Asymptotically stable particle-in-cell methods for the Vlasov-Poisson system with a strong external magnetic field

TL;DR

This paper introduces an asymptotic-preserving Particle-In-Cell method for the Vlasov-Poisson system with strong magnetic fields, overcoming classical stability constraints and accurately capturing guiding-center dynamics.

Contribution

It develops a novel semi-implicit PIC scheme that remains stable under strong magnetic fields and converges to the guiding-center limit, improving simulation robustness.

Findings

The method is stable without traditional time/space step restrictions.

It accurately reproduces guiding-center equations in strong magnetic regimes.

Numerical experiments validate the scheme's effectiveness and stability.

Abstract

This paper deals with the numerical resolution of the Vlasov-Poissonsystem with a strong external magnetic field by Particle-In-Cell(PIC) methods. In this regime, classical PIC methods are subject tostability constraints on the time and space steps related to the smallLarmor radius and plasma frequency. Here, we propose anasymptotic-preserving PIC scheme which is not subjected to theselimitations. Our approach is based on first and higher order semi-implicit numericalschemes already validated on dissipative systems. Additionally, when the magnitude of the external magneticfield becomes large, this method provides a consistent PICdiscretization of the guiding-center equation, that is, incompressibleEuler equation in vorticity form. We propose several numerical experiments which provide a solid validation of the method and its underlying concepts.