Anomalous beam diffusion near beam-beam synchro-betatron resonances

TL;DR

This paper investigates the anomalous diffusion of particle beams near synchro-betatron resonances caused by beam-beam interactions, revealing non-Markovian dynamics and deriving fractional diffusion equations to model the process.

Contribution

It introduces a detailed analysis of microscopic and macroscopic beam behaviors near resonances and develops a novel fractional diffusion model for non-Markovian diffusion processes.

Findings

Diffusion near resonances is anomalous and non-Markovian.

Derived a fractional diffusion equation for beam density evolution.

Provided evidence of non-Markovian dynamics in beam diffusion.

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.