STUDIES OF ENERGY RECOVERY LINACS AT ... - CASA

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7.8 Threshold current versus the feedback time delay. . . . . . . . . . . . 176 7.9 The maximum threshold current that can be achieved with feedback as a function of time delay. . . . . . . . . . . . . . . . . . . . . . . . . 177 7.10 The threshold current as a function of feedback gain for several different time delays. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 178 7.11 The feedback time delay as a function of gain. . . . . . . . . . . . . . 179 A.1 A pillbox cavity exhibiting azimuthal symmetry. . . . . . . . . . . . . 186 B.1 Relationship of the S-parameters in terms of the incident and reflected voltages from ports 1 and 2 for a network analyzer. . . . . . . . . . . 190 C.1 Impedance and frequency of dipole HOMs in zone 3 cavity 8. . . . . . 192 C.2 Impedance and frequency of dipole HOMs in zone 3 cavity 7. . . . . . 192 C.3 Impedance and frequency of dipole HOMs in zone 3 cavity 6. . . . . . 193 C.4 Impedance and frequency of dipole HOMs in zone 3 cavity 5. . . . . . 193 C.5 Impedance and frequency of dipole HOMs in zone 3 cavity 4. . . . . . 194 C.6 Impedance and frequency of dipole HOMs in zone 3 cavity 3. . . . . . 194 C.7 Impedance and frequency of dipole HOMs in zone 3 cavity 2. . . . . . 195 C.8 Impedance and frequency of dipole HOMs in zone 3 cavity 1 . . . . . 195 xviii
ABSTRACT An energy recovering linac (ERL) offers an attractive alternative for generating intense beams of charged particles by approaching the operational efficiency of a storage ring while maintaining the superior beam quality typical of a linear accelerator. Two primary physics challenges exist in pushing the frontier of ERL performance. The first is energy recovering a high energy beam while demonstrating operational control of two coupled beams in a common transport channel. The second is controlling the high average current effects in ERLs, specifically a type of beam instability called multipass beam breakup (BBU). This work addresses both of these issues. A successful 1 GeV energy recovery demonstration with a maximum-to-injection energy ratio of 51:1 was carried out on the Continuous Electron Beam Accelerator Facility at Jefferson Laboratory in an effort to address issues related to beam quality preservation in a large scale system. With a 1.3 km recirculation length and containing 312 superconducting radio frequency (SRF) cavities, this experiment has demonstrated energy recovery on the largest scale, and through the largest SRF environment, to date. The BBU instability imposes a potentially severe limitation to the average current that can be accelerated in an ERL. Simulation results for Jefferson Laboratory’s 10 kW free electron laser (FEL) Upgrade Driver predict the occurrence of BBU below the nominal operating current. Measurements of the threshold current are described and shown to agree to within 10% of predictions from BBU simulation codes. This represents the first time the codes have been benchmarked with experimental data. With BBU limiting the beam current, several suppression schemes were developed. These include direct damping of the higher-order mode using two different cavity-based feedbacks and modifying the electron beam optics to reduce the coupling between the beam and mode. Specifically the effect of implementing (1) point-to-point focusing (2) a reflection of the betatron planes about 45 ◦ and (3) a rotation of the betatron planes by 90 ◦ is measured. Each method increased the threshold current for stability. Beam optical control methods proved to be so effective that they are routinely used in the operation of the 10 kW FEL Upgrade. xix
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 and 16: 5.1 Successive frames in time (prog
Page 17: 6.8 A plot of 1/Qeff versus average
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
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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
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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
Page 221 and 222:
[79] L. Merminga et al., in Proceed
Page 223 and 224:
VITA Christopher D. Tennant Christo
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