Rotating Electromagnetic Waves in Toroid-Shaped Regions

TL;DR

This paper numerically investigates electromagnetic waves confined in toroid-shaped regions, analyzing their shape and properties, and explores spherical vortex ring analogs with explicit solutions for unique configurations.

Contribution

It introduces numerical solutions for rotating electromagnetic waves in toroid-shaped regions and analyzes their geometric properties and vortex ring analogs.

Findings

Electromagnetic waves can be confined in toroid-shaped regions.

Shape of the wave sections depends on rotation speed and size.

Explicit solutions are provided for certain vortex ring configurations.

Abstract

Electromagnetic waves, solving the full set of Maxwell equations in vacuum, are numerically computed. These waves occupy a fixed bounded region of the three dimensional space, topologically equivalent to a toroid. Thus, their fluid dynamics analogs are vortex rings. An analysis of the shape of the sections of the rings, depending on the angular speed of rotation and the major diameter, is carried out. Successively, spherical electromagnetic vortex rings of Hill's type are taken into consideration. For some interesting peculiar configurations, explicit numerical solutions are exhibited.