Self-force approach to synchrotron radiation

TL;DR

This paper investigates the self-force in synchrotron radiation using a multipole expansion, confirming the consistency of the self-force with radiated power and the Abraham-Lorentz-Dirac equation.

Contribution

It introduces a multipole expansion method to analyze radiation reaction in synchrotron radiation, aligning near-field self-force with radiated power and established equations.

Findings

Self-force component matches radiated power in the radiation zone.

Agreement with Abraham-Lorentz-Dirac equation for radiation reaction.

Mode-by-mode consistency in multipole decomposition.

Abstract

We analyze radiation reaction for synchrotron radiation by computing, via a multipole expansion, the near field evaluated on the world-line of the charge. We find that the temporal component of the self four-force agrees with the radiated power, which one calculates in the radiation zone. This is the case for each mode in the multipole decomposition. We also find agreement with the Abraham-Lorentz-Dirac equation.