Dynamics of ultrarelativistic charged particles with strong radiation reaction. I. Aristotelian equilibrium state

TL;DR

This paper analyzes the behavior of ultrarelativistic charged particles under strong radiation reaction, revealing an equilibrium state where particles move along principal null directions of the electromagnetic field, with detailed analytical and numerical insights.

Contribution

It provides a detailed analytical framework for Aristotelian equilibrium states of particles influenced by radiation reaction, using the Landau-Lifshitz equation and Frenet-Serret frame.

Findings

Particles tend to move along principal null directions of the electromagnetic field.

Derived conditions necessary for equilibrium in specific field configurations.

Analytic formulas agree with numerical solutions of the Landau-Lifshitz equation.

Abstract

Previous studies from the astrophysics and laser physics communities have identified an interesting phenomenon wherein ultrarelativistic charged particles experiencing strong radiation reaction tend to move along special directions fixed by the local electromagnetic field. In the relativity literature these are known as the "principal null directions" (PNDs) of the Maxwell field. A particle in this regime has "Aristotelian" dynamics in the sense that its velocity (rather than acceleration) is determined by the local field. We study this Aristotelian equilibrium in detail, starting from the Landau-Lifshitz equation describing charged particle motion including radiation reaction. Using a Frenet-Serret frame adapted to the PNDs, we derive the Lorentz factor describing motion along the local PND, together with drift velocities reflecting slower passage from one PND to another. We derive conditions on the field configuration that are necessary for such an equilibrium to occur. We demonstrate agreement of our analytic formulas with full numerical solutions of the Landau-Lifshitz equation in the appropriate regime.