Paper detail

A Dynamical-Time Framework for the Dynamics of Charged Particles

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.