Anomalous beam diffusion near beam-beam synchro-betatron resonances

摘要

The diffusion process near low order synchro-betatron resonances driven bybeam-beam interactions at a crossing angle is investigated. Macroscopicobservables such as beam emittance, lifetime and beam profiles are calculated.These are followed with detailed studies of microscopic quantities such as theevolution of the variance at several initial transverse amplitudes and singleparticle probability distribution functions. We present evidence to show thatthe observed diffusion is anomalous and the dynamics follows a non-Markoviancontinuous time random walk process. We derive a modified master equation toreplace the Chapman-Kolmogorov equation in action-angle space and a fractionaldiffusion equation to describe the density evolution for this class ofprocesses.