Trajectories of charged particles in knotted electromagnetic fields

TL;DR

This paper studies how charged particles move in complex, knotted electromagnetic fields, revealing diverse behaviors like acceleration, trajectory convergence, and twisting, which enhances understanding of these fields and their potential experimental uses.

Contribution

It introduces a detailed analysis of charged particle trajectories in electromagnetic knot solutions generated by the de Sitter method, highlighting new dynamic behaviors.

Findings

Particles can accelerate from rest to ultrarelativistic speeds.

Trajectories tend to converge into narrow cones at high coupling.

Particles exhibit pronounced twisting and turning in the fields.

Abstract

We investigate the trajectories of point charges in the background of finite-action vacuum solutions of Maxwell's equations known as knot solutions. More specifically, we work with a basis of electromagnetic knots generated by the so-called "de Sitter method". We find a variety of behaviors depending on the field configuration and the parameter set used. This includes an acceleration of particles by the electromagnetic field from rest to ultrarelativistic speeds, a quick convergence of their trajectories into a few narrow cones asymptotically for sufficiently high value of the coupling, and a pronounced twisting and turning of trajectories in a coherent fashion. This work is part of an effort to improve the understanding of knotted electromagnetic fields and the trajectories of charged particles they generate, and may be relevant for experimental applications.