Effect of interparticle fields and radiation reaction on beam dynamics

TL;DR

This paper develops a comprehensive theoretical and numerical framework for analyzing relativistic particle beam dynamics in intense electromagnetic fields, emphasizing the importance of interparticle fields and radiation reaction for energy-momentum conservation and beam behavior.

Contribution

It introduces a generalized Landau-Lifshitz equation including interparticle fields and validates it through first-principles simulations, ensuring energy-momentum conservation in complex interactions.

Findings

Interparticle fields and radiation reaction significantly influence the tail of the energy distribution.

Energy-momentum conservation is maintained when both effects are included in simulations.

Interparticle field effects diminish when radiated energy is predominantly incoherent.

Abstract

The dynamics of relativistic particles in an intense electromagnetic field can be described by the Landau-Lifshitz (LL) equation, where the adiation reaction (RR) is accounted for via a self-force, and interparticle fields are often neglected as an approximation. However, the inclusion of interparticle fields is necessary to ensure energy-momentum conservation, particularly during coherent emission. Here we present (i) an analytical proof showing that the energy-momentum conservation law of the Hamilton-Rohrlich-Dirac action, which is divergence free and describes a generic system of interacting charges, respects causality and provides physically sensible results; (ii) a simple generalization of the LL equation for many particles evaluated as a function of the total field, i.e., the sum of the external and interparticle fields. By performing first-principles numerical simulations of a neutral, relativistic bunch of electrons and positrons ($e^-/e^+$) colliding with a laser pulse, this theory is shown to satisfy energy-momentum conservation when interparticle fields and RR are simultaneously taken into account; and (iii) the combined effect of interparticle fields and RR primarily affects the tail of the particle energy distribution. Additionally, our first-principles simulations show that the effect of interparticle fields on beam energy loss becomes smaller when most of the radiated energy is incoherent.