Electromagnetic helicity flux density for radiative systems

TL;DR

This paper introduces a new way to analyze electromagnetic helicity flux density, distinguishing it from magnetic helicity, with applications to radiative systems and potential relevance to pulsar physics.

Contribution

It derives the helicity flux density for accelerating charges and generalizes Larmor's formula, providing new tools for studying electromagnetic radiation and helicity transfer.

Findings

Helicity flux density differs from magnetic helicity by analyzing Hopf solitons.

Derived multipole expansion of helicity flux density, extending Larmor's formula.

Applied formulas to toy models and discussed implications for pulsar systems.

Abstract

We show that the helicity flux density is distinguished from magnetic helicity by analysing Hopf solitons. The electromagnetic (EM) helicity flux and the magnetic helicity are Chern-Simons terms at different hypersurfaces. We find the helicity flux density for a point charge moving with an acceleration, extending the Li\'enard-Wiechert angular distribution of radiant power. We also derive the multipole expansion of the helicity flux density, generalizing the Larmor's formula for the radiant power. These formulae have been applied to discuss the helicity flux density in several toy models such as circular and helical motion as well as soft bremsstrahlung. We also comment on the potential applications of the EM helicity flux density to pulsar systems.