Motion of charged particles in an electromagnetic knot

TL;DR

This paper investigates the classical relativistic trajectories of charged particles, specifically electrons, in knotted electromagnetic fields derived from the Hopf map, revealing significant acceleration to ultrarelativistic speeds.

Contribution

It introduces a method to construct electromagnetic knots and analyzes particle motion within these complex fields, highlighting the acceleration effects caused by knotted electromagnetic configurations.

Findings

Electrons are strongly accelerated by knotted electromagnetic fields.

Electrons become ultrarelativistic depending on knot energy and size.

The study provides insights into particle dynamics in complex electromagnetic topologies.

Abstract

In this paper we consider the classical relativistic motion of charged particles in a knotted electromagnetic field. After reviewing how to construct electromagnetic knots from maps between the three-sphere and the two-sphere, we introduce a mean quadratic radius of the energy density distribution in order to study some properties of this field. We study the classical relativistic motion of electrons in the electromagnetic field of the Hopf map, and compute their trajectories. It is observed that these electrons initially at rest are strongly accelerated by the electromagnetic force, becoming ultrarelativistic in a period of time that depends on the knot energy and size.