A heuristic derivation of radiative power loss and radiation reaction from the kinetic power of electric inertial mass of a charge

TL;DR

This paper presents a heuristic derivation of the radiative power loss and radiation reaction for a non-relativistic charge based on the kinetic power of its electric inertial mass, linking electromagnetic field changes to charge motion.

Contribution

It introduces a simple, heuristic method to derive radiation reaction formulas from the kinetic power of electric inertial mass, applicable to arbitrary non-relativistic motions.

Findings

Power loss occurs only with changing acceleration.

Instantaneous power loss is proportional to velocity and the rate of change of acceleration.

Derived radiation reaction formula matches previous complex derivations.

Abstract

It is shown that formulas for the radiative power loss and radiation reaction from a charge can be derived in a heuristic manner from the kinetic power (rate of change of the kinetic energy) of its electric inertial mass. The derivation assumes a non-relativistic but otherwise an arbitrary motion of the charge. We exploit the fact that as the charge velocity changes because of a constant acceleration, there are accompanying modifications in its electromagnetic fields which can remain concurrent with the charge motion because the velocity as well as acceleration information enters into the field expression. However, if the acceleration of the charge is varying, information about that being not present in the field expressions, the electromagnetic fields get `out of step' with the actual charge motion. Accordingly we arrive at a radiation reaction formula for an arbitrarily moving charge, obtained hitherto in literature from the self-force, derived in a rather cumbersome way from the detailed mutual interaction between various constituents of a small charged sphere. This way we demonstrate that a power loss from a charge occurs only when there is a change in its acceleration and the derived instantaneous power loss is directly proportional to the scalar product of the velocity and the rate of change of the acceleration of the charge.