Asymptotic-preserving particle-in-cell method for the magnetized Vlasov--Poisson--Fokker--Planck equation

TL;DR

This paper introduces a new particle-in-cell method for the magnetized Vlasov--Poisson--Fokker--Planck system that overcomes dimensionality and time step limitations, with proven asymptotic-preserving properties and validated by numerical experiments.

Contribution

The paper presents a novel asymptotic-preserving particle method with semi-implicit schemes for the magnetized Vlasov--Poisson--Fokker--Planck system, addressing key computational challenges.

Findings

Proves asymptotic-preserving and uniform convergence properties.

Demonstrates accurate long-term plasma simulations.

Validates effectiveness through extensive numerical experiments.

Abstract

In this work, we develop and rigorously analyze a new class of particle methods for the magnetized Vlasov--Poisson--Fokker--Planck system. The proposed approach addresses two fundamental challenges: (1) the curse of dimensionality, which we mitigate through particle methods while preserving the system's asymptotic properties, and (2) the temporal step size limitation imposed by the small Larmor radius in strong magnetic fields, which we overcome through semi-implicit discretization schemes. We establish the theoretical foundations of our method, proving its asymptotic-preserving characteristics and uniform convergence through rigorous mathematical analysis. These theoretical results are complemented by extensive numerical experiments that validate the method's effectiveness in long-term simulations. Our findings demonstrate that the proposed numerical framework accurately captures key physical phenomena, particularly the magnetic confinement effects on plasma behavior, while maintaining computational efficiency.