STUDIES OF ENERGY RECOVERY LINACS AT ... - CASA

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5.14 A plot of 1/Qeff versus the average beam current from the data in Fig. 5.13. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 129 5.15 The HOM voltage measured from an unstable cavity for 9 ms long macropulses with 4.5 mA of average current (blue) and 5.0 mA of average current (red). . . . . . . . . . . . . . . . . . . . . . . . . . . . 131 5.16 HOM voltage measured from an unstable cavity for 16 ms (blue) and 18 ms (red) long macropulses with an average current of 3.5 mA. . . . 132 5.17 A plot of the HOM power of the 2106 MHz mode as a function of time for three different values of macropulse current (note the logarithmic scale of the vertical axis). . . . . . . . . . . . . . . . . . . . . . . . . . 133 5.18 A plot of the three values of 1/τeff corresponding to each macropulse current from Fig. 5.17 versus the macropulse current. . . . . . . . . . 134 5.19 The model optics in response to a horizontal kick immediately following zone 4 (line) and the expected displacements at the BPMs used in the difference orbits (open circles). . . . . . . . . . . . . . . . . . . 135 6.1 Schematic of a FODO cell of length ℓ. . . . . . . . . . . . . . . . . . . 140 6.2 A plot of the threshold current versus the change in quadrupole strength showing the effect of point-to-point focusing. . . . . . . . . . 143 6.3 Beam envelopes (horizontal in red and vertical in blue) for the 3F region of the FEL with the five skew quadrupoles (blue) activated and illustrating the exchange of horizontal and vertical phase spaces. 146 6.4 Beam position monitor readings for a cosine-like trajectory launched at the entrance to the local reflector in the horizontal plane. . . . . . 147 6.5 Beam position monitor readings for a sine-like trajectory launched at the entrance to the local reflector in the horizontal plane. . . . . . . . 147 6.6 Beam position monitor readings for a cosine-like trajectory launched at the entrance to the local reflector in the vertical plane. . . . . . . . 148 6.7 Beam position monitor readings for a sine-like trajectory launched at the entrance to the local reflector in the vertical plane. . . . . . . . . 148 xvi
6.8 A plot of 1/Qeff versus average beam current for the 2106 MHz mode with the local reflector activated. . . . . . . . . . . . . . . . . . . . . 150 6.9 A schematic illustrating the effect of a 90 ◦ rotation of the betatron planes. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 151 6.10 Nominal betatron functions in the 4F region of the FEL (top) and with a solenoid (blue) activated to produce a 90 ◦ rotation of betatron planes with the upstream and downstream quadrupole triplets used for matching (bottom). . . . . . . . . . . . . . . . . . . . . . . . . . . 153 6.11 A plot of 1/Qeff versus average beam current for the 2106 MHz mode with the rotator activated. . . . . . . . . . . . . . . . . . . . . . . . . 154 6.12 Threshold current for nominal, decoupled optics as a function of the number of dipole modes per cavity and the HOM rotation angle. . . . 156 6.13 Threshold current utilizing a local reflector as a function of the number of dipole modes per cavity and the HOM rotation angle. . . . . . 157 6.14 Threshold current utilizing a rotator as a function of the number of dipole modes per cavity and the HOM rotation angle. . . . . . . . . . 158 7.1 A schematic of the feedback circuit used to damp the loaded Q of a mode. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 164 7.2 The effect on the loaded Q of the 2106 MHz mode with the cavitybased, narrowband feedback off (red curve represents Q = 6.2 × 10 6 ) and on (blue curve represents Q = 1.3 × 10 6 ). . . . . . . . . . . . . . 165 7.3 A plot of 1/Qeff versus average beam current for the 2106 MHz mode with the Q-damping feedback circuit on. . . . . . . . . . . . . . . . . 165 7.4 A coaxial 3-stub tuner used for Q-damping. . . . . . . . . . . . . . . 166 7.5 Schematic of the experimental setup using a 3-stub tuner to damp the loaded Q of a mode. . . . . . . . . . . . . . . . . . . . . . . . . . 167 7.6 Generic layout for a feedback system in an ERL. . . . . . . . . . . . . 170 7.7 The threshold current as a function of gain for td = 0 from the analytic model (red line) and the results of the simulation code (black open circles). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 174 xvii
Page 1 and 2: STUDIES OF ENERGY RECOVERY LINACS A
Page 3 and 4: DEDICATION To my wife Danielle and
Page 5 and 6: 2 CEBAF with Energy Recovery . . .
Page 7 and 8: 5.2 HOM Power . . . . . . . . . . .
Page 9 and 10: ACKNOWLEDGMENTS First and foremost
Page 11 and 12: 6.1 Summary of the measured effects
Page 13 and 14: 2.10 Illustration of quadrupole sca
Page 15: 5.1 Successive frames in time (prog
Page 19 and 20: ABSTRACT An energy recovering linac
Page 21 and 22: CHAPTER 1 Introduction An increasin
Page 23 and 24: FIG. 1.1: Schematic of a generic li
Page 25 and 26: FIG. 1.2: A CEBAF 5-cell cavity wit
Page 27 and 28: The solution to Eq. (1.3) is U(t) =
Page 29 and 30: y reducing the impedance of HOMs, a
Page 31 and 32: Despite its success, this method of
Page 33 and 34: design parameters, most notably ach
Page 35 and 36: 1.4.2 Machine Optics The second cat
Page 37 and 38: analytic model elucidates many impo
Page 39 and 40: CHAPTER 2 CEBAF with Energy Recover
Page 41 and 42: FIG. 2.1: Energy versus average cur
Page 43 and 44: FIG. 2.3: Additional hardware insta
Page 45 and 46: FIG. 2.4: A picture of the energy r
Page 47 and 48: dipoles and beam diagnostics such a
Page 49 and 50: FIG. 2.7: Horizontal (red) and vert
Page 51 and 52: FIG. 2.8: Illustration of the cryom
Page 53 and 54: linac and θNL is the RF phase. The
Page 55 and 56: 2.4 Transverse Emittance One of the
Page 57 and 58: where σ2 is the rms beam size meas
Page 59 and 60: eams. The effects of varying the qu
Page 61 and 62: FIG. 2.12: A typical wire scan near
Page 63 and 64: quadratic fit and a multiple regres
Page 65 and 66: ting the data is difficult. Without
Page 67 and 68:
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
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FIG. 2.19: The GASK signal measured
Page 79 and 80:
FIG. 2.20: The measured normalized
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CHAPTER 3 The Jefferson Laboratory
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FIG. 3.1: Schematic of the 10 kW FE
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FIG. 3.2: Layout of the DC photocat
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accelerating gradient at the front
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eason for making the endloops achro
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FIG. 3.7: Illustration of path leng
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3.5 Longitudinal Dynamics This sect
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FIG. 3.9: The effect of a thin focu
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Under the constraint that each orde
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form of beam breakup not only occur
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4.1 The Pillbox Cavity Although the
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FIG. 4.2: Electric field (red) and
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where the full 4×4 transfer matrix
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The threshold is inversely proporti
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4.3 BBU Simulation Codes: Particle
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6. The second pass beam bunch then
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which excites it. The BBU instabili
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Equation (4.41) is a dispersion rel
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FIG. 4.4: Output from MATBBU showin
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FIG. 4.5: Setup for measuring cavit
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Consequently, depending on the exte
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The projection of the beam displace
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TABLE 4.1: Experimental measurement
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FIG. 4.10: A plot showing the effec
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these cryomodules. Modes from these
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CHAPTER 5 Experimental Measurements
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threshold current - preferably with
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occurred at approximately 2 mA of a
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FIG. 5.5: FFT of a pure 2106.007 MH
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FIG. 5.6: Illustration to show the
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5.4 Measuring the Threshold Current
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for the HOM-beam system and is deri
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FIG. 5.10: Schematic of the experim
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FIG. 5.12: A plot of 1/Qeff versus
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measured HOMs in zone 3, a BTF meas
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FIG. 5.16: HOM voltage measured fro
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FIG. 5.18: A plot of the three valu
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the beam’s response in regions wh
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CHAPTER 6 BBU Suppression: Beam Opt
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FIG. 6.1: Schematic of a FODO cell
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plane [85]. Equations (6.7) and (6.
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6.2.3 Discussion The method of poin
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FIG. 6.3: Beam envelopes (horizonta
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FIG. 6.6: Beam position monitor rea
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FIG. 6.8: A plot of 1/Qeff versus a
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⎛ ⎞ ⎜ ⎝ 0 0 0 0 0 −1/K 0
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FIG. 6.11: A plot of 1/Qeff versus
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FIG. 6.12: Threshold current for no
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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
Page 213 and 214:
FIG. C.5: Impedance and frequency o
Page 215 and 216:
BIBLIOGRAPHY [1] M. Tigner, Nuovo C
Page 217 and 218:
[22] L. Merminga, in Proceedings of
Page 219 and 220:
[50] C. Hernandez-Garcia et al., in
Page 221 and 222:
[79] L. Merminga et al., in Proceed
Page 223 and 224:
VITA Christopher D. Tennant Christo
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