STUDIES OF ENERGY RECOVERY LINACS AT ... - CASA

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Using this process to verify that the reflector is operating correctly, virtually no remnant coupling is observed through the back end of the recirculator. In fact, the coupling introduced from the RF cavities (see Sections 2.2.3 and 3.3) prove to be more of an operational concern [61]. 6.3.2 Measured Effect on the Threshold Current The threshold current was first established to be 1.8 mA and caused by the 2106 MHz mode without the reflector. The reflector was then activated and opera- tion with 5.0 mA of average beam current was achieved with no indications of BBU. Since direct observation was not possible, a BTF measurement of the 2106 MHz mode was performed. The results of the measurement yielded a new threshold current of (9.2 ± 0.4) mA; an increase by a factor of 5.1 (Fig. 6.8). Additional BTF measurements were performed for the 2116 MHz mode (also located in cavity 7) and the 2114 MHz mode (cavity 4). The concern was that by producing a reflection in the betatron planes, these modes which were stabilized for decoupled optics may become unstable. However, the results of the measurements indicate that the modes remained stabilized and did not pose a threat for causing the instability. 6.4 Global Rotation The reflector described in Section 6.3 interchanges horizontal and vertical phase spaces, imaging each identically into the other. This will map a horizontal kick into the vertical plane, and a vertical kick to the horizontal plane, and thus is effective for suppressing BBU driven by modes with these specific polarizations. However, it will equally map a diagonal kick back into a similar diagonal displacement, thus failing to suppress BBU driven by an HOM of arbitrary polarization. Therefore a more robust scheme for BBU suppression can be achieved by generating a 90 ◦ 149
FIG. 6.8: A plot of 1/Qeff versus average beam current for the 2106 MHz mode with the local reflector activated. The best fit line is used to determine that the threshold current is 9.2 mA. rotation of the betatron planes from cavity 7 back to itself. The 4×4 recirculation transfer matrix for a 90 ◦ rotation is completely coupled and the off-diagonal 2×2 matrices are of opposite sign ⎛ ⎜ ⎝ 0 M −M 0 ⎞ 150 ⎟ ⎠ (6.11) From Eq. (6.11), M12 = M34 = 0, M32 = −M14 and the threshold current given by Eq. (4.21) is infinite independent of the mode orientation, α. For a single mode the idea is conceptually simple and is illustrated in Fig. 6.9. If on the first pass an offending mode imparts an angular deflection α, to a bunch, then on the second pass (and after a 90 ◦ rotation), the resultant displacement will be orthogonal to the deflection. Thus the bunch will be unable to couple energy to the mode that caused the deflection. A rotation implemented in a two-pass system effectively
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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
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 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: FIG. 6.6: Beam position monitor rea
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
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
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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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