STUDIES OF ENERGY RECOVERY LINACS AT ... - CASA

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7 BBU Suppression: Feedback Mechanisms . . . . . . . . . . . . 162 7.1 Cavity-based Feedback . . . . . . . . . . . . . . . . . . . . . . . . 163 7.1.1 Active Q-damping Circuit . . . . . . . . . . . . . . . . . . 163 7.1.2 Passive Q-damping with a Stub Tuner . . . . . . . . . . . 164 7.1.3 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . 166 7.2 Beam-based Feedback . . . . . . . . . . . . . . . . . . . . . . . . . 166 7.2.1 Overview . . . . . . . . . . . . . . . . . . . . . . . . . . . . 167 7.2.2 Analytic Model of BBU with Feedback . . . . . . . . . . . 169 7.2.3 BBU Code with Feedback . . . . . . . . . . . . . . . . . . 172 7.2.4 Simulation Results . . . . . . . . . . . . . . . . . . . . . . 175 7.2.5 Conclusions and Implications . . . . . . . . . . . . . . . . 177 8 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 180 8.1 CEBAF with Energy Recovery . . . . . . . . . . . . . . . . . . . . 180 8.2 Studies of Beam Breakup . . . . . . . . . . . . . . . . . . . . . . . 181 8.3 Future Work . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 183 APPENDIX A The Pillbox Cavity . . . . . . . . . . . . . . . . . . . . . . . . . . . 184 APPENDIX B Network Analyzer . . . . . . . . . . . . . . . . . . . . . . . . . . . . 189 APPENDIX C Zone 3 HOM Impedances and Frequencies . . . . . . . . . . . . . 191 Bibliography . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 196 Vita . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 204 viii
ACKNOWLEDGMENTS First and foremost I must thank my committee for their wise counsel and guidance over the past several years. It is incumbent upon a student’s advisors to choose an appropriate topic of research, and I could not have asked for a more intriguing and rewarding topic to study than the one presented in this dissertation. Specifically I would like to thank David Douglas who, being the first person I met at Jefferson Laboratory, has literally been there for me from day one. Despite his eternal pessimism, it has been a privilege to learn from one of the best in the “ERL business”. I would also like to thank Lia Merminga, whose eternal optimism, steadfastness and demand for perfection have ultimately led to this dissertation. And while their work has largely been behind the scene, I am equally grateful to Fred Dylla and Keith Griffioen for their guidance and quiet leadership. Although we worked less than three years together, the results presented in this dissertation would not have been possible without Eduard Pozdeyev. I gratefully acknowledge his unwavering support, guidance and friendship during the course of my studies. I suspect there have never been two people who have devoted so much time as we did looking at a screen - computer, network analyzer, spectrum analyzer or oscilloscope - over the course of three years. I must also thank Raphael Littauer, with whom I had the great privilege to work under while doing research as an undergraduate. The wealth of information which he shared so enthusiastically with me, in addition to his charming personality and pleasant demeanor, greatly influenced my decision to pursue a career in the field of accelerator physics. There are a number of other individuals whose help over the past several years has been indispensable and I am grateful to them all. They are Kevin Beard, Steve Benson, Jim Coleman, Kevin Jordan, Geoffrey Krafft, Tom Powers, Richard Walker, Haipeng Wang and Byung Yunn from Jefferson Laboratory, Stefan Simrock from DESY, Todd Smith from Stanford and John Dirk Walecka from The College of William and Mary. Thank you. ix
Page 1 and 2: STUDIES OF ENERGY RECOVERY LINACS A
Page 3 and 4: DEDICATION To my wife Danielle and
Page 5 and 6: 2 CEBAF with Energy Recovery . . .
Page 7: 5.2 HOM Power . . . . . . . . . . .
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
Page 57 and 58: where σ2 is the rms beam size meas
Page 59 and 60:
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
Page 215 and 216:
BIBLIOGRAPHY [1] M. Tigner, Nuovo C
Page 217 and 218:
[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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