STUDIES OF ENERGY RECOVERY LINACS AT ... - CASA
STUDIES OF ENERGY RECOVERY LINACS AT ... - CASA STUDIES OF ENERGY RECOVERY LINACS AT ... - CASA
FIG. 5.2: The Schottky diode assembly showing the directional coupler, attenuator and Schottky diode. Each of the 16 Schottky diodes were calibrated by measuring the output voltage as a function of incident power using an RF signal generator at a frequency of 2000 MHz (the HOM signals of primary interest are around 2100 MHz, however the signal generator did not extend that far in frequency). The resulting data was fit with a polynomial up to second order in the voltage. 5.2.2 Observations of BBU A thorough experimental investigation of BBU commenced in early 2005. The nominal machine setup for the extent of the study was an 88 MeV configuration with decoupled transverse optics. The injector was set to provide 7.3 MeV electrons into the linac where the accelerating gradients were set such that zone 2, zone 3 and zone 4 provided 28.7 MeV, 15.1 MeV and 36.3 MeV of energy gain, respectively. Operating in cw mode, the average beam current was slowly increased until exponential growth of the HOM power was observed from cavity 7, which occurred 115 simultaneously with a machine trip caused by excessive beam losses. These trips
occurred at approximately 2 mA of average beam current. The process of slowly ramping up the current was repeated several times to ensure that the instability developed at the same current each time. With the FEL Upgrade Driver in a configuration to readily observe beam breakup, the mode causing the instability was identified (Section 5.3) and measurements of the threshold current were conducted (Section 5.4) to benchmark BBU simulation codes. 5.3 HOM Voltage Upon identifying cavity 7 as containing the unstable mode, the next measure- ment was identifying the frequency of the mode. To do this, the signals from the HOM coupler are split further after the −20 dB directional coupler, with one part connected to a Schottky diode to measure the power while the other part is sent di- rectly to an oscilloscope to measure the voltage. A schematic of this setup is shown in Fig. 5.3. If the oscilloscope is fast enough and the signal sufficiently sampled, the frequency of the offending mode can be extracted by Fourier analysis. A screen shot of the oscilloscope screen showing the HOM power and voltage during BBU is given in Fig. 5.4. Taking the FFT of the voltage signal reveals that the mode frequency is 2106.007 MHz (see Fig. 5.5). The results of the measurements show that with nominal, decoupled optics for an 88 MeV machine configuration, the most dangerous mode is at a frequency of 2106.007 MHz and located in cavity 7. This is in agreement with simulation results presented in Section 4.8.2. The 2106 MHz mode was considered one of the prime candidates for causing BBU because it has the second highest impedance, (R/Q)QL, of the 224 modes measured in zone 3. In fact, the highest impedance mode is also in cavity 7, at a frequency of 2116 MHz. However subsequent measurements, described 116 in Section 5.4.3, confirmed that this HOM was not a threat for causing BBU because
- Page 83 and 84: FIG. 3.1: Schematic of the 10 kW FE
- Page 85 and 86: FIG. 3.2: Layout of the DC photocat
- Page 87 and 88: accelerating gradient at the front
- Page 89 and 90: eason for making the endloops achro
- Page 91 and 92: FIG. 3.7: Illustration of path leng
- Page 93 and 94: 3.5 Longitudinal Dynamics This sect
- Page 95 and 96: FIG. 3.9: The effect of a thin focu
- Page 97 and 98: Under the constraint that each orde
- Page 99 and 100: form of beam breakup not only occur
- 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: threshold current - preferably with
- 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 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
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FIG. 5.2: The Schottky diode assembly showing the directional coupler, attenuator and<br />
Schottky diode.<br />
Each of the 16 Schottky diodes were calibrated by measuring the output voltage<br />
as a function of incident power using an RF signal generator at a frequency of<br />
2000 MHz (the HOM signals of primary interest are around 2100 MHz, however the<br />
signal generator did not extend that far in frequency). The resulting data was fit<br />
with a polynomial up to second order in the voltage.<br />
5.2.2 Observations of BBU<br />
A thorough experimental investigation of BBU commenced in early 2005. The<br />
nominal machine setup for the extent of the study was an 88 MeV configuration<br />
with decoupled transverse optics. The injector was set to provide 7.3 MeV electrons<br />
into the linac where the accelerating gradients were set such that zone 2, zone 3 and<br />
zone 4 provided 28.7 MeV, 15.1 MeV and 36.3 MeV of energy gain, respectively.<br />
Operating in cw mode, the average beam current was slowly increased until<br />
exponential growth of the HOM power was observed from cavity 7, which occurred<br />
115<br />
simultaneously with a machine trip caused by excessive beam losses. These trips
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