Green ' s Function Analysis of Bunched Charged Particle

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 (ReM) 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 2m; / m; necessary for confining the bunched beam, where mp is the effective plasma frequency and OJe is the cyclotron frequency. The ReM 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 2m; / m;,nns for confinement, where mc•nns 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. W,? model bunches with zero longitudinal thickness and azimuthally symmetric [mite transverse distributions in the RBDB model. We derive a limit on 2m; / m; , and apply this limit to bunched annular electron beams. The LANL 1.3 GHz relativistic klystron amplifier (RKA), a high-power microwave source using bunched annular electron beams, is found to be operating slightly above this limit, which may explain the observance of beam loss and anomalous beam halo foonation. Finally, we present preliminary results of a Green's function based code called PFB3D, which simulates the dynamics of bunched charged particle beams in a cylindrical conducting pipe. We utilize this code to simulate the dynamics of the LANL 1.3 GHz RKA experiment.