STUDIES OF ENERGY RECOVERY LINACS AT ... - CASA
STUDIES OF ENERGY RECOVERY LINACS AT ... - CASA STUDIES OF ENERGY RECOVERY LINACS AT ... - CASA
FIG. 4.6: A screenshot of a typical HOM resonance curve. Markers are placed at the center frequency and at the −3 dB points to extract the QL. modes created difficulty because only a partial bandwidth could be measured. In such cases the ±45 ◦ points of the phase spectrum were used to calculate the band- width. A summary of the measured data is presented in graphical form and given in Appendix C. 4.6.2 Beam-based HOM Polarization Measurements In light of Eq. (4.21), an important parameter in characterizing HOMs is the polarization of the modes. Prior to experimentally measuring these values, BBU simulations were performed with dipole HOM pairs assigned orientations of 0 ◦ and 90 ◦ and then repeated with orientations of 90 ◦ and 0 ◦ degrees, with the threshold taken as the lowest of the two cases. Essentially only worst case scenarios were sim- ulated. In principle, bead pull measurements can be used to extract mode polariza- tions. However, the small geometric perturbations from cavity to cavity introduced 101 during the fabrication process leads to a unique HOM spectrum for each cavity.
Consequently, depending on the extent of the perturbations, the same mode can be oriented differently from one cavity to the next. Therefore, it becomes necessary to use beam-based methods to accurately measure HOM polarizations. The measurement required that only the first pass beam be transported through the linac. To prevent the second pass (energy recovered) beam from propagating through the linac, the beam was directed to an insertable dump in the recirculator. Because it is a low power dump it could only tolerate tune-up beam (250 µs long macropulses with a 4.678 MHz bunch repetition rate every 2 Hz). Initial attempts to measure the polarizations used a NWA to excite a specific HOM frequency through the cavity HOM coupler. Using a downstream BPM, the resulting displacement in the vertical and horizontal planes due to the angular kick imparted to the beam by the dipole HOM could be monitored and used to calculate the polarization. In principle this is a straightforward measurement, but was never successful because cw beam is required to adequately couple to the HOM. The experimental setup that finally enabled the polarizations to be measured was based on the idea that, rather than excite the HOM externally and measure its effect on the beam, one should use the electron beam to excite the HOM and measure the response of the HOM itself. When the beam passes through a cavity, it can excite cavity HOMs. The voltage of dipole HOMs induced by a beam pulse depends on a number of beam and HOM parameters such as the bunch repetition rate, pulse length and the HOM frequency. However, most importantly for our measurement is the fact that the voltage of dipole HOMs depends linearly on the beam displacement in the cavity. The beam was displaced in each plane independently using either an upstream vertical corrector or a horizontal corrector. The corrector was changed by ±150 G- cm, in increments of 50 G-cm, from its nominal setpoint while the response of the 102 HOM of interest was measured by a network analyzer, zero-spanned at the frequency
- Page 69 and 70: identified, although the phase dela
- Page 71 and 72: TABLE 2.3: Comparison of Twiss para
- Page 73 and 74: the results of the fits. The vertic
- Page 75 and 76: FIG. 2.18: Schematic illustrating t
- Page 77 and 78: FIG. 2.19: The GASK signal measured
- Page 79 and 80: FIG. 2.20: The measured normalized
- Page 81 and 82: CHAPTER 3 The Jefferson Laboratory
- 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: FIG. 4.5: Setup for measuring cavit
- 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
Consequently, depending on the extent of the perturbations, the same mode can be<br />
oriented differently from one cavity to the next. Therefore, it becomes necessary to<br />
use beam-based methods to accurately measure HOM polarizations.<br />
The measurement required that only the first pass beam be transported through<br />
the linac. To prevent the second pass (energy recovered) beam from propagating<br />
through the linac, the beam was directed to an insertable dump in the recirculator.<br />
Because it is a low power dump it could only tolerate tune-up beam (250 µs long<br />
macropulses with a 4.678 MHz bunch repetition rate every 2 Hz).<br />
Initial attempts to measure the polarizations used a NWA to excite a specific<br />
HOM frequency through the cavity HOM coupler. Using a downstream BPM, the<br />
resulting displacement in the vertical and horizontal planes due to the angular kick<br />
imparted to the beam by the dipole HOM could be monitored and used to calculate<br />
the polarization. In principle this is a straightforward measurement, but was never<br />
successful because cw beam is required to adequately couple to the HOM.<br />
The experimental setup that finally enabled the polarizations to be measured<br />
was based on the idea that, rather than excite the HOM externally and measure<br />
its effect on the beam, one should use the electron beam to excite the HOM and<br />
measure the response of the HOM itself. When the beam passes through a cavity,<br />
it can excite cavity HOMs. The voltage of dipole HOMs induced by a beam pulse<br />
depends on a number of beam and HOM parameters such as the bunch repetition<br />
rate, pulse length and the HOM frequency. However, most importantly for our<br />
measurement is the fact that the voltage of dipole HOMs depends linearly on the<br />
beam displacement in the cavity.<br />
The beam was displaced in each plane independently using either an upstream<br />
vertical corrector or a horizontal corrector. The corrector was changed by ±150 G-<br />
cm, in increments of 50 G-cm, from its nominal setpoint while the response of the<br />
102<br />
HOM of interest was measured by a network analyzer, zero-spanned at the frequency
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