Shunt Impedance Measurement of the Aps Bbc Gun∗

The injector test stand (ITS) at Advanced Photon Source (APS) presently incorporates a ballistic bunch compression (BBC) gun, and it is used as a beam source for a number of experiments, including THz generation, beam position monitor testing for the Linac Coherent Light Source (LCLS), novel cathode testing, and radiation therapy source development. The BBC gun uses three independently powered and phased rf cavities, one cathode cell, and two full cells to provide beam energies from 2 to 10 MeV with variable energy spread, energy chirp, and, to an extent, bunch duration. The shunt impedance of an rf accelerator determines how effectively the accelerator can convert supplied rf power to accelerating gradient. The calculation of the shunt impedance can be complicated if the beam energy changes substantially during its transit through a cavity, such as in a cathode cell. We present the results of direct measurements of the shunt impedance of the APS BBC gun on an individual cavity basis, including the cathode cell, and report on achieved gradients. We also present a comparison of the measured shunt impedance with theoretical values calculated from the rf models of the cavities. DEFINITIONS The shunt impedance serves as a figure of merit for the accelerating efficiency: the larger the accelerating field per unit supplied rf power, the more efficient the accelerator. For an accelerating cavity, the shunt impedance is defined, such as in the code Superfish [1], as Zf = (∫ zf zi Ez(z)dz )2 LPT = V 2 ins LPT , (1) where zi is the entrance of the cavity field on z-axis and zf is the exit, L = zf − zi is the length of the cavity, PT is the total power loss in the absence of beam, Ez(z) = Ez(r = 0, z) is the axial longitudinal electric field, and Vins = ∫ zf zi Ez(z)dz. Alternatively, one can define the shunt impedance as Zb = V 2 g LPT , (2) where Vg is the voltage gain of an electron passing through the cavity. The latter definition is well suited for beambased measurement of the shunt impedance as described in the next section. For a normal conducting cavity with close ∗Work supported by U.S. Department of Energy, Office of Science, Office of Basic Energy Sciences, under Contract No. W-31-109-ENG-38. † [email protected] to critical coupling, we can assume that all the forward power PFWD is lost in the cavity so that PT ≈ PFWD . Generally speaking, the two definitions of the shunt impedance, Zf and Zb, do not agree since the beam-based definition implicitly includes all transit-time and velocitychange-related effects via the voltage gain Vg . These are explicitly absent in the definition of Zf . EXPERIMENT Experimental Setup The BBC gun is a 2+1/2 cell rf cavity. Each cell has a separate rf feed which allows its field amplitude and phase to be independently controlled. A photo of the gun before installation is shown in Fig. 1. Figure 1: The BBC gun before installation in the beamline. A dispenser photocathode mounted on the back plate of the half-cell cavity can produce electron bunches with charges exceeding 1 nC [2]. The beam’s final energy ranges from approximately 2 to 10 MeV. Downstream of the gun the beamline includes quadrupoles, magnetic steerers, and a dipole spectrometer. Measurement of Full-Cell Shunt Impedance By keeping the power into the cathode cell constant and measuring the beam energy as the first full cell forward power is varied, we can obtain the shunt impedance of the first full cell via Eq. (2). The result of the measurements is shown in Fig. 2. A linear regression of the data yields a shunt impedance value of approximately Z fc b = 79 ± 6 MΩ/m. The maximum average accelerating gradient reached in this set of measurements is about 75 MV/m. TUP044 Proceedings of LINAC 2006, Knoxville, Tennessee USA 346 Technology, Components, and Subsystems Particle Sources and Injectors 3.5 4 4.5 5 5.5 0.5 1 1.5 2 2.5 3 3.5 total voltage gain (MV) P F W D ( M W ) measurement quadratic fit Figure 2: The forward power of the first full cell versus the total voltage gain from the cathode cell and the first full cell. The shunt impedance of the second full cell is approximately the same as the first full cell by observing that the beam energy is about the same when powering either (1) the cathode cell and the first cell or (2) the cathode cell and the second full cell at the same power level. Both cells are operated for maximum energy gain in this measurement. Measurement of Cathode-Cell Shunt Impedance With the two full cells downstream of the cathode cell turned off, the cathode cell forward power is set to about PFWD = 1.8 MW. The corresponding maximum beam voltage gain is measured to be Vg = 2.8 MV, indicating a shunt impedance of approximately Z cc b ≈ 135 MΩ/m for the 3.22-cm-long cathode cell. The average accelerating gradient is about 87 MV/m, corresponding to a peak field of ∼ 125 MV/m. THEORETICAL MODEL Full Cell The ratio of two shunt impedances given by Eq. (1) and Eq. (2) is Zb Zf = (∫ zf zi Ez(z) cos (kz + φ0) dz ∫ zf zi Ez(z)dz )2 , (3) where φ0 is the launching phase and k= 2π λ is the wave number. Let’s consider a beam with normalized velocity β = 1. To evaluate the numerator integrand in Eq. (3), we chose φ0 to provide the maximum energy gain; see Fig. 3 for a plot of the two integrands. A numerical integration using the on-axis field profile obtained from Superfish gives ∫ zf zi Ez(z)dz = 40.47 kV and ∫ zf zi Ez(z) cos (kz + φ0) dz = 30.40 kV, resulting in a ratio Z b /Z fc f ≈ 0.56. The shunt impedance given by Superfish for the full cell is Z f =148 MΩ/m, therefore the expected Z b = 83 MΩ/m. This agrees very well with our measurement result 79 ± 6 MΩ/m as reported in the last section, given that any real cavity generally has imperfections that lower the shunt impedance, such as the pumping ports, power feeds, etc. −0.04 −0.02 0 0.02 0.04 0 0.2 0.4 0.6 0.8 1