STUDIES OF ENERGY RECOVERY LINACS AT ... - CASA

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mode can translate into a transverse displacement at the cavity after recirculation. The recirculated beam induces an HOM voltage which depends on the magnitude and direction of the beam displacement. Thus, the recirculated beam completes the feedback loop which can become unstable if the average beam current exceeds the threshold current for stability. Beam breakup is of particular concern in the design of high average current ERLs utilizing superconducting RF (SRF) technology. If not sufficiently damped by the HOM couplers, dipole modes with quality factors several orders of magnitude higher than in normal conducting cavities can exist, providing a real threat for BBU to develop. The effect of the instability is to limit the average current that can be accelerated, which can severely affect machine performance when this occurs at currents below the designed operational current. 1.2 Superconducting Radio Frequency Technol- ogy While in principle there is nothing that prohibits the use of normal conducting RF cavities for energy recovery, superconducting RF has many advantages which have made it the technology of choice for nearly all ERL designs, past and present. The primary features which make it so attractive are the high quality factor of the accelerating mode and the ability to operate in continuous wave (cw) mode while maintaining relatively high accelerating gradients. The basic building block of the linacs at Jefferson Laboratory’s electron acceler- ators - the Continuous Electron Beam Accelerator Facility (CEBAF) and the 10 kW FEL Upgrade Driver - is the SRF cavity shown in Fig. 1.2. The standard CEBAF style cavity is based on a Cornell University design and consists of five elliptically 5
FIG. 1.2: A CEBAF 5-cell cavity with a waveguide higher-order mode coupler (left) and fundamental power coupler (right). shaped resonators, or cells, which are coupled. The cavity is a standing wave struc- ture and operates in the π-mode with a fundamental frequency of 1497 MHz. The elliptical cell shape prevents multipactoring, which plagued early cavity designs, and also provides good mechanical rigidity to combat the effects of external mechanical vibrations, known as microphonics [2]. Each cavity is equipped with two couplers, a fundamental power coupler (FPC) on one end and an HOM coupler on the other. The cavities are constructed from niobium which becomes superconducting below 9.2 K. Cavities are hermetically paired and installed in cryounits where they are immersed in a liquid helium bath at 2.1 K. A single cryomodule is comprised of four cryounits. Each of the two linacs in CEBAF contain 20 cryomodules, while the FEL Upgrade Driver’s linac consists of 3 cryomodules. A brief introduction to some of the most important figures of merit used to characterize an SRF cavity is given below. 6
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 and 8: 5.2 HOM Power . . . . . . . . . . .
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: FIG. 1.1: Schematic of a generic li
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
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
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FIG. 3.1: Schematic of the 10 kW FE
Page 85 and 86:
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
Page 103 and 104:
FIG. 4.2: Electric field (red) and
Page 105 and 106:
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
Page 131 and 132:
CHAPTER 5 Experimental Measurements
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threshold current - preferably with
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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
Page 145 and 146:
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
Page 151 and 152:
FIG. 5.16: HOM voltage measured fro
Page 153 and 154:
FIG. 5.18: A plot of the three valu
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the beam’s response in regions wh
Page 157 and 158:
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
Page 177 and 178:
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
Page 195 and 196:
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
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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