bunches, <strong>the</strong> electro-optic detecti<strong>on</strong> method makes use of <strong>the</strong> fact<br />
that <strong>the</strong> local electric field of a highly relativistic electr<strong>on</strong> bunch moving in a straight<br />
line is almost entirely c<strong>on</strong>centrated perpendicular to its directi<strong>on</strong> of moti<strong>on</strong>. The<br />
limitati<strong>on</strong>s to temporal resoluti<strong>on</strong> are discussed in Berden et al. [234] <strong>and</strong> include <strong>the</strong><br />
EO material selecti<strong>on</strong>, crystal thickness, wavelength dependence <strong>and</strong> <strong>beam</strong> <strong>–</strong> probe<br />
displacement. Philips et al. [235] have dem<strong>on</strong>strated measurement of electr<strong>on</strong> bunch<br />
lengths of 118 fs FWHM using a 35 fs probe laser at <strong>the</strong> Flash facility.<br />
The method can be used to m<strong>on</strong>itor <strong>the</strong> relative timing of an external laser with<br />
<strong>the</strong> electr<strong>on</strong> bunch, <strong>and</strong> using this informati<strong>on</strong> to improve <strong>the</strong> resoluti<strong>on</strong> of crosscorrelati<strong>on</strong><br />
data. A proof-of-principle experiment has been carried out at Flash by<br />
Azima et al. [236] where <strong>the</strong>y have measured <strong>the</strong> relative arrival time of <strong>the</strong> electr<strong>on</strong><br />
bunch<strong>and</strong> <strong>the</strong>laser pulseat <strong>the</strong>entrance to<strong>the</strong>free electr<strong>on</strong> laser as well as measuring<br />
<strong>the</strong> side-b<strong>and</strong> formati<strong>on</strong> in <strong>the</strong> photo-electr<strong>on</strong> spectra from Xe in <strong>the</strong> presence of <strong>the</strong><br />
laser field. A plot of side-b<strong>and</strong> intensity against <strong>the</strong> delay between <strong>the</strong> laser <strong>and</strong> <strong>the</strong><br />
free electr<strong>on</strong> laser has a rms width of 410 fs which is mainly due to jitter in <strong>the</strong> free<br />
electr<strong>on</strong> laser pulse. When <strong>the</strong> electro-optical data are used to correct for <strong>the</strong> jitter,<br />
<strong>the</strong> rms width of <strong>the</strong> curve is reduced to 100 fs. They call this technique TEO <strong>–</strong><br />
timing by electro-optic sampling.<br />
9.4 Autocorrelati<strong>on</strong> techniques<br />
The advent of ultra-short (< 100 fs) optical pulses from lasers has driven a significant<br />
amount of development into measuring <strong>the</strong> temporal profile of such pulses. Since<br />
<strong>the</strong>re are no detectors with a fast enough temporal resp<strong>on</strong>se to directly measure <strong>the</strong><br />
intensity profile of pulses with lengths shorter than a few hundred femtosec<strong>on</strong>ds,<br />
<strong>the</strong> approach taken has been to probe <strong>the</strong> pulse with ano<strong>the</strong>r short phot<strong>on</strong> pulse. Of<br />
course, this leads to <strong>the</strong> immediate problem of producing a suitably short probe pulse.<br />
In autocorrelati<strong>on</strong> measurements, <strong>the</strong> probe is created by splitting <strong>the</strong> original pulse<br />
into two (or in some cases more) parts that are each a replica of <strong>the</strong> original <strong>and</strong> <strong>on</strong>e<br />
part is used to probe <strong>the</strong> o<strong>the</strong>r. Since <strong>the</strong> pulse being measured is its own reference,<br />
autocorrelati<strong>on</strong> is thus used to study shape of pulses ra<strong>the</strong>r than timing jitter (though
156 9. Pulse length, profile <strong>and</strong> jitter<br />
a technique such as Spider (q.v.) can be used to derive <strong>the</strong> time correlati<strong>on</strong> functi<strong>on</strong><br />
of a train of pulses).<br />
Intensity autocorrelati<strong>on</strong><br />
When optical lasers producing ultra-short pulses were first developed, <strong>the</strong> instrument<br />
that was most likely to be employed to measure <strong>the</strong> pulses was a simple intensity<br />
autocorrelator. This was not because <strong>the</strong> autocorrelator was especially good at this<br />
job, but ra<strong>the</strong>r because autocorrelati<strong>on</strong> was about <strong>the</strong> <strong>on</strong>ly technique that could be<br />
used to measure pulses with durati<strong>on</strong>s below 100 fs since <strong>the</strong> fastest alternative<br />
instruments, such as streak cameras, were limited to temporal resoluti<strong>on</strong>s of several<br />
hundred femtosec<strong>on</strong>ds at best <strong>and</strong> more generally picosec<strong>on</strong>ds.<br />
A sec<strong>on</strong>d-order intensity autocorrelator is relatively easy to produce. The key<br />
comp<strong>on</strong>ents are a <strong>beam</strong> splitter to divide <strong>the</strong> <strong>beam</strong> into two (in principle identical)<br />
replicas of <strong>the</strong> input pulse, a means of altering <strong>the</strong> path length travelled by <strong>on</strong>e of <strong>the</strong><br />
replicas so as to vary <strong>the</strong> relative temporal delay between <strong>the</strong>m in precise increments,<br />
<strong>and</strong> a means of recombining <strong>the</strong>m so that <strong>the</strong>y overlap spatially. There must also be<br />
some means of measuring <strong>the</strong> temporal overlap as a functi<strong>on</strong> of <strong>the</strong> delay. Typically,<br />
this is achieved by spatially overlapping <strong>the</strong> two <strong>beam</strong>s in some instantaneouslyresp<strong>on</strong>ding,<br />
n<strong>on</strong>-linear medium so that a signal is produced that is proporti<strong>on</strong>al to<br />
<strong>the</strong> overlap intensity I(t)I(t−τ).<br />
A detector records <strong>the</strong> intensity of this signal, after separating it by some means<br />
from <strong>the</strong> transmitted replica pulses. Since <strong>the</strong> detector will inevitably have a resp<strong>on</strong>se<br />
thatisveryslowcomparedwith<strong>the</strong>ultra-shortpulselength, itautomatically performs<br />
a time integrati<strong>on</strong> of <strong>the</strong> signal. The signal as afuncti<strong>on</strong> of <strong>the</strong> relative temporal delay<br />
τ is thus <strong>the</strong> autocorrelati<strong>on</strong> functi<strong>on</strong> of <strong>the</strong> temporal intensity profile of <strong>the</strong> original<br />
pulse.<br />
�∞<br />
A(τ) = dtI(t)I(t−τ) (9.1)<br />
−∞<br />
Because <strong>the</strong> phase informati<strong>on</strong> is lost in this measurement, <strong>the</strong> Fourier transform of<br />
<strong>the</strong> autocorrelati<strong>on</strong> functi<strong>on</strong> is just <strong>the</strong> power spectrum of <strong>the</strong> original pulse. Autocorrelati<strong>on</strong><br />
thus gives <strong>the</strong> pulse length but not <strong>the</strong> pulse profile. Indeed, <strong>on</strong>e has to<br />
assume a pulse profile even to extract a pulse length. The autocorrelati<strong>on</strong> also tends<br />
to smear out any structure (such as satellite pulses) <strong>and</strong> in general any number of<br />
pulse shapes can give <strong>the</strong> same autocorrelati<strong>on</strong> functi<strong>on</strong>. Thus, changing <strong>the</strong> assumed<br />
pulse profile can give significant changes to <strong>the</strong> extracted pulse length. In general,<br />
autocorrelati<strong>on</strong> measurements are pr<strong>on</strong>e to systematic errors (for example caused by<br />
misalignment) since <strong>the</strong> <strong>on</strong>ly c<strong>on</strong>straints <strong>on</strong> <strong>the</strong> trace are that it should have a maximum<br />
at zero relative delay, be zero at delays much larger than <strong>the</strong> pulse width, <strong>and</strong><br />
be symmetric with respect to zero delay. In fact, <strong>the</strong> autocorrelati<strong>on</strong> of complicated<br />
pulses always tends to a sharp spike sitting <strong>on</strong> a smooth pedestal 1 .<br />
In <strong>the</strong> visible <strong>and</strong> UV regi<strong>on</strong>s <strong>the</strong> n<strong>on</strong>-linear medium is usually a sec<strong>on</strong>d harm<strong>on</strong>ic<br />
generati<strong>on</strong> (SHG) crystal which has a sec<strong>on</strong>d-order n<strong>on</strong>-linearity in its electric susceptibility<br />
<strong>and</strong> produces light at twice <strong>the</strong> frequency of <strong>the</strong> input light <strong>and</strong> with <strong>and</strong><br />
intensity that is proporti<strong>on</strong>al to <strong>the</strong> product of <strong>the</strong> intensities of <strong>the</strong> two input pulses.<br />
1 See, for instance, http://www.swampoptics.com/tutorials autocorrelati<strong>on</strong>.htm
9.4. Autocorrelati<strong>on</strong> techniques 157<br />
The SHG signal thus rises quadratically with intensity of <strong>the</strong> original pulse. The SHG<br />
signal is generally detected through a spectrometer to isolate it from <strong>the</strong> fundamental<br />
light.<br />
The short wavelength limit for SHG producti<strong>on</strong> is determined by <strong>the</strong> transmissi<strong>on</strong><br />
of <strong>the</strong> n<strong>on</strong>-linear crystals. The crystal must be transparent at half <strong>the</strong> wavelength<br />
of <strong>the</strong> incident light for <strong>the</strong> SHG signal to be detectable. Petrov et al. [237] have<br />
dem<strong>on</strong>strated autocorrelati<strong>on</strong> measurements to 250 nm (5 eV) using SrB4O7 (SBO),<br />
which is transparent to 125 nm. A fur<strong>the</strong>r limitati<strong>on</strong> of SHG is <strong>the</strong> finite b<strong>and</strong>width<br />
over which <strong>the</strong> crystal will functi<strong>on</strong>. It is important that <strong>the</strong> SHG signal be phasematched<br />
to <strong>the</strong> original pulses since o<strong>the</strong>rwise <strong>the</strong>re can be a spectral filtering effect<br />
that can significantly distort <strong>the</strong> autocorrelati<strong>on</strong> functi<strong>on</strong>[238]. For very short pulses,<br />
this means <strong>the</strong> crystals have to be very thin. The crystals also need to be thin to<br />
limit dispersi<strong>on</strong> that will change <strong>the</strong> pulse being measured. To overcome some of <strong>the</strong><br />
limitati<strong>on</strong>s of SHG from crystals, Dai et al. [239] have dem<strong>on</strong>strated using SHG from<br />
metal surfaces. This will work from <strong>the</strong> far-infrared to <strong>the</strong> plasma frequency of <strong>the</strong><br />
metal being used (e.g. about 10 eV for gold).<br />
Autocorrelati<strong>on</strong> measurements have also been dem<strong>on</strong>strated using two-phot<strong>on</strong> absorpti<strong>on</strong><br />
inside a semic<strong>on</strong>ductor-based phot<strong>on</strong> detector [240]. The advantage here is<br />
that <strong>the</strong> n<strong>on</strong>-linear medium <strong>and</strong>detector are combined <strong>and</strong> so <strong>the</strong> experimental set-up<br />
is simplified. However, a detector with a b<strong>and</strong>gap that is between <strong>the</strong> phot<strong>on</strong> energy<br />
<strong>and</strong> twice <strong>the</strong> phot<strong>on</strong> energy is required <strong>and</strong> so different materials will be required for<br />
different wavelengths. Extending <strong>the</strong> technique to <strong>the</strong> XUV is also unlikely to be possible.<br />
Worth noting is that Liu et al. [241, 242] have shown that autocorrelati<strong>on</strong> can<br />
give <strong>the</strong> full pulse profile if <strong>the</strong> pulse is split into three <strong>beam</strong>s. In this triple-optical<br />
autocorrelati<strong>on</strong> for direct pulse shape measurement (Toad), <strong>the</strong> delay between all <strong>the</strong><br />
pulses must be varied <strong>and</strong> <strong>the</strong> <strong>beam</strong>s are focused into a third-harm<strong>on</strong>ic generati<strong>on</strong><br />
(THG) crystal. Thus, although <strong>the</strong> technique requires <strong>on</strong>ly time-domain measurements,<br />
<strong>the</strong> extensi<strong>on</strong> to wavelengths shorter than <strong>the</strong> optical will be significantly<br />
more challenging than extending two-<strong>beam</strong> autocorrelati<strong>on</strong>.<br />
Making a two-<strong>beam</strong> autocorrelator that works at VUV <strong>and</strong> shorter wavelengths is<br />
challenging but not impossible. A successful instrument has been built for Flash by<br />
BESSY[137] <strong>and</strong> a simpler system has been made by <strong>the</strong> University of Hamburg[243]<br />
(cross-correlators between X-ray <strong>and</strong> optical pulses have also been achieved[244]).<br />
A significant challenge is achieving <strong>the</strong> initial <strong>beam</strong> splitting. Amplitude divisi<strong>on</strong><br />
whilst preserving <strong>the</strong> quality of <strong>the</strong> original pulse-fr<strong>on</strong>t is probably impossible at<br />
VUV to SXR wavelengths. In <strong>the</strong> BESSY instrument, <strong>the</strong> <strong>beam</strong> is divided spatially<br />
(i.e. wavefr<strong>on</strong>t divisi<strong>on</strong>) using a knife-edged mirror <strong>and</strong> <strong>on</strong>e must thus assume that<br />
<strong>the</strong> temporal profile of <strong>the</strong> <strong>beam</strong> is <strong>the</strong> same over <strong>the</strong> <strong>beam</strong> cross-secti<strong>on</strong>. Diffracti<strong>on</strong><br />
effects from <strong>the</strong> wavefr<strong>on</strong>t divisi<strong>on</strong> are a c<strong>on</strong>cern but are said to be minor in <strong>the</strong> focal<br />
plane[137]. A sec<strong>on</strong>d knife-edged mirror after <strong>the</strong> delay line is used to overlap <strong>the</strong><br />
two <strong>beam</strong>s by angling <strong>on</strong>e of <strong>the</strong>m slightly with respect to <strong>the</strong> o<strong>the</strong>r. The delay of<br />
<strong>on</strong>e <strong>beam</strong> with respect to <strong>the</strong> o<strong>the</strong>r is achieved through an optical delay line using<br />
translating mirrors. The relative delay range available is -3/+25 ps <strong>and</strong> is limited<br />
by <strong>the</strong> overall mechanical design <strong>and</strong> <strong>the</strong> size of <strong>the</strong> delay line mirrors, since <strong>the</strong><br />
<strong>beam</strong> moves al<strong>on</strong>g <strong>the</strong>se as <strong>the</strong> delay is varied. The mechanical specificati<strong>on</strong>s (e.g.<br />
mirror quality, angular precisi<strong>on</strong>, translati<strong>on</strong> accuracy <strong>and</strong> overall stability) are very<br />
challenging for short wavelength operati<strong>on</strong>.<br />
The shortest wavelength that can be measured is determined by <strong>the</strong> reflectivity<br />
of <strong>the</strong> mirrors since <strong>the</strong>re are four mirrors per <strong>beam</strong> path. Making <strong>the</strong> instrument
158 9. Pulse length, profile <strong>and</strong> jitter<br />
relatively compact prevents <strong>the</strong> use of extremely grazing angles of incidence; <strong>the</strong> fixed<br />
path arm uses 3 ◦ grazing whilst <strong>the</strong> variable path arm uses 6 ◦ grazing <strong>and</strong> <strong>the</strong>refore<br />
<strong>the</strong> intensity of <strong>the</strong>two pulses is not <strong>the</strong> same. With carb<strong>on</strong> coatings, good reflectivity<br />
is possible from 30 to 200 eV. Different coatings (e.g. nickel) could be used to extend<br />
this range to higher phot<strong>on</strong> energies.<br />
A mechanically much simpler instrument has been developed at Synchrotr<strong>on</strong> Soleil<br />
for use as a VUV Fourier Transform interferometer[245]. This also uses wavefr<strong>on</strong>t<br />
divisi<strong>on</strong> to split <strong>the</strong> <strong>beam</strong> but in this design two roof-mirrors are used so that <strong>the</strong><br />
optical assembly for each <strong>beam</strong> path is m<strong>on</strong>olithic. However, this means <strong>the</strong>re are<br />
two 90 ◦ deflecti<strong>on</strong>s in each path <strong>and</strong> so <strong>the</strong> l<strong>on</strong>gest operating wavelength is in <strong>the</strong><br />
VUV.<br />
Autocorrelati<strong>on</strong> measurements <strong>on</strong> pulses from an HHG source using ano<strong>the</strong>r splitmirror<br />
approach have been reported by Tzallas et al. [246]. In <strong>the</strong>ir work, a focusing<br />
wavefr<strong>on</strong>t divideris madebysplittingaspherical mirror intotwohalves. Atranslati<strong>on</strong><br />
of <strong>on</strong>e half-mirror al<strong>on</strong>g <strong>the</strong> surface normal gives a relative delay between <strong>the</strong> parts of<br />
<strong>the</strong> <strong>beam</strong> reflected from each half whilst <strong>the</strong> mirror also focuses <strong>the</strong> split <strong>beam</strong>s to a<br />
comm<strong>on</strong> positi<strong>on</strong> in <strong>the</strong> detecti<strong>on</strong> medium. Two-phot<strong>on</strong> i<strong>on</strong>ized He gas is used as <strong>the</strong><br />
n<strong>on</strong>-linear medium <strong>and</strong> <strong>the</strong> He i<strong>on</strong> yield measured by a time-of-flight spectrometer.<br />
Stigmatic imaging with a spherical mirror requires <strong>the</strong> system to operate at nearnormal<br />
incidence. The upperphot<strong>on</strong> energy is thus limited ifasimple metallic coating<br />
is used. Multilayer coatings could be used to allow operati<strong>on</strong> at shorter wavelengths,<br />
though <strong>the</strong> operating b<strong>and</strong>width would be quite narrow for a given multilayer.<br />
The final challenge in <strong>the</strong> XUV autocorrelator is a means of measuring <strong>the</strong> autocorrelati<strong>on</strong><br />
signal. In <strong>the</strong> measurements reported in [247] using <strong>the</strong> BESSY/Flash<br />
instrument, <strong>the</strong> temporal coherence was deduced from <strong>the</strong> fringe visibility of <strong>the</strong> spatial<br />
interference pattern as a functi<strong>on</strong> of relative delay. In <strong>the</strong>se measurements, <strong>the</strong><br />
mutual coherence functi<strong>on</strong>, which is closely related to <strong>the</strong> auto-correlati<strong>on</strong> functi<strong>on</strong>,<br />
is measured. The mutual coherence functi<strong>on</strong> is defined by[248]:<br />
�<br />
Γ12(τ) =<br />
u1(t+τ)u ∗<br />
2(t)dt<br />
where ui:s are <strong>the</strong> field values at <strong>the</strong> two slits.<br />
An alternative detecti<strong>on</strong> technique that gives a sec<strong>on</strong>d-order signal like SHG is<br />
two-phot<strong>on</strong> i<strong>on</strong>isati<strong>on</strong> [249<strong>–</strong>251]. The strength of <strong>the</strong> two-phot<strong>on</strong> i<strong>on</strong>isati<strong>on</strong> signal<br />
produced when <strong>on</strong>e phot<strong>on</strong> is c<strong>on</strong>tributed from each <strong>beam</strong> is clearly proporti<strong>on</strong>al <strong>the</strong><br />
temporal intensity overlap of <strong>the</strong> two <strong>beam</strong>s. The wavelength range over which such<br />
schemes will work depends <strong>on</strong> <strong>the</strong> i<strong>on</strong>isati<strong>on</strong> potential of <strong>the</strong> gas. For first i<strong>on</strong>isati<strong>on</strong><br />
potentials, this ranges from 12-24 eV for helium to 4.5 to 9 eV for toluene.<br />
Two-phot<strong>on</strong> single-i<strong>on</strong>isati<strong>on</strong> above 24 eV is unlikely to be practical due to <strong>the</strong><br />
need to discriminate against single-phot<strong>on</strong> i<strong>on</strong>isati<strong>on</strong> events which will give an increasingly<br />
str<strong>on</strong>g background of first order signal as <strong>the</strong> phot<strong>on</strong> energy increases.<br />
Nakajima <strong>and</strong> Nikolopoulos [252, 253] have made a <strong>the</strong>oretical study of using twophot<strong>on</strong><br />
doublei<strong>on</strong>isati<strong>on</strong> of helium, which would cover <strong>the</strong> range 40 to 54 eV. This<br />
scheme could be extended to shorter wavelengths by using heavier elements (Li, Be,<br />
B etc) <strong>and</strong> <strong>the</strong>ir higher i<strong>on</strong>isati<strong>on</strong> stages [254]. Never<strong>the</strong>less, c<strong>on</strong>tinuous coverage of<br />
a wide phot<strong>on</strong> energy range will not be possible with i<strong>on</strong>isati<strong>on</strong> based techniques. In<br />
summary, autocorrelati<strong>on</strong> is a feasible pulse length measuring technique in <strong>the</strong> VUV<br />
<strong>and</strong> XUV, though <strong>on</strong>ly <strong>the</strong> pulse length is measured <strong>and</strong> <strong>the</strong> technique is usually
9.4. Autocorrelati<strong>on</strong> techniques 159<br />
multi-shot, though adapti<strong>on</strong> to single shot should be possible (see for example <strong>the</strong><br />
descripti<strong>on</strong> of single shot Frog in secti<strong>on</strong> 3.2.1). The pulse length extracti<strong>on</strong> is also<br />
not particularly robust due to <strong>the</strong> need to assume a pulse profile <strong>and</strong> <strong>the</strong> susceptibility<br />
to systematic errors. Autocorrelators do not give informati<strong>on</strong> of pulse timing (jitter).<br />
The mechanical dem<strong>and</strong>s of <strong>the</strong> instrument are high but can be surmounted. Finding<br />
a suitable n<strong>on</strong>-linear detecti<strong>on</strong> technique to measure <strong>the</strong> auto-correlati<strong>on</strong> signal is<br />
even more dem<strong>and</strong>ing <strong>and</strong> unlikely to give c<strong>on</strong>tinuous wavelength coverage. Autocorrelators<br />
are invasive in that <strong>the</strong>y modify <strong>the</strong> <strong>beam</strong> passing through <strong>the</strong>m, but <strong>the</strong>y<br />
can be designed so that <strong>the</strong>y can be inserted into or removed from <strong>the</strong> <strong>beam</strong> path<br />
without affecting <strong>the</strong> operati<strong>on</strong> of downstream optical elements.<br />
Autocorrelati<strong>on</strong> techniques for complete pulse characterizati<strong>on</strong><br />
Complete characterisati<strong>on</strong> of <strong>the</strong> pulse intensity profile requires <strong>the</strong> measurement of<br />
both <strong>the</strong> spectral <strong>and</strong> phase informati<strong>on</strong> so that <strong>the</strong> electric field can be computed<br />
as a functi<strong>on</strong> of time. There are three distinct approaches to this that have been<br />
used in <strong>the</strong> visible <strong>and</strong> near-visible spectral regi<strong>on</strong>s, viz. spectrographic, tomographic<br />
<strong>and</strong> interferometric. In all cases, filtering of <strong>the</strong> pulses is required. It is <strong>the</strong> practical<br />
realizati<strong>on</strong> of some of <strong>the</strong>se filters that make extending <strong>the</strong> techniques to shorter<br />
wavelengths so difficult.<br />
The two classes of filter that are important in current pulse length analysis techniques<br />
are time-stati<strong>on</strong>ary filters (in which <strong>the</strong> time of incidence of <strong>the</strong> input pulse<br />
does not affect <strong>the</strong> output) <strong>and</strong> frequency stati<strong>on</strong>ary filters (where <strong>the</strong> output is not<br />
changed by arbitrary shifts in frequency of <strong>the</strong> input). Frequency-stati<strong>on</strong>ary filters<br />
are time n<strong>on</strong>-stati<strong>on</strong>ary. These filters can be fur<strong>the</strong>r classified as amplitude-<strong>on</strong>ly or<br />
phase-<strong>on</strong>ly i.e. <strong>the</strong>y modulate <strong>on</strong>ly <strong>the</strong> amplitude or <strong>on</strong>ly <strong>the</strong> phase of <strong>the</strong> input.<br />
Finally, <strong>the</strong> filter may have a linear or n<strong>on</strong>-linear resp<strong>on</strong>se (with frequency or time as<br />
appropriate).<br />
A n<strong>on</strong>-dispersive delay line is a simple filter that adds <strong>the</strong> same time delay to all<br />
<strong>the</strong> frequency comp<strong>on</strong>ents in <strong>the</strong> pulse. A delay line is thus a linear spectral phase<br />
modulator, since a linear (with frequency) shift in <strong>the</strong> spectral phase is equivalent to<br />
a time shift. A spectrometer is an example of spectral amplitude filter.<br />
These are both time-stati<strong>on</strong>ary filters. Both <strong>the</strong>se types of filter are relatively easy<br />
to implement across a wide range of wavelengths, though some thought must be given<br />
to <strong>the</strong> frequency resp<strong>on</strong>se functi<strong>on</strong> (e.g. b<strong>and</strong>width, resoluti<strong>on</strong>) of practical devices.<br />
The simplest time-n<strong>on</strong>-stati<strong>on</strong>ary filters are a time-gate <strong>and</strong> a frequency shifter.<br />
A time gate is a time-n<strong>on</strong>stati<strong>on</strong>ary amplitude filter <strong>and</strong> is used to take time slices<br />
of a pulse. A linear temporal phase modulator gives a linear variati<strong>on</strong> of phase with<br />
time, which is <strong>the</strong> same as a translati<strong>on</strong> or shift of <strong>the</strong> frequency axis, <strong>and</strong> thus gives<br />
a spectral shift or shear to <strong>the</strong> pulse. Time-n<strong>on</strong>-stati<strong>on</strong>ary filters are more difficult to<br />
implement, especially for ultra-short pulses.<br />
Spectrographic techniques are probably <strong>the</strong> most widely used pulse profiling techniques.<br />
They work by measuring a two-dimensi<strong>on</strong>al representati<strong>on</strong> of <strong>the</strong> <strong>on</strong>e- dimensi<strong>on</strong>al<br />
field, i.e. <strong>the</strong>y are phase-space measurements. This is <strong>the</strong> critical step since it<br />
allows a generally unambiguous retrieval of <strong>the</strong> phase informati<strong>on</strong> in a way that is not<br />
possible with a <strong>on</strong>e-dimensi<strong>on</strong>al measurement. The <strong>on</strong>ly ambiguities are <strong>the</strong> absolute<br />
phase <strong>and</strong> absolute arrival time.
160 9. Pulse length, profile <strong>and</strong> jitter<br />
Frequency Resolved Optical Gating (FROG)<br />
An example of a spectrographic technique is Frog or Frequency-Resolved Optical<br />
Gating. This uses a sequential spectral filter <strong>and</strong> a time-gate, in ei<strong>the</strong>r order, followed<br />
by an intensity detector. Depending <strong>on</strong> <strong>the</strong> order of <strong>the</strong> filters, <strong>the</strong> recorded signal<br />
is a measure ei<strong>the</strong>r of <strong>the</strong> spectrum of a series of time slices or a measure of <strong>the</strong><br />
time of arrival of a series of spectral slices. The technique is thus operating in <strong>the</strong><br />
timefrequency domain (phase-space) <strong>and</strong> is both temporally <strong>and</strong> spectrally resolved.<br />
The technique is not limited to just autocorrelati<strong>on</strong> measurements (i.e. it will work<br />
with external gate pulses), but in all practical applicati<strong>on</strong>s <strong>the</strong> pulse is used to analyse<br />
itself in manner that is an extensi<strong>on</strong> of intensity autocorrelati<strong>on</strong>.<br />
τ<br />
input-pulse<br />
Beam-splitter<br />
Probe, E(t)<br />
Gate, E(t − τ)<br />
Spectrometer<br />
N<strong>on</strong>-linear medium<br />
Figure 9.2: The basic layout of a Frog experiment; τ marks <strong>the</strong> variable time-delay between <strong>the</strong> probe <strong>and</strong><br />
gate pulses.<br />
In <strong>the</strong> first descripti<strong>on</strong> of Frog by Kane <strong>and</strong> Trebino [255], a replica of <strong>the</strong> pulse<br />
to be measured is used as <strong>the</strong> time gate. Thus, <strong>the</strong> initial pulse is split into two pulses<br />
(gate g(t) <strong>and</strong> probe E(t)) <strong>and</strong> <strong>the</strong> gate pulse has a variable temporal delay applied<br />
to it <strong>–</strong> see Figure 9.2. The two pulses are focused <strong>and</strong> overlapped spatially in an<br />
instantaneous n<strong>on</strong>-linear medium (in this case, self-diffracti<strong>on</strong> due to <strong>the</strong> electr<strong>on</strong>ic<br />
Kerr effect in glass is <strong>the</strong> n<strong>on</strong>-linear process). The diffracted light is <strong>the</strong>n passed to a<br />
spectrometer <strong>and</strong> a complete spectrum recorded, i.e. <strong>the</strong> spectrogram:<br />
�<br />
� �∞<br />
�<br />
SE(ω,τ) = �<br />
� E(t)g(t−τ)e<br />
�<br />
−iωt �<br />
�2<br />
�<br />
dt�<br />
�<br />
�<br />
−∞<br />
The spectrogram is recorded for a range of relative delays of <strong>the</strong> probe <strong>and</strong> gate that<br />
is sufficiently wide to give zero temporal overlap of <strong>the</strong> gate as it is shifted from before<br />
to after <strong>the</strong> probe pulse. Frog is thus essentially a spectrally resolved autocorrelati<strong>on</strong><br />
(as seen from <strong>the</strong> similarity of <strong>the</strong> equati<strong>on</strong> above <strong>and</strong> Equati<strong>on</strong> 9.1).
9.4. Autocorrelati<strong>on</strong> techniques 161<br />
If self-diffracti<strong>on</strong> is used as <strong>the</strong> n<strong>on</strong>-linear effect <strong>the</strong> signal pulse is given by<br />
ES(t,τ) ∝ [E(t)] 2 E ∗ (t−τ), which yields<br />
�<br />
� �<br />
�<br />
Ifrog(ω,τ) = �<br />
�<br />
�<br />
∞<br />
−∞<br />
[E(t)] 2 E ∗ (t−τ)e −iωt dt<br />
It does not matter (i.e. it does not degrade <strong>the</strong> temporal resoluti<strong>on</strong>) that <strong>the</strong> gate<br />
has <strong>the</strong> same time-width as <strong>the</strong>pulse beingmeasured, though ashorter pulse would be<br />
preferable. However, <strong>the</strong> gate pulse should not be too short as an infinitely short gate<br />
yields <strong>on</strong>ly intensity informati<strong>on</strong>, (whilst a CW gate would yield <strong>on</strong>ly <strong>the</strong> spectrum).<br />
The use of <strong>the</strong> pulse to gate itself does however complicate <strong>the</strong> inversi<strong>on</strong> process since<br />
<strong>on</strong>e cannot input any knowledge of <strong>the</strong> gate pulse into <strong>the</strong> analysis.<br />
Ano<strong>the</strong>rpointt<strong>on</strong>oteis that, if<strong>the</strong>Frog measurement recordsan equalnumberN<br />
temporal slices <strong>and</strong> spectral slices, <strong>the</strong>n N 2 measurements are made in total. But <strong>the</strong><br />
analysis will yield <strong>on</strong>ly N intensity <strong>and</strong> N phase values, i.e. 2N derived values. There<br />
is thus a lot of data redundancy in <strong>the</strong> measurement, though this does c<strong>on</strong>tribute<br />
to making <strong>the</strong> data inversi<strong>on</strong> give unambiguous results. In fact, <strong>the</strong> unambiguous<br />
nature of Frog is a <strong>on</strong>e of its most important features (<strong>and</strong> is quite c<strong>on</strong>trary to<br />
simple autocorrelati<strong>on</strong>). Although <strong>the</strong> technique as described above is multi-shot<br />
due to <strong>the</strong> need to scan <strong>the</strong> time delay, <strong>the</strong> technique can be adapted for single shot<br />
measurements [255, 256]. This is achieved by focusing <strong>the</strong> pulses to lines in a comm<strong>on</strong><br />
plane <strong>and</strong> crossing <strong>the</strong> lines at an angle. The positi<strong>on</strong> al<strong>on</strong>g ei<strong>the</strong>r of <strong>the</strong> line foci<br />
is now a linear functi<strong>on</strong> of relative delay between <strong>the</strong> two pulses. If <strong>the</strong> line foci are<br />
orthog<strong>on</strong>al to <strong>the</strong> dispersi<strong>on</strong> plane of <strong>the</strong> spectrometer, <strong>the</strong>n an imaging spectrometer<br />
with 2-D detector will be able to record spectrum in <strong>on</strong>e plane simultaneously with<br />
delay in <strong>the</strong> orthog<strong>on</strong>al plane. Thus <strong>the</strong> spectrum can be recorded as a functi<strong>on</strong> of<br />
delay <strong>and</strong> frequency in <strong>on</strong>e shot. The length of <strong>the</strong> line foci <strong>and</strong> relative angle will<br />
determine <strong>the</strong> range of delays that is recorded, which must be sufficient to give zero<br />
overlap of <strong>the</strong> pulses at each end for <strong>the</strong> Frog measurement to be successful. The size<br />
of <strong>the</strong> delay step is determined by <strong>the</strong> spatial resoluti<strong>on</strong> of <strong>the</strong> spectrometer detector.<br />
The experimental c<strong>on</strong>figurati<strong>on</strong> as described in [255] is quite simple since both<br />
<strong>the</strong> delay line <strong>and</strong> spectrometer are straightforward. Though <strong>the</strong> technique has <strong>the</strong><br />
disadvantage of being invasive, it would seem to be extensible to wavelengths shorter<br />
than <strong>the</strong> visible <strong>and</strong> UV. The key limitati<strong>on</strong>s are <strong>the</strong> need to find a suitable <strong>beam</strong><br />
splitter, <strong>and</strong> in particular <strong>the</strong> need for a n<strong>on</strong>-linear process to mix <strong>the</strong> two <strong>beam</strong>s<br />
<strong>and</strong> give a signal proporti<strong>on</strong>al to <strong>the</strong> combined intensity. As with autocorrelati<strong>on</strong>,<br />
two-phot<strong>on</strong> i<strong>on</strong>isati<strong>on</strong> would be possible n<strong>on</strong>-linear process, at least at lower phot<strong>on</strong><br />
energies.<br />
Norin et al. [257] used two-photo i<strong>on</strong>isati<strong>on</strong> from Xen<strong>on</strong> to study <strong>the</strong> chirp of <strong>the</strong><br />
5th harm<strong>on</strong>ic (15.5 eV) radiati<strong>on</strong> produced by HHG in a method that is described<br />
as similar to Frog. The HHG is produced from xen<strong>on</strong> from frequency doubled IR<br />
radiati<strong>on</strong> (Ti:Sapph)whilst<strong>the</strong>probepulseissplitofffrom <strong>the</strong>mainIR<strong>beam</strong>. Amagnetic<br />
bottle spectrometer is used to collect <strong>the</strong> photoelectr<strong>on</strong> spectrum as a functi<strong>on</strong><br />
of probe <strong>beam</strong> delay. The intensity of <strong>the</strong> sideb<strong>and</strong> corresp<strong>on</strong>ding to <strong>the</strong> absorpti<strong>on</strong><br />
of <strong>on</strong>e 15.5 eV <strong>and</strong> <strong>on</strong>e IR phot<strong>on</strong> is measured as a functi<strong>on</strong> of relative delay. This<br />
allowed <strong>the</strong> extracti<strong>on</strong> of <strong>the</strong> linear chirp in <strong>the</strong> HHG pulse <strong>and</strong> its length, but not<br />
<strong>the</strong> actual pulse shape.<br />
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2
162 9. Pulse length, profile <strong>and</strong> jitter<br />
Sekikawa et al. [258] were able to fully characterize <strong>the</strong> 5th harm<strong>on</strong>ic pulse of a<br />
Ti:Sapphire laser using twophot<strong>on</strong> i<strong>on</strong>isati<strong>on</strong> in Frog (TPI Frog). This is because<br />
<strong>the</strong>y show that <strong>the</strong> TPI spectrum is equivalent to <strong>the</strong> spectrally resolved SHG used<br />
in ”c<strong>on</strong>venti<strong>on</strong>al” Frog. They also claim <strong>the</strong> technique is scaleable to XUV <strong>and</strong> SXR<br />
pulses through <strong>the</strong> detecti<strong>on</strong> of two-phot<strong>on</strong> absorpti<strong>on</strong> from <strong>the</strong> K-shell to a free state<br />
in bor<strong>on</strong>.<br />
Frog is probably <strong>the</strong> most widely used technique for measuring <strong>the</strong> pulse profile of<br />
ultra-short optical pulses. There are a number of different geometries for measuring<br />
Frog as described by Trebino et al. [256]. They are summarized briefly below.<br />
Polarizati<strong>on</strong>-gate FROG (PG FROG)<br />
The basic layout of PG Frog is shown in Figure 9.3. The input pulse is split into two<br />
equal replicas. One replica (<strong>the</strong>probe) is sent throughcrossed polarisers <strong>and</strong> <strong>the</strong>o<strong>the</strong>r<br />
(<strong>the</strong> gate) through a half-wave plate to give a ±45 ◦ linear polarisati<strong>on</strong> with respect<br />
to <strong>the</strong> first. The two replicas are <strong>the</strong>n spatially overlapped in a material with a fast<br />
third-order susceptibility such as fused silica. The gate pulse induces birefringence<br />
in <strong>the</strong> silica through <strong>the</strong> electr<strong>on</strong>ic Kerr effect <strong>and</strong> so <strong>the</strong> silica acts as a wave plate<br />
<strong>and</strong> rotates <strong>the</strong> polarisati<strong>on</strong> of <strong>the</strong> probe <strong>beam</strong> slightly which allows some light to be<br />
transmitted through a polarisati<strong>on</strong> analyser. Because this occurs <strong>on</strong>ly when <strong>the</strong> gate<br />
pulse is present in <strong>the</strong> silica, <strong>the</strong> transmitted intensity as a functi<strong>on</strong> of relative delay<br />
is an autocorrelati<strong>on</strong> measurement of <strong>the</strong> pulse. Spectrally resolving <strong>the</strong> transmitted<br />
light thus gives <strong>the</strong> Frog measurement.<br />
λ 2 -plate<br />
τ<br />
Polariser<br />
input-pulse<br />
Beam-splitter<br />
Probe, E(t)<br />
Gate, E(t − τ)<br />
Photodetector<br />
Figure 9.3: The basic layout of PG Frog.<br />
Fused Silica<br />
Filter<br />
Polariser<br />
The biggest advantage of PG Frog is that <strong>the</strong>re are no ambiguities <strong>on</strong> inversi<strong>on</strong><br />
so that <strong>the</strong> pulse characterisati<strong>on</strong> is complete in all cases. Ano<strong>the</strong>r advantage is that<br />
<strong>the</strong> n<strong>on</strong>-linear process is automatically phase matched so alignment is easy. The main<br />
disadvantage is that <strong>the</strong> polarisers must be of high quality; an extincti<strong>on</strong> coefficient
9.4. Autocorrelati<strong>on</strong> techniques 163<br />
of better than 10 −5 is recommended. This makes <strong>the</strong> polarisers expensive <strong>and</strong> more<br />
importantly fairly thick, which can introducedispersi<strong>on</strong> to<strong>the</strong> pulse<strong>and</strong> sochange <strong>the</strong><br />
pulse being measured, a particular problem for <strong>the</strong> shortest of pulses. Also, because<br />
a third-order n<strong>on</strong>-linearity is used, <strong>the</strong> sensitivity of <strong>the</strong> technique is reduced.<br />
The fact that PG Frog polarises <strong>the</strong> <strong>beam</strong> is <strong>the</strong> biggest impediment to extending<br />
<strong>the</strong> technique to wavelengths shorter than <strong>the</strong> UV. Polarisers <strong>and</strong> half-wave plates<br />
with <strong>the</strong>requiredperformance are impossible tomakefor <strong>the</strong>XUV<strong>and</strong>X-rayregimes.<br />
Achieving a large phase shift in this spectral range is <strong>on</strong>ly possible using anomalous<br />
dispersi<strong>on</strong> near an absorpti<strong>on</strong> edge <strong>and</strong> so polarisers would be limited to narrow<br />
spectral ranges. Even <strong>the</strong>n, absorpti<strong>on</strong> is str<strong>on</strong>g <strong>and</strong> <strong>the</strong> performance would not meet<br />
<strong>the</strong> exacting requirements for PG Frog. Finally, a third-order n<strong>on</strong>-linear process<br />
wouldbeneededtoextract<strong>the</strong>Frog signal. Thereseemslittle possibilityofextending<br />
PG FROG to wavelengths shorter than 250 nm (5 eV).<br />
Self-diffracti<strong>on</strong> FROG (SD FROG)<br />
Self-diffracti<strong>on</strong>Frogis<strong>the</strong>techniqueasoriginally describedbyKane<strong>and</strong>Trebino[255]<br />
<strong>–</strong> see Figure 9.2. As with PG Frog, <strong>the</strong> electr<strong>on</strong>ic Kerr effect is used as a third-order<br />
n<strong>on</strong>-linear process. In SD Frog however, <strong>the</strong> intensity oscillati<strong>on</strong>s of <strong>the</strong> interfering<br />
<strong>beam</strong>s induce a refractive-index grating in <strong>the</strong> silica <strong>and</strong> this diffracts each of<br />
<strong>the</strong> <strong>beam</strong>s in a different directi<strong>on</strong>. The first order diffracti<strong>on</strong> of <strong>on</strong>e of <strong>the</strong> <strong>beam</strong>s is<br />
spectrally resolved to make <strong>the</strong> Frog measurement.<br />
The advantage of SD Frog <strong>the</strong>refore, is that <strong>the</strong> <strong>beam</strong>s can have <strong>the</strong> same polarisati<strong>on</strong><br />
<strong>and</strong> polarisers are not required. Applicati<strong>on</strong> to bey<strong>on</strong>d <strong>the</strong> UV is <strong>the</strong>refore<br />
potentially more straightforward than with PG Frog.<br />
However, a third-order n<strong>on</strong>-linear process is still required. Self-diffracti<strong>on</strong> is not actually<br />
ideal even in <strong>the</strong> visible since it is not a phase-matched process. The n<strong>on</strong>-linear<br />
medium must <strong>the</strong>refore be kept thin (
164 9. Pulse length, profile <strong>and</strong> jitter<br />
as sec<strong>on</strong>d-order processes are inherently more efficient than third-order <strong>on</strong>es. The<br />
probe <strong>and</strong> gate <strong>beam</strong>s are overlapped spatially in an SHG crystal <strong>and</strong> a signal at<br />
twice <strong>the</strong>ir frequency is produced with intensity that is proporti<strong>on</strong>al to <strong>the</strong> product<br />
of <strong>the</strong> individual intensities. The SHG signal is spectrally resolved as functi<strong>on</strong> of <strong>the</strong><br />
relative pulse delay. Since each frequency in <strong>the</strong> original pulse is up-c<strong>on</strong>verted by <strong>the</strong><br />
crystal, <strong>the</strong> SHG spectrum is directly correlated to <strong>the</strong> original pulse spectrum. It<br />
is thus important to ensure that <strong>the</strong> crystal works over a wide enough b<strong>and</strong>width to<br />
up-c<strong>on</strong>vert <strong>the</strong> entire b<strong>and</strong>width of <strong>the</strong> original pulse.<br />
Failure to record <strong>the</strong> entire pulse b<strong>and</strong>width will prevent <strong>the</strong> Frog inversi<strong>on</strong> from<br />
working. Since <strong>the</strong> crystal b<strong>and</strong>width is inversely proporti<strong>on</strong>al to crystal thickness,<br />
short pulses require very thin crystals, e.g. for measuring 100 fs pulse at 800 nm,<br />
<strong>the</strong> maximum crystal thickness should be ∼ 300 µm for KDP (potassium dihydrogen<br />
phosphate) <strong>and</strong> ∽ 100 µm for BBO (β-barium borate).<br />
Of course, operati<strong>on</strong> at VUV to X-ray wavelengths will require <strong>the</strong> crystal to be<br />
replaced by ano<strong>the</strong>r n<strong>on</strong>-linear medium in any case. The opti<strong>on</strong>s for this are discussed<br />
in Secti<strong>on</strong> 9.4. SHG Frog has <strong>the</strong> most potential to be extended to operati<strong>on</strong> at<br />
wavelengths shorter than <strong>the</strong> visible/UV part of <strong>the</strong> spectrum. A final point that<br />
should be noted with SHG Frog is that it is ambiguous with respect to <strong>the</strong> directi<strong>on</strong><br />
of time since SHG Frog traces are always symmetric with delay. Thus it is not<br />
possible to tell if a pulse with a satellite has <strong>the</strong> satellite before or after <strong>the</strong> main<br />
pulse.<br />
Third-harm<strong>on</strong>ic-generati<strong>on</strong> FROG (THG FROG)<br />
THG Frog is very similar to SHG Frog except that third-harm<strong>on</strong>ic generati<strong>on</strong> is<br />
used as <strong>the</strong> n<strong>on</strong>-linear process. The advantage of this is that <strong>the</strong> third-order n<strong>on</strong>linear<br />
process removes <strong>the</strong> time-directi<strong>on</strong> ambiguity inherent in SHG Frog (except<br />
in <strong>the</strong> particular case of a Gaussian pulse profile with a purely linear chirp).<br />
A potentially important variati<strong>on</strong> of THG Frog is where surface third-harm<strong>on</strong>ic<br />
generati<strong>on</strong> is used (STHG)[259]. Not <strong>on</strong>ly is STHG a relatively efficient process<br />
(compared to o<strong>the</strong>r third-order processes) but by interacting <strong>on</strong>ly at <strong>the</strong> surface <strong>the</strong><br />
phase-matching b<strong>and</strong>width is very large. This is of particular value when measuring<br />
pulses of <strong>on</strong>ly a few fs in durati<strong>on</strong> which require SHG crystals of <strong>on</strong>ly a few tens of<br />
µm in thickness.<br />
Table 9.1: Different FROG Schemes<br />
Type Esig(t,τ)<br />
SHG E(t)E(t−τ)<br />
Pol. Gate E(t)|E(t−τ)| 2<br />
Self. diff. E(t) 2 E(t−τ) ∗<br />
THG E(t) 2 E(t−τ)
9.5. SPIDER 165<br />
9.5 Spectral Phase Interferometry for Direct Electric-field Rec<strong>on</strong>structi<strong>on</strong><br />
An example of an interferometric pulse profiling technique is Spectral Phase Interferometry<br />
for Direct Electric-field Rec<strong>on</strong>structi<strong>on</strong> or Spider[260]. The c<strong>on</strong>cept of <strong>the</strong><br />
technique is to have a linear spectral phase filter in parallel with a linear temporal<br />
phase filter. These are followed by a spectral amplitude filter before an intensity<br />
detector. The input pulse is divided into two replicas <strong>and</strong> <strong>on</strong>e replica passes through<br />
each of <strong>the</strong> phase filters before being recombined <strong>and</strong> passing through <strong>the</strong> amplitude<br />
filter before reaching <strong>the</strong> detector. If <strong>the</strong> linear temporal phase filter is adjusted from<br />
null, <strong>the</strong>n <strong>on</strong>e of <strong>the</strong> replicas is given a spectral shift relative to <strong>the</strong> o<strong>the</strong>r. On recombining<br />
<strong>the</strong> pulses <strong>the</strong>y interfere spectrally (beat) <strong>and</strong> <strong>the</strong> apparatus becomes a<br />
spectral shearing interferometer. The spectral interferogram is recorded <strong>on</strong> <strong>the</strong> detector<br />
as <strong>the</strong> spectral amplitude filter is tuned over <strong>the</strong> b<strong>and</strong>width of <strong>the</strong> pulse, i.e. <strong>the</strong><br />
spectrometer resolves <strong>the</strong> frequency mixed signal. This informati<strong>on</strong> toge<strong>the</strong>r with<br />
knowledge of <strong>the</strong> applied spectral shear is sufficient to rec<strong>on</strong>struct <strong>the</strong> electric field of<br />
<strong>the</strong> pulse through direct inversi<strong>on</strong>.<br />
The linear spectral phase filter can be used to introduce a temporal delay between<br />
<strong>the</strong> two replica pulses. This additi<strong>on</strong>al degree of freedom allows <strong>the</strong> correlati<strong>on</strong> of<br />
pulses in a train of n<strong>on</strong>-identical pulses to be calculated[260], but o<strong>the</strong>rwise can, in<br />
principle, besettoanarbitraryvalue. Inpracticehowever, <strong>the</strong>timedelayisimportant<br />
as it adds an extra phase to <strong>the</strong> frequency spectrum of <strong>on</strong>e pulse replica relative<br />
to <strong>the</strong> o<strong>the</strong>r <strong>and</strong> this is used to ensure several fringes per independent frequency<br />
comp<strong>on</strong>ent. This makes an unambiguous reading of <strong>the</strong> spectral phases from <strong>the</strong><br />
spectral interferogram possible (because <strong>the</strong> ac <strong>and</strong> dc terms of <strong>the</strong> Fourier transform<br />
are well separated) <strong>and</strong> thus ensures that <strong>the</strong> inversi<strong>on</strong> can successfully recover <strong>the</strong><br />
electric field.<br />
In terms of <strong>the</strong> practical implementati<strong>on</strong> of Spider, <strong>the</strong> all-important temporal<br />
phase filter is <strong>the</strong> hardest to implement. The spectral phase filter is just a n<strong>on</strong>dispersive<br />
delay line <strong>and</strong> <strong>the</strong> spectral amplitude filter is a spectrometer with sufficient<br />
b<strong>and</strong>width <strong>and</strong> resoluti<strong>on</strong> to record <strong>the</strong> pulse b<strong>and</strong>width <strong>and</strong> resolve <strong>the</strong> spectral<br />
interference fringes. Because <strong>the</strong> final measurement is spectral, Spidercan be applied<br />
to single pulses (assuming <strong>the</strong>re is enough signal to noise to extract <strong>the</strong> interferogram<br />
accurately).<br />
Returning to <strong>the</strong> temporal phase filter, it is necessary to achieve an appropriate<br />
amountofspectralshear. In[260], <strong>the</strong>useofelectro-opticphasemodulator(EOPM)is<br />
c<strong>on</strong>sidered togive insufficientspectral shear. Therefore, amethodusingup-c<strong>on</strong>versi<strong>on</strong><br />
of <strong>the</strong>two replica pulses is described. A broadb<strong>and</strong>n<strong>on</strong>-linear material is required <strong>and</strong><br />
eachof<strong>the</strong>replicapulses isup-c<strong>on</strong>vertedthroughmixingwithaquasi-c<strong>on</strong>tinuouswave<br />
of different centre frequency. The up-c<strong>on</strong>verted pulses are thus centred at a different<br />
frequency <strong>and</strong> <strong>the</strong> required spectral shift is achieved.<br />
In [261], up-c<strong>on</strong>versi<strong>on</strong> is again used, but <strong>the</strong> two replica pulses are temporally<br />
displaced <strong>and</strong> mixed with a str<strong>on</strong>gly chirped pulse in <strong>the</strong> n<strong>on</strong>-linear material. The<br />
temporal delay results in mixing with a different frequency range of <strong>the</strong> chirped pulse<br />
<strong>and</strong> again <strong>the</strong> spectral shift is achieved. The fringe separati<strong>on</strong> in <strong>the</strong> interferogram is<br />
now inversely proporti<strong>on</strong>al to <strong>the</strong> temporal separati<strong>on</strong>. Note that <strong>the</strong> spectral phase<br />
filter (delay line) of <strong>the</strong> original c<strong>on</strong>cept is now linked to<strong>the</strong> role of <strong>the</strong> temporal phase<br />
filter <strong>and</strong> cannot thus be adjusted independently. Indeed, <strong>the</strong> temporal delay <strong>and</strong><br />
spectral shear are linked through <strong>the</strong> chirp of <strong>the</strong> pulse used to drive<strong>the</strong> upc<strong>on</strong>versi<strong>on</strong>.
166 9. Pulse length, profile <strong>and</strong> jitter<br />
The spectral <strong>and</strong> temporal shifts must be chosen to suit <strong>the</strong> length of <strong>the</strong> input<br />
pulse <strong>and</strong> <strong>the</strong> spectrometer resoluti<strong>on</strong>, <strong>and</strong> this places c<strong>on</strong>straints <strong>on</strong> <strong>the</strong> length of<br />
pulses that can be measured. The most important factor is to ensure that <strong>the</strong> delay<br />
is small enough to ensure <strong>the</strong> fringes can be resolved whilst not so small that <strong>the</strong> inversi<strong>on</strong><br />
process cannot unambiguously determine <strong>the</strong> phases. It is thus apparent that<br />
extending <strong>the</strong> Spider technique to shorter (XUV, SXR) wavelengths is dependent <strong>on</strong><br />
a satisfactory method of achieving <strong>the</strong> required spectral shear. (We will assume that<br />
splitting <strong>the</strong> <strong>beam</strong> by means of a knife-edged mirror will prove to be satisfactory since<br />
true amplitude divisi<strong>on</strong> is likely to be impossible). The use of n<strong>on</strong>-linear materials<br />
is prevented by str<strong>on</strong>g absorpti<strong>on</strong>. Ano<strong>the</strong>r approach that has been suggested for<br />
<strong>the</strong> XUV is to use two-colour, two-phot<strong>on</strong> atomic i<strong>on</strong>isati<strong>on</strong> to transfer <strong>the</strong> frequency<br />
spectrum of <strong>the</strong> phot<strong>on</strong> to <strong>the</strong> photoelectr<strong>on</strong> energy spectrum[262]. This however<br />
brings additi<strong>on</strong>al problems since an electr<strong>on</strong> spectrometer is now needed to resolve<br />
<strong>the</strong> photoelectr<strong>on</strong> spectrum, which c<strong>on</strong>tains <strong>the</strong> interferogram. Matching <strong>the</strong> fringe<br />
spacing <strong>and</strong> interferogram b<strong>and</strong>width to <strong>the</strong> performance of available electr<strong>on</strong> spectrometers<br />
will place limits <strong>on</strong> <strong>the</strong> range of pulses that can be analysed. For example,<br />
an electr<strong>on</strong> spectrometer with a challenging high resoluti<strong>on</strong> of 1 meV can <strong>on</strong>ly probe<br />
a temporal range of 660 fs from <strong>the</strong> uncertainty relati<strong>on</strong>.<br />
In [263], Smirnova et al. describe an approach for measuring fast processes with<br />
phot<strong>on</strong> pulses that are l<strong>on</strong>g relative to <strong>the</strong> process. The approach is to spectrally<br />
shear, by dressing with a weak IR field, a correlated two-electr<strong>on</strong> spectrum of photoi<strong>on</strong>isati<strong>on</strong><br />
<strong>and</strong> Auger electr<strong>on</strong>s created when an XUV pulse interacts with <strong>the</strong> sample.<br />
The spectrally shifted electr<strong>on</strong> spectrum interferes with <strong>the</strong> original spectrum <strong>and</strong> <strong>the</strong><br />
phase is mapped to an amplitude modulati<strong>on</strong> in <strong>the</strong> spectral intensity <strong>and</strong> thus can be<br />
measured. The technique is thus Spider with electr<strong>on</strong>s. The relevance here is that<br />
<strong>the</strong>re is no reas<strong>on</strong> in principal why <strong>the</strong> same approach cannot be used to measure<br />
<strong>the</strong> field of <strong>the</strong> X-ray pulse since <strong>the</strong> spectral c<strong>on</strong>tent of <strong>the</strong> pulse will be encoded<br />
into <strong>the</strong> electr<strong>on</strong> spectrum. The key requirement for <strong>the</strong> technique is that very tight<br />
synchr<strong>on</strong>isati<strong>on</strong> (sub-fs) between <strong>the</strong> XUV pulse profile <strong>and</strong> <strong>the</strong> phase of <strong>the</strong> IR pulse<br />
is required. The technique will also be flux intensive since <strong>the</strong> correlated two-electr<strong>on</strong><br />
spectrum must be measured, but given sufficient phot<strong>on</strong>s per pulse a single shot<br />
measurement can be made.<br />
In summary, <strong>the</strong> extensi<strong>on</strong> of optical techniques like Frog <strong>and</strong> Spiderto <strong>the</strong> XUV<br />
<strong>and</strong> shorter wavelengths looks challenging. Progress in this area has no doubt been<br />
limited by <strong>the</strong> lack of sources giving ultra-short pulses in this spectral range, <strong>and</strong> <strong>on</strong>e<br />
might <strong>the</strong>refore reas<strong>on</strong>ably expectmore progress in<strong>the</strong>future. The advantage of<strong>the</strong>se<br />
techniques is that <strong>the</strong>y give <strong>the</strong> exact pulse profile by calculating <strong>the</strong> electric field <strong>and</strong><br />
thus provide complete informati<strong>on</strong>. But <strong>the</strong> techniques are also invasive. The input<br />
pulse must be divided <strong>and</strong> manipulated <strong>and</strong> as such <strong>the</strong>y are not <strong>the</strong> obvious choice<br />
for a pulse-by pulse diagnostic even when single pulse characterisati<strong>on</strong> is possible.<br />
9.6 Reflectivity modulati<strong>on</strong><br />
Maltezopoulos et al. [264] describe how <strong>the</strong> free electr<strong>on</strong> laser <strong>beam</strong> incident at a<br />
glancing angle <strong>on</strong> <strong>the</strong> surface of a GaAs substrate modifies <strong>the</strong> reflectivity of <strong>the</strong><br />
GaAs to visible light in proporti<strong>on</strong> to <strong>the</strong> intensity of <strong>the</strong> X-rays. Thus, a visible laser<br />
(frequency doubled from near-infrared 800 nm) is used to simultaneously illuminate<br />
<strong>the</strong> area of <strong>the</strong> GaAs illuminated by <strong>the</strong> X-ray pulse <strong>and</strong> <strong>the</strong> reflected visible light
9.7. Streak cameras 167<br />
imaged <strong>on</strong>to a CCD. The intensity distributi<strong>on</strong> <strong>and</strong> positi<strong>on</strong> of <strong>the</strong> visible image give<br />
<strong>the</strong> free electr<strong>on</strong> laser pulse profile <strong>and</strong> timing.<br />
The technique is inherently pulse-by-pulse, <strong>and</strong> does not use co-propagati<strong>on</strong>, but<br />
is not transparent. Also, <strong>the</strong> visible light must overlap <strong>the</strong> entire area of illuminati<strong>on</strong><br />
from <strong>the</strong> free electr<strong>on</strong> laser <strong>and</strong> so some sort of focus of <strong>the</strong> X-rays may be required.<br />
The technique is thus not an <strong>on</strong>-line diagnostic but could be used for checking <strong>the</strong><br />
<strong>beam</strong> at <strong>the</strong> experimental end-stati<strong>on</strong> (where <strong>the</strong>re is likely to be a focus anyway).<br />
Alternatively, since this technique does not require such high <strong>beam</strong> intensities as <strong>the</strong><br />
cross-correlati<strong>on</strong> methods described in Secti<strong>on</strong> 9.3, it may be possible to split off a<br />
small part of <strong>the</strong> FEL <strong>beam</strong> <strong>and</strong> use that to m<strong>on</strong>itor <strong>the</strong> arrival time of <strong>the</strong> pulse. In<br />
any case, <strong>the</strong> temporal resoluti<strong>on</strong> is limited by <strong>the</strong> length of <strong>the</strong> visible pulse <strong>and</strong> <strong>the</strong><br />
space-to-time correlati<strong>on</strong> of <strong>the</strong> visible imaging system. The work presented gives a<br />
resoluti<strong>on</strong> of about 40 fs rms.<br />
Gahl et al. [244] suggest that <strong>the</strong> key limitati<strong>on</strong> to <strong>the</strong> temporal resoluti<strong>on</strong> is<br />
<strong>the</strong> visible probe pulse length, of <strong>the</strong> order 120 <strong>–</strong> 150 fs in this example. They<br />
also suggest that <strong>the</strong> time required for <strong>the</strong> GaAs surface to recover to its original<br />
level of reflectivity could be of <strong>the</strong> order of hundreds of picosec<strong>on</strong>ds, but this would<br />
<strong>on</strong>ly be a limit in multi-shot measurements at repetiti<strong>on</strong> rates in <strong>the</strong> GHz regi<strong>on</strong>.<br />
A fur<strong>the</strong>r c<strong>on</strong>siderati<strong>on</strong> is <strong>the</strong> potential for radiati<strong>on</strong> damage of <strong>the</strong> GaAs surface.<br />
Maltezopoulos et al. [264] used an optimised <strong>beam</strong> fluence of 13 ± 5 mJ/cm 2 rms<br />
for <strong>the</strong>ir measurements, commenting that permanent damage was observed at an<br />
unstated higher fluence, thus requiring <strong>the</strong> GaAs surface to be renewed. C<strong>on</strong>versely,<br />
measurements at a lower average fluence led to very weak c<strong>on</strong>trast in <strong>the</strong> images,<br />
making temporal determinati<strong>on</strong> unreliable.<br />
A related technique has been recently proposed by Krejcik [265]. In his scheme,<br />
<strong>the</strong> X-rays strike a magnetised film <strong>and</strong> cause a change in <strong>the</strong> magnetisati<strong>on</strong> which<br />
is probed using MOKE (Magneto- Optical Kerr Effect). An IR laser illuminates<br />
<strong>the</strong> magnetic film <strong>and</strong> undergoes a small relative polarisati<strong>on</strong> rotati<strong>on</strong> (∼ 1 ◦ ) in <strong>the</strong><br />
part that is reflected from <strong>the</strong> area <strong>the</strong> X-rays illuminated. The polarisati<strong>on</strong> of <strong>the</strong><br />
reflected IR <strong>beam</strong> is analysed <strong>and</strong> mapped over <strong>the</strong> <strong>beam</strong> profile. Thus, a time to<br />
space mapping of <strong>the</strong> arrival time of <strong>the</strong> X-ray pulse is achieved. The advantage of<br />
<strong>the</strong> MOKE analysis is that <strong>the</strong> magnetisati<strong>on</strong> change is extremely rapid <strong>and</strong> so <strong>the</strong>re<br />
is no issue with <strong>the</strong> resp<strong>on</strong>se time of <strong>the</strong> process reducing <strong>the</strong> temporal resoluti<strong>on</strong><br />
achieved. The disadvantage is that <strong>the</strong> magnetic material needs a res<strong>on</strong>ance at a<br />
magnetically active orbital at <strong>the</strong> X-ray wavelength of interest. Thus <strong>the</strong> technique<br />
is not applicable to arbitrary wavelengths.<br />
9.7 Streak cameras<br />
Streak cameras work <strong>on</strong> similar principles to oscilloscopes <strong>and</strong> cathode-ray tubes <strong>and</strong><br />
work by mapping time to a spatial coordinate in <strong>the</strong> detector. The incident phot<strong>on</strong><br />
<strong>beam</strong> is focused <strong>on</strong>to a slit <strong>and</strong> <strong>the</strong>n passes through a photocathode. The photoemitted<br />
electr<strong>on</strong>s are drawn between two parallel plates that are also parallel to <strong>the</strong><br />
slit. A high-speed sweep voltage, synchr<strong>on</strong>ised to <strong>the</strong> pulse arrival, is applied across<br />
<strong>the</strong> plates. This gives an angular deflecti<strong>on</strong> of <strong>the</strong> electr<strong>on</strong>s that is directly related to<br />
<strong>the</strong>ir time of arrival <strong>and</strong> thus to <strong>the</strong> durati<strong>on</strong> of <strong>the</strong> pulse. The deflected electr<strong>on</strong>s are<br />
<strong>the</strong>n multiplied with a micro-channel plate (MCP) before impacting <strong>on</strong> a phosphor<br />
screen. The streak pattern <strong>on</strong> <strong>the</strong> screen is imaged by a CCD or o<strong>the</strong>r suitable
168 9. Pulse length, profile <strong>and</strong> jitter<br />
detector, using a light intensifier tube if required. The advantages of streak cameras<br />
are <strong>the</strong> applicability across a wide wavelength range (X-rays to near-IR, although not<br />
with a single camera), single-shot time resoluti<strong>on</strong> in <strong>the</strong> picosec<strong>on</strong>d range for off-<strong>the</strong>shelf<br />
systems, <strong>and</strong> <strong>the</strong> ability to work at high repetiti<strong>on</strong> rate, albeit with reduced<br />
temporal resoluti<strong>on</strong>. They can also provide informati<strong>on</strong> <strong>on</strong> intensity <strong>and</strong> positi<strong>on</strong> in<br />
additi<strong>on</strong> to <strong>the</strong> temporal informati<strong>on</strong> in a single measurement.<br />
Historically, <strong>the</strong> resoluti<strong>on</strong> of streak cameras has been restricted to several picosec<strong>on</strong>ds<br />
in single-shot mode. In multiple-shot averaging systems, <strong>the</strong> use of a synchr<strong>on</strong>ised<br />
sine-wave sweep voltage adversely affects temporal resoluti<strong>on</strong> by making <strong>the</strong>se<br />
systems highly susceptible to source jitter. However, <strong>the</strong>re have been recent improvements<br />
in off <strong>the</strong> shelf systems <strong>and</strong> <strong>the</strong> fastest commercially available streak cameras<br />
claim a time resoluti<strong>on</strong> of
9.8. Summary 169<br />
ties, we ideally need to be able to measure each <strong>and</strong> every pulse that is used in <strong>the</strong><br />
experiment.<br />
The temporal diagnostics techniques thus need to be automatic, reliable, n<strong>on</strong>invasive<br />
<strong>and</strong> capable of h<strong>and</strong>ling large amounts of data. And yet a key point to note<br />
is that many of <strong>the</strong> techniques are currently at <strong>the</strong> level of experiments in <strong>the</strong>mselves.<br />
This is not unexpected since sources of ultra-short pulses at VUV <strong>and</strong> shorter<br />
wavelengths are a relatively new phenomen<strong>on</strong>, <strong>and</strong> it is <strong>on</strong>ly through availability of<br />
such sources that <strong>the</strong> diagnostic techniques can be developed. In <strong>the</strong> early days of<br />
ultra-short optical wavelength pulses, <strong>the</strong> principal diagnostic was <strong>the</strong> relatively uninformative<br />
autocorrelator, <strong>and</strong> yet sophisticated diagnostics that fully characterize<br />
<strong>the</strong> pulse profile can now be bought ”off <strong>the</strong> shelf”.<br />
We should not however be complacent that developments to shorter wavelengths<br />
will rapidly follow <strong>the</strong> availability of <strong>the</strong> sources. Certainly, basic sec<strong>on</strong>d-order autocorrelati<strong>on</strong><br />
as been successfully dem<strong>on</strong>strated into <strong>the</strong> soft X-ray, but this gives<br />
<strong>on</strong>ly informati<strong>on</strong> about <strong>the</strong> pulse length, <strong>and</strong> even <strong>the</strong>n assumpti<strong>on</strong>s have to be made<br />
about <strong>the</strong> pulse profile.<br />
Atoptical wavelengths, autocorrelati<strong>on</strong> was extendedthrough <strong>the</strong> additi<strong>on</strong> of spectral<br />
analysis (e.g. FROG) <strong>and</strong> this allowed complete pulse profile retrieval. But a key<br />
requirement in autocorrelati<strong>on</strong> techniques is a n<strong>on</strong>-linear process that can mix <strong>the</strong><br />
two pulses <strong>and</strong> produce a signal that is proporti<strong>on</strong>al to <strong>the</strong> autocorrelati<strong>on</strong> functi<strong>on</strong>.<br />
Here we are limited not <strong>on</strong>ly by <strong>the</strong> availability of suitable physical processes but<br />
also by detectors since <strong>the</strong> n<strong>on</strong>-linear signal may be accompanied by a str<strong>on</strong>g background<br />
that is hard to discriminate from <strong>the</strong> signal of interest. This is particularly<br />
true when <strong>the</strong> physical process produces electr<strong>on</strong>s ra<strong>the</strong>r than light, as will generally<br />
be <strong>the</strong> case at short wavelengths where i<strong>on</strong>izati<strong>on</strong> is a dominant process. Two-phot<strong>on</strong><br />
i<strong>on</strong>izati<strong>on</strong> is <strong>the</strong> most widely cited physical process that might fulfill <strong>the</strong> requirements<br />
<strong>and</strong> auto-correlati<strong>on</strong> measurements have been successfully performed into <strong>the</strong> XUV.<br />
The wavelength range over which two-phot<strong>on</strong> i<strong>on</strong>isati<strong>on</strong> will work is limited by<br />
<strong>the</strong> i<strong>on</strong>isati<strong>on</strong> potentials of available gases <strong>and</strong> so different gases are needed to cover<br />
different wavelength ranges. Fur<strong>the</strong>rmore, <strong>on</strong>ce <strong>the</strong> energy of a single phot<strong>on</strong> is above<br />
<strong>the</strong> gas IP, <strong>the</strong>n <strong>the</strong> large background of single-phot<strong>on</strong> i<strong>on</strong>isati<strong>on</strong> events is likely to<br />
swamp <strong>the</strong> two-phot<strong>on</strong> signal. Thus two-phot<strong>on</strong> i<strong>on</strong>isati<strong>on</strong> is <strong>on</strong>ly viable at phot<strong>on</strong><br />
energies between half of <strong>and</strong> <strong>the</strong> full IP of <strong>the</strong> gas. Two-phot<strong>on</strong> double i<strong>on</strong>isati<strong>on</strong><br />
may <strong>the</strong>n be <strong>the</strong> way forward into <strong>the</strong> soft X-ray, but at <strong>the</strong> moment such schemes<br />
are untested.<br />
A fundamental limitati<strong>on</strong> of autocorrelati<strong>on</strong> techniques is that <strong>the</strong>y cannot provide<br />
informati<strong>on</strong> about <strong>the</strong> timing of <strong>the</strong> pulse since it is measured against itself. Thus,<br />
<strong>the</strong>re has been a lot of development in crosscorrelati<strong>on</strong> techniques in which <strong>the</strong> free<br />
electr<strong>on</strong> laser pulse is measured against a known pulse from an IR laser. As well<br />
as pulse length informati<strong>on</strong>, we can gain informati<strong>on</strong> <strong>on</strong> timing jitter relative to <strong>the</strong><br />
laser, which is often very c<strong>on</strong>venient, for example when <strong>the</strong> laser is also used in pumpprobe<br />
experiments. A significant amount of work has been undertaken in this area<br />
<strong>and</strong> many possible approaches to cross-correlati<strong>on</strong> have been dem<strong>on</strong>strated or at least<br />
suggested.<br />
A well-established approach is to measure <strong>the</strong> intensity <strong>and</strong>/or number of sideb<strong>and</strong>s<br />
that appear <strong>on</strong> <strong>the</strong> photo-i<strong>on</strong>isati<strong>on</strong> spectrum of a gas as <strong>the</strong> infrared laser falls<br />
in <strong>and</strong> out of temporal overlap with <strong>the</strong> free electr<strong>on</strong> laser pulse. This requires <strong>the</strong><br />
infrared laser <strong>and</strong> X-ray pulse to be spatially overlapped in <strong>the</strong> i<strong>on</strong>isati<strong>on</strong> chamber,<br />
<strong>and</strong> thus has some implicati<strong>on</strong>s for <strong>the</strong> optical layout of <strong>the</strong> <strong>beam</strong>line. Never<strong>the</strong>less,
170 9. Pulse length, profile <strong>and</strong> jitter<br />
<strong>the</strong> gas absorbs so little that <strong>the</strong> X-ray pulse is unaltered <strong>and</strong> <strong>the</strong> diagnostic meets our<br />
requirement for being n<strong>on</strong>-invasive. In <strong>the</strong> first implementati<strong>on</strong>s of this sort of crosscorrelator,<br />
complete pulse characterisati<strong>on</strong> required measurement over a successi<strong>on</strong><br />
of free electr<strong>on</strong> laser pulses with differing infrared pulse delays. The pulse profile<br />
measure was thus an average profile <strong>and</strong> not shot-by-shot. This limitati<strong>on</strong> can be<br />
overcome byc<strong>on</strong>verting<strong>the</strong> temporal informati<strong>on</strong> tospatial informati<strong>on</strong> <strong>and</strong> recording<br />
<strong>the</strong> photo-electr<strong>on</strong> spectrum with an imaging detector. Proof of principle experiments<br />
have been d<strong>on</strong>e but more development is needed to improve sensitivity <strong>and</strong> temporal<br />
resoluti<strong>on</strong>.<br />
There are o<strong>the</strong>r approaches to cross-correlati<strong>on</strong> that have been proposed, using<br />
for example Auger electr<strong>on</strong>s <strong>and</strong> chirped infrared pulses. This is an active area of<br />
research at <strong>the</strong> moment. The comm<strong>on</strong> <strong>the</strong>me is detecti<strong>on</strong> through <strong>the</strong> i<strong>on</strong>isati<strong>on</strong> of<br />
gases, thus all <strong>the</strong>se schemes rely <strong>on</strong> electr<strong>on</strong> detectors, which adds significantly to<br />
<strong>the</strong> complexity of <strong>the</strong> measurement.<br />
A different approach to cross-correlati<strong>on</strong> is that of reflectivity modulati<strong>on</strong>. Although<br />
this is an invasive measurement, it is more sensitive than gas based measurements<br />
<strong>and</strong> so not all <strong>the</strong> <strong>beam</strong> is needed. Thus, a small part of <strong>the</strong> <strong>beam</strong> can be<br />
split off <strong>and</strong> sent to <strong>the</strong> cross-correlator whilst <strong>the</strong> rest of <strong>the</strong> <strong>beam</strong> is passed to <strong>the</strong><br />
experiment. Since <strong>the</strong> technique is relatively simple <strong>and</strong> is inherently pulse resolved<br />
(but limited to <strong>the</strong> external laser repetiti<strong>on</strong> rate), it is quite attractive. Some work is<br />
needed to improve <strong>the</strong> temporal resoluti<strong>on</strong> however.<br />
Streak cameras are a l<strong>on</strong>g established instrument for measuring short pulses. However,<br />
current instruments are too limited in terms of temporal resoluti<strong>on</strong> <strong>and</strong> repetiti<strong>on</strong><br />
rate. There are a number of active development programs aimed at addressing<br />
<strong>the</strong>se points <strong>and</strong> it seems likely that temporal resoluti<strong>on</strong> of 100 fs will be possible<br />
whilst <strong>the</strong> use of ’smart’ detectors will give operati<strong>on</strong> to several kHz.<br />
Electro-optical techniques are not useful for directly measuring <strong>the</strong> profile of <strong>the</strong><br />
free electr<strong>on</strong> laser pulses since <strong>the</strong>y <strong>on</strong>ly functi<strong>on</strong> at THz frequencies. But <strong>the</strong>y can<br />
be usefully employed for m<strong>on</strong>itoring <strong>the</strong> timing of <strong>the</strong> electr<strong>on</strong> bunch relative to an<br />
external laser. This is likely to give important informati<strong>on</strong> <strong>on</strong> <strong>the</strong> overall timing of<br />
<strong>the</strong> X-ray pulses.
9.8. Summary 171<br />
Summary<br />
• Pulse length <strong>and</strong>jitter can bediagnosed with cross-correlati<strong>on</strong><br />
techniques. They rely <strong>on</strong> encoding <strong>the</strong> electr<strong>on</strong>s emanating<br />
from a photoi<strong>on</strong>izati<strong>on</strong> of a gas spectrally with energy from<br />
a known laser pulse. The main photoi<strong>on</strong>izati<strong>on</strong> peaks will<br />
<strong>the</strong>n get side-b<strong>and</strong>s (also called satellites) whose intensity is<br />
proporti<strong>on</strong>al to <strong>the</strong> delay between <strong>the</strong> laser phot<strong>on</strong> pulse <strong>and</strong><br />
that of <strong>the</strong> free electr<strong>on</strong> laser. With a chirped laser pulse (<strong>the</strong><br />
phot<strong>on</strong>-energy varies over <strong>the</strong> pulse) <strong>the</strong> pulse length may also<br />
be extracted from such a measurement.<br />
• Autocorrelati<strong>on</strong> techniques uses <strong>the</strong> pulse itself, <strong>the</strong> pulse<br />
length is deduced from splitting <strong>the</strong> pulse <strong>and</strong> recombining<br />
it after <strong>the</strong> two parts of <strong>the</strong> pulse have traversed different<br />
optical paths. The correlati<strong>on</strong> between different parts of <strong>the</strong><br />
pulse can <strong>the</strong>n be measured. Although <strong>the</strong> technique is single<br />
shot a pulse shape has to be assumed to extract <strong>the</strong> length of<br />
<strong>the</strong> pulse. More advanced autocorrelati<strong>on</strong> techniques Frog<br />
<strong>and</strong> Spider can also deduce <strong>the</strong> pulse shape.<br />
• Reflectivity modulati<strong>on</strong> of a GaAs surface induced by an optical<br />
laser can be used to extract <strong>the</strong> pulse length since <strong>the</strong><br />
free electr<strong>on</strong> laser <strong>beam</strong> modifies <strong>the</strong> reflectivity of <strong>the</strong> surface.<br />
The positi<strong>on</strong> <strong>and</strong> intensity of <strong>the</strong> visible reflected light<br />
can <strong>the</strong>n be recorded <strong>on</strong> a pulse-by-pulse basis but not in a<br />
manner transparent to <strong>the</strong> experiments. The resoluti<strong>on</strong> limit<br />
is quoted to <strong>the</strong> 40 fs rms currently. Modulati<strong>on</strong> of o<strong>the</strong>r processes<br />
have also been suggested, such as <strong>the</strong> Magneto-optical<br />
Kerr effect.<br />
• Streak cameras work <strong>on</strong> similar principles to oscilloscopes <strong>and</strong><br />
cathode-ray tubes <strong>and</strong> work by mapping time to a spatial coordinate<br />
in <strong>the</strong> detector. The incident phot<strong>on</strong> <strong>beam</strong> is focused<br />
<strong>on</strong>to a slit <strong>and</strong> <strong>the</strong>n passes through a photocathode.<br />
The photo-emitted electr<strong>on</strong>s are drawn between two parallel<br />
plates that are also parallel to <strong>the</strong> slit. A high-speed sweep<br />
voltage, synchr<strong>on</strong>ised to <strong>the</strong> pulse arrival, is applied across<br />
<strong>the</strong> plates. This gives an angular deflecti<strong>on</strong> of <strong>the</strong> electr<strong>on</strong>s<br />
that is directly related to <strong>the</strong>ir time of arrival <strong>and</strong> thus to<br />
<strong>the</strong> durati<strong>on</strong> of <strong>the</strong> pulse. The deflected electr<strong>on</strong>s are <strong>the</strong>n<br />
multiplied with a micro-channel plate before impacting <strong>on</strong> a<br />
phosphor screen. Current time-resoluti<strong>on</strong> for streak cameras<br />
are about 300 fs.
10. Free electr<strong>on</strong> laser experiments<br />
Written by: A. Lindblad<br />
A free electr<strong>on</strong> laser provide a tunable pulsed (transversely) coherent phot<strong>on</strong> <strong>beam</strong><br />
with unprecedented brilliance. The <strong>beam</strong> can thus be focussed to small spots where<br />
a very high X-ray phot<strong>on</strong> density can be acquired.<br />
The properties outlined, enable a number of experiments that are, more or less,<br />
unique. The large number of phot<strong>on</strong>s per pulse (often tens of billi<strong>on</strong>s or more) allow<br />
time-resolved imaging <strong>and</strong> spectroscopies <strong>–</strong> where combinati<strong>on</strong>s of <strong>the</strong> free electr<strong>on</strong><br />
laser <strong>beam</strong> <strong>and</strong> laser <strong>beam</strong>s make pump <strong>and</strong> probe experiments more advanced. The<br />
high degree of coherence make single-shot imaging of nano-structures possible. The<br />
high X-ray phot<strong>on</strong> density enable <strong>the</strong> study of n<strong>on</strong>-linear processes in <strong>the</strong> X-ray<br />
regime, as well as <strong>the</strong> ability to study processes with low cross-secti<strong>on</strong>s or with low<br />
target density (e.g. imaging of single unsupported nanostructures/molecules).<br />
In this chapter some of <strong>the</strong> experiments carried out at free electr<strong>on</strong> laser will be<br />
highlighted <strong>–</strong> our treatment here will not by any means be all encompassing but is<br />
ra<strong>the</strong>r intended to give an introducti<strong>on</strong> to which kinds of experiments successfully<br />
exploits <strong>the</strong> unique properties of this kind of X-ray source.<br />
One may c<strong>on</strong>dense <strong>the</strong> experimental efforts into: imaging <strong>and</strong> measuring atoms<br />
<strong>and</strong> atomic processes <strong>on</strong> <strong>the</strong> nanometer <strong>and</strong> femtosec<strong>on</strong>d scales. Adding that <strong>the</strong><br />
development is towards ˚Angström <strong>and</strong> attosec<strong>on</strong>d time-scales.<br />
10.1 The ”holy grails” of free electr<strong>on</strong> laser experiments<br />
”Molecular movies”<br />
The short pulse length of free electr<strong>on</strong> laser sources makes it possible, ei<strong>the</strong>r via<br />
splitting or sub-pulse structure, to get a X-ray pump - X-ray probe experiment. With<br />
<strong>the</strong> additi<strong>on</strong> of external lasers X-ray pump, UV/Vis Laser-probe or UV/Vis-pump<br />
X-ray probe is made possible. All of this in <strong>the</strong> femtosec<strong>on</strong>d regime.<br />
This, potentially, makes it possible to follow a photo-excited process like a movie,<br />
but with a femtosec<strong>on</strong>d frame-rate.<br />
173
174 10. Free electr<strong>on</strong> laser experiments<br />
”Single-molecule/nanostructure imaging”<br />
Real-space imaging of nanostructures <strong>and</strong> ultimately single-molecules can be realized<br />
by <strong>the</strong> rec<strong>on</strong>structi<strong>on</strong> of <strong>the</strong> image via a recorded image in momentum space obtained<br />
from X-ray scattering from <strong>the</strong> object.<br />
”Single-shot spectroscopy/imaging”<br />
Single-shot experiments are made possible by <strong>the</strong> large number of phot<strong>on</strong>s available<br />
that can get focussed down to a very small point owing to <strong>the</strong> <strong>beam</strong> quality. Since <strong>the</strong><br />
pulses are short <strong>and</strong> intense <strong>the</strong> data for imaging <strong>and</strong> spectroscopy can be acquired<br />
before <strong>the</strong> sample explodes. This is also a cornerst<strong>on</strong>e for <strong>the</strong> success of time-resolved<br />
measurements as outlined above.<br />
In <strong>the</strong> following some examples from each field will be given. Both planned <strong>and</strong><br />
already performed experimentsare presentedas toshowwhat is d<strong>on</strong>etoday <strong>and</strong>where<br />
different groups <strong>and</strong> facilities intends to head in <strong>the</strong> near future.<br />
10.2 Time-resolved spectroscopies<br />
Core-level photo-electr<strong>on</strong> spectroscopies give informati<strong>on</strong> about <strong>the</strong> chemical state<br />
of <strong>the</strong> c<strong>on</strong>stituting atoms (being in free molecules or atoms, molecules or atoms <strong>on</strong><br />
surfaces or in solids). By using phot<strong>on</strong>-pulses time-resolved spectroscopies can be<br />
performed. Atsynchrotr<strong>on</strong>s<strong>and</strong>HHGlaser sources <strong>the</strong>numberofphot<strong>on</strong>sperpulse is<br />
verylowcomparedtothoseatafreeelectr<strong>on</strong>laser (atleast generally)whichiswhythis<br />
kind of experiments needs to be performed at X-ray free electr<strong>on</strong> laser facilites[271].<br />
Many fundamental properties of matter can be studied with this type of spectroscopy,<br />
e.g. magnetizati<strong>on</strong> dynamics, reflectivity changes <strong>and</strong> molecular dissociati<strong>on</strong><br />
dynamics.<br />
UV/Vis pump-X-ray probe spectroscopy<br />
With an ordinary laser synchr<strong>on</strong>ized (with a known time-delay) to <strong>the</strong> free electr<strong>on</strong><br />
laser X-rays it is possible to study <strong>the</strong> development of <strong>the</strong> core level photo-electr<strong>on</strong><br />
spectrum. At Flash, <strong>the</strong> Ge 3d photoemissi<strong>on</strong> from a n-doped Ge crystal have been<br />
studied in this manner[272].<br />
Time-resolved pump-probe experiments at <strong>the</strong> Lcls[273]: N2 molecule studied<br />
with 1.05 keV X-rays (10 11 phot<strong>on</strong>s/pulse) with a Wiley-McLaren i<strong>on</strong> time-of-flight<br />
spectrometer. The counting rate was about 3 Hz. Comparing to <strong>the</strong> 30 Hz repetiti<strong>on</strong><br />
rate of <strong>the</strong> X-ray source focussed <strong>on</strong> 3 µm 2 <strong>and</strong> 10 13 molecules/cm 3 .<br />
Timeresolvedcorelevelphoto-electr<strong>on</strong>spectroscopy(asdescribedalsoinRef.[274])<br />
studied of atoms <strong>and</strong> molecules (in gases, clusters, liquids <strong>and</strong> solids) combined with<br />
lasers will be an important investigative tool at free electr<strong>on</strong> laser to study how <strong>the</strong><br />
chemical state of an atom can change with time depending <strong>on</strong> how its neigbours are<br />
excited.<br />
Velocity map imaging have been used sucessfully for characterizati<strong>on</strong> of <strong>the</strong> overlap<br />
between free electr<strong>on</strong> laser X-rays <strong>and</strong> 800 nm optical laser <strong>–</strong> for instance using<br />
hydrogen[275] as <strong>the</strong> target.<br />
X-ray/X-ray Auto-correlati<strong>on</strong> spectroscopy at <strong>the</strong> X-Fel have been discussed by<br />
Grübel[276].
10.3. Imaging <strong>and</strong> Crystallography 175<br />
Nexafs<br />
Ce:YAG screen<br />
Sample<br />
Free electr<strong>on</strong> laser <strong>beam</strong><br />
Grating<br />
Figure 10.1: Possible set-up for a single shot Nexafs measurement (adapted from Ref. [278]).<br />
X-ray absorpti<strong>on</strong> near an i<strong>on</strong>izati<strong>on</strong> threshold (Nexafs) allow for <strong>the</strong> mapping of<br />
unoccupied states in a sample <strong>–</strong> <strong>the</strong> absorpti<strong>on</strong> intensity is recorded as a functi<strong>on</strong><br />
of phot<strong>on</strong>-energy. The absorpti<strong>on</strong> may be studied with any decay product from<br />
<strong>the</strong> excitati<strong>on</strong>, e.g. i<strong>on</strong>s, electr<strong>on</strong>s, phot<strong>on</strong>s. A possible way of doing Nexafs in a<br />
single-shot fashi<strong>on</strong> is depicted in Figure 10.1 <strong>–</strong> a grating acts as a <strong>beam</strong>splitter which<br />
c<strong>on</strong>tinuously disperse <strong>the</strong> X-ray pulse over a sample, thus <strong>the</strong> need for sweeping <strong>the</strong><br />
phot<strong>on</strong>-energy is eliminated <strong>and</strong> a single-shot measurement made possible[277, 278].<br />
10.3 Imaging <strong>and</strong> Crystallography<br />
The high fluence of free electr<strong>on</strong> laser <strong>beam</strong>s allow imaging of micro- <strong>and</strong> nanoparticles<br />
via X-ray scattering <strong>on</strong> a shot-to-shot basis. A problem that needs to be<br />
circumvented is <strong>the</strong> radiati<strong>on</strong> damage <strong>and</strong> subsequent explosi<strong>on</strong> of <strong>the</strong> particles up<strong>on</strong><br />
<strong>the</strong> multi-i<strong>on</strong>izati<strong>on</strong> <strong>–</strong> this problem becomes more <strong>and</strong> more substantial with decreasing<br />
particles size. For a 50 femtosec<strong>on</strong>d l<strong>on</strong>g pulse <strong>the</strong> resoluti<strong>on</strong> limit have been<br />
estimated to 0.2 nm because of <strong>the</strong> blurring caused by <strong>the</strong> Coulumb-explosi<strong>on</strong> of <strong>the</strong><br />
sample[279].<br />
A dem<strong>on</strong>strati<strong>on</strong> of single nano-sized particle X-ray diffractive imaging have been<br />
performedbyBogan<strong>and</strong>co-workers[280]whereanærodynamiclensprovidednanoparticles<br />
from an electrospray source. A part of <strong>the</strong>ir set-up is shown in Figure 10.2.<br />
There is clearly a strive towards imaging ever smaller objects[281] <strong>–</strong> <strong>and</strong> ultimately<br />
single molecules, both in free form <strong>and</strong> in <strong>the</strong>ir natural envir<strong>on</strong>ment, i.e. in water or
176 10. Free electr<strong>on</strong> laser experiments<br />
Figure 10.2: A prototypical single particle X-ray diffractive imaging (after Ref. [280]).<br />
in cells[282]. Recently a virus particle was imaged using overlays of recorded patterns<br />
from single particles <strong>–</strong> which shows that even if <strong>the</strong> object explodes because of <strong>the</strong><br />
deposited X-ray energy it survives l<strong>on</strong>g enough to be imaged[283].<br />
The imaging activities at Flash have recently been reviewed[284], as well as <strong>the</strong><br />
specific strives towards coherent diffractive imaging [50]. At <strong>the</strong> Lcls <strong>the</strong>re is an<br />
endstati<strong>on</strong> dedicated to coherent X-ray imaging[285]: <strong>the</strong> (CXI) instrument[286]. At<br />
Fermi@Elettra <strong>the</strong> first operati<strong>on</strong>al <strong>beam</strong>line is intended for coherent scattering experiments.<br />
As free electr<strong>on</strong> laser promise to deliver X-rays of sufficient quality to allow singleparticle/single-molecule<br />
imaging <strong>and</strong> that phase-retrieval algorithms become ever<br />
more sophisticated this area of research attracts a lot of effort. With phase-retrieval<br />
informati<strong>on</strong> (lost in <strong>the</strong> imaging process) this will ultimately allow for single-particle<br />
tomographic measurements of nano-particles, proteins <strong>and</strong> parts of cells.<br />
Figure 10.3 depicts X-ray scattering through a r<strong>and</strong>omly ordered sample (powder<br />
diffracti<strong>on</strong>). If <strong>the</strong> <strong>beam</strong> is incoherent <strong>and</strong> wide (Debeye-Scherrer scattering) <strong>the</strong><br />
scattering angle is proporti<strong>on</strong>al to <strong>the</strong> mean distance between <strong>the</strong> scattering centers in<br />
<strong>the</strong>samples. If<strong>the</strong><strong>beam</strong>issmall <strong>and</strong>sufficientlycoherent<strong>on</strong>estill obtainsinformati<strong>on</strong><br />
about <strong>the</strong> mean distances in <strong>the</strong> film via <strong>the</strong> scattering angle <strong>–</strong> but <strong>on</strong> <strong>the</strong> detector<br />
a speckle interference pattern occur instead of diffuse rings. The speckles angular<br />
extent is inversely proporti<strong>on</strong>al to <strong>the</strong> <strong>beam</strong> width.<br />
By overlaying <strong>the</strong> X-ray scattering images from two time-delayed pulses Gün<strong>the</strong>r<br />
<strong>and</strong> co-workers have recently dem<strong>on</strong>strated that sequential imaging with femtosec<strong>on</strong>d<br />
resoluti<strong>on</strong> is indeed possible to obtain for nanometer sized objects[287]. This is a<br />
significant step towards time-resolved imaging of objects at <strong>the</strong> atomic scale.<br />
10.4 N<strong>on</strong>-linear X-ray science<br />
Photoi<strong>on</strong>izati<strong>on</strong><br />
Withveryhigh irradiance levels (towards 10 16 W/cm 2 )at 93eV phot<strong>on</strong>energy, Xe 21+<br />
have been observed in i<strong>on</strong>-time of flight spectra <strong>–</strong> this corresp<strong>on</strong>ds to <strong>the</strong> absorpti<strong>on</strong>
10.4. N<strong>on</strong>-linear X-ray science 177<br />
a<br />
d<br />
∼ λ/a<br />
∼ λ/d<br />
Figure 10.3: X-ray diffracti<strong>on</strong> using diffuse <strong>and</strong> coherent <strong>beam</strong>s.<br />
of about 57 phot<strong>on</strong>s for that atom (or 5 keV absorbed X-ray energy)[288]. This<br />
amount of energy deposited in a single atom allow <strong>the</strong> study for many processes of<br />
fundamental nature. With shorter pulses in <strong>the</strong> attosec<strong>on</strong>d regime (<strong>the</strong> ”atomic unit<br />
of time” being 24 as) processes may even be possible to study <strong>on</strong> <strong>the</strong> same time-scale<br />
as <strong>the</strong> electr<strong>on</strong>’s travel-time around <strong>the</strong> nucleus.<br />
Sequential i<strong>on</strong>izati<strong>on</strong> of atomic arg<strong>on</strong> have been studied at <strong>the</strong> Scss free electr<strong>on</strong><br />
laser. They find evidence of a sequential electr<strong>on</strong> emissi<strong>on</strong> from <strong>the</strong> absorbing atoms<br />
during <strong>the</strong> pulse durati<strong>on</strong>[289], access to even shorter pulses would naturally benefit<br />
<strong>the</strong> study of this kind of physical phenomena.<br />
A summary of <strong>the</strong> findings <strong>on</strong> different rare gases is provided in Ref [98]. In this<br />
reference a survey of different possible experimental set-ups is also provided.<br />
Multiphot<strong>on</strong> i<strong>on</strong>izati<strong>on</strong> of atomic clusters have also been studied in this regard<br />
(see, e.g. Ref. [290]) since this allows for a detailed study of <strong>the</strong> Coulomb explosi<strong>on</strong><br />
from <strong>the</strong> interacti<strong>on</strong> of nano-particles with free electr<strong>on</strong> laser light.<br />
Recently Fang <strong>and</strong> colleagues have reported <strong>on</strong> an experiment where double corehole<br />
i<strong>on</strong>izati<strong>on</strong> in nitrogen molecules[291] is dem<strong>on</strong>strated. This type of experiment<br />
give insight in how fast phot<strong>on</strong>s are absorbed during <strong>the</strong> pulse since <strong>the</strong> single corei<strong>on</strong>izedspecies<br />
havealifetime in<strong>the</strong>lowfemtosec<strong>on</strong>dregime. Anexperimentinvolving<br />
X-ray emissi<strong>on</strong> following two-phot<strong>on</strong> absorpti<strong>on</strong> have also been suggested by Sun <strong>and</strong><br />
coworkers[292].
178 10. Free electr<strong>on</strong> laser experiments<br />
Diff. pumping<br />
Open multiplier<br />
TOF<br />
I<strong>on</strong>s<br />
±2 cm<br />
Figure 10.4: Focussed free electr<strong>on</strong> laser <strong>beam</strong> set-up for <strong>the</strong> study of multi-phot<strong>on</strong> i<strong>on</strong>izati<strong>on</strong> of gases (from<br />
Figure 8.11).<br />
Summary<br />
• Free electr<strong>on</strong> lasers enable <strong>the</strong> study of atoms <strong>and</strong> atomic<br />
processes, ei<strong>the</strong>r via imaging or spectroscopic measurements,<br />
<strong>on</strong> nanometer <strong>and</strong> femtosec<strong>on</strong>d scales.<br />
• Current source developments strive to refine <strong>the</strong> scales to<br />
atomic <strong>on</strong>es, i.e. ˚Angströms <strong>and</strong> attosec<strong>on</strong>ds.<br />
• Naturally an free electr<strong>on</strong> laser experimentshould exploit <strong>on</strong>e,<br />
or several of <strong>the</strong> source’s unique properties vis-à-vis:<br />
<strong>–</strong> Coherence<br />
<strong>–</strong> Brilliance<br />
<strong>–</strong> Fluence<br />
<strong>–</strong> Time structure<br />
• The holy grails of free electr<strong>on</strong> laser experiments are:<br />
<strong>–</strong> Single-shot imaging of single molecules<br />
<strong>–</strong> Single-shot spectroscopy of single molecules<br />
<strong>–</strong> Molecular-movies<br />
-<br />
+
11. Free Electr<strong>on</strong> Laser facilities<br />
Written by: A. Lindblad<br />
Inthischapter, free electr<strong>on</strong> laser facilites around<strong>the</strong>world will beinvestigated visà-vis<br />
<strong>the</strong> different technology choices made <strong>and</strong> how <strong>the</strong> performance of <strong>the</strong> facilites<br />
have been affected by those choices. Naturally such an overview will be somewhat<br />
limited <strong>and</strong> <strong>the</strong> focus lies <strong>on</strong> <strong>the</strong> currently operating facilites <strong>and</strong> <strong>the</strong> intended developments<br />
of <strong>the</strong>m <strong>–</strong> also, <strong>on</strong>ly free electr<strong>on</strong> lasers that lase in <strong>the</strong> VUV- <strong>and</strong> X-ray<br />
regimes are c<strong>on</strong>sidered here.<br />
Facility E εn λmin Rate Pol.<br />
Flash O SC 1.2 < 2 4.45 8·10 3<br />
No<br />
Lcls O NC 14 1 0.12 120 No<br />
XFEL C SC 17.5 1.4 0.1 27·10 3 Yes<br />
XFEL/SPring-8 C NC 8 0.8 0.1 60 No<br />
Fermi@Elettra C NC 1.7 1 4 50 Yes<br />
SwissFEL D NC 6 0.4 0.1 100 Yes<br />
Pal XFEL D NC 10 1 0.1 60 No<br />
Lcls-II D NC 14 1 0.6 120 Yes<br />
Flash-II D SC 1.2 1-1.5 4 10 No<br />
Table 11.1: The electr<strong>on</strong> energy is given in GeV <strong>and</strong> <strong>the</strong> repetiti<strong>on</strong> rate in Hz; <strong>the</strong> normalized emittance is<br />
given in µm; <strong>the</strong> minimum wavelength in nm. Informati<strong>on</strong> in <strong>the</strong> table is adapted from <strong>the</strong> review by McNiel<br />
<strong>and</strong> Thomps<strong>on</strong>[293].<br />
In Table 11.1 <strong>the</strong> facilites around <strong>the</strong> world currently operati<strong>on</strong>al (O), under c<strong>on</strong>structi<strong>on</strong><br />
(C) <strong>and</strong> in advanced technical planning <strong>and</strong> design phases (D) are listed<br />
toge<strong>the</strong>r with <strong>the</strong> facilities’ choice <strong>on</strong> normally c<strong>on</strong>ducting technology (NC) or superc<strong>on</strong>ducting<br />
technology (SC) <strong>and</strong> some o<strong>the</strong>r parameters.<br />
The locati<strong>on</strong>s of <strong>the</strong> facilites around <strong>the</strong> world are as follows: <strong>the</strong> Flash <strong>and</strong><br />
<strong>the</strong> European X-Fel[89] are located in Hamburg, Germany; <strong>the</strong> Lcls free electr<strong>on</strong><br />
laser uses <strong>the</strong> SLAC linear accelerator, which can be found in Stanford, USA[294];<br />
<strong>the</strong> XFEL/SPring-8 is located in <strong>the</strong> Harima area in Japan[295]; Fermi@Elettra<br />
is in Trieste, Italy; <strong>the</strong> SwissFEL[49] can be found in Switerl<strong>and</strong> <strong>and</strong> <strong>the</strong> Pal XFEL<br />
in Korea[296].<br />
179
180 11. Free Electr<strong>on</strong> Laser facilities<br />
Lcls-II <strong>and</strong> Flash-II[297] are extensi<strong>on</strong>s of those currently operating facilities.<br />
11.1 Operating facilities<br />
11.2 Flash<br />
Flash is situated in Hamburg, Germany (www.flash.de). The facility deliver ultrashort<br />
femtosec<strong>on</strong>d coherent radiati<strong>on</strong> in <strong>the</strong> wavelength range between 47 <strong>and</strong> 4.12<br />
nm. The shorter wavelength lies inside <strong>the</strong>, so called, water window where water is<br />
transparent to X-rays.<br />
Since 2005, Flash is a user facility serving a large variety of experiments. Typical<br />
user operati<strong>on</strong> parameters during <strong>the</strong> 2 nd user period from Nov 26, 2007 to Aug 16,<br />
2009:<br />
Wavelength range (fundamental) 4.12 <strong>–</strong> 47 nm<br />
Average single pulse energy 10 <strong>–</strong> 100 µJ<br />
Pulse durati<strong>on</strong> (FWHM) 10<strong>–</strong>400 fs<br />
Peak power (from av.) 1 <strong>–</strong> 5 GW<br />
Average power (at 500 pulses/s) ∼ 15 mW<br />
Spectral width (FWHM) ∼ 1 %<br />
Peak Brilliance 10 29 −10 30<br />
Flash is a high-gain Sase free electr<strong>on</strong> laser. The lasing process is initiated by<br />
<strong>the</strong> sp<strong>on</strong>taneous undulator radiati<strong>on</strong>, <strong>and</strong> <strong>the</strong> free electr<strong>on</strong> laser works <strong>the</strong>n in <strong>the</strong> socalled<br />
Self-Amplified Sp<strong>on</strong>taneous Emissi<strong>on</strong> (Sase)mode without needingan external<br />
input signal.The electr<strong>on</strong> bunches are produced in a laser-driven photoinjector <strong>and</strong><br />
accelerated by a superc<strong>on</strong>ducting linear accelerator. The RF-gun based photoinjector<br />
allows <strong>the</strong> generati<strong>on</strong> of electr<strong>on</strong> bunches with tiny emittances - m<strong>and</strong>atory for an<br />
efficient SASE process.The superc<strong>on</strong>ductingtechniques allows to accelerate thous<strong>and</strong>s<br />
of bunches per sec<strong>on</strong>d, which is not possible with o<strong>the</strong>r technologies.<br />
At intermediate energies of 130 <strong>and</strong> 470 MeV <strong>the</strong> electr<strong>on</strong> bunches are l<strong>on</strong>gitudinally<br />
compressed, <strong>the</strong>reby increasing <strong>the</strong> peak current from initially 50-80 A to 1-2<br />
kA - as required for <strong>the</strong> lasing process in <strong>the</strong> undulator. The 30 m l<strong>on</strong>g undulator<br />
c<strong>on</strong>sists of permanent NdFeB magnets with a fixed gap of 12 mm, a period length of<br />
27.3 mm <strong>and</strong> peak magnetic field of 0.47 T. The electr<strong>on</strong>s interact with <strong>the</strong> undulator<br />
field in such a way, that so called micro bunches are developed. These micro bunches<br />
radiate coherently <strong>and</strong> produce intense X-ray pulses. Finally, a dipole magnet deflects<br />
<strong>the</strong> electr<strong>on</strong> <strong>beam</strong> safely into a dump, while <strong>the</strong> X-ray radiati<strong>on</strong> propagates to <strong>the</strong><br />
experimental hall.<br />
e - -gun<br />
Accelerator<br />
Figure 11.1: Schematic of <strong>the</strong> Flash free electr<strong>on</strong> laser facility.<br />
Sase undulator
11.2. Flash 181<br />
Injector <strong>and</strong> accelerator<br />
Cs2Te photocathode inside a 1.3 GHz normally-c<strong>on</strong>ducting radiofrequency cavity. 0.5<br />
to 1 nC per pulse at 10 Hz. L-b<strong>and</strong> cavity (1.3 GHz). The pulse trains generated<br />
can be up to 800 microsec<strong>on</strong>ds l<strong>on</strong>g <strong>and</strong> <strong>the</strong> pulse spacing is usually 1 mikrosec<strong>on</strong>d<br />
(1 MHz). The peak current of <strong>the</strong> uncompresssed bunch is around 70 A. The bunch<br />
compressi<strong>on</strong> occurring during <strong>the</strong> acclerati<strong>on</strong>-stages in two steps up to 2 kA.<br />
The accelerator secti<strong>on</strong> c<strong>on</strong>sists of 5 TESLA linear accelerator secti<strong>on</strong>s (each c<strong>on</strong>taining<br />
eight superc<strong>on</strong>ducting radiofrequency cavities) that can accelerate <strong>the</strong> electr<strong>on</strong>s<br />
to 1.2 GeV.<br />
Undulators<br />
The Flash undulator system c<strong>on</strong>sists of six 4.5 meter l<strong>on</strong>g permanent magnet undulators<br />
having 27.3 mm period with a fixed 12 mm gap. The undulator parameter K<br />
is 1.23 (corresp<strong>on</strong>ding to a peak magnetic field of 0.48 T).<br />
Infrared/THz undulator<br />
An electromagnetic l<strong>on</strong>g period undulator (400 mm period) placed after <strong>the</strong> SASE-<br />
FELundulatorsystemprovidesfar-infrared pulsesthataresynchr<strong>on</strong>izedto<strong>the</strong>VUV/soft<br />
X-ray phot<strong>on</strong> pulses <strong>–</strong> <strong>the</strong>y are emitted from <strong>the</strong> same electr<strong>on</strong> bunch[298]. The<br />
wavelength can be tuned between 1 <strong>and</strong> 200 µm (300 THz-1.5 THz). For wavelengths<br />
shorter than 20 µm <strong>the</strong> pulse energies of 10 µJ can be obtained.<br />
sFlash<br />
Undulator placed before <strong>the</strong> Sase undulator secti<strong>on</strong> of Flash.<br />
e - -gun<br />
Accelerator<br />
Seed<br />
sFlash undulator<br />
sFlash out<br />
Figure 11.2: Schematic of <strong>the</strong> sFlash seeding extensi<strong>on</strong> to Flash.<br />
Sase undulator<br />
C<strong>on</strong>sists of an extra 10 m l<strong>on</strong>g variable gap undulator before <strong>the</strong> current Flash<br />
undulator system. The seed laser system is a HHG setup using an arg<strong>on</strong> gas jet,<br />
<strong>the</strong> 21st harm<strong>on</strong>ic of a 800 nm Ti:Sa laser is used with a pulse length of 40 fs. The<br />
seeded free electr<strong>on</strong> laser radiati<strong>on</strong> is <strong>the</strong>n <strong>transport</strong>ed to a different experimental hall<br />
situated <strong>on</strong> top of <strong>the</strong> Flash hall.<br />
Flash-II<br />
Is a proposed extensi<strong>on</strong> of <strong>the</strong> Flash facility in Hamburg, Germany (see page 180)<br />
(http://flash.desy.de/flash ii/).<br />
Besides <strong>the</strong> operating FEL undulator at Flash, a sec<strong>on</strong>d undulator line with a<br />
separate tunnel<strong>and</strong> experimental hall is envisaged toextend<strong>and</strong> enhance <strong>the</strong>capacity<br />
of <strong>the</strong> Flash facility.
182 11. Free Electr<strong>on</strong> Laser facilities<br />
The facility will use a two stage Hghg seeding scheme (see page 17) with variable<br />
gap undulators to ensure shot-to-shot pulse reproducibility with variable femtosec<strong>on</strong>d<br />
durati<strong>on</strong>, gigawatt peak power, <strong>and</strong> full transverse <strong>and</strong> l<strong>on</strong>gitudinal coherence. A<br />
seeding opti<strong>on</strong> using HHG (High Harm<strong>on</strong>ic Generati<strong>on</strong>) laser generati<strong>on</strong> in gases to<br />
reach short seeding wavelengths is also c<strong>on</strong>tained within this project[299].<br />
The new experimental hall will house about six new <strong>beam</strong>lines with <strong>on</strong>e user<br />
<strong>beam</strong>line housing phot<strong>on</strong> diagnostics <strong>and</strong> <strong>beam</strong> manipulati<strong>on</strong> facilities.<br />
The electr<strong>on</strong> <strong>beam</strong> from <strong>the</strong> linear accelerator will be shared between <strong>the</strong> two<br />
Flash undulator chains with a fast <strong>beam</strong> switch. The project is currently in <strong>the</strong><br />
technical design phase[297, 299].<br />
e - -gun<br />
Accelerator<br />
Experimental stati<strong>on</strong>s:<br />
seed<br />
Seed<br />
sFlash und.<br />
Flash-II undulator<br />
Figure 11.3: Schematic of <strong>the</strong> Flash-II free electr<strong>on</strong> laser.<br />
sFlash out<br />
Flash-1 Sase und.<br />
• PG1<strong>–</strong>am<strong>on</strong>ochromatizedsmall focus<strong>beam</strong>linewithapermanenthigh-resoluti<strong>on</strong><br />
two-stage phot<strong>on</strong> spectrometer for inelastic scattering experiments.<br />
• PG2 <strong>–</strong> 50 µm focus after a high-resoluti<strong>on</strong> plane-grating m<strong>on</strong>ochromator.<br />
• BL1 <strong>–</strong> 100 µm spot after a toroidal mirror.<br />
• BL2 <strong>–</strong> 25 µm spot after an ellipsoidal mirror.<br />
• BL3 <strong>–</strong> a <strong>beam</strong>line without focussing optics.<br />
• THz undulator <strong>beam</strong>line <strong>–</strong> provides pulsed, coherent THz pulses that can be<br />
usedincombinati<strong>on</strong>with<strong>the</strong>freeelectr<strong>on</strong>laserradiati<strong>on</strong>from<strong>the</strong>Sase-undulator.
11.3. Scss <strong>–</strong> X-fel 183<br />
11.3 Scss <strong>–</strong> X-fel<br />
Scss<br />
The Spring-8 compact SASE source, Japan[295] is a test-bed for technologies to be<br />
used for <strong>the</strong> japanese X-fel. It has also been used to do accelerator research, for<br />
instance <strong>the</strong> first seeding experiments using a HHG laser[300].<br />
e - -gun<br />
Injector & accelerator<br />
Accelerator<br />
Undulators<br />
Figure 11.4: Schematic of <strong>the</strong> Scss free electr<strong>on</strong> laser test facility.<br />
The electr<strong>on</strong> gun used in <strong>the</strong> injector is of <strong>the</strong> <strong>the</strong>rmi<strong>on</strong>ic type, based <strong>on</strong> a singlecrystal<br />
CeB6 cathode which provides a <strong>beam</strong> current of 1 A at <strong>the</strong> initial <strong>beam</strong><br />
energy of 500 keV. In <strong>the</strong> accelerating structure <strong>the</strong> peak current becomes 300 A after<br />
bunch-compressi<strong>on</strong> with bunch-charges of 0.3 nC. The accelerating structure after<br />
<strong>the</strong> injector (which c<strong>on</strong>tains two S-b<strong>and</strong> accelerating structures) is composed C-b<strong>and</strong><br />
accelerating structures operating at 35 MV/m <strong>–</strong> yielding a final <strong>beam</strong> energy of 250<br />
MeV.<br />
Undulators<br />
Two, in vacuum, 600 period permanent magnet undulators with a minimum gap of<br />
3 mm <strong>and</strong> a period length of 15 mm. The maximum K is 1.5 <strong>and</strong> <strong>the</strong> radiati<strong>on</strong><br />
wavelength is between 30 <strong>and</strong> 61 nm.<br />
X-ray free electr<strong>on</strong> laser/ Spring-8<br />
This project was founded in 2006. The c<strong>on</strong>structi<strong>on</strong> is scheduled between 2006-2010<br />
<strong>and</strong> <strong>the</strong> start of operati<strong>on</strong>s is planned to 2011. The aim is to produce coherent<br />
radiati<strong>on</strong> of 1 ˚Angström wavelength with an 8 GeV electr<strong>on</strong> <strong>beam</strong> from a normalc<strong>on</strong>ducting<br />
C-b<strong>and</strong> (5.712 GHz) accelerator.<br />
Injector & accelerator<br />
The electr<strong>on</strong> gun was developed at <strong>the</strong> SCSS (see above) <strong>and</strong> is of <strong>the</strong> <strong>the</strong>rmi<strong>on</strong>ic<br />
type. The repetiti<strong>on</strong> rate of <strong>the</strong> accelerator is 60 Hz for macropulses c<strong>on</strong>taining 50<br />
sub-pulses. The X-ray pulse frequency is thus 3000 Hz. The peak current is 4 kA<br />
after <strong>the</strong> accelerati<strong>on</strong> up to 8 GeV (with bunch charges of 0.2 nC). The 128 C-b<strong>and</strong><br />
accelerators operating around 35 MV/m.
184 11. Free Electr<strong>on</strong> Laser facilities<br />
Undulators<br />
The in vacuum undulators is of hybrid type using permanent magnets <strong>and</strong> ir<strong>on</strong> yokes.<br />
The gap can be varied between 2 <strong>and</strong> 40 mm with a nominal operati<strong>on</strong> point at 4 mm<br />
gap (giving K=1.9). The resulting X-ray wavelength range is between 3 <strong>and</strong> 0.1 nm<br />
in bunches that are 50 fs l<strong>on</strong>g. At 1 ˚Angström wavelength <strong>the</strong> output power is 0.4<br />
mJ per pulse, <strong>the</strong> phot<strong>on</strong> flux is estimated to be 2·10 11 phot<strong>on</strong>s per pulse. The peak<br />
brightness is calculated to be in <strong>the</strong> order of 10 33 phot<strong>on</strong>s/mm 2 /mrad 2 /0.1%bw.<br />
11.4 Fermi@Elettra<br />
The Italian X-ray free electr<strong>on</strong> laser 1 is located near Trieste in Italy[301].<br />
e - -gun<br />
Injector & accelerator<br />
”Cern”-type, ”Fermi”-type acc. struct.<br />
Fel-1<br />
Fel-2<br />
Figure 11.5: Schematic of <strong>the</strong> Fermi@Elettra free electr<strong>on</strong> laser.<br />
The injector is of <strong>the</strong> photocathode variety with a copper target photoi<strong>on</strong>ized by <strong>the</strong><br />
3 rd harm<strong>on</strong>ic ofaTi:Salaser. Thephotocathodeis placedinanS-b<strong>and</strong>radiofrequency<br />
accelerating structure (1.6 cells).<br />
Seven”Cern”-type accelerating structures followed by seven S-b<strong>and</strong>”Fermi” structures<br />
provide <strong>the</strong> accelerati<strong>on</strong> up to 1.5 GeV. The repetiti<strong>on</strong> rate is 50 Hz.<br />
After <strong>the</strong> accelerator <strong>the</strong> electr<strong>on</strong> <strong>beam</strong> can be steered ei<strong>the</strong>r into <strong>the</strong> first or <strong>the</strong><br />
sec<strong>on</strong>d undulator arrays.<br />
Undulators<br />
Following <strong>the</strong> linear accelerator part of <strong>the</strong> facility, <strong>the</strong>re is a switch for <strong>the</strong> electr<strong>on</strong><br />
<strong>beam</strong> <strong>–</strong> allowing <strong>the</strong> alternate usage of two different free electr<strong>on</strong> laser undulator<br />
systems; <strong>the</strong> first of which have been installed <strong>and</strong> <strong>the</strong> sec<strong>on</strong>d <strong>on</strong>e is to follow.<br />
Fel-1<br />
The first undulator system is a seeded Hghg cascade utilizing a tunable seed laser in<br />
<strong>the</strong> wavelength range 240-360 nm.<br />
The first undulator, referred to as <strong>the</strong> modulator where <strong>the</strong> microbunching density<br />
modulati<strong>on</strong> occurs is a 160 mm period 3.04 m l<strong>on</strong>g planar permanent magnet<br />
undulator with an undulator strength between K=3.9 to 4.9. This provided <strong>the</strong> basic<br />
wavelength that is to be up-c<strong>on</strong>verted in <strong>the</strong> radiator undulator system.<br />
Between <strong>the</strong> modulator <strong>and</strong> <strong>the</strong> sec<strong>on</strong>d undulator system <strong>the</strong>re is a 1 meter l<strong>on</strong>g<br />
<strong>beam</strong> <strong>transport</strong> secti<strong>on</strong> (which is a small chicane). The radiator undulator system<br />
1 http://www.elettra.trieste.it/FERMI/.
11.4. Fermi@Elettra 185<br />
c<strong>on</strong>sists of four Apple-type variable polarizati<strong>on</strong> undulators <strong>–</strong> tuned to a harm<strong>on</strong>ic<br />
n of <strong>the</strong> modulator wavelength (thus optimized for λ/n). They have a undulator<br />
period of 65 mm installed in four 2.34 meter l<strong>on</strong>g segments separated by 1.06 meter<br />
l<strong>on</strong>g <strong>transport</strong> secti<strong>on</strong>s, yielding a total length of <strong>the</strong> radiator system of 12.48 meters.<br />
Their undulator strengths are between 2.4 <strong>and</strong> 4.<br />
Including <strong>transport</strong> secti<strong>on</strong>s, <strong>the</strong> total length of <strong>the</strong> Fel-1 system is thus 16.5<br />
meters. This part of <strong>the</strong> free electr<strong>on</strong> laser facility provides radiati<strong>on</strong> in <strong>the</strong> range<br />
between 20 <strong>and</strong> 100 nm (see Table 11.2).<br />
Fel-2<br />
The sec<strong>on</strong>d free electr<strong>on</strong> laser of <strong>the</strong> Fermi will be built after <strong>the</strong> first <strong>on</strong>e is completed.<br />
It is intended to be a cascaded double HGHG scheme (using two modulators<br />
<strong>and</strong> two radiators). This scheme is flexible enough to also allow HHG seeding <strong>and</strong><br />
Echo-enabled harm<strong>on</strong>ic generati<strong>on</strong> in <strong>the</strong> future. By using Apple-II undulators <strong>the</strong><br />
polarizati<strong>on</strong> can be c<strong>on</strong>trolled <strong>and</strong> tuned in a range around 10% of <strong>the</strong> energy defined<br />
by <strong>the</strong> <strong>beam</strong> energy[302].<br />
Parameter Fel-1 Fel-2<br />
Wavelength range (fundamental) 20 <strong>–</strong> 100 nm 3-20 nm<br />
Phot<strong>on</strong> energy 62 <strong>–</strong> 12 eV 413<strong>–</strong>62 eV<br />
Pulse durati<strong>on</strong> (FWHM) 20 <strong>–</strong> 40 fs < 100 fs<br />
Repetiti<strong>on</strong> rate 10-50 Hz 10-50 Hz<br />
Peak power (from av.) 1 <strong>–</strong> 5 GW 1 GW<br />
Spectral width (FWHM) ∼ 20−40 meV ∼ 20−40 meV<br />
Phot<strong>on</strong>s per pulse 2·10 14 at 100 nm 10 13 at 10 nm<br />
Peak Brilliance 10 29 −10 30<br />
Table 11.2: Phot<strong>on</strong> output parameters for Fermi@Elettra. Taken from <strong>the</strong> laboratory homepage.<br />
Experiments:<br />
• DIPROI <strong>–</strong> Diffracti<strong>on</strong> <strong>and</strong> projecti<strong>on</strong> imaging<br />
• LDM <strong>–</strong> Low density matter<br />
• EIS <strong>–</strong> Elastic <strong>and</strong> inelastic scattering.
186 11. Free Electr<strong>on</strong> Laser facilities<br />
11.5 Lcls <strong>–</strong> Linac Coherent Light Source<br />
The Lcls was designed to become <strong>the</strong> world’s first hard X-ray free electr<strong>on</strong> laser with<br />
<strong>the</strong> fundamental wavelength lying between 0.55 <strong>and</strong> 10 keV[96, 294, 303]. The facility<br />
is located at <strong>the</strong>SLACnati<strong>on</strong>al accelerator laboratory inMenloPark, California, USA<br />
<strong>and</strong> went into operati<strong>on</strong> during <strong>the</strong> year 2009 2 .<br />
e - -gun<br />
Injector <strong>and</strong> accelerator<br />
Accelerator<br />
Figure 11.6: Schematic of <strong>the</strong> Lcls free electr<strong>on</strong> laser.<br />
Undulator<br />
The Lcls free electr<strong>on</strong> laser is currently utilizing <strong>the</strong> last kilometre of <strong>the</strong> SLAClinear<br />
electr<strong>on</strong> accelerator (which is 3 km l<strong>on</strong>g in total). The SLAC accelerator use S-b<strong>and</strong><br />
radiofrequency-fields (2,856 MHz) in copper cavities <strong>and</strong> can accelerate electr<strong>on</strong>s up<br />
to 50 GeV - if <strong>the</strong> whole three kilometers available is used. As <strong>the</strong> Lcls uses <strong>on</strong>ly<br />
<strong>on</strong>e kilometer electr<strong>on</strong> energies of 3.5 to 15 GeV can be delivered to <strong>the</strong> undulators.<br />
A photocathode radiofrequency electr<strong>on</strong> gun serves as injector; <strong>the</strong> gun c<strong>on</strong>sists<br />
of a copper target that is photoi<strong>on</strong>ized by a frequency trippled Ti:Sapphire system.<br />
This can operate up to 120 Hz with bunch charges of 0.25 nC (with a peak current of<br />
35 A). With bunch compressi<strong>on</strong> during <strong>the</strong> accelerati<strong>on</strong> <strong>the</strong> peak current is amplified<br />
up to 3.5 kA.<br />
Undulators<br />
The undulator secti<strong>on</strong> of Lcls is 132 m l<strong>on</strong>g in total <strong>and</strong> c<strong>on</strong>sists of thirty-three 3.4<br />
m l<strong>on</strong>g planar permanent magnet undulators - separated by short <strong>and</strong> l<strong>on</strong>g <strong>transport</strong><br />
secti<strong>on</strong>s. The undulator period is 30 mm with a fixed gap of 6.8 mm. The undulator<br />
parameter K is 3.5 (corresp<strong>on</strong>ding to a magnetic field of 1.25 T at <strong>the</strong> menti<strong>on</strong>ed<br />
gap).<br />
Lcls-II proposal<br />
Proposed extensi<strong>on</strong> of <strong>the</strong> Linac Coherent Light Source in Stanford, California, USA<br />
[304] (see page 186). This proposal c<strong>on</strong>siders <strong>the</strong> use of <strong>the</strong> 2 nd km (of 3 km in total,<br />
<strong>the</strong> first kilometer remains untouched) of <strong>the</strong> SLAC linear accelerator. By adding<br />
a sec<strong>on</strong>d electr<strong>on</strong> gun <strong>and</strong> injector 1 km upstream from <strong>the</strong> Lcls injector <strong>the</strong> mid<br />
kilometer of <strong>the</strong> accelerator could be used to operate a soft X-ray free electr<strong>on</strong> laser in<br />
2 Lcls homepage: https://slacportal.slac.stanford.edu.
11.5. Lcls <strong>–</strong> Linac Coherent Light Source 187<br />
parallel to <strong>the</strong> existing Lcls if <strong>the</strong> electr<strong>on</strong> bunches are made to travel in a bypass<br />
line running side by side to <strong>the</strong> last kilometer (used for <strong>the</strong> accelerati<strong>on</strong> of <strong>the</strong> electr<strong>on</strong><br />
bunches for <strong>the</strong> o<strong>the</strong>r free electr<strong>on</strong> laser). Besides extending <strong>the</strong> phot<strong>on</strong>-energy range<br />
of <strong>the</strong> facility this would also allow simultaneous operati<strong>on</strong> of two free electr<strong>on</strong> laser in<br />
parallel which would increase <strong>the</strong> number of users significantly.<br />
e<br />
Bypass<br />
- -gun Undulators<br />
Accelerator<br />
Figure 11.7: Schematic of <strong>the</strong> Lcls-II proposal. The grey area marks <strong>the</strong> existing Lcls facility.<br />
Upgrade of <strong>the</strong> existing facility<br />
An upgrade of <strong>the</strong> current Lcls is c<strong>on</strong>sidered to allow a larger gap (<strong>and</strong> thus higher<br />
energies). A sec<strong>on</strong>d harm<strong>on</strong>ic afterburner optimizing <strong>the</strong> bunching at 0.62 ˚A wavelength<br />
will be added in 2010 to produce half <strong>the</strong> fundamental wavelength efficiently.<br />
This will be achieved by increasing <strong>the</strong> gap of <strong>the</strong> last 8-10 undulators to give <strong>the</strong>m<br />
a K of 2.26 (as opposed to 3.5 for <strong>the</strong> 23-25 undulators).<br />
The soft X-ray undulators<br />
Withtwoundulators, each36ml<strong>on</strong>ghaving6-60˚Awavelengthrange throughvariable<br />
gap, a number of possible opportunities are given: self-seeding by placing a grating<br />
between <strong>the</strong> undulators, Eehg-seeding, etc. It is also possible to c<strong>on</strong>trol <strong>the</strong> polarizati<strong>on</strong><br />
of <strong>the</strong> light by adding Apple-II type undulators at <strong>the</strong> end of each undulator<br />
that would offer variable polarizati<strong>on</strong>.<br />
Since <strong>the</strong> accelerator for <strong>the</strong> soft X-ray free electr<strong>on</strong> laser operate in <strong>the</strong> 3-7 GeV<br />
range, <strong>the</strong> repetiti<strong>on</strong> rate can be increased to 320 Hz.<br />
Experiments:<br />
• AMO <strong>–</strong> Atomic, molecular <strong>and</strong> optical science.<br />
• CXI <strong>–</strong> Coherent X-ray imaging.<br />
• MEC <strong>–</strong> Matter in extreme c<strong>on</strong>diti<strong>on</strong>s.<br />
• SXR <strong>–</strong> Soft X-ray materials science.<br />
• XCS <strong>–</strong> X-ray correlati<strong>on</strong> spectroscopy.<br />
• X<strong>PP</strong> <strong>–</strong> X-ray pump probe.
188 11. Free Electr<strong>on</strong> Laser facilities<br />
11.6 Facilities under c<strong>on</strong>structi<strong>on</strong><br />
11.7 The European Xfel<br />
The European Xfel will be 3.4 km l<strong>on</strong>g, starting at <strong>the</strong> DESY-Bahrenfeld site in<br />
Hamburg, Germany <strong>and</strong> <strong>the</strong> research campus will be situated south of <strong>the</strong> town of<br />
Schenefeld[305]. Thestartofoperati<strong>on</strong>s isplannedtobein2014(http://www.xfel.eu/).<br />
Injector <strong>and</strong> accelerator<br />
The injector is of <strong>the</strong> radio-frequency accelerated photocathode variety with a Cs2Te<br />
target (very similar to <strong>the</strong> <strong>on</strong>e used at Flash presented above). Both <strong>the</strong> injector <strong>and</strong><br />
<strong>the</strong> linear accelerator c<strong>on</strong>sists of superc<strong>on</strong>ducting L-b<strong>and</strong> (1.3 GHz) Tesla cavities<br />
that will operate at 23.6 MV/m. The repetiti<strong>on</strong> rate between macropulses is 10 Hz,<br />
each such pulse can house 3000 pulses.<br />
In total <strong>the</strong> accelerator will be 1.6 km l<strong>on</strong>g with 116 accelerator modules, each 12<br />
m l<strong>on</strong>g. The peak current is projected to be 5 kA with a bunch charge of 1 nC. The<br />
maximum <strong>beam</strong> energy attainable is 20 GeV, but normal operati<strong>on</strong> will be at 17.5<br />
Gev electr<strong>on</strong> energy.<br />
Undulators<br />
Sase 2<br />
Sase 1<br />
U 1<br />
Sase 3<br />
U 2<br />
e - dump<br />
Figure 11.8: The electr<strong>on</strong> <strong>beam</strong> distributi<strong>on</strong> between different undulators in <strong>the</strong> European Xfel.<br />
Toaccommodate <strong>the</strong>differentdem<strong>and</strong>sfrom <strong>the</strong>experimentalside<strong>–</strong><strong>and</strong>toprovide<br />
maximum flexibility for future upgrades <strong>–</strong> <strong>the</strong> 17.5 GeV electr<strong>on</strong> <strong>beam</strong> can be sent<br />
al<strong>on</strong>g two different paths (Figure 11.8) servicing five different undulators.<br />
Sase 1 is a planar permanent magnet undulator optimized to deliver 12.4 keV<br />
hard X-rays (λ = 0.1 nm) <strong>–</strong> <strong>the</strong> magnetic period is 35.6 <strong>and</strong> <strong>the</strong> gap is 10 mm (giving<br />
K=3.3). The total undulator length is 201.3 m.<br />
Sase 2 provides tunable hard X-rays between 3.1 <strong>and</strong> 12.4 keV. It is a planar permanent<br />
magnet undulator that thus provides linearly polarized light. This undulator<br />
have a magnet period of 47.9 mm with a gap adjustable between 19 <strong>and</strong> 10 mm (K
11.7. The European Xfel 189<br />
between 2.8 <strong>and</strong> 6.1). The total length is 256.2 m.<br />
Sase 3 is an Apple II device which can deliver circularly or linearly polarized light<br />
in <strong>the</strong> range between 0.8-3.1 keV. If <strong>the</strong> accelerator is operated at 10 GeV electr<strong>on</strong><br />
energy <strong>the</strong> range becomes 0.25-1.0 keV. The undulator’s period is 80 mm with gaps<br />
between 23 <strong>and</strong> 10 mm. The total length is 128.1 m.<br />
U 1 & U 2 provides sp<strong>on</strong>taneous synchrotr<strong>on</strong> radiati<strong>on</strong> in <strong>the</strong> range between<br />
20-100 keV by utilizing <strong>the</strong> ”spent” electr<strong>on</strong> <strong>beam</strong> after <strong>the</strong> Sase 2 undulator. The<br />
length is 61 m each.<br />
To attain <strong>the</strong> accuracy <strong>and</strong> maintainability of such a large undulator system <strong>the</strong><br />
undulators are built up from 5 m l<strong>on</strong>g magnet arrays intersected by 1.1 m l<strong>on</strong>g<br />
<strong>transport</strong> secti<strong>on</strong>s.<br />
Sase 1 Sase 2 Sase 3 Unit<br />
Ee− 17.5 17.5 17.5 10 GeV<br />
λ 0.1 0.1-0.4 0.4-1.6 4.9 nm<br />
EPhot. 12.4 12.4-3.1 3.1-0.8 0.25 keV<br />
Ppeak 20 20-80 80-130 150 GW<br />
˜P 65 65-260 260-420 490 W<br />
Phot./pulse 10 12<br />
0.1−1.6·10 13<br />
0.16−1.0·10 13<br />
3.7·10 14 #<br />
Flux 3.0·10 16<br />
0.3−4.8·10 17<br />
0.48−4.8·10 17<br />
1.1·10 19 #/s<br />
Peak brill. 5.0·10 33<br />
0.5−2.2·10 33<br />
0.22−2.3·10 33<br />
1.0·10 32<br />
a)<br />
Aver. brill. 1.6·10 25<br />
0.16−6.5·10 34<br />
0.65−5.9·10 24<br />
2.8·10 23<br />
a)<br />
Table 11.3: Radiati<strong>on</strong> parameters of <strong>the</strong> three free electr<strong>on</strong> laser undulators at <strong>the</strong> European Xfel <strong>–</strong> from<br />
simulati<strong>on</strong>s[89]. a)brilliance is given in <strong>the</strong> unit phot<strong>on</strong>/0.1% bw/s/mm 2 /mrad 2 . The pulse durati<strong>on</strong> is 100 fs<br />
overall.<br />
Experiments:<br />
• FXE Femtosec<strong>on</strong>d X-ray Experiments<br />
• HED High-Energy Density matter experiments<br />
• SPB Single Particles, Clusters & Biomolecules<br />
• MID Materials Imaging <strong>and</strong> Dynamics<br />
• SQS Small Quantum Systems<br />
• SCS Spectroscopy & Coherent Scattering
190 11. Free Electr<strong>on</strong> Laser facilities<br />
11.8 SwissFEL<br />
SwissFEL injector test facility<br />
Currently in operati<strong>on</strong> at <strong>the</strong> Paul Scherrer Institut (PSI) in Switerl<strong>and</strong> is <strong>the</strong> injector<br />
testbed[306]for<strong>the</strong>proposedSwissFEL. Theintentwiththisfacility istodevelop<strong>the</strong><br />
electr<strong>on</strong> gun <strong>and</strong> injector technology sufficiently to achieve low enough emittance for<br />
free electr<strong>on</strong> laser operati<strong>on</strong>. An important parameter for <strong>the</strong> intended free electr<strong>on</strong><br />
laser is that it will have two pulses per macrobunch with a defined delay between <strong>the</strong><br />
(i.e. minimal jitter) subpulses <strong>–</strong> this to allow very precise X-ray pump- X-ray probe<br />
experiments <strong>–</strong> something which also is being developed at <strong>the</strong> PSI.<br />
A photocathode electr<strong>on</strong> gun enclosed in a radiofrequency S-b<strong>and</strong> accelerating<br />
module provides <strong>the</strong> electr<strong>on</strong> bunches for <strong>the</strong> linear accelerator, at <strong>the</strong> cathode (depending<br />
<strong>on</strong> l<strong>on</strong>g or short pulse mode) it delivers 22 or 3 A at <strong>the</strong> cathode. The accelerator<br />
structure is based <strong>on</strong> four normally c<strong>on</strong>ducting S-b<strong>and</strong> accelerati<strong>on</strong> modules<br />
(operating at 20 MV/m) followed by a fourth harm<strong>on</strong>ic X-b<strong>and</strong> cavity (which decelerates<br />
<strong>the</strong> electr<strong>on</strong>s somewhat to attain a better bunch compressi<strong>on</strong>, giving shorter<br />
pulses). The repetiti<strong>on</strong> rate of <strong>the</strong> source is 100 Hz <strong>and</strong> <strong>the</strong> <strong>beam</strong> energy is 250 MeV.<br />
<strong>the</strong> SwissFEL proposal<br />
e - gun<br />
Accelerator secti<strong>on</strong>s<br />
Seed<br />
Figure 11.9: Schematic of <strong>the</strong> proposed SwissFEL.<br />
d’Artagnan Athos<br />
Aramis<br />
Undulators<br />
The time-schedule <strong>on</strong> <strong>the</strong> project’s homepage 3 indicates that <strong>the</strong> planned start of<br />
operati<strong>on</strong>s is targeted towards in 2016.<br />
This seeded free electr<strong>on</strong> laser is envisi<strong>on</strong>ed to deliver transform-limited pulses in<br />
<strong>the</strong> soft X-ray range. The highest electr<strong>on</strong> <strong>beam</strong> energy at <strong>the</strong> entrance of <strong>the</strong> hard<br />
X-ray undulator secti<strong>on</strong> is 5.8 GeV. To facilitate experiments examining temporal<br />
processes <strong>the</strong> macropulse durati<strong>on</strong> range between 6 <strong>and</strong> 30 femtosec<strong>on</strong>ds with 50 ns<br />
separati<strong>on</strong> between two subpulses. To achieve short pulses <strong>the</strong> bunch charge is kept<br />
between 10 <strong>and</strong> 200 pC. For <strong>the</strong> soft X-rays (less than 1.6 keV) circular polarizati<strong>on</strong><br />
can be employed (for instance for magnetism measurements).<br />
3 http://www.psi.ch/swissfel/swissfel
11.8. SwissFEL 191<br />
Wavelength range 7-0.1 nm<br />
Rep. Rate 100 Hz (of 2 sub-pulses, 50 ns separati<strong>on</strong>)<br />
Pulse durati<strong>on</strong> (FWHM) 30 or 6 fs (high/low charge mode)<br />
Peak power 10 GW<br />
Peak Brilliance 1-10·10 32<br />
Injector & accelerator<br />
Table 11.4: Main parameters of <strong>the</strong> SwissFEL.<br />
The photocathode injector uses a S-b<strong>and</strong> <strong>and</strong> X-b<strong>and</strong> accelerati<strong>on</strong> before <strong>the</strong> first<br />
bunch-compressi<strong>on</strong>, about 24 meters l<strong>on</strong>g. This is followed by three C-b<strong>and</strong> accelerating<br />
linear accelerati<strong>on</strong> secti<strong>on</strong>s, in total 208 meters l<strong>on</strong>g. The C-b<strong>and</strong> parts were<br />
chosen over <strong>the</strong> S-b<strong>and</strong> (used for <strong>the</strong> test facility) as <strong>the</strong>y preserve <strong>the</strong> emittance<br />
better (provided a good alignment)[307], <strong>the</strong> power c<strong>on</strong>sumpti<strong>on</strong> is lower <strong>and</strong> <strong>the</strong><br />
number of RF stati<strong>on</strong>s fewer[308]. For <strong>the</strong> soft-X-ray secti<strong>on</strong> <strong>on</strong>ly two are used before<br />
<strong>the</strong> electr<strong>on</strong> <strong>beam</strong> enter <strong>the</strong> undulator system, giving a final electr<strong>on</strong> <strong>beam</strong> energy<br />
of 2.1 or 3.4 GeV <strong>–</strong> <strong>the</strong> electr<strong>on</strong> <strong>beam</strong> is accelerated to 5.8 GeV in <strong>the</strong> last secti<strong>on</strong>,<br />
exclusively serving <strong>the</strong> hard X-ray undulator system. The total length of <strong>the</strong> whole<br />
free electr<strong>on</strong> laser is 715 meters. Two pulse modes are envisi<strong>on</strong>ed with 13 or 2.1 fs.<br />
Undulators<br />
The details <strong>on</strong> <strong>the</strong> undulators is from a presentati<strong>on</strong> given by T. Garvey at <strong>the</strong> 32 nd<br />
free electr<strong>on</strong> laser c<strong>on</strong>ference[308].<br />
• Aramis <strong>–</strong> an in-vacuum planar undulator system with variable gap to produce<br />
Sase free electr<strong>on</strong> laser radiati<strong>on</strong> in <strong>the</strong> 0.1 to 70 nm range. The undulator<br />
period is 15 mm (with a gap larger than 4 mm <strong>and</strong> K=1.2) <strong>and</strong> <strong>the</strong> total length<br />
is 60 meters in 4 meter secti<strong>on</strong>s.<br />
• Athos <strong>–</strong> <strong>the</strong> undulator system is built up from 40 mm period Apple-II type<br />
undulators with a fixed 6.5 mm gap <strong>and</strong> full polarizati<strong>on</strong> c<strong>on</strong>trol. Intended<br />
for both Sase <strong>and</strong> seeded free electr<strong>on</strong> laser operati<strong>on</strong> in <strong>the</strong> wavelength range<br />
between 0.7 <strong>and</strong> 7 nm.<br />
• d’Artagnan <strong>–</strong> intended for use as <strong>the</strong> radiator in aHHG seeded HGHG cascade<br />
toge<strong>the</strong>r with <strong>the</strong> Athos undulator as radiator. This extends <strong>the</strong> energy range<br />
of this part of <strong>the</strong> SwissFEL to l<strong>on</strong>ger wavelengths.<br />
Experiments<br />
The scientific program at <strong>the</strong> SwissFEL is focussed towards <strong>the</strong> study of ultra-fast<br />
phenomena at <strong>the</strong> nanoscale. The double pulse structure <strong>and</strong> <strong>the</strong> strive to create very<br />
short pulses is a testament to this goal.<br />
According to <strong>the</strong> scinece case 4 for <strong>the</strong> Swissfel <strong>the</strong> scientific program will focus<br />
up<strong>on</strong> five areas:<br />
4 http://www.psi.ch/swissfel/CurrentSwissFELPublicati<strong>on</strong>sEN/SwissFEL Science Case<br />
small.pdf
192 11. Free Electr<strong>on</strong> Laser facilities<br />
1. Ultrafast magnetizati<strong>on</strong> dynamics at <strong>the</strong> nanoscale.<br />
2. Catalysis <strong>and</strong> soluti<strong>on</strong> chemistry, i.e. <strong>the</strong> lifetime <strong>and</strong> structure of short-lived<br />
intermediate states <strong>on</strong> surfaces or in soluti<strong>on</strong>.<br />
3. Coherent diffracti<strong>on</strong> of nanostructures <strong>–</strong> lens-less imaging can provide atomic<br />
resoluti<strong>on</strong> of biological <strong>and</strong> inorganic nanostructures.<br />
4. Ultrafast biochemistry<br />
5. Time-resolved spectroscopies of correlated electr<strong>on</strong> materials.<br />
11.9 Proposed facilities<br />
Besides <strong>the</strong> proposed extensi<strong>on</strong>s of currently existing facilites (as <strong>the</strong> Flash-II, Lcls-<br />
II, SwissFEL) <strong>and</strong> projects under c<strong>on</strong>structi<strong>on</strong> as <strong>the</strong> European <strong>and</strong> <strong>the</strong> Spring-8<br />
X-fels included here <strong>the</strong> Korean X-fel project.<br />
11.10 PAL-X-fel<br />
The X-fel at <strong>the</strong> Poohang accelerator laboratory in Korea is currently in <strong>the</strong> technical<br />
design phase[309]. Here we will c<strong>on</strong>sider <strong>the</strong> design assuming a 10 GeV linear<br />
accelerator. Shorter more compact designs using 3.7 GeV linear accelerators envisi<strong>on</strong>ing<br />
<strong>the</strong> use of <strong>on</strong>ly <strong>the</strong> third harm<strong>on</strong>ic for free electr<strong>on</strong> laser radiati<strong>on</strong> have been<br />
c<strong>on</strong>sidered.<br />
Accelerator<br />
The accelerator secti<strong>on</strong> c<strong>on</strong>sists of three S-b<strong>and</strong> secti<strong>on</strong>s (4, 28 <strong>and</strong> 96 three meter<br />
l<strong>on</strong>g radiofrequency accelerating structures) <strong>and</strong> <strong>on</strong>e short (0.6 m) X-b<strong>and</strong> secti<strong>on</strong> <strong>–</strong><br />
<strong>the</strong> total length of <strong>the</strong> S-b<strong>and</strong> secti<strong>on</strong> is 550 m. The accelerating gradients in <strong>the</strong><br />
S-b<strong>and</strong> structures is 27 MV/m. Simulati<strong>on</strong>s of both 1 nC <strong>and</strong> <strong>and</strong> 0.2 nC charges<br />
have been d<strong>on</strong>e. With 1 nC <strong>the</strong> radiated output power is 6 GW, 0.2 nC gives about<br />
2 GW.<br />
Undulators<br />
The undulator c<strong>on</strong>sidered is a 94 m l<strong>on</strong>g (or around 100 m) in vacuum undulator with<br />
a period of 2.23 cm <strong>and</strong> undulator parameter K=2.22.<br />
As this facility is in <strong>the</strong> technical design stage no informati<strong>on</strong> <strong>on</strong> <strong>the</strong> intended<br />
experimental program is available in <strong>the</strong> time of writing.
11.10. PAL-X-fel 193<br />
Summary<br />
• The currently two operating soft <strong>and</strong> hard X-ray free electr<strong>on</strong>laser<br />
are Flash, Hamburg, Germany<strong>and</strong>Lcls, Stanford,<br />
USA.<br />
• Facilities currently being built is <strong>the</strong> Fermi@Elettra, Trieste,<br />
Italy; <strong>the</strong> european <strong>and</strong> <strong>the</strong> japanese X-fels.<br />
• Am<strong>on</strong>g facilities in detailed technical design phase are <strong>the</strong><br />
SwissFel in Switzerl<strong>and</strong> <strong>and</strong> <strong>the</strong> PAL-X-fel in Korea.<br />
• In c<strong>on</strong>trast to <strong>the</strong> o<strong>the</strong>r facilities <strong>the</strong> Flash free electr<strong>on</strong><br />
laser have less permanent in house experiments (encouraging<br />
users to bring <strong>the</strong>ir own set-ups).<br />
• Both Flash <strong>and</strong> <strong>the</strong> Lcls are currently specifying upgrades<br />
to <strong>the</strong> facilites. Flash have a seeding experiment already.<br />
Both are c<strong>on</strong>sidering additi<strong>on</strong>s to <strong>the</strong> current accelerator layout<br />
that would increase <strong>the</strong> number of experimental secti<strong>on</strong>s.<br />
Notably both facilites, currently producing Sase free electr<strong>on</strong><br />
laser radiati<strong>on</strong> <strong>–</strong> aims to install seeded HGHG or EEHG cascades.<br />
• Most facilites are trying to (or at least have <strong>the</strong> opti<strong>on</strong> to) run<br />
with lower bunch charges as to shorten <strong>the</strong> pulses.<br />
• The overall length of <strong>the</strong> newer facilites is shorter, owing to<br />
advances made in technology to reduce <strong>the</strong> emittance of <strong>the</strong><br />
electr<strong>on</strong> <strong>beam</strong>.
12. Outlook & C<strong>on</strong>clusi<strong>on</strong>s<br />
Written by: A. Lindblad<br />
12.1 Current trends<br />
More compact sources <strong>and</strong> alternative approaches<br />
A significant effort is currently being undertaken to find technology that reduce <strong>the</strong><br />
normalized emittance of <strong>the</strong> electr<strong>on</strong> <strong>beam</strong> <strong>and</strong> <strong>the</strong> length of <strong>the</strong> undulators <strong>–</strong> both<br />
factors that severely impacts <strong>the</strong> overall length <strong>and</strong> cost of a free electr<strong>on</strong> laser.<br />
The radiofrequency systems driving <strong>the</strong> cavities of <strong>the</strong> linear accelerators are also<br />
important cost drivers.<br />
The European X-fel <strong>and</strong> <strong>the</strong> Lcls is 3.4 km <strong>and</strong> 3 km l<strong>on</strong>g respectively. They use<br />
L-b<strong>and</strong> <strong>and</strong> S-b<strong>and</strong> accelerator technology respectively toge<strong>the</strong>r with photocathode<br />
electr<strong>on</strong> guns. In c<strong>on</strong>trast <strong>the</strong> X-fel at Spring-8 will use C-b<strong>and</strong> accelerators (with<br />
frequencies four times that of L-b<strong>and</strong> <strong>and</strong> twice that of S-b<strong>and</strong>) <strong>and</strong> a <strong>the</strong>rmi<strong>on</strong>ic gun<br />
<strong>–</strong> both c<strong>on</strong>tributing to <strong>the</strong> significantly shorter accelerator part of <strong>the</strong> facility of 750<br />
m. Also c<strong>on</strong>tributing to this is <strong>the</strong> in vacuum undulators with small gaps that allow<br />
<strong>the</strong> undulator period to be shortened[310] <strong>–</strong> similar undulators are c<strong>on</strong>sidered for <strong>the</strong><br />
SwissFel.<br />
The incentives are thus many to make more compact X-ray sources, not <strong>on</strong>ly<br />
motivated by cost reducti<strong>on</strong> but also scientifically[311], <strong>on</strong>e such source would be <strong>the</strong><br />
plasma wake-field accelerators[312]. In such a device electr<strong>on</strong>s are accelerated in a<br />
bubble created in a plasma by a str<strong>on</strong>g laser propagating through a medium (often<br />
a gas). A plasma wake-field accelerator can be used toge<strong>the</strong>r with an undulator to<br />
create sp<strong>on</strong>taneous X-ray radiati<strong>on</strong>[313]. A questi<strong>on</strong> yet to be answered is if <strong>the</strong><br />
electr<strong>on</strong> <strong>beam</strong> in <strong>the</strong> plasma wake-field can be made with high enough quality to <strong>and</strong><br />
if collective effects like microbunching can occur to allow free electr<strong>on</strong> lasing. The<br />
repetiti<strong>on</strong> rate of <strong>the</strong> driving lasers is currently slow, in <strong>the</strong> order of 10’s of Hz.<br />
XFELO (X-ray free electr<strong>on</strong> laser oscillator) <strong>and</strong> <strong>the</strong> regenerative free electr<strong>on</strong><br />
laser amplifier are suggested low gain amplificati<strong>on</strong> systems, both use cavity feedback<br />
to achieve lasing with cavities made from highly reflecting diam<strong>on</strong>d mirrors that work<br />
in <strong>the</strong> X-ray range. Unlike <strong>the</strong> single-pass high-gain systems described in this book<br />
both <strong>the</strong> XFELO <strong>and</strong> <strong>the</strong> regenerative FEL amplifiers dem<strong>and</strong> high repetiti<strong>on</strong> rate<br />
195
196 12. Outlook & C<strong>on</strong>clusi<strong>on</strong>s<br />
electr<strong>on</strong> guns <strong>–</strong> o<strong>the</strong>rwise <strong>the</strong> electr<strong>on</strong>bunches do not arrive in time to meet <strong>the</strong> pulse<br />
in <strong>the</strong> cavity.<br />
Higher repetiti<strong>on</strong> rates<br />
Normally c<strong>on</strong>ducting accelerator technology limits <strong>the</strong> repetiti<strong>on</strong> rate to about 100<br />
Hz, e.g. at <strong>the</strong> Lcls. Currently Flash <strong>and</strong>, in <strong>the</strong> near future, <strong>the</strong> European X-Fel<br />
operate with phot<strong>on</strong> pulses that have MHz substructures.<br />
Achieving high average brilliance is an active area of pursuit <strong>–</strong> as it opens up<br />
new fields of research <strong>and</strong> allows for serving many user experiments in parallel or in<br />
series (at reduced intensity or repetiti<strong>on</strong> rate respectively). The technology (superc<strong>on</strong>ducting<br />
accelerator secti<strong>on</strong>s? electr<strong>on</strong> guns, etc.) for driving a X-ray free electr<strong>on</strong><br />
laser with MHz frequency exist in principle with <strong>the</strong> cost being <strong>the</strong> biggest obstacle.<br />
With o<strong>the</strong>r comp<strong>on</strong>ents of <strong>the</strong> free electr<strong>on</strong> laser becoming shorter <strong>and</strong> more efficient<br />
this deterring factor may be less str<strong>on</strong>g in <strong>the</strong> future. Generic c<strong>on</strong>cepts for what<br />
would be <strong>the</strong> necessary comp<strong>on</strong>ents in a free electr<strong>on</strong> laser facility achieving MHz<br />
repetiti<strong>on</strong> rates have been studied by J. Corlett <strong>and</strong> co-workers[314].<br />
Polarizati<strong>on</strong> c<strong>on</strong>trol<br />
We fleetingly touched up<strong>on</strong> <strong>the</strong> subject of polarizati<strong>on</strong>s different from <strong>the</strong> linear inplane<br />
variety produced by planar undulators with a vertical magnetic field in chapter<br />
3 when different types of undulators were discussed.<br />
Typically <strong>the</strong> first generati<strong>on</strong> free electr<strong>on</strong> laser in <strong>the</strong> VUV <strong>and</strong> X-ray ranges<br />
utilize <strong>the</strong> aforementi<strong>on</strong>ed planar undulators with vertical magnetic fields to generate<br />
<strong>the</strong> phot<strong>on</strong> <strong>beam</strong> generating linearly polarized light. Many experiments, for instance<br />
those c<strong>on</strong>cerning spin properties <strong>and</strong> dynamics of materials, e.g. magnetic properties<br />
<strong>and</strong>magnetizati<strong>on</strong>/de-magnetizati<strong>on</strong> processes, requirecircularly (helically) polarized<br />
light for <strong>the</strong>ir inquiry.<br />
On paper <strong>the</strong>re it is not harder to produce helical light than linearly polarized, in<br />
practice helical undulators involve more moving parts <strong>and</strong> are thus more intricate to<br />
build <strong>and</strong> utilize. This is probably <strong>the</strong> main reas<strong>on</strong> why <strong>the</strong> first generati<strong>on</strong> of X-ray<br />
free electr<strong>on</strong> laser have chosen to operate with planar undulators <strong>–</strong> as seen earlier <strong>the</strong><br />
error tolerances for <strong>the</strong> undulator systems are tight without <strong>the</strong> complexity of, e.g. an<br />
Apple type undulator.<br />
Above roughtly 2 keV phot<strong>on</strong> energies it is possible to produce befringement transparent<br />
materials that c<strong>on</strong>vert linearly polarized X-rays to helical polarizati<strong>on</strong>s given<br />
that <strong>the</strong> thickness <strong>and</strong> orientati<strong>on</strong> of <strong>the</strong> crystals c<strong>on</strong>spire to do so (e.g. diam<strong>on</strong>d<br />
crystals with <strong>the</strong> proper thickness will do this). In many cases this will be a true<br />
<strong>on</strong>e-shot experiment which destroys <strong>the</strong> crystal <strong>–</strong> <strong>the</strong> cost is though microscopical<br />
compared to installing a new undulator secti<strong>on</strong> in a free electr<strong>on</strong> laser.<br />
In <strong>the</strong> soft X-ray regime it is however necessary to use an undulator to create<br />
helical polarizati<strong>on</strong>, am<strong>on</strong>g o<strong>the</strong>r things <strong>the</strong> absorbance for soft X-rays in materials<br />
is too high for experiments to be efficiently executed.<br />
Besides <strong>the</strong> Apple type of undulators described earlier, two planar undulators with<br />
<strong>the</strong> undulator planes rotated with respect to each o<strong>the</strong>r can be used to produce tilted<br />
linear <strong>and</strong> helical polarizati<strong>on</strong>s. The c<strong>on</strong>figurati<strong>on</strong> drawn in <strong>the</strong> top of Figure 12.1<br />
will create tilted linearly polarized light if <strong>the</strong> undulators are placed at a distance
12.1. Current trends 197<br />
that cause <strong>the</strong>m to emit in phase. If, <strong>on</strong> <strong>the</strong> o<strong>the</strong>r h<strong>and</strong>, a magnetic chicane secti<strong>on</strong> is<br />
installed between <strong>the</strong>undulators <strong>the</strong>delay between <strong>the</strong>exit of<strong>the</strong> electr<strong>on</strong> bunchfrom<br />
<strong>the</strong> first <strong>and</strong> entrance of <strong>the</strong> sec<strong>on</strong>d undulator can be varied with <strong>the</strong> magnetic field<br />
strength (as <strong>the</strong> path becomes l<strong>on</strong>ger for str<strong>on</strong>ger magnetic fields since <strong>the</strong> deviati<strong>on</strong><br />
becomes larger). Theintroduceddelaycase aphase-shift of<strong>the</strong>emittedphot<strong>on</strong>swhich<br />
give rise to a (tunable) polarizati<strong>on</strong> change from linear tofully circular polarized light.<br />
Chicane<br />
Figure 12.1: Planar undulators with <strong>the</strong> plane shifted (here 90 ◦ ) can produce light with tilted linear polarizati<strong>on</strong><br />
when <strong>the</strong>y emit in phase <strong>–</strong> or circular polarizati<strong>on</strong> if <strong>the</strong> phase can be shifted with a delay introduced with a<br />
chicane secti<strong>on</strong> between <strong>the</strong> undulators.<br />
It is not necessary for <strong>the</strong> whole undulator array of <strong>the</strong> free electr<strong>on</strong> laser to be<br />
composed of helical undulators. An electr<strong>on</strong> bunch which is microbunched in a planar<br />
undulator emit coherently in a helical undulator as well if <strong>the</strong> undulators are tuned<br />
to <strong>the</strong> same wavelength. C<strong>on</strong>siderable effort can thus be saved in c<strong>on</strong>structing an<br />
undulator array that can produce all kinds of polarizati<strong>on</strong> of <strong>the</strong> light. Most upgrades<br />
to currently operating facilities <strong>and</strong> new facilities have this capacity included in <strong>on</strong>e<br />
way or ano<strong>the</strong>r since <strong>the</strong> experiments enabled are numerous <strong>and</strong> studies phenomena<br />
of general scientific interest.<br />
Coherence & Seeding<br />
Throughout this book we have noted that nei<strong>the</strong>r l<strong>on</strong>gitudinal, nor transverse coherence<br />
of a free electr<strong>on</strong> laser is perfect. This is reflected in <strong>the</strong> spectral b<strong>and</strong>width,<br />
which is inversely proporti<strong>on</strong>al to <strong>the</strong> number of undulator periods. We may improve<br />
up<strong>on</strong> this number with a m<strong>on</strong>ochromator before <strong>the</strong> experiment, trading intensity for<br />
higher m<strong>on</strong>ochromaticity.<br />
Differentup-shiftingschemesinvolvingtraditi<strong>on</strong>allasers <strong>and</strong>HHGlasers, e.g.Hghg,<br />
Eehg <strong>and</strong> o<strong>the</strong>r seeding schemes are an integral part of most new free electr<strong>on</strong><br />
laser projects <strong>–</strong> notably <strong>the</strong> Fermi@Elettra, <strong>the</strong> next free electr<strong>on</strong> laser to come<br />
<strong>on</strong>-line. A significant improvement up<strong>on</strong> <strong>the</strong> coherence properties of <strong>the</strong> free electr<strong>on</strong><br />
laser radiati<strong>on</strong> can be expected from this, especially if <strong>the</strong> seed power dominates <strong>the</strong><br />
initial Sase power. Currently, <strong>the</strong> limit of effective seeding using an HHG laser source<br />
is around 10 nm <strong>–</strong> mainly set by <strong>the</strong> power of <strong>the</strong> driving lasers. Up-shifting schemes<br />
<strong>the</strong>refore often use ordinary lasers because of <strong>the</strong>ir higher repetiti<strong>on</strong> rate, which will<br />
be needed for many newfree electr<strong>on</strong> laser facilites operating in <strong>the</strong> kHz/MHz regi<strong>on</strong>s.<br />
At<strong>the</strong>Lcls aself-seedingopti<strong>on</strong>is includedin<strong>the</strong>upgradeproposal, whichwill use<br />
<strong>the</strong> generated radiati<strong>on</strong> to seed <strong>the</strong> Sase process in <strong>the</strong> following undulator secti<strong>on</strong>s
198 12. Outlook & C<strong>on</strong>clusi<strong>on</strong>s<br />
<strong>–</strong> something which potentially overcomes <strong>the</strong> limits imposed <strong>on</strong> external laser seeding<br />
schemes vis-à-vis wavelength <strong>and</strong> repetiti<strong>on</strong> rate.<br />
The use of low bunch charges reduce <strong>the</strong> emittance of <strong>the</strong> <strong>beam</strong> <strong>and</strong> increases <strong>the</strong><br />
probability of <strong>on</strong>ly <strong>on</strong>e Sase mode radiating efficiently (which improves <strong>the</strong> pulse<br />
length).<br />
Harder X-rays<br />
It is problematic to reduce <strong>the</strong> phot<strong>on</strong>-wavelength fur<strong>the</strong>r than 1 ˚A while maintaining<br />
free electr<strong>on</strong> laser amplificati<strong>on</strong> efficiently <strong>–</strong> <strong>the</strong> main limits being electr<strong>on</strong> <strong>beam</strong><br />
emittance <strong>and</strong> for very hard X-rays <strong>the</strong> recoil up<strong>on</strong> phot<strong>on</strong> emissi<strong>on</strong> smears out <strong>the</strong><br />
microbunching (having an extremely short period as is at those wavelengths). At <strong>the</strong><br />
Lcls a significant porti<strong>on</strong> of <strong>the</strong> density modulati<strong>on</strong> of <strong>the</strong> electr<strong>on</strong> <strong>beam</strong> is present<br />
at half of <strong>the</strong> fundamental wavelength, giving access to sub-˚A wavelengths when <strong>the</strong><br />
first undulator secti<strong>on</strong> is followed by undulators that have <strong>the</strong> sec<strong>on</strong>d harm<strong>on</strong>ic of<br />
<strong>the</strong> radiati<strong>on</strong> as fundamental wavelength. The expected power at 16 keV is about<br />
10% of that found in <strong>the</strong> 8 keV fundamental[303]. A proposal for a free electr<strong>on</strong><br />
laser producing 50 keV X-rays is actively worked up<strong>on</strong>[315].<br />
γ-rays <strong>and</strong> <strong>the</strong> quantum free electr<strong>on</strong> laser<br />
The c<strong>on</strong>cept of <strong>the</strong> quantum free electr<strong>on</strong> laser (QFEL) have been introduced by<br />
R. B<strong>on</strong>ifacio <strong>and</strong> o<strong>the</strong>rs (see [316] <strong>and</strong> references <strong>the</strong>rein). We may check when<br />
<strong>the</strong> phot<strong>on</strong>’s momentum becomes comparable to <strong>the</strong> electr<strong>on</strong> momentum spread in<br />
<strong>the</strong> <strong>beam</strong> using <strong>the</strong> Pierce parameter ρ (see chapter 2). Classically, <strong>the</strong> momentum<br />
spread in <strong>the</strong> electr<strong>on</strong> <strong>beam</strong> is mcγrρ. The phot<strong>on</strong>’s momentum is proporti<strong>on</strong>al to<br />
<strong>the</strong> wavenumber k with � as <strong>the</strong> proporti<strong>on</strong>ality c<strong>on</strong>stant.<br />
Letting <strong>the</strong> ratio between <strong>the</strong> two momenta define <strong>the</strong> ”quantum FEL parameter”<br />
as:<br />
¯ρ = ρ mcγr<br />
�k<br />
in <strong>the</strong> soft X-ray regime <strong>the</strong> wavenumber of <strong>the</strong> phot<strong>on</strong>s is small compared to <strong>the</strong><br />
momentum spread in <strong>the</strong> electr<strong>on</strong> <strong>beam</strong>, for a normal Sase-free electr<strong>on</strong> laser this<br />
means that ¯ρ ≫ 1. For very high momenta <strong>the</strong> phot<strong>on</strong> momentum will have comparable<br />
magnitude to <strong>the</strong> electr<strong>on</strong> momenta. In this limit we must take into account<br />
that <strong>the</strong> momentum recoil can <strong>on</strong>ly assume discrete values (i.e. multiples of �k). If<br />
nothing is d<strong>on</strong>e to synchr<strong>on</strong>ize <strong>the</strong> phot<strong>on</strong> emissi<strong>on</strong> <strong>the</strong> recoils will occur r<strong>and</strong>omly<br />
<strong>and</strong> widen <strong>the</strong> momentum distributi<strong>on</strong> in <strong>the</strong> <strong>beam</strong> with loss of <strong>the</strong> microbunching.<br />
For an electr<strong>on</strong> <strong>beam</strong> with small enough energy spread, <strong>the</strong> quantum free electr<strong>on</strong><br />
laser operate by colliding this electr<strong>on</strong> <strong>beam</strong> with a counterpropagating laser <strong>beam</strong><br />
having very high power 1 . The laser <strong>beam</strong> (which can be operated at µm wavlengths)<br />
<strong>the</strong>n effectively acts as an undulator with extremely short period. If <strong>on</strong>e is in <strong>the</strong><br />
regime where ¯ρ ≤ 1 all electr<strong>on</strong>s experience <strong>the</strong> same recoil losing �k. The radiati<strong>on</strong><br />
from this process is temporally coherent up into γ-ray energies.<br />
Experiments with this type of radiati<strong>on</strong> may extend <strong>the</strong> applicability of free electr<strong>on</strong><br />
laser (in a broad sense) into <strong>the</strong> sub-atomic regimes with <strong>the</strong> study of processes<br />
involving, e.g. nuclear transiti<strong>on</strong>s.<br />
1 For <strong>the</strong> so inclined, <strong>the</strong> process is that of collective Compt<strong>on</strong> backscattering.
12.2. C<strong>on</strong>clusi<strong>on</strong> 199<br />
A X-ray free-prot<strong>on</strong> laser have been suggested as a way to overcome <strong>the</strong> ”quantum<br />
momentumlimitati<strong>on</strong>”of<strong>the</strong>Saseprocess, thisbyusingprot<strong>on</strong>sra<strong>the</strong>rthanelectr<strong>on</strong>s<br />
in <strong>the</strong> particle <strong>beam</strong> <strong>–</strong> although feasible, it would require a huge scale facility such<br />
as <strong>the</strong> LHC as a driver[317]. As noted in <strong>the</strong> reference though, this may be tested<br />
as a parasitic undertaking at <strong>the</strong> storage ring, much as synchrotr<strong>on</strong> radiati<strong>on</strong> studies<br />
started out in <strong>the</strong> late 1940’s.<br />
12.2 C<strong>on</strong>clusi<strong>on</strong><br />
Free electr<strong>on</strong> laser operating in <strong>the</strong> VUV <strong>and</strong> X-ray ranges offer scientists a light<br />
source with unique spectral properties. The success of Flash <strong>and</strong> Lcls <strong>and</strong> <strong>the</strong><br />
pi<strong>on</strong>eering experiments carried out <strong>the</strong>re mark <strong>the</strong> potential for a broad <strong>and</strong> deep<br />
endeavor to investigate nature in ways hi<strong>the</strong>rto not possible with X-rays using that<br />
degree of precisi<strong>on</strong>: nanometers <strong>and</strong> femtosec<strong>on</strong>ds with developments pushing those<br />
limits towards ˚Angströms <strong>and</strong> attosec<strong>on</strong>ds <strong>–</strong> <strong>the</strong> true atomic scales of space <strong>and</strong> time.<br />
With <strong>the</strong> advent of successful improvements of <strong>the</strong> spectral characteristics of <strong>the</strong><br />
Sase experimental work <strong>and</strong> interpretati<strong>on</strong> of data will become easier <strong>and</strong> facilitate<br />
<strong>the</strong> utilizati<strong>on</strong> of this type of source for a broader user community.<br />
As <strong>the</strong> first generati<strong>on</strong> of X-ray free electr<strong>on</strong> laser is augmented, upgraded <strong>and</strong> <strong>the</strong><br />
sec<strong>on</strong>d generati<strong>on</strong> of facilities are brought <strong>on</strong>-line in <strong>the</strong> future <strong>the</strong> number of possible<br />
experiments will surely increase as well as <strong>the</strong> intricacy of <strong>the</strong> investigati<strong>on</strong>s.
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This <str<strong>on</strong>g>compendium</str<strong>on</strong>g> serves both as a summary of <strong>the</strong> reports generated<br />
by <strong>the</strong> <strong>IRUVX</strong> experts <strong>on</strong> optics <strong>and</strong> phot<strong>on</strong> diagnostics <strong>and</strong> as an<br />
introducti<strong>on</strong> to Free Electr<strong>on</strong> Lasers, <strong>the</strong>ir functi<strong>on</strong>, <strong>and</strong> some of <strong>the</strong><br />
necessary technologies to make <strong>the</strong>m work.<br />
The ambiti<strong>on</strong> has been to encompass <strong>the</strong> subject of Free Electr<strong>on</strong> Laser<br />
technology in an introductory manner (part I), which supports <strong>the</strong> ra<strong>the</strong>r<br />
deep excursi<strong>on</strong> into phot<strong>on</strong> diagnostic methods that follows (part II). The<br />
list of references is extensive <strong>and</strong> could be used for more in depth studies.<br />
Members of <strong>IRUVX</strong>-<strong>PP</strong> WP7 <strong>and</strong> WP3 Expert Groups Phot<strong>on</strong> Beam<br />
Transport <strong>and</strong> Diagnostics <strong>and</strong> Metrology for FEL Optics:<br />
Rafael Abela, Günter Brenner, Anna Bianco, Mari<strong>on</strong> Bowler, Roberto<br />
Cimino, Daniele Cocco, Henrik Enquist, Uwe Flechsig, Christopher Gerth,<br />
Anth<strong>on</strong>y Glees<strong>on</strong>, Fini Jastrow, Ulf Johanss<strong>on</strong>, Libor Juha, Pavle Juranić,<br />
Barbara Keitel, Jörgen Larss<strong>on</strong>, Andreas Lindblad, Eric Louis, Bernd<br />
Löchel, Rolf Mitzner, Paul Morin, Robert Nietubyć, Luca Poletto, Paul<br />
Radcliffe, Amparo Rommeveaux, Mark Roper, Frank Siewert, Ryszard<br />
Sobierajski, Andrey Sorokin, Giovanni Sostero, Sibylle Spielmann-Jaeggi,<br />
Svante Svenss<strong>on</strong>, Cristian Svetina, Muriel Thomasset, Kai Tiedtke, Peter<br />
van der Slot, Hubertus Wabnitz, Christian Weniger, Marco Zangr<strong>and</strong>o.<br />
This work is supported by <strong>IRUVX</strong>-<strong>PP</strong>, an EU co-funded project under FP7<br />
(Grant Agreement 211285).<br />
www.eurofel.eu