Theory of perturbation of the magnetostatic field by an anisotropic magnetic toroid

TL;DR

This paper develops a mathematical framework to analyze how an anisotropic magnetic toroid perturbs a magnetostatic field, revealing the effects of material anisotropy near the toroid.

Contribution

It introduces a novel solution method for the perturbation of magnetostatic fields by anisotropic toroids using toroidal coordinate solutions and affine transformations.

Findings

Anisotropy significantly affects the perturbation near the toroid.

Series expansion coefficients are related through a transition matrix.

The approach clarifies the influence of material properties on magnetic fields.

Abstract

The perturbation of a magnetostatic field by a toroid made of a homogeneous anisotropic magnetic material was formulated using the solutions of the Laplace equation in the toroidal coordinate system. That was straightforward in the region outside the toroid, but an affine coordinate transformation had to be employed inside the toroid. The coefficients of the series expansion of the perturbation potential in terms of appropriate toroidal basis functions were related to the coefficients of the series expansion of the source potential in terms of appropriate toroidal basis functions by a transition matrix. As a result of the solution of this novel problem, the consequences of material anisotropy on perturbing the magnetostatic field are clearly evident in the region near the toroid.