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

Hamad M. Alkhoori, Akhlesh Lakhtakia, Nikolaos L. Tsitsas
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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.
各向异性磁环对磁静电场的扰动理论
利用各向同性磁性材料制成的环状体在环状体坐标系中的拉普拉斯方程解法,计算了磁静力场对环状体的扰动。这在环状体外的区域很简单,但在环状体内必须使用仿射坐标变换。以适当的环状基函数为单位的扰动势的级数展开系数与以适当的环状基函数为单位的源势的级数展开系数通过一个过渡矩阵联系起来。由于解决了这一新颖问题,材料各向异性对磁静场扰动的影响在环状体附近区域清晰可见。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
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