STUDIES OF ENERGY RECOVERY LINACS AT ... - CASA

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sense it measures the strength of the coupling between the mode and beam. One of the primary challenges in designing a cavity is to ensure that the accelerating mode has a large (R/Q) while minimizing the (R/Q) of higher-order modes. 1.2.2 ERLs Utilizing SRF Technology There is an increasing demand for accelerators to provide high duty factor, or cw, beams. The duty factor refers to the percentage of time the beam is on and a continuous wave beam is one in which the duty factor is 100%. In this case the beam pulse is continuously on at the RF repetition rate or at one of its subharmonics. The high Qo of SRF cavities means very little power is dissipated on the cavity walls, which in turn allows cavities to operate in cw mode while maintaining relatively high gradients. This is in stark contrast to normal conducting cavities. Because of the resistive heating in the normal conducting material (e.g. copper), the linac can only operate in pulsed mode, requiring large time gaps between accelerated bunches to allow the cavities to cool. Operating copper cavities in cw mode limits gradients to less than 2 MV/m. On the other hand, at the Jefferson Laboratory FEL SRF-based Driver, cw beam is provided by operating up to the 20 th subharmonic of the fundamental RF frequency, while maintaining cavity gradients in excess of 10 MV/m. Thus, the operation of a high duty factor accelerator necessitates the use of SRF technology. Another important advantage of SRF cavities is the ability to increase the beam aperture. While this decreases the (Ra/Qo) of the fundamental mode, the effect can be absorbed by the extremely high Qo since the goal is to minimize the dissipated power, which from Eq. (1.5) is inversely proportional to (Ra/Qo)Qo. A larger aperture ensures increased beam quality by reducing the short range wakefields and thereby reducing emittance growth along the linac, it ensures greater beam stability 9
y reducing the impedance of HOMs, and reduces beam loss from scraping. All of these benefits combine to make it possible to accelerate and preserve a high quality beam. Furthermore, in SRF cavities there is a high RF power to beam power efficiency compared to their normal conducting counterparts. As a way to quantify the efficiency of an ERL, the concept of a multiplication factor is used and defined as [4] κ = Pb PRF ≈ Io(Emax/e) Io(Einj/e) + PRF,linac 10 (1.7) where Pb is the power of the beam and PRF is the power required to operate the RF cavities. The beam power is given by the product of the average beam current and the maximum energy (i.e. before energy recovery) divided by the charge of the electron, e. For a machine operating in the regime of perfect energy recovery (the accelerated and energy recovered beams cancel), PRF consists of two terms; the first is the power required to accelerate a beam current Io in the injector (which is not energy recovered) to an energy Einj and PRF,linac, is the power required to establish the accelerating field in the linac cavities. Note that the last term is independent of beam current. This term is inversely proportional to QL which, in SRF cavities, is typically three orders of magnitude greater than in normal conducting cavities. Consequently, for an ERL with energy and average beam current comparable to a storage ring, using SRF technology would ensure an efficiency several orders of magnitude greater than for the same machine based on normal conducting technology. 1.3 Historical Development of ERLs To provide the proper context for the research presented in this dissertation, a brief historical overview of the development of ERLs is given [5]. Particular atten- tion will be given to ERLs at Jefferson Laboratory where, for the past decade, the
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 and 18: 6.8 A plot of 1/Qeff versus average
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: The solution to Eq. (1.3) is U(t) =
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
Page 69 and 70: identified, although the phase dela
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
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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
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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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