Radiation reaction on a classical charged particle: a modified form of the equation of motion

TL;DR

This paper introduces a numerically solvable, covariant modified equation of motion for a charged particle that incorporates radiation reaction, with technical improvements over previous models, and demonstrates its advantages through examples.

Contribution

A new, linear-in-acceleration covariant equation of motion for charged particles that simplifies numerical solutions and ensures physical consistency.

Findings

The equation is linear in the highest derivative, simplifying numerical integration.

Total four-force is constructed to be perpendicular to four-velocity.

The model ensures forces and accelerations vanish when external forces are absent.

Abstract

We present and numerically solve a modified form of the equation of motion for a charged particle under the influence of an external force, taking into account the radiation reaction. This covariant equation is integrodifferential, as Dirac-R\"ohrlich's, but has several technical improvements. First, the equation has the form of the second Newton law, with acceleration isolated on the left hand side, and the force depending only on positions and velocities: thus, the equation is linear in the highest derivative. Second, the total four-force is by construction perpendicular to the four-velocity. And third, if the external force vanishes for all future times, the total force and the acceleration automatically vanish at present time. We show the advantages of this equation by solving it numerically for several examples of external force.