Space-charge limit for a finite-size bunched beam in a circular conducting pipe

Abstract

We derive the space-charge limit for a train of periodic finite-size charged bunches which are slightly displaced from the axis of a circular, perfectly conducting pipe. The general calculation assumes that the bunches, while periodic, may have arbitrary radial and longitudinal density distributions with respect to the beam axis. We present results for a few specific distributions, as well as the limits of unbunched and single-bunch beams. Finally, we show how the bunched beam space-charge limit along with the radial rms envelope equation for a bunched beam is applied to predict operational limits of periodic permanent magnet focusing klystrons, such as the SLAC 11.4 GHz 75 MW XP-3 device.