Post-Newtonian dynamics at order 1.5 in the Vlasov-Maxwell system

TL;DR

This paper analyzes higher-order relativistic corrections to the Vlasov-Maxwell system, focusing on dissipative effects due to radiation damping at order |v/c|^3, extending previous work on Darwin order corrections.

Contribution

It provides an explicit derivation and control of dissipative radiation damping effects at order |v/c|^3 in the Vlasov-Maxwell system, beyond the Darwin correction.

Findings

Derived the order |v/c|^3 dissipative correction terms.

Established conditions under which radiation damping effects vanish.

Extended the understanding of relativistic corrections in plasma dynamics.

Abstract

We study the dynamics of many charges interacting with the Maxwell field. The particles are modeled by means of non-negative distribution functions $f^+$ and $f^-$ representing two species of charged matter with positive and negative charge, respectively. If their initial velocities are small compared to the speed of light, $c$, then in lowest order, the Newtonian or classical limit, their motion is governed by the Vlasov-Poisson system. We investigate higher order corrections with an explicit control on the error terms. The Darwin order correction, order $|v/c|^2$, has been proved previously. In this contribution we obtain the dissipative corrections due to radiation damping, which are of order $|v/c|^3$ relative to the Newtonian limit. If all particles have the same charge-to-mass ratio, the dissipation would vanish at that order.