STUDIES OF ENERGY RECOVERY LINACS AT ... - CASA

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3.4.2 Backleg Region . . . . . . . . . . . . . . . . . . . . . . . . 73 3.4.3 Energy Recovery Transport . . . . . . . . . . . . . . . . . 73 3.5 Longitudinal Dynamics . . . . . . . . . . . . . . . . . . . . . . . . 74 3.5.1 Analogy to Transverse Dynamics . . . . . . . . . . . . . . 74 3.5.2 Deriving Proper Momentum Compactions . . . . . . . . . 76 4 Theory and Simulation of Multipass BBU . . . . . . . . . . . 79 4.1 The Pillbox Cavity . . . . . . . . . . . . . . . . . . . . . . . . . . 82 4.1.1 TMmn0 Modes . . . . . . . . . . . . . . . . . . . . . . . . . 82 4.2 Derivation of the BBU Threshold Current . . . . . . . . . . . . . 83 4.2.1 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . 89 4.3 BBU Simulation Codes: Particle Tracking . . . . . . . . . . . . . 90 4.3.1 Generic Algorithm . . . . . . . . . . . . . . . . . . . . . . 90 4.3.2 TDBBU . . . . . . . . . . . . . . . . . . . . . . . . . . . . 92 4.3.3 ERLBBU . . . . . . . . . . . . . . . . . . . . . . . . . . . 92 4.4 Alternate Derivation of the BBU Threshold Current . . . . . . . . 93 4.5 BBU Simulation Codes: Eigenvalue Solutions . . . . . . . . . . . . 97 4.5.1 M<strong>AT</strong>BBU . . . . . . . . . . . . . . . . . . . . . . . . . . . 97 4.6 Measuring HOM Parameters . . . . . . . . . . . . . . . . . . . . . 98 4.6.1 RF Measurements of the Zone 3 Cryomodule . . . . . . . . 99 4.6.2 Beam-based HOM Polarization Measurements . . . . . . . 101 4.7 Validity of Single Mode Threshold Current Formula . . . . . . . . 106 4.8 Results of BBU Simulations . . . . . . . . . . . . . . . . . . . . . 109 4.8.1 FEL Upgrade Without Zone 3 . . . . . . . . . . . . . . . . 109 4.8.2 FEL Upgrade With Zone 3 . . . . . . . . . . . . . . . . . . 110 5 Experimental Measurements of Multipass BBU . . . . . . . . 112 5.1 Overview . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 113 vi
5.2 HOM Power . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 114 5.2.1 Schottky Diodes . . . . . . . . . . . . . . . . . . . . . . . . 114 5.2.2 Observations of BBU . . . . . . . . . . . . . . . . . . . . . 115 5.3 HOM Voltage . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 116 5.3.1 Stable Modes Being Driven Unstable . . . . . . . . . . . . 118 5.4 Measuring the Threshold Current . . . . . . . . . . . . . . . . . . 122 5.4.1 Evolution of the HOM Voltage . . . . . . . . . . . . . . . . 122 5.4.2 Direct Observation . . . . . . . . . . . . . . . . . . . . . . 124 5.4.3 Beam Transfer Function . . . . . . . . . . . . . . . . . . . 124 5.4.4 Growth Rate Measurements . . . . . . . . . . . . . . . . . 130 5.5 Characterizing the Beam Optics . . . . . . . . . . . . . . . . . . . 133 5.6 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 136 6 BBU Suppression: Beam Optical Control . . . . . . . . . . . . 138 6.1 Overview . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 138 6.2 Point-to-Point Focusing . . . . . . . . . . . . . . . . . . . . . . . . 139 6.2.1 Implementing Point-to-Point Focusing . . . . . . . . . . . 140 6.2.2 Measured Effect on the Threshold Current . . . . . . . . . 142 6.2.3 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . 144 6.3 Local Reflection . . . . . . . . . . . . . . . . . . . . . . . . . . . . 144 6.3.1 Implementing a Local Reflector . . . . . . . . . . . . . . . 145 6.3.2 Measured Effect on the Threshold Current . . . . . . . . . 149 6.4 Global Rotation . . . . . . . . . . . . . . . . . . . . . . . . . . . . 149 6.4.1 Implementing a Global Rotation . . . . . . . . . . . . . . . 151 6.4.2 Measured Effect on the Threshold Current . . . . . . . . . 153 6.4.3 Simulations of Coupled Optics Suppression Techniques . . 154 6.5 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 160 vii
Page 1 and 2: STUDIES OF ENERGY RECOVERY LINACS A
Page 3 and 4: DEDICATION To my wife Danielle and
Page 5: 2 CEBAF with Energy Recovery . . .
Page 9 and 10: ACKNOWLEDGMENTS First and foremost
Page 11 and 12: 6.1 Summary of the measured effects
Page 13 and 14: 2.10 Illustration of quadrupole sca
Page 15 and 16: 5.1 Successive frames in time (prog
Page 17 and 18: 6.8 A plot of 1/Qeff versus average
Page 19 and 20: ABSTRACT An energy recovering linac
Page 21 and 22: CHAPTER 1 Introduction An increasin
Page 23 and 24: FIG. 1.1: Schematic of a generic li
Page 25 and 26: FIG. 1.2: A CEBAF 5-cell cavity wit
Page 27 and 28: The solution to Eq. (1.3) is U(t) =
Page 29 and 30: y reducing the impedance of HOMs, a
Page 31 and 32: Despite its success, this method of
Page 33 and 34: design parameters, most notably ach
Page 35 and 36: 1.4.2 Machine Optics The second cat
Page 37 and 38: analytic model elucidates many impo
Page 39 and 40: 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
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where σ2 is the rms beam size meas
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eams. The effects of varying the qu
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FIG. 2.12: A typical wire scan near
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quadratic fit and a multiple regres
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ting the data is difficult. Without
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primary source of error is measurin
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identified, although the phase dela
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TABLE 2.3: Comparison of Twiss para
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the results of the fits. The vertic
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FIG. 2.18: Schematic illustrating t
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FIG. 2.19: The GASK signal measured
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FIG. 2.20: The measured normalized
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CHAPTER 3 The Jefferson Laboratory
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FIG. 3.1: Schematic of the 10 kW FE
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FIG. 3.2: Layout of the DC photocat
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accelerating gradient at the front
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eason for making the endloops achro
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FIG. 3.7: Illustration of path leng
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3.5 Longitudinal Dynamics This sect
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FIG. 3.9: The effect of a thin focu
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Under the constraint that each orde
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form of beam breakup not only occur
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4.1 The Pillbox Cavity Although the
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FIG. 4.2: Electric field (red) and
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where the full 4×4 transfer matrix
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The threshold is inversely proporti
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4.3 BBU Simulation Codes: Particle
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6. The second pass beam bunch then
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which excites it. The BBU instabili
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Equation (4.41) is a dispersion rel
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FIG. 4.4: Output from MATBBU showin
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FIG. 4.5: Setup for measuring cavit
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Consequently, depending on the exte
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The projection of the beam displace
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TABLE 4.1: Experimental measurement
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FIG. 4.10: A plot showing the effec
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these cryomodules. Modes from these
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CHAPTER 5 Experimental Measurements
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threshold current - preferably with
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occurred at approximately 2 mA of a
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FIG. 5.5: FFT of a pure 2106.007 MH
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FIG. 5.6: Illustration to show the
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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
Page 221 and 222:
[79] L. Merminga et al., in Proceed
Page 223 and 224:
VITA Christopher D. Tennant Christo
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