STUDIES OF ENERGY RECOVERY LINACS AT ... - CASA
STUDIES OF ENERGY RECOVERY LINACS AT ... - CASA STUDIES OF ENERGY RECOVERY LINACS AT ... - CASA
polarization and (2) to determine if a global rotation is more robust in its ability to increase the threshold current than a local reflector. Before discussing the details of each case, a brief explanation of how the sim- ulations were performed is required. Initially, all of the fourteen measured dipole HOMs in each of the eight cavities of zone 3 were simulated for each of the three machine optics. Dipole HOMs were then removed according to their impedance, (R/Q)QL, the lowest impedance modes being removed first, so that for the case of a single dipole HOM per cavity only the mode with the highest impedance is simulated. Each dipole HOM is assumed to be comprised of two orthogonal polar- izations. These polarizations are then rotated by an angle with standard deviations of (0, 5, 10, 15, 20, 25, 30, 35, 40, 45) ◦ . A total of 140 simulations (14 dipole modes × 10 rotation angles) were performed for each optics configuration with the results presented by the two-dimensional surface plots shown in Figs. 6.12, 6.13 and 6.14 for the decoupled optics, local reflector and global rotation, respectively. In the instance of decoupled optics, the threshold current remains relatively insensitive to changes in the HOM polarizations. As the deviation of the mode orientations from 0 ◦ and 90 ◦ increases, the threshold current also increases, albeit only slightly, consistent with Eq. (4.21). Because the optics is decoupled and the modes well separated in frequency, coupling between modes is negligible and the current for stability can be determined by the threshold current due to the worst individual mode. The optics describing the local reflector were derived from machine all-save values used for the measurements described in Section 6.3.1. From the arguments of Section 6.3, the expected increase in the threshold current is observed. The point of interest however, is that as the HOM rotation angle increases, the effectiveness of the local reflector rapidly diminishes. Thus, unless it is known that dangerous 155 HOMs are oriented very nearly to 0 ◦ or 90 ◦ , a reflection scheme may not adequately
FIG. 6.12: Threshold current for nominal, decoupled optics as a function of the number of dipole modes per cavity and the HOM rotation angle. 156
- 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 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: FIG. 6.11: A plot of 1/Qeff versus
- 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
- 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
FIG. 6.12: Threshold current for nominal, decoupled optics as a function of the number<br />
of dipole modes per cavity and the HOM rotation angle.<br />
156