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tics could not be loaded. Because the quadrupoles were running at strengths (Emax/Einj) = 51 times smaller than in standard CEBAF operations, scanning the quadrupole by tens of Gauss has a negligible effect on the emittance measurement - despite not producing compensatory optics. An expression for the relative change in the beta functions due to a focusing error is given by [42] δβ βo = ∓ βi f 47 sin(2∆ψ) (2.15) where βi is the initial, unperturbed beta function, ∆ψ is the phase advance for a single revolution in the machine starting from the location of βi, f is the focal length of the focusing error and the upper (lower) sign applies to the horizontal (vertical) plane. To first order the betatron phase advances can be determined from the model optics and are 60 ◦ and 145 ◦ for the vertical and horizontal planes, respectively. Assuming a focusing error of 150 G (the extent to which each quadrupole was scanned) gives δβ βo δβ βo = −βi = βi 150 sin(2 · 145 33.365 · 1020 ◦ ) βi(0.004) (2.16) 150 sin(2 · 60 33.365 · 1020 ◦ ) βi(0.004) (2.17) where Eq. (2.16) corresponds to the horizontal plane and Eq. (2.17) corresponds to the vertical plane. For the first pass beam with an initial unperturbed beta function of 100 m, the result of the focusing perturbation caused by not producing compensating optics leads to a contribution of 40 cm to the beta function on the second pass. Because the beta functions are on the order of 35 m, the contribution is approximately 1% and can safely be ignored. Other sources of error include errors in the magnet-to-harp distance, magnet power supplies, quadrupole excitation calibration, and beam energy. However, the
primary source of error is measuring the beam spot diameters with the other sources of error being negligible in comparison [43]. 2.4.4 Emittance Measurement Using Multiple Monitors In addition to the quadrupole scan technique, the emittance can also be measured using multiple wire scanners in conjunction with multiple beam optics. The latter method is used in standard CEBAF operations to measure transverse emit- tances in the injector and in the arcs. In the injector region, a single quadrupole is scanned three times while five downstream wire scanners record the transverse beam sizes. A chicane used to merge the injected beam into the main linac provides a region of dispersion where the energy spread can be measured in addition to the emittance. For the emittance measurement in the arcs, an insertable dump was used to intercept the beam prior to re-entry into the north linac. In this way only the accelerating pass is transported in arc 1 and the emittance is readily measured using standard CEBAF procedures. The measurement uses two wire scanners in each arc. One wire scanner is located in a region of zero dispersion and used to extract the emittance, while the second is located downstream in a region of high dispersion and used to measure the energy spread. The method requires varying the quadrupoles between a location upstream of the wire scanners where the emittance will be measured (referred to as the fit point) and the first wire scanner. To ensure a good measurement, two primary criteria must be satisfied; first, the emittance measurement must be done in a region of zero dispersion and second, the matrix that defines the transport between the location of the fit point to the wire scanners must be well known. A scheme to measure the emittance and energy spread of the second pass beam proved to be too difficult. Hence the only quantitative measurement of 48
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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
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
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: ting the data is difficult. Without
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
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
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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
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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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