Coherent transverse instability of bunched beams in circular accelerators

Abstract

Coherent transverse oscillations of a bunch in a ring accelerator are considered. Three different models of the bunch are used: a hollow bunch in a square potential well, a square bunch in a parabolic potential well, and a parabolic bunch in a parabolic well. The bunch space-charge field, wakefield, and chromaticity are taken into account in all the cases. The bunch eigenmodes and various instabilities are studied. The results are compared and analyzed to establish the range of applicability of the models. Role of the Landau damping due to dependence of the SC field on the longitudinal coordinate is discussed.