Radiation Reaction of an accelerating Point Charge: A new Approach

TL;DR

This paper introduces a novel expression for radiation reaction force based on instantaneous velocity change, avoiding the pathological issues of traditional formulas and applicable to non-periodic motion.

Contribution

A new approach deriving radiation reaction from Larmor formula considering instantaneous velocity change, eliminating longstanding issues in classical equations.

Findings

New radiation reaction expression free of pathological solutions

Applicable to non-periodic, realistic particle motion

Resolves issues present in AL and ALD formulas

Abstract

Abraham Lorentz (AL) formula of Radiation Reaction and its relativistic generalization, Abraham Lorentz Dirac (ALD) formula, are valid only for periodic (accelerated) motion of a charged particle, where the particle returns back to its original state. Thus, they both represent time averaged solutions for radiation reaction force. In this paper, another expression has been derived for radiation reaction following a new approach, starting from Larmor formula, considering instantaneous change (rather than periodic change) in velocity, which is a more realistic situation. Further, it has been also shown that the new expression for Radiation Reaction is free of pathological solutions; which were unpleasant parts of AL as well as ALD equations; and remained unresolved for about 100 years.