A second order differential equation for a point charged particle

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.

arXiv commentSeveral arguments simplified; accepted version to appear in International Journal of Geometric Methods in Modern Physics

References in corpus (8)

• The critical manifold of the Lorentz-Dirac equation
• A Rigorous Derivation of Electromagnetic Self-force
• Evidence for Maximal Acceleration and Singularity Resolution in Covariant Loop Quantum Gravity
• An introduction to the Lorentz-Dirac equation
• Asymptotic analysis of ultra-relativistic charge
• On a covariant version of Caianiello's Model
• Geometry of generalized higher order fields and applications to classical linear electrodynamics
• Fiber averaged dynamics associated with the Lorentz force equation

Cited by in corpus (10)

• Theories with maximal acceleration
• Geometry of generalized higher order fields and applications to classical linear electrodynamics
• Maximal acceleration geometries and spacetime curvature bounds
• Some consequences of theories with maximal acceleration in laser-plasma acceleration
• Maximal acceleration and black hole evaporation
• On the effect of the maximal proper acceleration in the inertia
• Spacetimes of maximal proper acceleration and muon mean lifetime
• $\mathcal{C}$, $\mathcal{P}$, $\mathcal{T}$ operations and classical point charged particle dynamics
• On the Unruh effect for hyperbolic observers in spacetimes of maximal proper acceleration
• On the notion of kinetic energy in a spacetime of maximal proper acceleration