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Superconducting Linac) machine [27]. Most recently, in 2004 beam breakup was observed for the first time in an ERL at the Jefferson Laboratory FEL Upgrade Driver [28]. 1.5 Outline The majority of the proposed applications for ERLs require an order of magnitude higher average beam current and/or an order of magnitude higher beam energy than has currently been demonstrated. Making these extrapolations raises many unanswered questions. The aim of this dissertation is to address issues with respect to both beam energy and average beam current. Chapter 2 describes an experiment that successfully energy recovered the beam in the CEBAF accelerator. By doing so, issues related to the energy recovery of a high energy beam and the preservation of beam quality of two co-propagating beams through a large-scale transport channel were addressed. In addition, operation with a lowered injection energy was demonstrated, thereby showing the viability of a high maximum-to-injector energy ratio (Emax/Einj) of 51:1. The remaining chapters are dedicated to studying the effects of high average current, specifically the multipass beam breakup instability, in Jefferson Labora- tory’s ERL-based FEL Upgrade Driver. Chapter 3 provides an overview of the Driver. The Upgrade’s predecessor, the IR FEL Demo, set the standard for ERL light sources by achieving a world-record (at the time) 2 kW of average laser power while also serving as a user facility. With the 10 kW FEL Upgrade, the frontier of energy recovering linacs continues to expand. Currently, the Upgrade Driver is the most substantial demonstration of energy recovery in the world, having recovered in excess of 1 MW of beam power. Chapter 4 derives an analytic model for BBU. Although relatively simple, the 17
analytic model elucidates many important features of the instability and yields a formula for the threshold current for beam stability. Application of this formula is restricted to simple systems (one cavity containing one HOM) and so it is neces- sary to use computer simulation codes to analyze more complex systems. A brief overview of three BBU codes developed at Jefferson Laboratory is given. Microwave measurements to characterize the HOMs in the FEL cryomodules were performed and used as inputs to the simulation codes. The results predict the onset of the BBU instability in the Upgrade Driver at 2 mA - well below the design operating current of 10 mA. Chapter 5 presents the results of experimental measurements to characterize BBU which was observed in the FEL Upgrade first in 2004. The primary goal of the measurements was to benchmark BBU simulation codes with experimental data. To that end, several methods to measure the threshold current for stability were developed. The beam transfer function measurement is described and shown to be a particularly useful technique as it can be used to extract the threshold current for a system while working in a regime where the beam is stable. This is in contrast to the method of measuring growth rates, which requires working in the regime where the beam is unstable. Together, however, these two techniques provide a complementary set of measurements. The measured threshold currents and the threshold current predicted from simulations were shown to agree to within 10% which represents the first time the codes have been benchmarked with experimental data. With the knowledge that BBU poses a threat to beam operations, Chapter 6 and Chapter 7 describe several BBU suppression techniques that were demonstrated - all with varying degrees of success. Chapter 6 discusses beam optical suppression techniques that require modifying the electron beam optics in a way so as to prevent the beam from coupling as strongly to harmful HOMs. These include implementing point-to-point focusing which is 18
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 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: 1.4.2 Machine Optics The second cat
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 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
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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
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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
Page 151 and 152:
FIG. 5.16: HOM voltage measured fro
Page 153 and 154:
FIG. 5.18: A plot of the three valu
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the beam’s response in regions wh
Page 157 and 158:
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
Page 177 and 178:
FIG. 6.14: Threshold current utiliz
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TABLE 6.1: Summary of the measured
Page 181 and 182:
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
Page 213 and 214:
FIG. C.5: Impedance and frequency o
Page 215 and 216:
BIBLIOGRAPHY [1] M. Tigner, Nuovo C
Page 217 and 218:
[22] L. Merminga, in Proceedings of
Page 219 and 220:
[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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