Green's function analysis of bunched charged particle beams

Abstract

In this thesis, we analyze the dynamics and equilibrium of bunched charged particle beams in the presence of perfectly conducting walls using a Green's function technique. Exact self-consistent electric and magnetic fields are obtained for charged particles in the vicinity of a conducting boundary with the use of Green's functions. We present three analytical models of bunched beams in a cylindrical conducting pipe which employ Green's functions, the Non-Relativistic Center-of-Mass (NRCM) model, the Relativistic Center-of-Mass (RCM) model, and the Relativistic Bunched Disk Beam (RBDB) model. The NRCM model assumes that the bunches are periodic and represented as point charges propagating non-relativistically in the presence of a constant magnetic focusing field. We derive a maximum limit on the effective self-field parameter ... necessary for confining the bunched beam, where wp, is the effective plasma frequency and at is the cyclotron frequency. The RCM model extends the analysis of the NRCM model to incorporate relativistic motion of the bunches in the presence of a periodic solenoidal focusing field. We derive a maximum limit on ... for confinement, where ... is the root-mean-square cyclotron frequency. We demonstrate how the self-field parameter limit can be used to predict a current limit in Periodic Permanent Magnet (PPM) klystrons. The 75 MW-XP PPM 11.4 GHz klystron designed by SLAC is found to be operating above this current limit, which may explain the observance of non-negligible beam loss in this experiment.