Low‐frequency electromagnetic scattering by a metal torus in a lossless medium with magnetic dipolar illumination

Abstract

The present contribution is concerned with an analytical presentation of the low‐frequency electromagnetic fields, which are scattered off a highly conductive ring torus that is embedded within an otherwise lossless ambient and interacting with a time‐harmonic magnetic dipole of arbitrary orientation, located nearby in the three‐dimensional space. Therein, the particular 3‐D scattering boundary value problem is modeled with respect to the solid impenetrable torus‐shaped body, where the toroidal geometry fits perfectly. The incident, the scattered, and the total non‐axisymmetric magnetic and electric fields are expanded in terms of positive integral powers of the real‐valued wave number of the exterior medium at the low‐frequency regime, whereas the static Rayleigh approximation and the first three dynamic terms provide the most significant part of the solution, because all the additional terms are small contributors and, hence, they are neglected. Consequently, the typical Maxwell‐type physical problem is transformed into intertwined either Laplace's or Poisson's potential‐type boundary value problems with the proper conditions, attached to the metallic surface of the torus. The fields of interest assume representations via infinite series expansions in terms of standard toroidal eigenfunctions, obtaining in that way analytical closed‐form solutions in a compact fashion. Although this mathematical procedure leads to infinite linear systems for every single case, these can be readily and approximately solved at a certain level of desired accuracy through standard cut‐off techniques. Copyright © 2016 John Wiley & Sons, Ltd.