STUDIES OF ENERGY RECOVERY LINACS AT ... - CASA
STUDIES OF ENERGY RECOVERY LINACS AT ... - CASA STUDIES OF ENERGY RECOVERY LINACS AT ... - CASA
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 MATBBU . . . . . . . . . . . . . . . . . . . . . . . . . . . 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
3.4.2 Backleg Region . . . . . . . . . . . . . . . . . . . . . . . . 73<br />
3.4.3 Energy Recovery Transport . . . . . . . . . . . . . . . . . 73<br />
3.5 Longitudinal Dynamics . . . . . . . . . . . . . . . . . . . . . . . . 74<br />
3.5.1 Analogy to Transverse Dynamics . . . . . . . . . . . . . . 74<br />
3.5.2 Deriving Proper Momentum Compactions . . . . . . . . . 76<br />
4 Theory and Simulation of Multipass BBU . . . . . . . . . . . 79<br />
4.1 The Pillbox Cavity . . . . . . . . . . . . . . . . . . . . . . . . . . 82<br />
4.1.1 TMmn0 Modes . . . . . . . . . . . . . . . . . . . . . . . . . 82<br />
4.2 Derivation of the BBU Threshold Current . . . . . . . . . . . . . 83<br />
4.2.1 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . 89<br />
4.3 BBU Simulation Codes: Particle Tracking . . . . . . . . . . . . . 90<br />
4.3.1 Generic Algorithm . . . . . . . . . . . . . . . . . . . . . . 90<br />
4.3.2 TDBBU . . . . . . . . . . . . . . . . . . . . . . . . . . . . 92<br />
4.3.3 ERLBBU . . . . . . . . . . . . . . . . . . . . . . . . . . . 92<br />
4.4 Alternate Derivation of the BBU Threshold Current . . . . . . . . 93<br />
4.5 BBU Simulation Codes: Eigenvalue Solutions . . . . . . . . . . . . 97<br />
4.5.1 M<strong>AT</strong>BBU . . . . . . . . . . . . . . . . . . . . . . . . . . . 97<br />
4.6 Measuring HOM Parameters . . . . . . . . . . . . . . . . . . . . . 98<br />
4.6.1 RF Measurements of the Zone 3 Cryomodule . . . . . . . . 99<br />
4.6.2 Beam-based HOM Polarization Measurements . . . . . . . 101<br />
4.7 Validity of Single Mode Threshold Current Formula . . . . . . . . 106<br />
4.8 Results of BBU Simulations . . . . . . . . . . . . . . . . . . . . . 109<br />
4.8.1 FEL Upgrade Without Zone 3 . . . . . . . . . . . . . . . . 109<br />
4.8.2 FEL Upgrade With Zone 3 . . . . . . . . . . . . . . . . . . 110<br />
5 Experimental Measurements of Multipass BBU . . . . . . . . 112<br />
5.1 Overview . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 113<br />
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