STUDIES OF ENERGY RECOVERY LINACS AT ... - CASA
STUDIES OF ENERGY RECOVERY LINACS AT ... - CASA STUDIES OF ENERGY RECOVERY LINACS AT ... - CASA
FIG. 4.8: Measured response of the 2106 MHz HOM due to vertical (red) and horizontal (blue) displacements through cavity 7. than its partner. It was found that these high Q modes are oriented approximately vertically, thereby making BBU less of threat in the horizontal plane (see Table 4.1). Comparison with Simulation Results The results of the polarization measurements, specifically the orientation of the 2106 MHz mode, was confirmed through computer simulations. Using the code Omega3P, the Advanced Computations Department at SLAC performed simulations of the Jefferson Laboratory 7-cell cavity. Among the information extracted from the simulations was the polarization of the 2106 MHz mode. The results of the simulated electric field contours for the mode are displayed in Fig. 4.9 which shows that the dipole HOM is split into horizontally and vertically polarized modes [74]. Because the vertically polarized mode has a higher QL, it takes longer to decay and interacts more strongly with the second pass beam, which in turn may lead to BBU. 105
TABLE 4.1: Experimental measurements of HOM polarizations of dangerous dipole modes in zone 3. Cavity Mode Frequency QL Orientation (MHz) (10 6 ) (degrees) 8 7 4 3 TM110 3π/7 TM110 4π/7 TM110 3π/7 TM110 4π/7 TM110 3π/7 TM110 4π/7 TM110 3π/7 TM110 4π/7 2102.591 2.61 84 ± 11 2103.009 0.21 8 ± 13 2113.346 3.10 80 ± 2 2114.154 0.35 11 ± 2 2105.999 6.11 88 ± 2 2106.697 0.33 4 ± 1 2116.583 6.66 86 ± 10 2117.225 0.49 4 ± 1 2102.537 0.27 25 ± 1 2102.642 0.63 63 ± 1 2113.991 0.37 33 ± 1 2114.151 5.21 87 ± 6 2104.201 2.49 38 ± 1 2104.408 0.29 14 ± 1 2115.386 2.88 75 ± 1 2115.683 0.39 18 ± 2 4.7 Validity of Single Mode Threshold Current Formula The analytical results of Sections 4.2 and 4.4 are very powerful provided they are applied properly. While Eq. (4.21) holds for coupled transverse optics, consider for the moment only decoupled optics (M14 = M32 = 0). The first criterion that must be satisfied is an assumption made in deriving the threshold current formula, namely, that the HOM voltage decay is negligible on the scale of the recirculation time. Furthermore, in any real world accelerator there will be more than one dipole HOM present in the linac, even if the linac consists of only a single cavity. So then, the second criterion for applying Eq. (4.21) to individual modes is that the modes 106 are separated in frequency by at least ω/2QL. Modes which are separated less than
- 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 and 122: Consequently, depending on the exte
- Page 123: The projection of the beam displace
- 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
- Page 173 and 174: FIG. 6.11: A plot of 1/Qeff versus
FIG. 4.8: Measured response of the 2106 MHz HOM due to vertical (red) and horizontal<br />
(blue) displacements through cavity 7.<br />
than its partner. It was found that these high Q modes are oriented approximately<br />
vertically, thereby making BBU less of threat in the horizontal plane (see Table 4.1).<br />
Comparison with Simulation Results<br />
The results of the polarization measurements, specifically the orientation of<br />
the 2106 MHz mode, was confirmed through computer simulations. Using the code<br />
Omega3P, the Advanced Computations Department at SLAC performed simulations<br />
of the Jefferson Laboratory 7-cell cavity. Among the information extracted from the<br />
simulations was the polarization of the 2106 MHz mode. The results of the simulated<br />
electric field contours for the mode are displayed in Fig. 4.9 which shows that the<br />
dipole HOM is split into horizontally and vertically polarized modes [74]. Because<br />
the vertically polarized mode has a higher QL, it takes longer to decay and interacts<br />
more strongly with the second pass beam, which in turn may lead to BBU.<br />
105
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