Electromagnetic helicity flux density for radiative systems

Abstract We show that the helicity flux density is distinguished from magnetic helicity by analyzing 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 Liénard–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.