A second order differential equation for a point charged particle

TL;DR

This paper introduces a Lorentz-invariant second order differential equation model for point charged particles interacting with jet fields, avoiding run-away solutions and aligning with classical physics principles.

Contribution

It presents a novel second order differential equation model for charged particle dynamics that eliminates problematic solutions found in previous models.

Findings

The new equation is free of run-away solutions.

It is compatible with Newton's laws and Larmor's radiation.

Implications for non-neutral plasma phenomenology are discussed.

Abstract

A model for the dynamics of a classical point charged particle interacting with higher order jet fields is introduced. In this model, the dynamics of the charged particle is described by an implicit ordinary second order differential equation. Such equation is free of run-away and pre-accelerated solutions of Dirac's type. The theory is Lorentz invariant, compatible with the first law of Newton and Larmor's power radiation formula. Few implications of the new equation in the phenomenology of non-neutral plasmas is considered.