STUDIES OF ENERGY RECOVERY LINACS AT ... - CASA
STUDIES OF ENERGY RECOVERY LINACS AT ... - CASA STUDIES OF ENERGY RECOVERY LINACS AT ... - CASA
FIG. 4.7: Schematic of the experimental setup used to measure dipole HOM polarizations. of a chosen HOM. A schematic of the setup is given in Fig. 4.7. To ensure that only the voltage of the chosen HOM was measured, the intermediate frequency (IF) bandwidth of the NWA was limited to 30 kHz. Note that only the input of the NWA was used to measure the signal while the output was terminated. Therefore, a spectrum analyzer could be used for this measurement as well. This process was repeated for eight of the most dangerous HOMs in zone 3, taking care to measure each pair of the dipole modes. Assume that initially the electron beam travels along the axis of the cavity and does not excite the dipole HOM. The position of the beam can be described by the vector 103 r = (xo, yo) (4.49) while the polarization of the HOM of interest is described by the unit vector êHOM = (cos α, sin α) (4.50) where α is the measured angle with respect to the horizontal plane. The induced voltage for a dipole HOM is proportional to the displacement of the electron bunch.
The projection of the beam displacement on the HOM is given by the dot product of Eq. (4.49) with Eq. (4.50) 104 V ∝ r · êHOM = xo cos α + yo sin α (4.51) As described above, the method of measuring the polarization requires varying the horizontal displacement of the electron beam while measuring the response of the induced HOM voltage ∆Vx ∝ ∆x cos α + yo sin α (4.52) and then varying the vertical beam displacement while measuring the response ∆Vy ∝ xo cos α + ∆y sin α (4.53) Because the beam is initially on-axis, (xo, yo), and cannot couple to the dipole HOM, by taking the ratio of Eq. (4.53) with Eq. (4.52), the polarization can be calculated using the following relation α = tan −1 ∆Vy ∆Vx where ∆Vy and ∆Vx are extracted from fits of the measured data. (4.54) An example of measured data is displayed in Fig. 4.8 which shows the results for a mode in cavity 7 with a frequency of 2106.007 MHz. From just an inspection of the HOM response, it is clear that this mode is polarized nearly vertically. A more thorough analysis where ∆Vy and ∆Vx were extracted and Eq. (4.54) used, yielded a polarization of (88 ± 2) ◦ . A summary of the measurements for all the HOMs is given in Table 4.1. Within each dipole HOM, the two polarizations are separated in frequency by a few hundred kHz, making it possible to excite each independently. In addition, one polarization typically has a loaded Q an order of magnitude larger
- 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 and 120: FIG. 4.5: Setup for measuring cavit
- Page 121: Consequently, depending on the exte
- 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
- Page 171 and 172: ⎛ ⎞ ⎜ ⎝ 0 0 0 0 0 −1/K 0
FIG. 4.7: Schematic of the experimental setup used to measure dipole HOM polarizations.<br />
of a chosen HOM. A schematic of the setup is given in Fig. 4.7. To ensure that only<br />
the voltage of the chosen HOM was measured, the intermediate frequency (IF)<br />
bandwidth of the NWA was limited to 30 kHz. Note that only the input of the<br />
NWA was used to measure the signal while the output was terminated. Therefore,<br />
a spectrum analyzer could be used for this measurement as well. This process was<br />
repeated for eight of the most dangerous HOMs in zone 3, taking care to measure<br />
each pair of the dipole modes.<br />
Assume that initially the electron beam travels along the axis of the cavity and<br />
does not excite the dipole HOM. The position of the beam can be described by the<br />
vector<br />
103<br />
r = (xo, yo) (4.49)<br />
while the polarization of the HOM of interest is described by the unit vector<br />
êHOM = (cos α, sin α) (4.50)<br />
where α is the measured angle with respect to the horizontal plane. The induced<br />
voltage for a dipole HOM is proportional to the displacement of the electron bunch.
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