STUDIES OF ENERGY RECOVERY LINACS AT ... - CASA
STUDIES OF ENERGY RECOVERY LINACS AT ... - CASA STUDIES OF ENERGY RECOVERY LINACS AT ... - CASA
FIG. 5.19: The model optics in response to a horizontal kick immediately following zone 4 (line) and the expected displacements at the BPMs used in the difference orbits (open circles). The latter half of the machine is characterized by only two points, at locations 4F12 and 5F05. Since the optics is transversely decoupled, the vertical response at the BPM locations is zero (blue markers). in the recirculator is such that they yield no useful data. That is, the betatron phase advance between the correctors used to kick the beam and the BPMs at 4F12 and 5F05 is nearly an integer multiple of π so that the BPMs do not register a displacement - regardless of the strength of the corrector kicks. The lack of sufficient difference orbit data is illustrated in Fig. 5.19. This plot was generated in the program TAO, developed at Cornell University, which was used to analyze the data [82]. The response to a horizontal kick immediately following zone 4, as predicted by the model optics, is plotted along with the expected displacements at the BPMs used in the difference orbits. While there is adequate BPM data in the first half of the machine, the latter half is characterized by only two points, at 4F12 and 5F05. The net result is that the data is sufficient to resolve only the optics through the first half of the machine. Although less than satisfactory, given the manner in which the machine was instrumented at the time and using the automated difference orbit software, this represents the best that can be done to experimentally characterize the optics. 135 It should be noted that a brute force method - utilizing beam viewers to measure
the beam’s response in regions where the BPMs are ineffective - can be used to reconstruct the machine optics. However, by the time the problem of the insufficient difference orbit data was revealed, the machine configuration had changed to such an extent that characterizing the optics in this manner would be meaningless with regard to the BBU studies. Fortunately for each machine configuration a record, or “all-save”, exists of the quadrupole and dipole strengths, the accelerating gradient for each cavity, the linac phasing, and the injection energy. This represents all the information required to reconstruct the optics in the BBU simulations. While not determined experimen- tally, this represents a good starting point. The results of simulations based on the all-save data to describe the beam optics are displayed in Table 5.1 and discussed in Section 5.6. 5.6 Summary A comparison between the predictions from simulations, experimental measure- ments and analytic calculation of the threshold current is displayed in Table 5.1. The simulations were performed with the three BBU codes developed at Jef- ferson Laboratory; TDBBU, MATBBU and ERLBBU as well as a code developed at Cornell University called BI [83]. For consistency all the codes were run with the HOM kicks placed before each accelerating cavity. As expected, the predictions from all four codes agree. A variety of experimental techniques were utilized to measure the threshold current and they all show excellent agreement amongst themselves. The BTF mea- surement used cw beam operating at currents below the threshold current, while the growth rate measurements employed pulsed beam operating at currents above the 136 threshold. Thus under a variety of beam conditions (cw and pulsed) and operating
- Page 103 and 104: 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: FIG. 5.18: A plot of the three valu
- 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 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
the beam’s response in regions where the BPMs are ineffective - can be used to<br />
reconstruct the machine optics. However, by the time the problem of the insufficient<br />
difference orbit data was revealed, the machine configuration had changed to such<br />
an extent that characterizing the optics in this manner would be meaningless with<br />
regard to the BBU studies.<br />
Fortunately for each machine configuration a record, or “all-save”, exists of the<br />
quadrupole and dipole strengths, the accelerating gradient for each cavity, the linac<br />
phasing, and the injection energy. This represents all the information required to<br />
reconstruct the optics in the BBU simulations. While not determined experimen-<br />
tally, this represents a good starting point. The results of simulations based on the<br />
all-save data to describe the beam optics are displayed in Table 5.1 and discussed<br />
in Section 5.6.<br />
5.6 Summary<br />
A comparison between the predictions from simulations, experimental measure-<br />
ments and analytic calculation of the threshold current is displayed in Table 5.1.<br />
The simulations were performed with the three BBU codes developed at Jef-<br />
ferson Laboratory; TDBBU, M<strong>AT</strong>BBU and ERLBBU as well as a code developed<br />
at Cornell University called BI [83]. For consistency all the codes were run with<br />
the HOM kicks placed before each accelerating cavity. As expected, the predictions<br />
from all four codes agree.<br />
A variety of experimental techniques were utilized to measure the threshold<br />
current and they all show excellent agreement amongst themselves. The BTF mea-<br />
surement used cw beam operating at currents below the threshold current, while the<br />
growth rate measurements employed pulsed beam operating at currents above the<br />
136<br />
threshold. Thus under a variety of beam conditions (cw and pulsed) and operating
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