STUDIES OF ENERGY RECOVERY LINACS AT ... - CASA

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TABLE 2.4: Fractional energy spread measured at various locations in the machine with the injector set to 56 MeV. Location ∆E/E (10 −3 ) Energy (MeV) Injector 0.32 ± 0.01 56 Arc 1 0.0080 ± 0.0023 556 Arc 2 0.020 ± 0.0018 1056 TABLE 2.5: Fractional energy spread measured at various locations in the machine with the injector set to 20 MeV. Location ∆E/E (10 −3 ) Energy (MeV) Injector 0.15 ± 0.01 20 Arc 1 0.0072 ± 0.0010 520 Arc 2 0.0100 ± 0.0014 1020 For example, with an injection energy of 20 MeV, the intrinsic fractional energy spread is 0.15 × 10 −3 . With appropriate scaling, and for a perfectly phased linac, the arc 1 energy spread is expected to be [48] ∆E = E 520 ∆E E 20 2 20 + 520 δφ4 2 55 (2.19) where δφ is the rms bunch length in radians. Using the measured data, the contribution to the energy spread from the bunch length can be calculated. Plugging in values and solving for the bunch length yields 0.14 ◦ (rms). The expected energy spread in arc 2 can be calculated using Eq. (2.19) by modifying the energy scaling factor from (20/520) to (20/1020). The result is 0.0052 × 10 −3 and is 74% smaller than the measured value. The effect of RF crest phasing errors can cause increases in the observed fractional energy spread and can account for this discrepancy. The effect is illustrated in Fig. 2.18 and described by ∆E = E cos(φo + δφ) − cos(φo − δφ) (2.20) where φo is the error in RF phase relative to on-crest acceleration. Equation (2.20)
FIG. 2.18: Schematic illustrating the effect of an RF crest phasing error on the fractional energy spread. can be rewritten more conveniently as 56 ∆E = 2 sin φo sin δφ (2.21) E phase Assuming a 0.06 ◦ RF crest phasing error and adding this contribution to to the expected relative energy spread in arc 2 yields a value of 0.02 × 10 −3 which agrees with the measured data. The 56 MeV case can be analyzed in much the same manner. It turns out, however, that the relative energy spread measured in arc 1 is much less than the expected value (0.033 × 10 −3 ). Because this expected value is based on a perfectly phased linac, there are no mechanisms which can account for the discrepancy and this may represent a poor data point. The expected energy spread in arc 2 can be calculated with ∆E = E 1056 ∆E E 56 2 56 + 1056 δφ4 + 2 ∆E E phase (2.22)
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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
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
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: the results of the fits. The vertic
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
Page 83 and 84: FIG. 3.1: Schematic of the 10 kW FE
Page 85 and 86: FIG. 3.2: Layout of the DC photocat
Page 87 and 88: accelerating gradient at the front
Page 89 and 90: eason for making the endloops achro
Page 91 and 92: FIG. 3.7: Illustration of path leng
Page 93 and 94: 3.5 Longitudinal Dynamics This sect
Page 95 and 96: FIG. 3.9: The effect of a thin focu
Page 97 and 98: Under the constraint that each orde
Page 99 and 100: form of beam breakup not only occur
Page 101 and 102: 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
Page 107 and 108: The threshold is inversely proporti
Page 109 and 110: 4.3 BBU Simulation Codes: Particle
Page 111 and 112: 6. The second pass beam bunch then
Page 113 and 114: which excites it. The BBU instabili
Page 115 and 116: Equation (4.41) is a dispersion rel
Page 117 and 118: FIG. 4.4: Output from MATBBU showin
Page 119 and 120: FIG. 4.5: Setup for measuring cavit
Page 121 and 122: Consequently, depending on the exte
Page 123 and 124: 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
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[22] L. Merminga, in Proceedings of
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[50] C. Hernandez-Garcia et al., in
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[79] L. Merminga et al., in Proceed
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VITA Christopher D. Tennant Christo
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