STUDIES OF ENERGY RECOVERY LINACS AT ... - CASA

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4.8 Results of BBU Simulations Modeling BBU requires information to fully characterize the HOMs of interest and also an accurate description of the machine optics. An HOM is characterized by its frequency, loaded quality factor, polarization, and R/Q. The first three were measured directly from the cold cryomodule while the R/Q was obtained from MAFIA models [75]. Machine optics describing an 88 MeV beam energy configuration were generated from “all-save” values of the magnet strengths and RF cavity gradients. A feature of each of the three BBU simulation codes is the ability to explicitly define transfer matrices for each accelerating cavity. In this way cavity RF focusing can be included, which is known to have an appreciable effect, particularly at the front end of the linac where the energy of the injected beam is 7 MeV. 4.8.1 FEL Upgrade Without Zone 3 Initial commissioning of the FEL Upgrade Driver proceeded with only zone 2 and zone 4 installed on the beamline. Microwave measurements to characterize the dipole HOMs in each cryomodule - similar to the methods described in Section 4.6.1 - had already been performed [76]. The only difference was the manner in which HOM polarizations were measured. Because the zone 2 and 4 cryomodules are based on the 5-cell cavity design and utilize waveguide HOM couplers, the polarization was measured by noting which mode was perturbed by inserting a probe in the vertical and then the horizontal waveguide. Simulating the measured modes from the two cryomodules for an 88 MeV machine configuration results in a threshold current of 43.1 mA. The mode responsible for the instability is vertically polarized and located in cavity 6 of zone 2 with a frequency of 1891.120 MHz, an R/Q of 22.1 Ω and a loaded Q of 2.1 × 10 5 . Thus, 109 beam breakup is not a problem for the designed operating current of 10 mA with
these cryomodules. Modes from these two zones which pose the biggest threat for beam breakup have frequencies around 1900 MHz and loaded Qs of a few 10 5 . The onset of BBU at currents below 10 mA was precipitated by the installation of the zone 3 cryomodule and is discussed in the following section. 4.8.2 FEL Upgrade With Zone 3 Simulations incorporating the measured modes from zone 3 and for the same 88 MeV setup used in simulations of Section 4.8.1 predict a threshold current of 2.1 mA. The drastic decrease in the threshold current is due to the fact that HOMs in the 7-cell cavities are insufficiently damped, the most dangerous having loaded Qs on the order of 10 6 and are an order of magnitude larger than those in the 5-cell cavities. The simulations were performed with all three of the BBU simulation codes developed at Jefferson Laboratory (TDBBU, M<strong>AT</strong>BBU, ERLBBU) and all predict a threshold current of 2.1 mA. The mode responsible for the instability is vertically polarized and located in cavity 7 of zone 3 with a frequency of 2106.007 MHz, an R/Q of 29.9 Ω and a loaded Q of 6.11 × 10 6 . The discussion in Section 4.7 explained that the FEL Upgrade Driver is in a regime such that the threshold current of the machine is determined by the threshold current of the worst individual mode. This condition was confirmed through simulations. Initially, a total of 432 individually measured dipole HOMs were simulated. Upon identifying the 2106 MHz mode as the dominant HOM, simulations were re- peated using only this mode. In both instances, the predicted threshold current was 2.1 mA. Simulations performed with M<strong>AT</strong>BBU not only predict the threshold current due to the worst HOM but also the threshold currents due to other HOMs as well. 110 Table 4.8.2 gives the results of the three lowest threshold currents and the corre-
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STUDIES OF ENERGY RECOVERY LINACS A
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DEDICATION To my wife Danielle and
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2 CEBAF with Energy Recovery . . .
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5.2 HOM Power . . . . . . . . . . .
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ACKNOWLEDGMENTS First and foremost
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6.1 Summary of the measured effects
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2.10 Illustration of quadrupole sca
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5.1 Successive frames in time (prog
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6.8 A plot of 1/Qeff versus average
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ABSTRACT An energy recovering linac
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CHAPTER 1 Introduction An increasin
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FIG. 1.1: Schematic of a generic li
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FIG. 1.2: A CEBAF 5-cell cavity wit
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The solution to Eq. (1.3) is U(t) =
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y reducing the impedance of HOMs, a
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Despite its success, this method of
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design parameters, most notably ach
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1.4.2 Machine Optics The second cat
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analytic model elucidates many impo
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CHAPTER 2 CEBAF with Energy Recover
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FIG. 2.1: Energy versus average cur
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FIG. 2.3: Additional hardware insta
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FIG. 2.4: A picture of the energy r
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dipoles and beam diagnostics such a
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FIG. 2.7: Horizontal (red) and vert
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FIG. 2.8: Illustration of the cryom
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linac and θNL is the RF phase. The
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2.4 Transverse Emittance One of the
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where σ2 is the rms beam size meas
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eams. The effects of varying the qu
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FIG. 2.12: A typical wire scan near
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quadratic fit and a multiple regres
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ting the data is difficult. Without
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primary source of error is measurin
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identified, although the phase dela
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TABLE 2.3: Comparison of Twiss para
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the results of the fits. The vertic
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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 and 124: The projection of the beam displace
Page 125 and 126: TABLE 4.1: Experimental measurement
Page 127: FIG. 4.10: A plot showing the effec
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
Page 175 and 176: FIG. 6.12: Threshold current for no
Page 177 and 178: FIG. 6.14: Threshold current utiliz
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TABLE 6.1: Summary of the measured
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CHAPTER 7 BBU Suppression: Feedback
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FIG. 7.1: A schematic of the feedba
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FIG. 7.4: A coaxial 3-stub tuner us
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All of these considerations are con
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FIG. 7.6: Generic layout for a feed
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in Section 4.2.1, however, in the p
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FIG. 7.7: The threshold current as
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FIG. 7.8: Threshold current versus
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FIG. 7.10: The threshold current as
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CHAPTER 8 Conclusions The work pres
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le were experimentally measured. Du
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APPENDIX A The Pillbox Cavity Start
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FIG. A.1: A pillbox cavity exhibiti
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Ez(ρ, φ) = ψ(ρ, φ) = E0Jm(γρ
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FIG. B.1: Relationship of the S-par
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FIG. C.1: Impedance and frequency o
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FIG. C.5: Impedance and frequency o
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BIBLIOGRAPHY [1] M. Tigner, Nuovo C
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[22] L. Merminga, in Proceedings of
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[50] C. Hernandez-Garcia et al., in
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[79] L. Merminga et al., in Proceed
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VITA Christopher D. Tennant Christo
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