Long time simulation of a beam in a periodic focusing channel via a two-scale PIC-method

TL;DR

This paper develops a two-scale PIC numerical method to efficiently simulate long-term evolution of a charged beam in a periodic focusing channel, accounting for rapid oscillations in the external electric field.

Contribution

It introduces a novel two-scale asymptotic analysis and a corresponding numerical scheme for long-time beam simulation in oscillatory electric fields.

Findings

Proved convergence to the asymptotic state.

Validated the efficiency of the numerical method.

Enabled long-time simulations with reduced computational cost.

Abstract

We study the two-scale asymptotics for a charged beam under the action of a rapidly oscillating external electric field. After proving the convergence to the correct asymptotic state, we develop a numerical method for solving the limit model involving two time scales and validate its efficiency for the simulation of long time beam evolution.