Second order equation of motion for electromagnetic radiation back-reaction

TL;DR

This paper proposes a second order equation of motion for electromagnetic radiation back-reaction, providing methods to determine the self-force and analyzing its effects on damping and external force influence.

Contribution

It introduces a novel second order equation of motion for radiation back-reaction and presents three methods to derive the self-force function, validated in nonrelativistic regimes.

Findings

Back-reaction causes velocity-proportional damping.

Back-reaction reduces the effect of external forces.

All three methods yield consistent results.

Abstract

We take the viewpoint that the physically acceptable solutions of the Lorentz--Dirac equation for radiation back-reaction are actually determined by a second order equation of motion, the self-force being given as a function of spacetime location and velocity. We propose three different methods to obtain this self-force function. For two example systems, we determine the second order equation of motion exactly in the nonrelativistic regime via each of these three methods, the three methods leading to the same result. We reveal that, for both systems considered, back-reaction induces a damping proportional to velocity and, in addition, it decreases the effect of the external force.