A Dynamical-Time Framework for the Dynamics of Charged Particles

TL;DR

This paper introduces a dynamical-time framework for modeling charged particle motion in electromagnetic fields, offering insights into asymptotic behavior and computational benefits over traditional methods.

Contribution

The paper develops a novel dynamical-time approach for charged particles, applicable to relativistic regimes, with advantages in accuracy and efficiency compared to conventional methods.

Findings

Massless and massive particles show identical asymptotic behavior in constant fields.

The new framework improves computational accuracy and efficiency.

Velocity space representation clarifies particle dynamics.

Abstract

We present a dynamical framework for modeling the motion of point-like charged particles, with or without mass, in general external electromagnetic fields. A key feature of this formulation is the treatment of time coordinate as a dynamical variable. The framework applies to the relativistic regime while consistently admitting a nonrelativistic limit. We also introduce a representation of particle trajectories in velocity space, which provides clear insight into the nature and asymptotic behavior of the dynamics. As an application, we compare the motion of massive and massless particles in a constant electromagnetic field and find that, for identical field configurations, their asymptotic behavior is independent of both mass and initial conditions. Finally, we explore the computational advantages of the dynamical-time formulation over the conventional uniform-time approach in two case studies: a uniform electromagnetic field, and an elliptically polarized wave propagating along a uniform magnetic field. In both scenarios, the proposed scheme exhibits improvements in accuracy and computational efficiency.