Abstract
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.
Highlights
Inductive electromagnetic means that are currently employed in several practical applications in physics, which are relative to electromagnetic activities, deal with many configurations of sources and receivers
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. We address this issue by incorporating the full series expansion of the potentials and utilizing the entire subspace of ellipsoidal harmonic eigenfunctions
The low-frequency electromagnetic scattering theory [1] is adopted in order to specify the kinds of the metallic targets with nondestructive analytical methods, which remains a subject of worthwhile investigation, even if there exist computational tools that could directly provide numerical data
Summary
Inductive electromagnetic means that are currently employed in several practical applications in physics, which are relative to electromagnetic activities, deal with many configurations of sources and receivers. The first stage of the work consists in the development of simple yet accurate models of the scattering problem itself, which can bring insight to the field behaviour and be employed at low computational cost, in view of a nonlinear inversion scheme, aiming at the retrieval of main geometrical and electrical parameters that characterize the object In such analytical or semianalytical approaches, we are confronted with a near-field problem, where planar skin depths are significantly larger than source-body or bodysensor distances and, therein, only diffusion phenomena occur, since conduction currents are predominant. Our devised modeling tools are based on a rigorous low-frequency analysis of the 3D vector electromagnetic fields (incident, scattered, and total ones) in positive integral powers of (ik)n for every order n ≥ 0, k denoting the complex-valued wave number of the exterior medium at the operation frequency Therein, both their real and imaginary parts are of equivalent significance in the development of a reliable model. Any future numerical implementation must include plots that depict the variation of the measurable magnetic scattered field, as we move towards the surface
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