Combined Mean Field Limit and Non-relativistic Limit of Vlasov-Maxwell Particle System to Vlasov-Poisson System

TL;DR

This paper rigorously derives the Vlasov-Poisson system from the relativistic Vlasov-Maxwell particle system by analyzing the mean field and non-relativistic limits using probabilistic methods.

Contribution

It provides a detailed mathematical analysis of the combined mean field and non-relativistic limits from Vlasov-Maxwell to Vlasov-Poisson, including estimates with respect to particle number and speed of light.

Findings

Established convergence of the particle system to Vlasov-Poisson in the combined limit.

Provided probabilistic estimates for the characteristic equations.

Validated the limits through rigorous mathematical analysis.

Abstract

In this paper we consider the mean field limit and non-relativistic limit of relativistic Vlasov-Maxwell particle system to Vlasov-Poisson equation. With the relativistic Vlasov-Maxwell particle system being a starting point, we carry out the estimates (with respect to $N$ and $c$) between the characteristic equation of both Vlasov-Maxwell particle model and Vlasov-Poisson equation, where the probabilistic method is exploited. In the last step, we take both large $N$ limit and non-relativistic limit (meaning $c$ tending to infinity) to close the argument.