STUDIES OF ENERGY RECOVERY LINACS AT ... - CASA
STUDIES OF ENERGY RECOVERY LINACS AT ... - CASA STUDIES OF ENERGY RECOVERY LINACS AT ... - CASA
FIG. 7.9: The maximum threshold current that can be achieved with feedback as a function of time delay. The best fit line has a slope of −0.93. the gain. Finally, the relationship between the required feedback time delay to achieve a threshold current of 2.1 mA as a function of the gain was investigated. The resulting isoline is given on the log-log plot in Fig. 7.11. The data is fit with a straight line of slope −0.86. Thus, for the parameters used in these studies and for a 2.1 mA threshold current, the feedback time delay scales as g −0.86 . For each value of the gain, time delays which lie below the best fit line will lead to a threshold current which exceeds 2.1 mA while points above lead to thresholds less than 2.1 mA. 7.2.5 Conclusions and Implications A simple BBU code has been developed to study, in particular, the effects of time delays for implementing a bunch-by-bunch feedback system. While the details 177 of the results reported in the previous section depend largely on the specific choice
FIG. 7.10: The threshold current as a function of feedback gain for several different time delays. The lower and upper dotted lines mark threshold currents of 2.1 mA and 21 mA, respectively. of simulation parameters, in general, the following conclusions can be drawn: 1. The most effective suppression for BBU occurs when td = 0, although effective suppression of BBU can be arranged for finite feedback time delays 2. The maximum threshold current that can be obtained by implementing feedback decreases as the time delay increases (the rate at which this occurs depends on the simulation input parameters) 3. For large time delays, a feedback system will only decrease the threshold - regardless of the gain. The last point is worth emphasizing; unless the required time budget can be met, the feedback will be completely ineffective. In fact, using the feedback in this regime will act to only decrease the threshold current further. 178
- 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 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: FIG. 7.8: Threshold current versus
- 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. 7.9: The maximum threshold current that can be achieved with feedback as a<br />
function of time delay. The best fit line has a slope of −0.93.<br />
the gain.<br />
Finally, the relationship between the required feedback time delay to achieve a<br />
threshold current of 2.1 mA as a function of the gain was investigated. The resulting<br />
isoline is given on the log-log plot in Fig. 7.11. The data is fit with a straight line<br />
of slope −0.86. Thus, for the parameters used in these studies and for a 2.1 mA<br />
threshold current, the feedback time delay scales as g −0.86 . For each value of the<br />
gain, time delays which lie below the best fit line will lead to a threshold current<br />
which exceeds 2.1 mA while points above lead to thresholds less than 2.1 mA.<br />
7.2.5 Conclusions and Implications<br />
A simple BBU code has been developed to study, in particular, the effects of<br />
time delays for implementing a bunch-by-bunch feedback system. While the details<br />
177<br />
of the results reported in the previous section depend largely on the specific choice
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