Convergence of Hamiltonian Particle methods for Vlasov--Poisson equations with a nonhomogeneous magnetic field

TL;DR

This paper analyzes the convergence of Hamiltonian particle methods applied to the Vlasov-Poisson equations with nonhomogeneous magnetic fields, crucial for plasma physics modeling, demonstrating that numerical solutions accurately approximate particle trajectories.

Contribution

It provides a new error analysis framework for Hamiltonian particle methods in the context of Vlasov-Poisson equations with external magnetic fields, establishing convergence results.

Findings

Numerical solutions converge to exact particle trajectories.

Error bounds are established for the particle and Hamiltonian methods.

The combined approach ensures reliable simulation of plasma dynamics.

Abstract

In high-temperature plasma physics, a strong magnetic field is usually used to confine charged particles. Therefore, for studying the classical mathematical models of the physical problems it is needed to consider the effect of external magnetic fields. One of the important model equations in plasma is the Vlasov-Poisson equation with an external magnetic field. In this paper, we study the error analysis of Hamiltonian particle methods for this kind of system. The convergence of particle method for Vlasov equation and that of Hamiltonian method for particle equation are provided independently. By combining them, it can be concluded that the numerical solutions converge to the exact particle trajectories.