Electron beam halo formation in high-power periodic permanent magnet focusing klystron amplifiers

Electron beam halo formation is studied as a potential mechanism for electron beam losses in high-power periodic permanent magnet focusing klystron amplifiers. In particular, a two-dimensional (2-D) self-consistent electrostatic model is used to analyze equilibrium beam transport in a periodic magnetic focusing field in the absence of a radio frequency (RF) signal, and the behavior of a high-intensity electron beam under a current-oscillation-induced mismatch between the beam and the periodic magnetic focusing field. Detailed simulation results are presented for choices of system parameters corresponding to the 50-MW, 11.4-GHz periodic permanent magnet (PPM) focusing klystron experiment performed at the Stanford Linear Accelerator Center (SLAC). It is found from the self-consistent simulations that sizable halos appear after the beam envelope undergoes several oscillations, and that the residual magnetic field at the cathode plays an important role in delaying the halo formation process