LCLS Conceptual Design Report - Stanford Synchrotron Radiation ...

L C L S C O N C E P T U A L D E S I G N R E P O R T
8.2.5.4 Resulting Power Gain Length Increase.
Gathering the results of Eqs. (8.17), (8.23), and (8.24),
F − F x + y ⎛ A A ⎞ L
F ⎝ A ⎠ L
2 2
0 m − 0 g 2
>− + ℜ 2 ⎜ ⎟ − ϕm
max
0 2σr0 2
where Lg = 1/[2Re(p)] is the power gain length.
, (8.28)
This reduction of the wave-electron interaction efficiency can be expressed as an effective
reduction of the undulator parameter K for the ideal magnetic system:
K − K 0
K 0
>− x 2 + y 2
2 2σ r
+ Re A m − A 0
A 0
− L g
2
2L ϕ m max
. (8.29)
Now one can use analytical theory [8] or computer code to calculate the corresponding
increase of the power gain length. For the LCLS magnetic system, a 3% increase in power gain
length corresponds to a 5.4% reduction in K. Taking σr 2 ≈εβ [8], one can make the tolerance
budget.
8.3 Undulator Measurement and Tuning
8.3.1 Requirements for the LCLS
The main tolerance requirements for alignment and field quality within a section of the
undulator line that includes an undulator segment and a quadrupole are given in Table 8.2.
Table 8.2 Alignment tolerances for undulator segment
Alignment Tolerance Value
Horizontal and vertical trajectory excursion 2 µm
“Radiation amplitude” deviation (see Eq., (8.5)) 2 %
Phase slip between two undulator segments 10 degrees
Vertical positioning error 50 µm
These tolerances correspond to approximately 3 % growth of the power gain length. They are
demanding, but achievable. They have already been met by the undulator segments that were
tuned magnetically for installation in the APS FEL. Those undulator segments have a period
length of 33 mm, close enough to the 30 mm period length of the LCLS undulator segments that
the tuning techniques developed for the APS undulator segments should transfer directly.
8-14 ♦ U N D U L A T O R