STUDIES OF ENERGY RECOVERY LINACS AT ... - CASA

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TABLE 5.1: Comparison of simulation predictions, experimental results and the analytic calculation of the threshold current. Method Threshold Current (mA) Simulation TDBBU 2.1 M<strong>AT</strong>BBU 2.1 ERLBBU 2.1 BI 2.1 Experimental Direct Observation 2.3 ± 0.2 Kicker-based BTF 2.3 ± 0.1 Cavity-based BTF 2.4 ± 0.1 Growth Rates 2.3 ± 0.2 (method 1) 2.3 ± 0.1 2.3 ± 0.1 (method 2) 2.2 ± 0.2 Analytic Analytic Formula 2.1 in different current regimes (above and below the threshold) and working in both the time and frequency domain, there is complete agreement in determining the threshold current. To emphasize the value of the single mode threshold current derived in Sec- tion 4.2, Table 5.1 includes the threshold current as determined by plugging values for the 2106 MHz mode in Eq. (4.21). The analytic formula agrees very well with both simulations and experimental data. The results summarized in Table 5.1 represent the first time BBU simulation codes have been benchmarked with experimental data. The measured data and the simulation predictions agree to within 10%. As a consequence of benchmarking the codes, the validity of the analytic model used to describe BBU, and the threshold current formula in particular, have been confirmed. 137
CHAPTER 6 BBU Suppression: Beam Optical Control 6.1 Overview With the average current limited in the FEL Upgrade Driver to approximately 2 mA, attention is now turned towards implementing suppression techniques. In- sights into how the threshold current can be increased are gained by considering the parametric dependence of the threshold as expressed in Eq. (4.21). There exist four primary means by which to increase the threshold current. First, since the threshold is directly proportional to the beam energy, the injection energy must be increased, or the cryomodule with the unstable mode can be placed in the back end of the linac where the energy is higher. Secondly, the ratio (R/Q) which is a property of the cavity’s geometry must be lowered. These first two methods are not technically feasible given that the cavities are already fabricated and the cryomodule is installed on the beamline. Thirdly, the properties of the mode itself can be modified by low- ering the loaded Q and/or modifying the frequency such that the phase term leads 138
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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
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
Page 117 and 118: FIG. 4.4: Output from MATBBU showin
Page 119 and 120: FIG. 4.5: Setup for measuring cavit
Page 121 and 122: Consequently, depending on the exte
Page 123 and 124: The projection of the beam displace
Page 125 and 126: TABLE 4.1: Experimental measurement
Page 127 and 128: FIG. 4.10: A plot showing the effec
Page 129 and 130: these cryomodules. Modes from these
Page 131 and 132: CHAPTER 5 Experimental Measurements
Page 133 and 134: threshold current - preferably with
Page 135 and 136: occurred at approximately 2 mA of a
Page 137 and 138: FIG. 5.5: FFT of a pure 2106.007 MH
Page 139 and 140: FIG. 5.6: Illustration to show the
Page 141 and 142: 5.4 Measuring the Threshold Current
Page 143 and 144: for the HOM-beam system and is deri
Page 145 and 146: FIG. 5.10: Schematic of the experim
Page 147 and 148: 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: the beam’s response in regions wh
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 and 200: CHAPTER 8 Conclusions The work pres
Page 201 and 202: le were experimentally measured. Du
Page 203 and 204: APPENDIX A The Pillbox Cavity Start
Page 205 and 206: 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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