STUDIES OF ENERGY RECOVERY LINACS AT ... - CASA

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3.5 An achromatic system comprised of four dipoles. . . . . . . . . . . . . 71 3.6 Understanding the layout of the Bates endloop in terms of the achromat in Fig. 3.5. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 71 3.7 Illustration of path length management using correctors embedded in the 180 ◦ dipole magnet. . . . . . . . . . . . . . . . . . . . . . . . . . 72 3.8 The effect of a drift length on a displaced bunch with no initial angle (left) and on a bunch with an initial angle with zero displacement (right). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 75 3.9 The effect of a thin focusing element on a displaced bunch with no initial angle (left) and on a bunch with an initial angle but with zero displacement (right). . . . . . . . . . . . . . . . . . . . . . . . . . . . 76 4.1 The evolution of BBU in the time domain (bottom plot) and frequency domain (top plots). . . . . . . . . . . . . . . . . . . . . . . . . 81 4.2 Electric field (red) and magnetic field (blue) in the ρ−φ plane for a TM110 mode in a pillbox cavity. . . . . . . . . . . . . . . . . . . . . . 84 4.3 A plot of the threshold current versus HOM frequency as described by Eq. (4.21). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 89 4.4 Output from M<strong>AT</strong>BBU showing the results of scanning the frequency in the complex current plane for the horizontal (red) and vertical (green) planes. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 98 4.5 Setup for measuring cavity HOMs of zone 3 in the FEL vault. . . . . 100 4.6 A screenshot of a typical HOM resonance curve. . . . . . . . . . . . . 101 4.7 Schematic of the experimental setup used to measure dipole HOM polarizations. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 103 4.8 Measured response of the 2106 MHz HOM due to vertical (red) and horizontal (blue) displacements through cavity 7. . . . . . . . . . . . 105 4.9 Simulated electric field contours of the 2106 MHz dipole HOM in the 7-cell cavity. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 107 4.10 A plot showing the effect of frequency separation between two polarizations of a single dipole HOM on the threshold current. . . . . . . . 108 xiv
5.1 Successive frames in time (progressing from left to right) from a movie of the synchrotron light monitor in the second endloop at the onset of BBU. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 113 5.2 The Schottky diode assembly showing the directional coupler, attenuator and Schottky diode. . . . . . . . . . . . . . . . . . . . . . . . . 115 5.3 Schematic of the experimental setup for simultaneously measuring the HOM power and voltage from a particular cavity. . . . . . . . . . 117 5.4 A screen shot of an oscilloscope showing the HOM voltage (red) and power (blue) of the 2106.007 MHz HOM in cavity 7 of zone 3 during BBU. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 117 5.5 FFT of a pure 2106.007 MHz signal (top) and FFT of the HOM voltage from cavity 7 during BBU (bottom). . . . . . . . . . . . . . . 118 5.6 Illustration to show the effect of sideband frequencies driving otherwise stable modes unstable. . . . . . . . . . . . . . . . . . . . . . . . 120 5.7 The output from simulations of the HOM voltage squared for 4 modes. The bunch repetition frequency is 1497 MHz and the sidebands generated by 2106 MHz do not drive the other modes. . . . . . . . . . . 121 5.8 The output from simulations of the HOM voltage squared for 4 modes. The bunch repetition frequency is 37.425 MHz and the sidebands generated by 2106 MHz resonantly drive the 1881 MHz and 1786 MHz modes. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 121 5.9 Signal from a beam current monitor at the time of a BBU induced machine trip. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 125 5.10 Schematic of the experimental setup used for the cavity-based beam transfer function measurement. . . . . . . . . . . . . . . . . . . . . . 126 5.11 The resonance curve for the 2106 MHz HOM as a function of average beam current with nominal, decoupled optics. . . . . . . . . . . . . . 127 5.12 A plot of 1/Qeff versus the average beam current from the data in Fig. 5.11. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 128 5.13 The resonance curve for the 2114 MHz HOM as a function of average beam current with nominal, decoupled optics. . . . . . . . . . . . . . 129 xv
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: 2.10 Illustration of quadrupole sca
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
Page 61 and 62: FIG. 2.12: A typical wire scan near
Page 63 and 64: 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
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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