Asymptotics of physical solutions to the Lorentz-Dirac equation for a planar motion in constant electromagnetic fields

TL;DR

This paper analyzes the long-term behavior of physical solutions to the Lorentz-Dirac equation for particles in a constant electromagnetic field, revealing a universal regime driven by radiation reaction effects.

Contribution

It reduces the Lorentz-Dirac equation to a second-order differential equation and derives the asymptotics of solutions, highlighting a universal behavior at large times in specific electromagnetic fields.

Findings

Charged particles tend to a universal momentum regime at large times.

The ratio of momentum components approaches a constant determined by the external field.

Radiation reaction causes effects not present in the Lorentz equation without radiation reaction.

Abstract

We present a study of planar physical solutions to the Lorentz-Dirac equation in a constant electromagnetic field. In this case, we reduced the Lorentz-Dirac equation to the one second order differential equation. We obtained the asymptotics of physical solutions to this equation at large proper times. It turns out that, in the crossed constant uniform electromagnetic field with vanishing invariants, a charged particle goes to a universal regime at large times. We found the ratio of momentum components which tends to a constant determined only by the external field. This effect is essentially due to a radiation reaction. There is not such an effect for the Lorentz equation in this field.