STUDIES OF ENERGY RECOVERY LINACS AT ... - CASA
STUDIES OF ENERGY RECOVERY LINACS AT ... - CASA STUDIES OF ENERGY RECOVERY LINACS AT ... - CASA
FIG. 2.13: A schematic of the 2L21 and 2L22 regions of CEBAF and the location of the quadrupoles used to measure the emittance. 2.4.3 Data Analysis Scanning the quadrupole at 2L22 to measure the vertical emittance constitutes a simple quadrupole-drift scheme. Based on simulated emittance measurements using design optics, measuring the horizontal emittance using the 2L22 quadrupole would require huge changes in field strength which create very large beta functions downstream. To remedy the problem, the quadrupole at 2L21 was used to measure the horizontal emittance. During the experiment a new cryomodule installed in the slot between the 2L21 and 2L22 quadrupoles was being commissioned. During emittance measurements the cavities in the cryomodule were set to zero accelerating gradient thereby effectively making the cryomodule a drift space. Consequently, the horizontal emittance is based on a quadrupole-drift-quadrupole-drift scheme where the 2L22 quadrupole remains at a fixed field and the 2L21 quadrupole strength is varied. Figure 2.13 shows a layout of the region. In terms of the analysis in Section 2.4.1, Eqs. (2.7), (2.8) and (2.9) remain the same and only Eq. (2.10) is modified to reflect the new beam line configuration. While the preceding analysis has modeled the quadrupoles as thin lenses, the program used to fit the experimental data was modified to model a thick lens quadrupole. The major difference in terms of analysis is that now, not only does the M11 transfer matrix element depend on the quadrupole strength, but so too does the M12 element. From Eq. (2.9) this rules out being able to perform a simple 43
quadratic fit and a multiple regression fit is required. The data for the four emittance measurements - two transverse planes (ver- tical and horizontal) for each of the two injector energy setups - are presented in Fig. 2.14 and Fig. 2.15. Before discussing the specifics of each measurement, some general comments are in order. Each plot displays the beam size squared versus the magnification, or M11 matrix element. The red data points in each plot represent the data on which the multiple-regression fit is being performed, whereas the blue data points represent those points which have been omitted (for reasons discussed below). The error bars on the data points are the errors associated with extracting the beam sizes from the raw wire scans. Horizontal Emittance: Einj= 56 MeV The limited number of data points reflects the fact that this was the first at- tempt at an emittance measurement. As with all future emittance measurements there was some local steering required to ensure that the signal of interest from the wire scan was not overlapping an adjacent peak. Despite the limited data the beta function passed through a minimum, which is critical for getting a good fit with a quadratic function. The leftmost data point - corresponding to a quadrupole strength furthest from the nominal set point - was omitted in the fit. The rea- son is that a fit on all data points results in an unphysical solution, namely ɛ 2 g < 0. Omitting the point results in a physically realizable emittance. Judiciously omitting data points which lead to nonsensical emittances was often required in subsequent measurements. Vertical Emittance: Einj = 56 MeV Despite the large number of data points, because the quadrupole was not scanned far enough to allow the beta function to pass through a minimum, fit- 44
- 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 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: FIG. 2.12: A typical wire scan near
- 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 and 88: accelerating gradient at the front
- Page 89 and 90: eason for making the endloops achro
- 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
quadratic fit and a multiple regression fit is required.<br />
The data for the four emittance measurements - two transverse planes (ver-<br />
tical and horizontal) for each of the two injector energy setups - are presented in<br />
Fig. 2.14 and Fig. 2.15. Before discussing the specifics of each measurement, some<br />
general comments are in order. Each plot displays the beam size squared versus the<br />
magnification, or M11 matrix element. The red data points in each plot represent<br />
the data on which the multiple-regression fit is being performed, whereas the blue<br />
data points represent those points which have been omitted (for reasons discussed<br />
below). The error bars on the data points are the errors associated with extracting<br />
the beam sizes from the raw wire scans.<br />
Horizontal Emittance: Einj= 56 MeV<br />
The limited number of data points reflects the fact that this was the first at-<br />
tempt at an emittance measurement. As with all future emittance measurements<br />
there was some local steering required to ensure that the signal of interest from<br />
the wire scan was not overlapping an adjacent peak. Despite the limited data the<br />
beta function passed through a minimum, which is critical for getting a good fit<br />
with a quadratic function. The leftmost data point - corresponding to a quadrupole<br />
strength furthest from the nominal set point - was omitted in the fit. The rea-<br />
son is that a fit on all data points results in an unphysical solution, namely ɛ 2 g < 0.<br />
Omitting the point results in a physically realizable emittance. Judiciously omitting<br />
data points which lead to nonsensical emittances was often required in subsequent<br />
measurements.<br />
Vertical Emittance: Einj = 56 MeV<br />
Despite the large number of data points, because the quadrupole was not<br />
scanned far enough to allow the beta function to pass through a minimum, fit-<br />
44
Change language