Asymptotically preserving particle methods for strongly magnetizedplasmas in a torus

TL;DR

This paper introduces a new class of semi-implicit particle methods for simulating strongly magnetized plasmas in a torus, effectively capturing guiding-center dynamics without restrictive time step constraints.

Contribution

It develops asymptotic-preserving particle schemes based on higher-order semi-implicit methods, validated through theoretical proofs and numerical experiments for strongly magnetized plasma simulations.

Findings

The scheme remains stable with large magnetic fields and small Larmor radii.

It accurately approximates guiding-center dynamics in a torus configuration.

Numerical experiments confirm the method's consistency and effectiveness.

Abstract

We propose and analyze a class of particle methods for the Vlasov equation with a strong external magnetic field in a torus configuration. In this regime, the time step can be subject to stability constraints related to the smallness of Larmor radius. To avoid this limitation, our approach is based on higher-order semi-implicit numerical schemes already validated on dissipative systems [3] and for magnetic fields pointing in a fixed direction [9, 10, 12]. It hinges on asymptotic insights gained in [11] at the continuous level. Thus, when the magnitude of the external magnetic field is large, this scheme provides a consistent approximation of the guiding-center system taking into account curvature and variation of the magnetic field. Finally, we carry out a theoretical proof of consistency and perform several numerical experiments that establish a solid validation of the method and its underlying concepts.