A kinetic model of radiating electrons

TL;DR

This paper develops a kinetic theory for radiating electrons based on the Lorentz-Dirac equation, deriving a generalized Vlasov equation and analyzing entropy changes and plasma wave damping.

Contribution

It introduces a novel kinetic model that incorporates radiation reaction effects into electron dynamics using a generalized Vlasov framework.

Findings

Derived a coupled set of equations for radiating electrons and phase space evolution.

Explored the entropy change due to radiation and its physical implications.

Calculated the damping rate of plasma waves caused by radiation reaction.

Abstract

A kinetic theory is developed to describe radiating electrons whose motion is governed by the Lorentz-Dirac equation. This gives rise to a generalized Vlasov equation coupled to an equation for the evolution of the physical submanifold of phase space. The pathological solutions of the 1-particle theory may be removed by expanding the latter equation in powers of $\tau := q^2/ 6\pi m$. The radiation-induced change in entropy is explored, and its physical origin is discussed. As a simple demonstration of the theory, the radiative damping rate of longitudinal plasma waves is calculated.