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