Radiation reaction from electromagnetic fields in the neighbourhood of a point charge

TL;DR

This paper derives a radiation reaction formula for a point charge based on electromagnetic field analysis near the charge, confirming the known self-force expression and extending it relativistically.

Contribution

It provides a derivation of the radiation reaction force directly from electromagnetic fields, including a relativistic generalization, without relying on a small charged sphere model.

Findings

Radiation reaction proportional to the first derivative of acceleration.

Derived a relativistic generalization of the radiation reaction formula.

Confirmed the self-force expression from electromagnetic field analysis.

Abstract

From the expression for the electromagnetic field in the neighborhood of a point charge we determine the rate of electromagnetic momentum flow, calculated using the Maxwell stress tensor, across a surface surrounding the charge. From that we derive for a `point charge' the radiation reaction formula, which turns out to be proportional to the first time-derivative of the acceleration of the charge, identical to the expression for the self-force, hitherto obtained in the literature from the detailed mutual interaction between constituents of a small charged sphere. We then use relativistic transformations to arrive at a generalized formula for radiation reaction for a point charge undergoing a relativistic motion.