STUDIES OF ENERGY RECOVERY LINACS AT ... - CASA

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FIG. 7.5: Schematic of the experimental setup using a 3-stub tuner to damp the loaded Q of a mode. systems. Like the cavity-based feedback, a beam-based feedback does not interfere with the machine optics and like beam optical control, the threshold current can, in principle, be increased by an order of magnitude or more. This section describes the results of initial studies concerning the viability of implementing a beam-based feedback system in an ERL and the anticipated effects on the BBU threshold current. 7.2.1 Overview Conceptually, a transverse feedback system is simple. A sensor, or pickup, is used to measure the beam displacement at a location in the machine. A kicker is located downstream and imparts an angular kick to the beam proportional to the offset signal detected at the pickup. The correcting kick may be applied on the same turn or on subsequent revolutions, it may be applied to the same bunch that 167 produced the signal at the pickup or it may act on preceding or following bunches.
All of these considerations are contingent upon the type of machine one is dealing with, the type and nature of the beam instability to control and the signal processing required of the system, among other things. Feedback systems have long been successfully used in storage rings. However, there are fundamental differences in designing a system for an energy recovery linac, namely the fact that the beam spends a relatively short time in the machine. Ideally the feedback system will correct the same bunch that produced the error signal, but in an ERL the beam typically makes only two passes through the machine, requiring that the bunch be corrected on the same turn on which the signal was detected. This imposes stringent requirements on the signal processing time and instrumentation electronics to the extent that such a system may not be practical. Consider, for example, the feedback time budget for the FEL Upgrade Driver. The recirculation time is 433.200 ns. In terms of time management, the ideal placement of the pickup is immediately downstream of zone 4 and the ideal placement of the kicker is immediately upstream of zone 2 and the distance between the two is approximately 50 m. For optimal feedback performance, for each bunch that gets a correcting kick, the error signal used is the one generated by that same bunch - that is, the condition where the feedback time delay, td, is zero. Yet, after taking into account the propagation time for a signal from the pickup to reach the kicker, only a few tens of nanoseconds remain in the time budget for processing the raw BPM signal, generating a suitable error signal and supplying sufficient gain. It is therefore not immediately clear whether adequate suppression can be achieved for td = 0. Using an analytic model of BBU which incorporates the effects of a feedback system and also using the results of a recently developed BBU code to simulate the effects of feedback on the system’s stability, it appears that a bunch-by-bunch feed- 168 back system may be feasible. Section 7.2.2 derives an expression for the threshold
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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
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FIG. 2.1: Energy versus average cur
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FIG. 2.3: Additional hardware insta
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FIG. 2.4: A picture of the energy r
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dipoles and beam diagnostics such a
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FIG. 2.7: Horizontal (red) and vert
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FIG. 2.8: Illustration of the cryom
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linac and θNL is the RF phase. The
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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
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
Page 143 and 144: for the HOM-beam system and is deri
Page 145 and 146: FIG. 5.10: Schematic of the experim
Page 147 and 148: FIG. 5.12: A plot of 1/Qeff versus
Page 149 and 150: measured HOMs in zone 3, a BTF meas
Page 151 and 152: FIG. 5.16: HOM voltage measured fro
Page 153 and 154: FIG. 5.18: A plot of the three valu
Page 155 and 156: the beam’s response in regions wh
Page 157 and 158: CHAPTER 6 BBU Suppression: Beam Opt
Page 159 and 160: FIG. 6.1: Schematic of a FODO cell
Page 161 and 162: plane [85]. Equations (6.7) and (6.
Page 163 and 164: 6.2.3 Discussion The method of poin
Page 165 and 166: FIG. 6.3: Beam envelopes (horizonta
Page 167 and 168: FIG. 6.6: Beam position monitor rea
Page 169 and 170: FIG. 6.8: A plot of 1/Qeff versus a
Page 171 and 172: ⎛ ⎞ ⎜ ⎝ 0 0 0 0 0 −1/K 0
Page 173 and 174: FIG. 6.11: A plot of 1/Qeff versus
Page 175 and 176: FIG. 6.12: Threshold current for no
Page 177 and 178: FIG. 6.14: Threshold current utiliz
Page 179 and 180: TABLE 6.1: Summary of the measured
Page 181 and 182: CHAPTER 7 BBU Suppression: Feedback
Page 183 and 184: FIG. 7.1: A schematic of the feedba
Page 185: FIG. 7.4: A coaxial 3-stub tuner us
Page 189 and 190: FIG. 7.6: Generic layout for a feed
Page 191 and 192: in Section 4.2.1, however, in the p
Page 193 and 194: FIG. 7.7: The threshold current as
Page 195 and 196: FIG. 7.8: Threshold current versus
Page 197 and 198: FIG. 7.10: The threshold current as
Page 199 and 200: CHAPTER 8 Conclusions The work pres
Page 201 and 202: le were experimentally measured. Du
Page 203 and 204: APPENDIX A The Pillbox Cavity Start
Page 205 and 206: FIG. A.1: A pillbox cavity exhibiti
Page 207 and 208: Ez(ρ, φ) = ψ(ρ, φ) = E0Jm(γρ
Page 209 and 210: FIG. B.1: Relationship of the S-par
Page 211 and 212: FIG. C.1: Impedance and frequency o
Page 213 and 214: 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
Page 219 and 220: [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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