On radiation reaction and the Abraham-Lorentz-Dirac equation

TL;DR

This paper investigates the radiation reaction problem in classical electrodynamics, proposing a minimal modification to the Abraham-Lorentz-Dirac equation to better align with physical expectations after external forces are removed.

Contribution

It introduces a Lorentz covariant term to the Abraham-Lorentz-Dirac equation ensuring the self-force vanishes instantly after external forces cease.

Findings

Modified equation prevents runaway acceleration in Dirac constant force example

Self-force vanishes immediately after external force removal

Maintains Lorentz covariance in the modified equation

Abstract

It is underlined that the Lienard-Wiechert solutions indicate that after the external force is instantly removed from a small charged particle, the field in its close neighborhood becomes a Lorentz boosted Coulomb field. It suggests that the force of the self-field on the particle should instantaneously vanish after a sudden removal of the external force. A minimal modification of Abraham-Lorentz-Dirac equation is searched seeking to implement this property. A term assuring this behavior is added to the equation by maintaining Lorentz covariance and vanishing scalar product with the four-velocity. The simple Dirac constant force example does not show runaway acceleration.