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首页> 外文期刊>Mathematical Problems in Engineering >Revisiting the Low-Frequency Dipolar Perturbation by an Impenetrable Ellipsoid in a Conductive Surrounding
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Revisiting the Low-Frequency Dipolar Perturbation by an Impenetrable Ellipsoid in a Conductive Surrounding

机译：重新探究导电环境中不可渗透的椭球体对低频偶极子摄动的影响

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摘要

This contribution deals with the scattering by a metallic ellipsoidal target, embedded in a homogeneous conductive medium, which is stimulated when a 3D time-harmonic magnetic dipole is operating at the low-frequency realm. The incident, the scattered, and the total three-dimensional electromagnetic fields, which satisfy Maxwell's equations, yield low-frequency expansions in terms of positive integral powers of the complex-valued wave number of the exterior medium. We preserve the static Rayleigh approximation and the first three dynamic terms, while the additional terms of minor contribution are neglected. The Maxwell-type problem is transformed into intertwined potential-type boundary value problems with impenetrable boundary conditions, whereas the environment of a genuine ellipsoidal coordinate system provides the necessary setting for tackling such problems in anisotropic space. The fields are represented via nonaxisymmetric infinite series expansions in terms of harmonic eigenfunctions, affiliated with the ellipsoidal system, obtaining analytical closed-form solutions in a compact fashion. Until nowadays, such problems were attacked by using the very few ellipsoidal harmonics exhibiting an analytical form. In the present article, we address this issue by incorporating the full series expansion of the potentials and utilizing the entire subspace of ellipsoidal harmonic eigenfunctions.
机译：该贡献涉及嵌入在均匀导电介质中的金属椭圆形目标的散射，当3D时谐波磁偶极子在低频范围内工作时，会激发该散射。满足麦克斯韦方程组的入射磁场，散射磁场和总的三维电磁场，根据外部介质的复数值波数的正整数幂，产生低频扩展。我们保留了静态瑞利近似和前三个动态项，而忽略了次要贡献的其他项。麦克斯韦型问题转化为交织的势型边值问题，具有不可渗透的边界条件，而真正的椭球坐标系的环境为解决各向异性空间中的此类问题提供了必要的条件。通过与椭圆系统相关的谐波特征函数，通过非轴对称无限级数展开表示这些场，从而以紧凑的方式获得解析的封闭形式的解。直到今天，通过使用极少数呈现解析形式的椭圆谐波来解决此类问题。在本文中，我们通过合并电位的全序列展开并利用椭球谐波本征函数的整个子空间来解决此问题。

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