Measuring the Electron Beam Energy in a Magnetic Bunch ... - DESY

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PMT BBO GDD PMT Two laser pulses: 800 nm 1550 nm Figure 3.4.1 Measurement of the arrival-time of the injector laser pulse relative to a timing laser reference (MLO) using a two-color single-crystal balanced optical cross-correlator. From S. Schulz, Synchronization of Injector Laser and Master Laser Oscillator PAC’10. In Fig. 3.4.1, the arrival-time of the injector laser pulse is measured relative to the optical reference laser in an optical cross-correlator. In a two-color optical cross-correlator, two laser pulses with different colors (800 nm and 1550 nm) are sent through a dichroic mirror that reflects the sum frequency (527.7 nm) and transmits the higher frequencies. The input laser pulses are then sent through a BBO crystal. When the pulses overlap in the crystal, new pulses with the sum frequency are generated and emitted in both forward and backward directions. With the aid of dichroic mirrors and a group delay generated in a dispersive medium, the pulses generated in the crystal each travel to a photomultiplier tube (PMT). The incoming laser pulses return from whence they came. In this balanced detection arrangement, the measurement of the relative arrival-times of the two input pulses is insensitive to laser noise and is background and drift free. 3.5 Third-harmonic Module Jitter The third-harmonic module is comprised of 4 cell cavities which are filled with 3.9 GHz. It is used to linearize the energy chirp of the beam. In the first bunch compressor, the energy of an electron at position z in the bunch is E Dichroic mirror: Reflects 527.7 nm Transmits 800 and 1550nm BBO crystal: second harmonic light generated when pulses overlap. = E0 + V1 cos( krf z + Φ1) + V3 cos(3k rf z + 3) (3.5.1) 1 Φ GDD: Generate a group delay in a dispersive medium Dichroic mirror: Transmits 527.7 nm Reflects 800 and 1550nm where (V 1 , Φ 1 , V 3 , Φ 3 ) are the RF amplitudes and phases of the first accelerator section and the thirdharmonic module. As in Eq. 1.7, the path-length through the chicane as a function of the energy of a given particle is written by 32
( ) E − E ⎛ E − E ⎜ ⎝ 0 0 L E = L0 + R56 + R566 E ⎜ ⎟ (3.5.2) 0 E0 where E 0 is the energy of the bunch center (z=0). The first and second order chirps of the beam energy as a function of the compression factor C are [30] ⎞ ⎟ ⎠ 2 E ⎜ ⎛ = 0 1 E' 1 − R ⎝ C 56 ⎞ ⎟ ⎠ 56 ( E ) 2 R566 ' E'' = −2 . (3.5.3) R E 0 Taken all together, we have three equations with four free parameters, (V 1 , Φ 1 , V 3 , Φ 3 ), in Eq. 3.5.1. To optimize this system, the second-order energy chirp will be compensated by an appropriate phase and amplitude setting in the third-harmonic module. Under the current plan for the operating parameters, the gradient of the thirdharmonic cavity is only a 9 th of the gradient of the downstream accelerator sections, so the amplitude jitter contribution will be only a 9 th of that of the downstream accelerator sections. This means that it doesn’t make sense to stabilize the gradient of the thirdharmonic module until the down-stream accelerator sections’ gradient stabilities are improved by a factor of nine. Because this has yet to be accomplished, the thirdharmonic module is a lesser worry. Schemes that attempt to compensate for the thirdorder energy chirp call for large amplitudes in the thirdharmonic module and this would begin to have an impact on the arrival-time stability. The jitter contribution of the phase of the third-harmonic module depends much more dramatically on the setpoint of the module. Some settings make the module the dominant contributor to bunch length jitter, while others make it the weakest contributor. It can be argued that the ideal setting for timing jitter and peak current considerations is one for which the phase jitter contributions of the 3.9 and 1.3 GHz modules are approximately equal [31]. 3.6 First Accelerator Section Jitter The first accelerator section needs to be stabilized on two fronts: the phase and the amplitude. The phase in this section determines primarily the bunch length, while the amplitude strongly affects the beam arrival-time and the energy. Following the argument given in Sect. 3.1 about arrival-time stability after a chicane, the desired energy stability in the first accelerator section is approximately 0.004%, a factor-of-ten improvement over the current 0.04% stability. A monitor for a feedback system should be at least two times better than the stability that it hopes to achieve, and so the monitor for an energy feedback should resolve 0.002% energy changes. By this logic, with an R 56 of 180 mm (550 ps) and an R 16 of 345 mm, an arrivaltime measurement of the beam’s time-of-flight through the first chicane of FLASH should resolve 10 femtoseconds and a position measurement in the chicane should resolve 7 μm (21 fs). It follows that the resolution required by the position measurement is lower than that required by a time-of-flight arrival-time measurement in proportion to the ratio between the R 16 and R 56 terms. In the case of the first bunch compressor of FLASH, this ratio is 2:1, in favor of the position measurement, whereas for the XFEL the 33
Page 1 and 2: Measuring the Electron Beam Energy
Page 3 and 4: Abstract Within this thesis, work w
Page 5 and 6: 9 Synchrotron Light Monitors 9.1 Pr
Page 7 and 8: List of Figures 1.0.1 Magnetic bunc
Page 9 and 10: 5.5.10 Dependence of the slope of p
Page 11 and 12: 8.3.6 RF phase measurement drift wi
Page 13 and 14: where α is the bending angle intro
Page 15 and 16: R 16 ( eBl / 2) d ⎛ ⎞ 1 eff 2 p
Page 17 and 18: 2 Free-electron Lasers The facility
Page 19 and 20: arrival-time and energy prior to a
Page 21 and 22: electrons travel faster than low-en
Page 23 and 24: efore bunch compressor energy chirp
Page 25 and 26: corresponds to terms that are linea
Page 27 and 28: spread will be larger and the trans
Page 29 and 30: (a) (b) Figure 2.3.4 Single chicane
Page 31 and 32: 3 Beam Arrival-time Stabilization A
Page 33 and 34: changes in the amplitude of the kly
Page 35 and 36: The problem of cavity field measure
Page 37 and 38: creates a single point-of-failure s
Page 39 and 40: accelerator section and it was firs
Page 41 and 42: ACC1 ~Gun 3rd ACC2 ACC3ACC4 ACC7 Ac
Page 43: • The lack of a normal-conducting
Page 47 and 48: 3.7 Second Accelerator Section Jitt
Page 49 and 50: 4 Beam Shape in the Bunch Compresso
Page 51 and 52: There has been some debate over the
Page 53 and 54: V T = V cos( k ⋅ z + = V T 0 rf
Page 55 and 56: Upstream of the first accelerator s
Page 57 and 58: Positive bump 5 8 deg off-crest in
Page 59 and 60: E (MeV) 4.75 4.74 4.73 4.72 4.71 4.
Page 61 and 62: leads one to suspect that as in the
Page 63 and 64: vacuum feedthroughs, the buttons we
Page 65 and 66: J image − ⎡ ⎛ ⎞ ⎤ = ⎢ +
Page 67 and 68: sensitivity of 8 and 20 mm diameter
Page 69 and 70: 1 v phase = . (5.1.21) LC Finally,
Page 71 and 72: some locations. Nevertheless, it is
Page 73 and 74: BPM BAM More power at lower frequen
Page 75 and 76: arrival-time monitor with and witho
Page 77 and 78: 5.2 Cavity BPM Cavity BPMs (Fig. 5.
Page 79 and 80: t=0 Z 0 t=L/c Z 0 2L Figure 5.3.1 L
Page 81 and 82: 0.2 nC beam charge and can handle b
Page 83 and 84: T1-T2=T3 X=T3*c T1 T2 Figure 5.5.2
Page 85 and 86: None of the designs suffered from a
Page 87 and 88: pickup functions appropriately over
Page 89 and 90: 35 Measured BPM Vertical amplitude
Page 91 and 92: 2.5 Beam position 2 position (cm) 1
Page 93 and 94: L( x0 , t) U 0 ( t) = λ( x0 , t) (
Page 95 and 96:
1 x beam = ) xdtdx Q ∫∫λ ( x,
Page 97 and 98:
0 BPM beam width dependence arrival
Page 99 and 100:
100 Vertical y position sensitiviy
Page 101 and 102:
Such an x-y tilt was measured with
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10 5 head x [mm] 0 tail -5 -5 -4 -3
Page 105 and 106:
3.5 x 10-3 Horizontal Charge Distri
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The problem that could arise due to
Page 109 and 110:
around their zero-crossings in orde
Page 111 and 112:
v i ( i i i t) = A sin(2π f t + θ
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strengths of the peaks seen in Fig.
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algorithm required to select the ph
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Downmixers for EBPM BPM-L BPM-R BPM
Page 119 and 120:
While this option was not built and
Page 121 and 122:
A Peltier element acts as a heat pu
Page 123 and 124:
For the measurement shown in Fig. 7
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2 1.5 1 BC2 x position (mm) 0.5 0 -
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0 BC2 arrival time (ps) 1.5 1 0.5 0
Page 129 and 130:
eality check BC2 PMT EBPM and PMT p
Page 131 and 132:
EBPM and PM positions (mm) 6 5 4 3
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If a limiter or nothing at all is u
Page 135 and 136:
Depending on the arrival-time of th
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20mW to BAM FARADAY 8m 80/20 60mW W
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can be placed anywhere prior to the
Page 141 and 142:
Insulation Peltier element on metal
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using the RF limiter. This might be
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compared. The length of the cable c
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eplaced with fiber. The advantage o
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Photodetector Photodetector Two las
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RF-Lock Box for FLASH MLO Synchroni
Page 153 and 154:
In Fig. 8.3.4, the spectral noise d
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Mixer Output (fs) 40 20 0 -20 MLO R
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For a frame of reference concerning
Page 159 and 160:
(Fig. 9.1.2). This method proved to
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N λ ∞ ∫ ω / ω Δω 9 3 ( ω)
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Finally, we can use this, together
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The highest energy resolution (ΔE/
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Good agreement between the RF chica
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10.3 Out-of-loop Vector Sum The out
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out. This was done in two ways: by
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1.8 1.6 stripline button 1.4 Upstre
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10 Conclusion and Outlook Six disti
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Appendix A The derivation of Eqs. 3
Page 179 and 180:
Solving Eq. 8 for E 1 ’ provides
Page 181 and 182:
Higher order terms and the 3 rd -ha
Page 183 and 184:
∂t ∂V 2 2 ⋅ ΔV 2 1 = T1 '( E
Page 185 and 186:
References [1] P. Castro. “Beam t
Page 187 and 188:
[28] H. Schlarb et al., “Beam bas
Page 189 and 190:
[55] C. Gerth, personal communicati
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