Longitudinal Space Charge Effects in RF Buckets

Abstract

Longitudinal space charge effects in RF buckets have been studied by means of an IBM 704 computer program. This program simulates the motion of the particles in a beam under the influences of space charge forces and RF fields. Initially, the beam is given a small perturbation to excite a particular mode. Stable and unstable beams with energy spreads much greater than, approximately equal to, and much less than the energy spread of an RF bucket in the absence of space charge forces have been studied. Duplicate runs are made with and without space charge forces and the results are compared. After a transitional period of time, with space charge forces acting, the stable phase region assumes a characteristic diamond shape which persists for more than five synchrotron periods. This stable phase region contains more particles than the corresponding RF bucket in the absence of space charge forces. When the initial distribution of particles in phase space is independent of phase angle and has an energy spread much less than the energy spread necessary to stabilize the beam against the negative mass instability, large clumps of particles form immediately. These clumps of particles execute phase oscillations and may coagulate with the particles in the stable phase region. If particles far from the stable phase region do not interact with particles in the stable phase region, the bucket assumes an elliptical shape, very narrow in phase angle, large in energy spread, with a lifetime of more than five synchrotron periods.