Confinement of high-intensity bunched beams in high-power periodic permanent magnet focusing klystrons

Beam confinement in periodic permanent magnet (PPM) focusing klystrons, is a major concern for successful operation of these devices. In an effort to study beam dynamics and confinement for PPM focusing klystrons, we present a model for a relativistic highly bunched beam propagating through a perfectly conducting cylinder in a PPM focusing field. By imposing confinement conditions on the beam, it is shown that the effect of bunching significantly reduces the maximum effective self-field parameter well below the Brillouin density limit for unbunched beams. We compare the self-field parameters of three SLAC PPM klystron experiments, the 50 MW XL-PPM, the 75 MW XP, and the Klystrino, with the theoretical limit. Our analysis shows that these experiments are operating relatively close to the theoretical result. We will discuss the implications of these results in preventing beam losses in these devices