Exact solutions in radiation reaction and the radiation-free direction

TL;DR

This paper derives exact solutions for particle motion with radiation reaction in intense fields, confirming that particles tend toward the radiation-free direction at high intensities and analyzing the spectral signals of this behavior.

Contribution

It provides new exact solutions to Landau-Lifshitz equations and compares different models' predictions regarding the radiation-free direction in intense electromagnetic fields.

Findings

Particles approach the radiation-free direction at high intensities

Analytical confirmation of RFD in several cases

Time-resolved radiation spectra show RFD behavior

Abstract

We present new exact solutions of the Landau-Lifshitz and higher-order Landau-Lifshitz equations describing particle motion, with radiation reaction, in intense electromagnetic fields. Through these solutions and others we compare the phenomenological predictions of different equations in the context of the conjectured `radiation-free direction' (RFD). We confirm analytically in several cases that particle orbits predicted by the Landau-Lifshitz equation indeed approach the RFD at extreme intensities, and give time-resolved signals of this behaviour in radiation spectra.