STUDIES OF ENERGY RECOVERY LINACS AT ... - CASA

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3.4.2 Backleg Region The backleg region consists of six 90 ◦ FODO cells. In addition to matching the beam to the undulator, the FODO lattice provides the additional freedom to vary the betatron phase advances [58]. This feature was implemented to allow control of BBU through modification of the recirculation phase advance and is discussed in detail in Section 6.2. The optical cavity chicane provides −0.5 m of momentum compaction, so that from the linac to undulator, the compaction is (+0.2 − 0.5) −0.3 m. Following the optical cavity chicane, a six quadrupole telescope is used to match the transverse beam envelopes to the undulator. Note that during experimental studies of BBU, the performance of the Driver itself, without lasing, was studied. 3.4.3 Energy Recovery Transport Following the undulator, a six quadrupole telescope is used to match the transverse beam envelopes to the second recirculation arc. The endloop is the same as the first, except that in addition to trim quadrupoles and sextupoles, there is a family of octupoles to provide tunable momentum compactions through third order. Following the undulator the electron bunch remains short, however there is a significant momentum spread induced by the lasing process. The transport following the undulator is designed to cleanly transport a beam with up to 10% full relative momentum spread and provide adequate energy compression so as to prevent adia- batic antidamping from generating a prohibitively large momentum spread. 73
3.5 Longitudinal Dynamics This section describes details of the off-crest acceleration/magnetic compression scheme that is used for bunch length compression at the undulator and energy compression at the energy recovered beam dump. 3.5.1 Analogy to Transverse Dynamics To gain a better understanding of longitudinal phase space manipulations, it is helpful to make an analogy to transverse dynamics, which can be more intuitive. Consider the effect of a drift and then of a thin focusing element on the transverse (e.g. horizontal) phase space. The transformation of a particle with an initial displacement (zero angle) due to a drift is given by ⎛ ⎜ ⎝ xf x ′ f ⎞ ⎟ ⎠ = ⎛ ⎜ ⎝ 1 M12 0 1 ⎞ ⎛ ⎟ ⎜ ⎠ ⎝ ±xi 0 ⎞ ⎟ ⎠ = ⎛ ⎜ ⎝ ±xi 0 ⎞ 74 ⎟ ⎠ (3.2) while the transformation of a particle with an initial angle (zero displacement) is given by ⎛ ⎜ ⎝ xf x ′ f ⎞ ⎟ ⎠ = ⎛ ⎜ ⎝ 1 M12 0 1 ⎞ ⎛ ⎟ ⎜ ⎠ ⎝ 0 ±x ′ i ⎞ ⎟ ⎠ = ⎛ ⎜ ⎝ ±M12x ′ i ±x ′ i The effect on the phase space is depicted graphically in Fig. 3.8. ⎞ ⎟ ⎠ (3.3) The transformation of a particle with an initial displacement (zero angle) due to a thin focusing element is given by ⎛ ⎜ ⎝ xf x ′ f ⎞ ⎟ ⎠ = ⎛ ⎜ ⎝ 1 0 M21 1 ⎞ ⎛ ⎟ ⎜ ⎠ ⎝ ±xi 0 ⎞ ⎛ ⎟ ⎜ ⎠ = ⎝ ±xi ±M21xi ⎞ ⎟ ⎠ (3.4) while the transformation of a particle with an initial angle (zero displacement) is given by
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STUDIES OF ENERGY RECOVERY LINACS A
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DEDICATION To my wife Danielle and
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2 CEBAF with Energy Recovery . . .
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5.2 HOM Power . . . . . . . . . . .
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ACKNOWLEDGMENTS First and foremost
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6.1 Summary of the measured effects
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2.10 Illustration of quadrupole sca
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5.1 Successive frames in time (prog
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6.8 A plot of 1/Qeff versus average
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ABSTRACT An energy recovering linac
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CHAPTER 1 Introduction An increasin
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FIG. 1.1: Schematic of a generic li
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FIG. 1.2: A CEBAF 5-cell cavity wit
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The solution to Eq. (1.3) is U(t) =
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y reducing the impedance of HOMs, a
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Despite its success, this method of
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design parameters, most notably ach
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1.4.2 Machine Optics The second cat
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analytic model elucidates many impo
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CHAPTER 2 CEBAF with Energy Recover
Page 41 and 42: FIG. 2.1: Energy versus average cur
Page 43 and 44: FIG. 2.3: Additional hardware insta
Page 45 and 46: FIG. 2.4: A picture of the energy r
Page 47 and 48: dipoles and beam diagnostics such a
Page 49 and 50: FIG. 2.7: Horizontal (red) and vert
Page 51 and 52: FIG. 2.8: Illustration of the cryom
Page 53 and 54: linac and θNL is the RF phase. The
Page 55 and 56: 2.4 Transverse Emittance One of the
Page 57 and 58: where σ2 is the rms beam size meas
Page 59 and 60: eams. The effects of varying the qu
Page 61 and 62: FIG. 2.12: A typical wire scan near
Page 63 and 64: quadratic fit and a multiple regres
Page 65 and 66: ting the data is difficult. Without
Page 67 and 68: primary source of error is measurin
Page 69 and 70: identified, although the phase dela
Page 71 and 72: TABLE 2.3: Comparison of Twiss para
Page 73 and 74: the results of the fits. The vertic
Page 75 and 76: FIG. 2.18: Schematic illustrating t
Page 77 and 78: FIG. 2.19: The GASK signal measured
Page 79 and 80: FIG. 2.20: The measured normalized
Page 81 and 82: CHAPTER 3 The Jefferson Laboratory
Page 83 and 84: FIG. 3.1: Schematic of the 10 kW FE
Page 85 and 86: FIG. 3.2: Layout of the DC photocat
Page 87 and 88: accelerating gradient at the front
Page 89 and 90: eason for making the endloops achro
Page 91: FIG. 3.7: Illustration of path leng
Page 95 and 96: FIG. 3.9: The effect of a thin focu
Page 97 and 98: Under the constraint that each orde
Page 99 and 100: form of beam breakup not only occur
Page 101 and 102: 4.1 The Pillbox Cavity Although the
Page 103 and 104: FIG. 4.2: Electric field (red) and
Page 105 and 106: where the full 4×4 transfer matrix
Page 107 and 108: The threshold is inversely proporti
Page 109 and 110: 4.3 BBU Simulation Codes: Particle
Page 111 and 112: 6. The second pass beam bunch then
Page 113 and 114: which excites it. The BBU instabili
Page 115 and 116: Equation (4.41) is a dispersion rel
Page 117 and 118: FIG. 4.4: Output from MATBBU showin
Page 119 and 120: FIG. 4.5: Setup for measuring cavit
Page 121 and 122: Consequently, depending on the exte
Page 123 and 124: The projection of the beam displace
Page 125 and 126: TABLE 4.1: Experimental measurement
Page 127 and 128: FIG. 4.10: A plot showing the effec
Page 129 and 130: these cryomodules. Modes from these
Page 131 and 132: CHAPTER 5 Experimental Measurements
Page 133 and 134: threshold current - preferably with
Page 135 and 136: occurred at approximately 2 mA of a
Page 137 and 138: FIG. 5.5: FFT of a pure 2106.007 MH
Page 139 and 140: FIG. 5.6: Illustration to show the
Page 141 and 142: 5.4 Measuring the Threshold Current
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for the HOM-beam system and is deri
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FIG. 5.10: Schematic of the experim
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FIG. 5.12: A plot of 1/Qeff versus
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measured HOMs in zone 3, a BTF meas
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FIG. 5.16: HOM voltage measured fro
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FIG. 5.18: A plot of the three valu
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the beam’s response in regions wh
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CHAPTER 6 BBU Suppression: Beam Opt
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FIG. 6.1: Schematic of a FODO cell
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plane [85]. Equations (6.7) and (6.
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6.2.3 Discussion The method of poin
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FIG. 6.3: Beam envelopes (horizonta
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FIG. 6.6: Beam position monitor rea
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FIG. 6.8: A plot of 1/Qeff versus a
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⎛ ⎞ ⎜ ⎝ 0 0 0 0 0 −1/K 0
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FIG. 6.11: A plot of 1/Qeff versus
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FIG. 6.12: Threshold current for no
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FIG. 6.14: Threshold current utiliz
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TABLE 6.1: Summary of the measured
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CHAPTER 7 BBU Suppression: Feedback
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FIG. 7.1: A schematic of the feedba
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FIG. 7.4: A coaxial 3-stub tuner us
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All of these considerations are con
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FIG. 7.6: Generic layout for a feed
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in Section 4.2.1, however, in the p
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FIG. 7.7: The threshold current as
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FIG. 7.8: Threshold current versus
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FIG. 7.10: The threshold current as
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CHAPTER 8 Conclusions The work pres
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le were experimentally measured. Du
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APPENDIX A The Pillbox Cavity Start
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FIG. A.1: A pillbox cavity exhibiti
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Ez(ρ, φ) = ψ(ρ, φ) = E0Jm(γρ
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FIG. B.1: Relationship of the S-par
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FIG. C.1: Impedance and frequency o
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FIG. C.5: Impedance and frequency o
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BIBLIOGRAPHY [1] M. Tigner, Nuovo C
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[22] L. Merminga, in Proceedings of
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[50] C. Hernandez-Garcia et al., in
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[79] L. Merminga et al., in Proceed
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VITA Christopher D. Tennant Christo
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