Transverse Coherent Resistive Instabilities of Azimuthally Bunched Beams in Particle Accelerators

Abstract

The transverse electromagnetic coupling of bunches of particles with each other is investigated theoretically, and shown to incorporate the possibility (due to the effect of imperfectly conducting vacuum chamber walls) of coherent instability even when the longitudinal distance between bunches is much larger than the transverse dimensions of the vacuum tank. The modes of oscillation in which the bunches move rigidly are investigated; criteria for stability, and expressions for the small amplitude growth rates under unstable conditions are presented. The case of a single bunch is considered in detail and demonstrated to be stable (even in the absence of Landau damping) provided v lies between an integer and the next higher half-integer, where v is the number of transverse free betatron oscillations occurring in one revolution; for many bunches which are sensibly different in intensity (a criterion for this is presented), all modes are stable provided v satisfies the same restriction. For equally spaced bunches of equal numbers of particles, approximately half the modes are unstable without Landau damping. Numerical examples are presented covering some intermediate situations.