STUDIES OF ENERGY RECOVERY LINACS AT ... - CASA

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• through the largest SRF environment (312 cavities) • with the highest final-to-injector energy ratio (51:1) 8.2 Studies of Beam Breakup The form of beam breakup discussed in this dissertation was first observed in an independent orbit recirculating linac (SCA) and then in a microtron (MUSL-2) in 1977. In 2004 BBU developed in the FEL Upgrade Driver and represents the first observations of the instability in an energy recovering linac. Beam breakup is well understood from a theoretical point of view and now, as result of the work presented in this dissertation, from an experimental point of view. The primary contribution is the successful benchmarking of BBU simulation codes with experimental data with agreement to within 10%. These codes are a valuable tool whose results dictate many of the most important parameters in the design of future high average current ERLs, such as HOM damping requirements of the SRF cavities and the means by which it is achieved and the choice of machine optics. With a number of design proposals for ERL drivers on the horizon, it is vitally important that the BBU codes can be applied with confidence. In the process of benchmarking the codes, several important auxiliary contri- butions were made. First, the validity of the analytic model used to describe BBU has been demonstrated in small machines where HOM frequencies do not overlap. In particular, the threshold current formula for a single cavity containing a single mode, if applied correctly, has been proven to describe BBU with a high degree of accuracy. Secondly, several important experimental techniques were introduced and applied to BBU-related measurements. 181 To adequately benchmark the codes, as many of the input parameters as possi-
le were experimentally measured. Due to the nature of BBU - that it involves the properties of the beam (average current and energy), the machine lattice (transfer matrices) and the properties of the HOMs (frequency, QL, (R/Q) and polarization) - a number of different measurements were required. There also is the necessity for techniques to accurately measure the threshold current. The beam transfer func- tion measurement has been used for many decades and has now been successfully applied, along with measuring the HOM growth rates, to measure the threshold current. It is important to keep in mind that BBU work reported in this dissertation addresses a specific regime; namely, a machine with only a few very high Q dipole modes which are localized in a single cryomodule in a relatively compact machine. Furthermore, in frequency space, the modes are well separated so that for decoupled optics, coupling between modes is not an issue. Because of these characteristics, all of the suppression techniques implemented were, to varying degrees, successful at increasing the threshold current for stability. Three different beam optical suppression techniques were implemented; point- to-point focusing, a rotator and a local reflector. The first two were able to suppress BBU due to the 2106 MHz mode completely, while the local reflector increased the threshold by a factor of 5.1. The latter two techniques are notable in that they required the introduction of strong transverse coupling in the electron beam optics. Additionally, two different cavity-based feedback systems were developed and proved to be successful at increasing the threshold current by factors of a few. Finally, some initial studies of the feasibility of a beam-based feedback system for an ERL were presented. Such a beam-based system incorporates the advantages of both beam optical control and cavity-based feedback methods of suppression. In addition to showing the validity of a modified threshold current formula to include 182 feedback, simulation results also explored the behavior of the BBU threshold current
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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
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FIG. 1.1: Schematic of a generic li
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FIG. 1.2: A CEBAF 5-cell cavity wit
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The solution to Eq. (1.3) is U(t) =
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y reducing the impedance of HOMs, a
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Despite its success, this method of
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design parameters, most notably ach
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1.4.2 Machine Optics The second cat
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analytic model elucidates many impo
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CHAPTER 2 CEBAF with Energy Recover
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FIG. 2.1: Energy versus average cur
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FIG. 2.3: Additional hardware insta
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FIG. 2.4: A picture of the energy r
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dipoles and beam diagnostics such a
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FIG. 2.7: Horizontal (red) and vert
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FIG. 2.8: Illustration of the cryom
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linac and θNL is the RF phase. The
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2.4 Transverse Emittance One of the
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where σ2 is the rms beam size meas
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eams. The effects of varying the qu
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FIG. 2.12: A typical wire scan near
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quadratic fit and a multiple regres
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ting the data is difficult. Without
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primary source of error is measurin
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identified, although the phase dela
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TABLE 2.3: Comparison of Twiss para
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the results of the fits. The vertic
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FIG. 2.18: Schematic illustrating t
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FIG. 2.19: The GASK signal measured
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FIG. 2.20: The measured normalized
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CHAPTER 3 The Jefferson Laboratory
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FIG. 3.1: Schematic of the 10 kW FE
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FIG. 3.2: Layout of the DC photocat
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accelerating gradient at the front
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eason for making the endloops achro
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FIG. 3.7: Illustration of path leng
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3.5 Longitudinal Dynamics This sect
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FIG. 3.9: The effect of a thin focu
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Under the constraint that each orde
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form of beam breakup not only occur
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4.1 The Pillbox Cavity Although the
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FIG. 4.2: Electric field (red) and
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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
Page 149 and 150: 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
Page 155 and 156: the beam’s response in regions wh
Page 157 and 158: CHAPTER 6 BBU Suppression: Beam Opt
Page 159 and 160: FIG. 6.1: Schematic of a FODO cell
Page 161 and 162: plane [85]. Equations (6.7) and (6.
Page 163 and 164: 6.2.3 Discussion The method of poin
Page 165 and 166: FIG. 6.3: Beam envelopes (horizonta
Page 167 and 168: FIG. 6.6: Beam position monitor rea
Page 169 and 170: FIG. 6.8: A plot of 1/Qeff versus a
Page 171 and 172: ⎛ ⎞ ⎜ ⎝ 0 0 0 0 0 −1/K 0
Page 173 and 174: FIG. 6.11: A plot of 1/Qeff versus
Page 175 and 176: FIG. 6.12: Threshold current for no
Page 177 and 178: FIG. 6.14: Threshold current utiliz
Page 179 and 180: TABLE 6.1: Summary of the measured
Page 181 and 182: CHAPTER 7 BBU Suppression: Feedback
Page 183 and 184: FIG. 7.1: A schematic of the feedba
Page 185 and 186: FIG. 7.4: A coaxial 3-stub tuner us
Page 187 and 188: All of these considerations are con
Page 189 and 190: FIG. 7.6: Generic layout for a feed
Page 191 and 192: in Section 4.2.1, however, in the p
Page 193 and 194: FIG. 7.7: The threshold current as
Page 195 and 196: FIG. 7.8: Threshold current versus
Page 197 and 198: FIG. 7.10: The threshold current as
Page 199: CHAPTER 8 Conclusions The work pres
Page 203 and 204: APPENDIX A The Pillbox Cavity Start
Page 205 and 206: FIG. A.1: A pillbox cavity exhibiti
Page 207 and 208: Ez(ρ, φ) = ψ(ρ, φ) = E0Jm(γρ
Page 209 and 210: FIG. B.1: Relationship of the S-par
Page 211 and 212: 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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