Anomalous beam diffusion near beam-beam synchrobetatron resonances

Abstract

The diffusion process near low order synchro-betatron resonances driven by beam-beam interactions at a crossing angle is investigated. Macroscopic observables such as beam emittance, lifetime and beam profiles are calculated. These are followed with detailed studies of microscopic quantities such as the evolution of the variance at several initial transverse amplitudes and single particle probability distribution functions. We present evidence to show that the observed diffusion is anomalous and the dynamics follows a non-Markovian continuous time random walk process. We derive a modified master equation to replace the Chapman-Kolmogorov equation in action-angle space and a fractional diffusion equation to describe the density evolution for this class of processes.