Exact solution to the Landau-Lifshitz equation in a constant electromagnetic field

TL;DR

This paper provides an exact, closed-form solution to the Landau-Lifshitz equation describing a charged particle's motion in a constant electromagnetic field, accounting for radiation reaction effects.

Contribution

It presents the first exact solution to the Landau-Lifshitz equation in a constant field, revealing the ultrarelativistic limit as eigenvalues and eigenvectors of the field tensor.

Findings

Exact solution to the Landau-Lifshitz equation derived

Ultrarelativistic limit characterized by eigenvalues/eigenvectors of the field tensor

Provides insights into radiation reaction effects in classical charge dynamics

Abstract

We are interested in the motion of a classical charge acted upon an external constant electromagnetic field where the back reaction of the particle's own field is taken into account. The Landau-Lifshitz approximation to the Lorentz-Abraham-Dirac equation is solved exactly and in closed form. It is shown that the ultrarelativistic limit of the Landau-Lifshitz equation for a radiating charge is the equation for eigenvalues and eigenvectors of the external electromagnetic field tensor.