STUDIES OF ENERGY RECOVERY LINACS AT ... - CASA

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FIG. 2.13: A schematic of the 2L21 and 2L22 regions of CEBAF and the location of the quadrupoles used to measure the emittance. 2.4.3 Data Analysis Scanning the quadrupole at 2L22 to measure the vertical emittance constitutes a simple quadrupole-drift scheme. Based on simulated emittance measurements using design optics, measuring the horizontal emittance using the 2L22 quadrupole would require huge changes in field strength which create very large beta functions downstream. To remedy the problem, the quadrupole at 2L21 was used to measure the horizontal emittance. During the experiment a new cryomodule installed in the slot between the 2L21 and 2L22 quadrupoles was being commissioned. During emittance measurements the cavities in the cryomodule were set to zero accelerating gradient thereby effectively making the cryomodule a drift space. Consequently, the horizontal emittance is based on a quadrupole-drift-quadrupole-drift scheme where the 2L22 quadrupole remains at a fixed field and the 2L21 quadrupole strength is varied. Figure 2.13 shows a layout of the region. In terms of the analysis in Section 2.4.1, Eqs. (2.7), (2.8) and (2.9) remain the same and only Eq. (2.10) is modified to reflect the new beam line configuration. While the preceding analysis has modeled the quadrupoles as thin lenses, the program used to fit the experimental data was modified to model a thick lens quadrupole. The major difference in terms of analysis is that now, not only does the M11 transfer matrix element depend on the quadrupole strength, but so too does the M12 element. From Eq. (2.9) this rules out being able to perform a simple 43
quadratic fit and a multiple regression fit is required. The data for the four emittance measurements - two transverse planes (vertical and horizontal) for each of the two injector energy setups - are presented in Fig. 2.14 and Fig. 2.15. Before discussing the specifics of each measurement, some general comments are in order. Each plot displays the beam size squared versus the magnification, or M11 matrix element. The red data points in each plot represent the data on which the multiple-regression fit is being performed, whereas the blue data points represent those points which have been omitted (for reasons discussed below). The error bars on the data points are the errors associated with extracting the beam sizes from the raw wire scans. Horizontal Emittance: Einj= 56 MeV The limited number of data points reflects the fact that this was the first at- tempt at an emittance measurement. As with all future emittance measurements there was some local steering required to ensure that the signal of interest from the wire scan was not overlapping an adjacent peak. Despite the limited data the beta function passed through a minimum, which is critical for getting a good fit with a quadratic function. The leftmost data point - corresponding to a quadrupole strength furthest from the nominal set point - was omitted in the fit. The rea- son is that a fit on all data points results in an unphysical solution, namely ɛ 2 g < 0. Omitting the point results in a physically realizable emittance. Judiciously omitting data points which lead to nonsensical emittances was often required in subsequent measurements. Vertical Emittance: Einj = 56 MeV Despite the large number of data points, because the quadrupole was not scanned far enough to allow the beta function to pass through a minimum, fit- 44
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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
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 and 60: eams. The effects of varying the qu
Page 61: FIG. 2.12: A typical wire scan near
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
Page 111 and 112: 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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