STUDIES OF ENERGY RECOVERY LINACS AT ... - CASA

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FIG. 2.11: A 3-wire scanner oriented at 45 ◦ with respect to the horizontal plane. In order to get sufficient resolution of the beam sizes, the horizontally focusing quadrupole at 2L21 was scanned to extract the horizontal emittance and the verti- cally focusing quadrupole at 2L22 was scanned to extract the vertical emittance. A 3-wire scanner - installed approximately 30 cm upstream of the dipole magnet used to deflect the energy recovered beam to the dump - was used to measure beam sizes. An actuator drives the wire scanner which is mounted at an angle of 45 ◦ with respect to the horizontal axis. Using a 3-wire scanner (to measure x, x-y, y profiles) each scan yielded six distinct peaks (3 wires × 2 beams). Initially, there was some con- cern as to how to differentiate each peak and assign them to the appropriate beam. However it soon became clear that the energy recovered beam (56 MeV or 20 MeV, depending on the injector setup) did not produce nearly as high, sharp peaks as the accelerated beam (1056 MeV or 1020 MeV). This fact was easily confirmed by using dipole correctors to locally steer the beam and identifying the displaced peaks with the lower energy beam. A typical scan is shown in Fig. 2.12. Because the capabil- ity to automatically extract beam sigmas from the wire scans did not exist at the 41
FIG. 2.12: A typical wire scan near the extraction region showing six distinct peaks as a result from a 3-wire scanner passing through two co-propagating beams. time of the experiment, analysis was performed off-line. This resulted in unforeseen difficulties which will be discussed in Section 2.4.3. The data analysis program Igor Pro [40] was used to analyze the raw wire scans. The program has the feature that only regions selected by the user are used for curve-fitting. This is convenient for the wire scans since there are multiple peaks and also because there is the possibility of peaks which are partially merged. The program applies a Gaussian fit to the data of the form y(x) = A √ 2πσ e − x−B √ 2σ 2 42 (2.14) To account for the effect of the 45 ◦ angle of the wire scanner on the x and y profiles (the x-y profile requires no correction) the extracted sigmas are divided by a factor of √ 2.
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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 . . . . . . . . . . .
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 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: eams. The effects of varying the qu
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
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
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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
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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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