Stochastic Cooling of Bunched Beams

Numerical simulation studies are presented for transverse and longitudinal stochastic cooling of bunched particle beams. Radio frequency buckets of various shapes (e.g. rectangular, parabolic well, single sinusoidal waveform) are used to investigate the enhancement of phase space cooling by nonlinearities of synchrotron motion. The connection between the notions of Landau damping for instabilities and mixing for stochastic cooling are discussed. In particular, the need for synchrotron frequency spread for both Landau damping and good mixing is seen to be comparable for bunched beams.