Electromagnetic wave scattering phenomena for target identification are important in many applications related to fundamental science and engineering. Here, we present an analytical formulation for the calculation of the magnetic and electric fields that scatter off a highly conductive ellipsoidal body, located within an otherwise homogeneous and isotropic lossless medium. The primary excitation source assumes a time‐harmonic magnetic dipole, precisely fixed and arbitrarily orientated that operates at low frequencies and produces the incident fields. The scattering problem itself is modeled with respect to rigorous expansions of the electromagnetic fields at the low‐frequency regime in terms of positive integral powers of the real wave number of the ambient. Obviously, the Rayleigh static term and a few dynamic terms are sufficient for the purpose of the present work, as the additional terms are neglected due to their minor contribution. Therein, the classical Maxwell's theory is suitably modified, leading to intertwined either Laplace's or Poisson's equations, accompanied by the impenetrable boundary conditions for the total fields and the limiting behavior at infinity. On the other hand, the complete spatial anisotropy of the three‐dimensional space is secured via the introduction of the genuine ellipsoidal coordinate system, being appropriate for tackling incrementally such scattering boundary value problems. The nonaxisymmetric fields are obtained via infinite series expansions in terms of ellipsoidal harmonic eigenfunctions, providing handy closed‐form solutions in a compact fashion, whose validity is verified by a straightforward reduction to simpler geometries of the metal object. The main idea is to demonstrate an efficient methodology, according to which the constructed analytical formulae can offer the appropriate environment for a fast numerical estimation of the scattered electromagnetic fields that could be useful for real data inversion.

中文翻译：

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固体椭球在无损环境中的低频偶极电磁散射

用于目标识别的电磁波散射现象在与基础科学和工程相关的许多应用中都很重要。在这里，我们提出了一种解析公式，用于计算从高传导性椭球体飞散的磁场和电场，该椭球体位于否则均匀且各向同性的无损介质中。初级激励源假设一个时谐磁偶极子，该偶极子被精确固定并任意定向，并在低频下工作并产生入射场。散射问题本身是针对低频状态下电磁场的严格扩展建模的，即环境的实波数的正整数幂。明显，Rayleigh静态项和一些动态项已足以满足本研究的目的，因为其他项因其贡献较小而被忽略。其中，对经典麦克斯韦理论进行了适当修改，导致拉普拉斯方程或泊松方程相互交织，并伴有总场的不可穿透边界条件和无穷大处的极限行为。另一方面，通过引入真正的椭球坐标系可以确保三维空间的完整空间各向异性，这适用于逐步解决此类散射边界值问题。非轴对称场是通过椭圆谐波本征函数通过无限级数展开获得的，从而以紧凑的方式提供了方便的闭式解，通过直接简化为更简单的金属物体几何形状可以验证其有效性。主要思想是演示一种有效的方法，根据该方法，所构造的分析公式可以为散射电磁场的快速数值估计提供适当的环境，这可能对实际数据反演有用。