Exact solution of the Landau-Lifshitz equation in a plane wave

TL;DR

This paper provides an exact, closed-form solution to the Landau-Lifshitz equation for particles in arbitrary plane wave fields, including special cases like constant crossed and monochromatic waves with various polarizations.

Contribution

It offers the first exact analytical solutions of the Landau-Lifshitz equation in general plane wave backgrounds, extending previous approximate or numerical approaches.

Findings

Explicit solutions for constant crossed fields

Solutions for monochromatic circular and linear polarized waves

Analytical expressions applicable to arbitrary plane wave shapes

Abstract

The Landau-Lifshitz form of the Lorentz-Abraham-Dirac equation in the presence of a plane wave of arbitrary shape and polarization is solved exactly and in closed form. The explicit solution is presented in the particular, paradigmatic cases of a constant crossed field and of a monochromatic wave with circular and with linear polarization.