STUDIES OF ENERGY RECOVERY LINACS AT ... - CASA
STUDIES OF ENERGY RECOVERY LINACS AT ... - CASA STUDIES OF ENERGY RECOVERY LINACS AT ... - CASA
1.2.1 Figures of Merit Radio frequency accelerating structures utilize the electromagnetic fields within microwave cavities to accelerate beams of charged particles. One of the most im- portant properties of a cavity is the accelerating gradient, which is quoted in units of accelerating voltage per meter. Typical values for SRF cavities in operation at CEBAF are 7 MV/m, although gradients exceeding 15 MV/m have been demon- strated in the FEL Upgrade Driver [3]. The maximum energy gained through a single cavity by an electron, for example, is (e × the gradient × the length of the cavity). Another important figure of merit is the quality factor of cavity modes. The unloaded quality factor is defined as the ratio of the energy stored to the energy dissipated in the cavity walls in one RF period and is written as Qo = ωU Pdiss 7 (1.1) where U is the energy stored in the cavity, ω is the angular frequency of the mode and Pdiss is the power dissipated on the cavity walls. Often it is more useful to quote the loaded quality factor of a mode which takes into account the total power loss due to leaks in the cavity couplers in addition to the ohmic heating of cavity walls. The loaded Q is defined as QL = ωU Ptot (1.2) where Ptot is the total power dissipated. The QL indicates how many oscillations it will take for the mode to dissipate its stored energy. For a cavity whose RF power source is turned off, the stored energy evolves as dU dt = −Ptot = − ωU . (1.3) QL
The solution to Eq. (1.3) is U(t) = Uoe −t/τL (1.4) where Uo is the stored energy at t = 0 and τL = QL/ω, is the decay time constant. Because SRF cavities are characterized by their very high quality factors, they are exceptionally good at storing energy. For example, an SRF cavity operating at 1500 MHz with a QL of 2×10 7 would have a time constant of 13 ms. On the other hand, for a normal conducting cavity operating at the same frequency, the loaded Q is typically 3 orders of magnitude lower and leads to a time constant of 13 µs. While a high quality factor for the accelerating mode is desirable, care must be taken to reduce, or damp, the quality factors of HOMs. If not sufficiently damped, the energy deposited into these modes by the beam will remain on time scales long enough such that multibunch instabilities, like beam breakup, develop. The shunt impedance is a quantity used to characterize losses in a cavity and is defined as Ra = V 2 acc Pdiss 8 (1.5) where Vacc is the accelerating voltage and Pdiss is the power dissipated on the cavity walls. From Eq. (1.5) it is clear that the goal is to maximize the shunt impedance for the accelerating mode in order to minimize the power dissipated. The reverse is true for higher-order modes, where the aim is to decrease the shunt impedance. Taking the ratio of Eq. (1.5) and Eq. (1.1) results in another useful figure of merit Ra Qo = V 2 acc ωU (1.6) which depends solely on the geometry of the cavity. The ratio (R/Q) of a mode is used to indicate the extent to which the mode is excited by passing charges. In that
- 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: FIG. 1.2: A CEBAF 5-cell cavity wit
- 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
- 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
1.2.1 Figures of Merit<br />
Radio frequency accelerating structures utilize the electromagnetic fields within<br />
microwave cavities to accelerate beams of charged particles. One of the most im-<br />
portant properties of a cavity is the accelerating gradient, which is quoted in units<br />
of accelerating voltage per meter. Typical values for SRF cavities in operation at<br />
CEBAF are 7 MV/m, although gradients exceeding 15 MV/m have been demon-<br />
strated in the FEL Upgrade Driver [3]. The maximum energy gained through a<br />
single cavity by an electron, for example, is (e × the gradient × the length of the<br />
cavity).<br />
Another important figure of merit is the quality factor of cavity modes. The<br />
unloaded quality factor is defined as the ratio of the energy stored to the energy<br />
dissipated in the cavity walls in one RF period and is written as<br />
Qo = ωU<br />
Pdiss<br />
7<br />
(1.1)<br />
where U is the energy stored in the cavity, ω is the angular frequency of the mode<br />
and Pdiss is the power dissipated on the cavity walls. Often it is more useful to<br />
quote the loaded quality factor of a mode which takes into account the total power<br />
loss due to leaks in the cavity couplers in addition to the ohmic heating of cavity<br />
walls. The loaded Q is defined as<br />
QL = ωU<br />
Ptot<br />
(1.2)<br />
where Ptot is the total power dissipated. The QL indicates how many oscillations it<br />
will take for the mode to dissipate its stored energy. For a cavity whose RF power<br />
source is turned off, the stored energy evolves as<br />
dU<br />
dt = −Ptot = − ωU<br />
. (1.3)<br />
QL
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