Asymptotic-preserving Particle-In-Cell methods for the Vlasov-Maxwell system near quasi-neutrality

TL;DR

This paper introduces Asymptotic-Preserving Particle-In-Cell methods for the Vlasov-Maxwell system that remain stable and accurate in the quasi-neutral limit, enabling efficient simulations of dense plasmas with localized non-neutral regions.

Contribution

The paper develops a novel reformulation of the Vlasov-Maxwell system that unifies models and enables stable, consistent discretizations in the quasi-neutral limit.

Findings

Methods effectively handle both quasi-neutral and non-neutral plasmas.

Numerical simulations demonstrate stability and accuracy in complex plasma scenarios.

Approach simplifies modeling of dense plasmas with localized non-neutral regions.

Abstract

In this article, we design Asymptotic-Preserving Particle-In-Cell methods for the Vlasov-Maxwell system in the quasi-neutral limit, this limit being characterized by a Debye length negligible compared to the space scale of the problem. These methods are consistent discretizations of the Vlasov-Maxwell system which, in the quasi-neutral limit, remain stable and are consistent with a quasi-neutral model (in this quasi-neutral model, the electric field is computed by means of a generalized Ohm law). The derivation of Asymptotic-Preserving methods is not straightforward since the quasi-neutral model is a singular limit of the Vlasov-Maxwell model. The key step is a reformulation of the Vlasov-Maxwell system which unifies the two models in a single set of equations with a smooth transition from one to another. As demonstrated in various and demanding numerical simulations, the Asymptotic-Preserving methods are able to treat efficiently both quasi-neutral plasmas and non-neutral plasmas, making them particularly well suited for complex problems involving dense plasmas with localized non-neutral regions.