Novel reaction force for ultra-relativistic dynamics of a classical point charge

TL;DR

This paper proposes a new equation for ultra-relativistic motion of a charged particle that conserves energy and aligns with the Liénard formula, addressing longstanding issues in electromagnetic radiation modeling.

Contribution

A novel energy-conserving equation for ultra-relativistic charged particles is introduced, improving upon previous models and aligning with established radiation formulas.

Findings

Energy lost by the charge matches Liénard formula

Good agreement with Landau-Lifshitz equation within its applicable range

Addresses limitations of previous equations of motion for charged particles

Abstract

The problem of the electromagnetic radiation of an accelerated charged particle is one of the most controversial issues in Physics since the beginning of the last century, representing one of the most popular unsolved problems of the Modern Physics. Different equations of motion have been proposed throughout history for a point charge including the electromagnetic radiation emitted, but all these expressions show some limitations. An equation based on the principle of conservation of energy is proposed in this work for the ultra-relativistic motion. Different examples are analyzed showing that the energy lost by the charge agrees with the Li\'enard formula. This proposed equation has been compared with the Landau-Lifshitz equation obtaining a good agreement in the range of application of the Landau-Lifshitz formula.