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

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1 Introduction Knowing the exact position of an electron beam under the influence of a magnetic field has been at the heart of many important experiments in the history of physics. From the first cathode ray tube that was placed next to a piece of magnetized metal to the highenergy beams of modern accelerators traveling through lattices of powerful electromagnets, the position of the beam under the influence of a magnetic field gives information about the momentum of the beam. High-precision knowledge of the beam momentum can enable higher precision control of the beam. Control of the beam momentum is critical for the stability of both the wavelength and arrival-time of the light pulses generated by free-electron lasers. The measurement of the beam momentum in a free-electron laser with magnetic bunch compressor chicanes is the topic of this thesis. The bending radius, r, of an electron with charge e traveling through a magnetic dipole field perpendicular to the beam direction, B, depends on the momentum, p, of the particle. 1 B = e⋅ (1.1) r p r r v is an equation derived from the Lorentz force law, F = q ( v × B) , and the relation between force and momentum F=dp/dt=pv/r. For a rectangular dipole magnet in which the electron beam enters perpendicularly to one of the magnet’s faces, the path length of the electron’s trajectory is given by l arc = r ⋅α , (1.2)
where α is the bending angle introduced by the magnet. This allows us to write the effective length of the dipole, l eff , in terms of the bending angle, l eff = r ⋅sinα , (1.3) As well as the x offset of the particle from a straight ahead trajectory, 1− cosα x offset = l eff ⋅ . (1.4) sinα We can use equations 1.3 and 1.4 to describe the situation that one finds in a magnetic bunch compressor chicane where, not one, but four magnetic fields are applied, two of which cause the beam to deviate from its straight-ahead trajectory and two of which bring the beam back to its original trajectory (Fig. 1.1). 0.6 Reference orbit in BC2 for 15, 18 and 21 deg 0.5 0.4 d 2 0.3 d 1 d 1 ά x [m] 0.2 0.1 0 x off l eff 1 -0.1 -0.2 -0.3 0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 z [m] Figure 1.1 Magnetic bunch compressor chicane. High-energy particles travel a shorter path than low-energy particles. The path-length of an electron traveling through the symmetric chicane shown above can be expressed by d1 l BC = 4rα + 2⋅ + d 2 (1.5) cosα and the x position in the middle of the chicane is 1− cosα x BC = 2 ⋅ r sinα ⋅ + d1 tanα (1.6) sinα
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: 8.3.6 RF phase measurement drift wi
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 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
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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,
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some locations. Nevertheless, it is
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BPM BAM More power at lower frequen
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arrival-time monitor with and witho
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5.2 Cavity BPM Cavity BPMs (Fig. 5.
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t=0 Z 0 t=L/c Z 0 2L Figure 5.3.1 L
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0.2 nC beam charge and can handle b
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T1-T2=T3 X=T3*c T1 T2 Figure 5.5.2
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None of the designs suffered from a
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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)
Page 163 and 164:
Finally, we can use this, together
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The highest energy resolution (ΔE/
Page 167 and 168:
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
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Solving Eq. 8 for E 1 ’ provides
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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
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[55] C. Gerth, personal communicati
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Measuring the Electron Beam Energy in a Magnetic Bunch ... - DESY

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