Two-scale semi-lagrangian simulation of a charged particle beam in a periodic focusing channel

TL;DR

This paper introduces a two-scale semi-lagrangian numerical method for simulating charged particle beams in periodic focusing channels, effectively capturing oscillatory electric fields and simplifying Poisson's equation solutions.

Contribution

The paper develops a novel two-scale numerical approach with a new phase space mesh, improving efficiency and accuracy in long-term simulations of charged particle beams.

Findings

Efficient long-time simulation of charged particle beams.

Validation of the method's accuracy against known models.

Simplification of Poisson's equation solution process.

Abstract

This paper is devoted to numerical simulation of a charged particle beam submitted to a strong oscillating electric field. For that, we consider a two-scale numerical approach as follows: we first recall the two-scale model which is obtained by using two-scale convergence techniques; then, we numerically solve this limit model by using a backward semi-lagrangian method and we propose a new mesh of the phase space which allows us to simplify the solution of the Poisson's equation. Finally, we present some numerical results which have been obtained by the new method, and we validate its efficiency through long time simulations.