STUDIES OF ENERGY RECOVERY LINACS AT ... - CASA
STUDIES OF ENERGY RECOVERY LINACS AT ... - CASA STUDIES OF ENERGY RECOVERY LINACS AT ... - CASA
FIG. 3.4: View of the second (as seen by the beam) Bates style endloop in the FEL Upgrade Driver. The dipoles are represented in blue, the quadrupoles in red and the sextupoles in green. endloop as a whole is achromatic. The endloops are achromatic in the sense that the outgoing orbit is independent of the incoming momentum [53]. This means that the M16, M26, M36 and M46 matrix elements are zero. A simple example is a magnetic chicane comprised of four dipoles and illustrated in Fig. 3.5. An off-momentum beam, one with a lower momentum than the reference beam for example, will follow a different orbit and make a longer excursion through the system. However, by symmetry, the off-momentum beam is brought parallel to the reference trajectory at the symmetry point and will exit with the same trajectory as the on-momentum, reference beam. The Bates-style endloop is simply a modification of the four dipole chicane, wherein a 180 ◦ dipole is inserted at the symmetry point as illustrated in Fig. 3.6 [54]. The underlying 69
eason for making the endloops achromatic is to support a large momentum spread, particularly in the second endloop following the undulator. The endloop has a momentum compaction, M56, of +0.2 m. Note that for storage rings, the momentum compaction is defined as αc ≡ ∆L/L ∆p/p 70 (3.1) whereas in the context of this dissertation, the momentum compaction refers to the M56 transfer matrix element which maps a change in momentum to a change in path length. Together with the momentum compaction of the downstream optical cavity chicane, the long bunch from the injector is rotated by 90 ◦ to a short bunch at the undulator. Trim quadrupoles and sextupoles located immediately upstream (downstream) of the 180 ◦ dipole’s entrance (exit) provide tunable linear (M56) and quadratic (T566) compactions from the linac to the undulator. In addition to providing longitudinal phase space matching to the undulator, the endloops are used to vary the path length of the electron beam. In earlier demonstrations of energy recovery, such as the injection line of CEBAF and at Stanford’s SCA, the required path length differential was achieved by physically moving a portion of the recirculator. In the FEL Driver, correction coils embedded in the 180 ◦ dipoles are used for path length management [55]. For a small deflection, θ, from the coils at the entrance of the magnet, the path length becomes (π + 2θ)ρ where ρ is the bending radius of the dipole. This is shown schematically in Fig. 3.7. Consequently a path length differential of 2θρ is created. To generate a path length differential of λRF /2 in a single 180 ◦ magnet (in practice both bends are used) with ρ = 1 m, requires a deflection of 0.05 radians. For complete energy recovery, the path length of the machine must be (n + 1 2 )λRF , where n is an integer and λRF is the wavelength of the accelerating RF frequency.
- 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
- 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: accelerating gradient at the front
- 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 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
FIG. 3.4: View of the second (as seen by the beam) Bates style endloop in the FEL<br />
Upgrade Driver. The dipoles are represented in blue, the quadrupoles in red and the<br />
sextupoles in green.<br />
endloop as a whole is achromatic.<br />
The endloops are achromatic in the sense that the outgoing orbit is independent<br />
of the incoming momentum [53]. This means that the M16, M26, M36 and M46 matrix<br />
elements are zero. A simple example is a magnetic chicane comprised of four dipoles<br />
and illustrated in Fig. 3.5. An off-momentum beam, one with a lower momentum<br />
than the reference beam for example, will follow a different orbit and make a longer<br />
excursion through the system. However, by symmetry, the off-momentum beam<br />
is brought parallel to the reference trajectory at the symmetry point and will exit<br />
with the same trajectory as the on-momentum, reference beam. The Bates-style<br />
endloop is simply a modification of the four dipole chicane, wherein a 180 ◦ dipole<br />
is inserted at the symmetry point as illustrated in Fig. 3.6 [54]. The underlying<br />
69
Change language