The Darwin Approximation of the Relativistic Vlasov-Maxwell System

TL;DR

This paper derives the Darwin approximation as a next-order correction to the relativistic Vlasov-Maxwell system, bridging the gap between relativistic and Newtonian models for particle interactions.

Contribution

The paper rigorously derives the Darwin approximation from the relativistic Vlasov-Maxwell system, providing a systematic next-order correction in the limit of large speed of light.

Findings

The Darwin approximation accurately captures relativistic effects at the next order.

The derivation clarifies the connection between relativistic and non-relativistic models.

The results facilitate more precise simulations of particle systems at high velocities.

Abstract

We study the relativistic Vlasov-Maxwell system which describes large systems of particles interacting by means of their collectively generated forces. If the speed of light $c$ is considered as a parameter then it is known that in the Newtonian limit $c\to\infty$ the Vlasov-Poisson system is obtained. In this paper we determine the next order approximate system, which in the case of individual particles usually is called the Darwin approximation.