STUDIES OF ENERGY RECOVERY LINACS AT ... - CASA
STUDIES OF ENERGY RECOVERY LINACS AT ... - CASA STUDIES OF ENERGY RECOVERY LINACS AT ... - CASA
FIG. 5.17: A plot of the HOM power of the 2106 MHz mode as a function of time for three different values of macropulse current (note the logarithmic scale of the vertical axis). are identical, as they should be, since this represents the natural decay time of the 2106 MHz mode that caused the instability. An alternate way of extracting the threshold current is to plot the three values of 1/τeff against the macropulse current and fit the data with a line in the same way as the BTF measurements. Finding the intersection of the extrapolated linear fit and the current axis indicates that the threshold current is (2.2 ± 0.2) mA as shown in Fig. 5.18. 5.5 Characterizing the Beam Optics To benchmark the BBU codes, it is important that the beam optics used in the simulations accurately describe the optics of the machine that the measurements 133 were performed on. In principle, standard difference orbit measurements are used
FIG. 5.18: A plot of the three values of 1/τeff corresponding to each macropulse current from Fig. 5.17 versus the macropulse current. The threshold current is 2.2 mA and is extracted in the same manner as the BTF measurements. to experimentally characterize the optics. Correctors immediately downstream of zone 4 are used to provide a known angular kick (horizontal and vertical) while downstream BPMs record the beam position. This is repeated with several corrector pairs. In preparation for these BBU studies, a program to automate the process of collecting the difference orbits was developed. The data is loaded into a machine model and the quadrupole strengths are varied to make the positional data and the positions predicted by the model match. These then are the actual quadrupole strengths in the machine. In principle this process is straightforward. However, for an ERL without beam position monitors with the capability to resolve two co-propagating beams through the linac, the ability to determine the betatron phase advance (horizontal and verti- 134 cal) is limited. Furthermore, in the Upgrade Driver the placement of several BPMs
- Page 101 and 102: 4.1 The Pillbox Cavity Although the
- 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: FIG. 5.16: HOM voltage measured fro
- 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 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
FIG. 5.17: A plot of the HOM power of the 2106 MHz mode as a function of time for<br />
three different values of macropulse current (note the logarithmic scale of the vertical<br />
axis).<br />
are identical, as they should be, since this represents the natural decay time of the<br />
2106 MHz mode that caused the instability.<br />
An alternate way of extracting the threshold current is to plot the three values<br />
of 1/τeff against the macropulse current and fit the data with a line in the same way<br />
as the BTF measurements. Finding the intersection of the extrapolated linear fit<br />
and the current axis indicates that the threshold current is (2.2 ± 0.2) mA as shown<br />
in Fig. 5.18.<br />
5.5 Characterizing the Beam Optics<br />
To benchmark the BBU codes, it is important that the beam optics used in the<br />
simulations accurately describe the optics of the machine that the measurements<br />
133<br />
were performed on. In principle, standard difference orbit measurements are used
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