Still The New Classical Relativistic Equation of Charge Motion in an Electromagnetic Field

TL;DR

This paper introduces a new covariant relativistic equation of motion for a point charge in an electromagnetic field, extending the non-relativistic Goedecke equation without runaway solutions, and relates it to existing equations.

Contribution

A novel covariant generalization of the Goedecke equation is proposed, providing a more accurate classical relativistic charge motion model that avoids runaway solutions.

Findings

The new equation has no runaway solutions.

It reduces to the Goedecke equation in the non-relativistic limit.

It shows that ALD and MP equations are approximate cases.

Abstract

The non-relativistic Goedecke equation (1975), which describes the motion of a point charge taking into account the radiation reaction, has no "runaway" solutions. A "physical" method of covariant generalization of this equation is proposed, a special case of which is based on the Lorentz transformations in a coordinate--free covariant representation. Two equivalent forms of a new classical relativistic equation of motion of a point charge are obtained. It is shown that the Abraham--Lorentz--Dirac (ALD) and the Mo--Papas (MP) equations are approximate consequences of the presented theory.