Exchange of helicity in a knotted electromagnetic field

TL;DR

This paper presents an exact vacuum solution to Maxwell's equations with nontrivial topology, demonstrating helicity exchange between electric and magnetic components, and analyzing their evolution over time.

Contribution

It introduces the first exact solution showing helicity exchange in a topologically nontrivial electromagnetic field.

Findings

Helicity is exchanged between electric and magnetic parts over time.

Both helicities converge to the same value as time approaches infinity.

The exchange process is explained using the Chern-Simons form.

Abstract

In this work we present for the first time an exact solution of Maxwell equations in vacuum, having non trivial topology, in which there is an exchange of helicity between the electric and magnetic part of such field. We calculate the temporal evolution of the magnetic and electric helicities, and explain the exchange of helicity making use of the Chern-Simon form. We also have found and explained that, as time goes to infinity, both helicities reach the same value and the exchange between the magnetic and electric part of the field stops.