Discrepancy between power radiated and the power loss due to radiation reaction for an accelerated charge

TL;DR

This paper investigates the difference between the radiated power and the power loss due to radiation reaction in an accelerated charge, clarifying their distinct physical meanings and showing they coincide only in time-averaged sense for periodic motions.

Contribution

It clarifies the distinction between radiated power and radiation reaction power, demonstrating their differences and similarities, especially for uniformly accelerated charges.

Findings

Time-averaged power loss matches radiated power in periodic motion.

Instantaneous power rates differ due to self-field energy changes.

Fields of a uniformly accelerated charge remain near the charge, not radiated away.

Abstract

We examine here the discrepancy between the radiated power, calculated from the Poynting flux at infinity, and the power loss due to radiation reaction for an accelerated charge. It is emphasized that one needs to maintain a clear distinction between the electromagnetic power received by distant observers and the mechanical power loss undergone by the charge. In literature both quantities are treated as almost synonymous, the two in general could, however, be quite different. It is shown that in the case of a periodic motion, the two formulations do yield the power loss in a time averaged sense to be the same, even though, the instantaneous rates are quite different. It is demonstrated that the discordance between the two power formulas merely reflects the difference in the power going in self-fields of the charge between the retarded and present times. In particular, in the case of a uniformly accelerated charge, power going into the self-fields at the present time is equal to the power that was going into the self-fields at the retarded time plus the power going in acceleration fields, usually called radiation. From a comparison of the far fields with the instantaneous location of the uniformly accelerated charge, it is shown that all its fields, including the acceleration fields, remain around the charge and are not {\em radiated away} from it.