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

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2 Σ t 0 σ A σ ϕ 2 Σ t Accelerating Section 2 Σ t / 2 Figure 3.2.1 Transformation of arrival-time jitter with an accelerator section followed by a bunch compressor. In Eq. 3.2.1, R 56 is the longitudinal dispersion constant of the chicane, C is the compression factor of the bunch (defined in Sect. 2.3), A is the amplitude of the upstream accelerating voltage, ϕ is the phase of the accelerating gradient, and Σ t0 is the arrival-time jitter upstream of the accelerator section. It makes several approximations: the bunch is short relative to the wavelength of the RF, the initial energy is small compared to the energy after the accelerator section, the incoming energy chirp is small compared to the energy chirp gained in the first accelerator section and the jitter is statistically uncorrelated. It was first published in [25] and a derivation is written in the Appendix A. The first thing to notice about the equation, reading it from left to right, is that the incoming arrival-time jitter, Σ t0 , is compressed in the chicane. The second thing to notice is that at FLASH, the amplitude stability, σ A /A , of the klystron will be more critical than the phase stability, σ ϕ /c 0 k rf , for most typical values of σ A /A and σ ϕ /c 0 k rf . This becomes more apparent when typical values from the first bunch compressor of FLASH (BC2) are inserted into the equation, giving: Σ after BC2 2 ≈ (0.2ps*0.1ps/ps injector ) 2 +( 0.04*5.5ps/% gradient ) 2 + (0.01*2ps/deg phase ) 2 With a compression factor of 10 in the first bunch compressor, the 200 fs injector jitter would be compressed to 20 fs arrival-time jitter after the bunch compressor. The 0.04% gradient stability of the first accelerator section would limit the arrival-time jitter downstream of BC2 to 220 fs. The 0.01 deg phase stability of the first accelerator section would limit the arrival-time jitter downstream of the first bunch compressor (BC2) to 20 fs. Given no additional contributions to arrival-time jitter from the second accelerator section amplitude or phase and further compression of the injector jitter by a factor of 2 in the second bunch compressor, the arrival-time stability at the end of the machine would be limited by the first accelerator section to 220 fs. An improvement by a factor of 10 in the gradient stability would make the arrival-time jitter contributions of the first accelerator section amplitude and phase approximately equal. The arrival-time stability at the end of the machine would then be 30 fs rms. This calculation has, however, ignored the second accelerator section. Because of the assumptions of Eq. 3.2.1, one cannot simply use the equation recursively for the second accelerator section. For the second accelerator section, the incoming energy chirp is not small compared to the outgoing chirp and the incoming energy is not small compared to the outgoing energy. Eq. 3.2.2 describes the arrival-time jitter after the second bunch compressor for a beam that is on-crest in the second 26
accelerator section and it was first published in [26]; the derivation of Eq. 3.2.2 is written in the Appendix A. Σ 2 2 2 1 ⎛ 2 ⎡ E1 ⎤ σ A ⎞ ⎛ E2 − E σ 1 1 1 A ⎞ ⎛ 2 ⎜ ⎟ ⎜ C − ⎜ ⎟ t = Σ 2 t0 + ⎢R1,56 + R2,56 ⎥ + R2,56 + C E 2 c0 A1 E2 c0 A2 C ⎝ ⎣ ⎦ ⎠ ⎝ ⎠ ⎝ σ ϕ 1 c 0 k rf ⎞ ⎟ ⎠ 2 Where the R 1,56 is from the first bunch compressor and R 2,56 is from the second bunch compressor. The RF amplitude, A, and beam energy, E, are given with indices corresponding to whether they refer to the first or second accelerator section. C=C 1*C2 is the compression factor for the combination of both bunch compressors, and σ φ1 is the phase stability of the first accelerator section. When the beam is on-crest in the second accelerator section, judging from Eq. 3.2.2, an arrival-time monitor after the second bunch compressor will measure primarily arrival-time jitter caused by the amplitude fluctuations of the first accelerator section for the following reasons: • Injector jitter will be compressed by both bunch compressors (C 1 =10, C 2 =2) • Arrival-time jitter induced by the first accelerator section amplitude jitter RF will not be compressed in the second chicane. • The R 56 of the second chicane is a factor of 5 smaller than that of the first chicane, so the amplitude jitter of the second accelerator section will make a smaller contribution to the total arrival-time jitter than the amplitude jitter of the first accelerator section. These are the reasons that when a single arrival-time monitor after the second chicane was used to feed back on the amplitude jitter of the first accelerator section, it was able to stabilize the beam arrival-time to within 30 fs [20]. This is possible when the second accelerator section is operated on-crest, but not when it is operated off-crest. When the beam is off-crest in the second accelerator section, the arrival-time jitter from the first accelerator section is compressed in the second chicane making the first and second accelerator section arrival-time jitter contributions more equal after the second bunch compressor. Given off-crest operation in the second accelerator section and a larger R 56 in the second bunch compressor, the amplitude stability of the second accelerator section amplitude becomes almost as important to the timing stability of the beam as that of the first accelerator section. This can partially be seen by using Eq. 3.2.1 recursively for the second bunch compressor, but because the ratio of the incoming energy chirp to the outgoing energy chirp and the ratio of the incoming energy to the outgoing energy are not small, as assumed in the derivation of the equation, the prediction of the equation will be wrong by up to 30%, depending on the machine configuration. In general, because a beam that arrives earlier or later on the falling slope of the RF wave will gain a lesser or greater amount of energy, whenever the accelerator section upstream of a bunch compressor is operated off-crest, it is not advisable to use the energy measurement from in the chicane or the arrival-time measurement from after the bunch compressor to directly feed back on the upstream accelerator section without first taking into account the effect of incoming arrival-time jitter on the quantity that is measured. Although, for large compression factors, the incoming arrival-time jitter may be compressed enough in the chicane that it can be ignored, this is not always the case. It is 27
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: creates a single point-of-failure s
Page 41 and 42: ACC1 ~Gun 3rd ACC2 ACC3ACC4 ACC7 Ac
Page 43 and 44: • The lack of a normal-conducting
Page 45 and 46: ( ) E − E ⎛ E − E ⎜ ⎝ 0 0
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
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35 Measured BPM Vertical amplitude
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2.5 Beam position 2 position (cm) 1
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L( x0 , t) U 0 ( t) = λ( x0 , t) (
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1 x beam = ) xdtdx Q ∫∫λ ( x,
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0 BPM beam width dependence arrival
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100 Vertical y position sensitiviy
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Such an x-y tilt was measured with
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10 5 head x [mm] 0 tail -5 -5 -4 -3
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3.5 x 10-3 Horizontal Charge Distri
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The problem that could arise due to
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around their zero-crossings in orde
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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
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While this option was not built and
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A Peltier element acts as a heat pu
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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
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eality check BC2 PMT EBPM and PMT p
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EBPM and PM positions (mm) 6 5 4 3
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If a limiter or nothing at all is u
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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
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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
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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
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(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
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∂t ∂V 2 2 ⋅ ΔV 2 1 = T1 '( E
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References [1] P. Castro. “Beam t
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[28] H. Schlarb et al., “Beam bas
Page 189 and 190:
[55] C. Gerth, personal communicati
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