Low‐frequency electromagnetic scattering by a metal torus in a lossless medium with magnetic dipolar illumination

Abstract

The present contribution is concerned with an analytical presentation of the low‐frequency electromagnetic fields, which are scattered off a highly conductive ring torus that is embedded within an otherwise lossless ambient and interacting with a time‐harmonic magnetic dipole of arbitrary orientation, located nearby in the three‐dimensional space. Therein, the particular 3‐D scattering boundary value problem is modeled with respect to the solid impenetrable torus‐shaped body, where the toroidal geometry fits perfectly. The incident, the scattered, and the total non‐axisymmetric magnetic and electric fields are expanded in terms of positive integral powers of the real‐valued wave number of the exterior medium at the low‐frequency regime, whereas the static Rayleigh approximation and the first three dynamic terms provide the most significant part of the solution, because all the additional terms are small contributors and, hence, they are neglected. Consequently, the typical Maxwell‐type physical problem is transformed into intertwined either Laplace's or Poisson's potential‐type boundary value problems with the proper conditions, attached to the metallic surface of the torus. The fields of interest assume representations via infinite series expansions in terms of standard toroidal eigenfunctions, obtaining in that way analytical closed‐form solutions in a compact fashion. Although this mathematical procedure leads to infinite linear systems for every single case, these can be readily and approximately solved at a certain level of desired accuracy through standard cut‐off techniques. Copyright © 2016 John Wiley & Sons, Ltd.

Dipolar Excitation of a Perfectly Electrically Conducting Spheroid in a Lossless Medium at the Low-Frequency Regime

“…which stand for the low-frequency equivalent expressions. However, for all the reasons described earlier, the behavior of the incident fields (5) and (6) with (7)-(11) reflects exactly the very same physical and mathematical treatment to the scattered fields (16) with (17) and 18; that is, we hold the corresponding nonvanishing terms, attaining fields up to the third order, since the rest of them consist of a minor correction. As a consequence, the scattered magnetic field reads…”

“…This project is focused now on the adjustment of the lowfrequency diffusive scattering theory in solving the particular problem of identifying impenetrable metallic bodies in a lossless, that is, perfect dielectric, medium, aiming to follow the similar successful path of other contributions to the field. Bearing in mind the few, but with quite good results, attempts of simulating the environment as lossless and not conductive (e.g., see [16] for the case of two metallic spheres almost touching and [17] for the toroidal case in this direction), we realize the necessity of dealing with such brute-force analytical models. Seeking for different body structures in order to attain the representation of all kind of anomalies in lossless media, as much effectively as possible, the present paper deals with the spheroidal configuration.…”

Revisiting the Low-Frequency Dipolar Perturbation by an Impenetrable Ellipsoid in a Conductive Surrounding

“…, 2ℓ + 1 stand for the constant coefficients to be determined. Thus, in terms of the primary field (13), in view of the unit dyadic, and taking the three projections of the magnetic dipole in Cartesian coordinates from (2), the condition (59), the gradient operator (36), and the unit normal vector (39) in ellipsoidal coordinates, we apply orthogonality of the surface ellipsoidal harmonics ℓ ( , ]) = ℓ ( ) ℓ (]) for ℓ ≥ 0 and = 1, 2, . .…”

“…However, the difficulty induced in performing analytical techniques when we are moving towards anisotropic geometrical models is strongly increasing due to the appearance of much more elaborate corresponding eigenfunctions of the introduced potentials, though the already rich literature with analytical works concerning the scattering by simple nonpenetrable metal shapes like spheres [7][8][9], spheroids [10,11], and as already mentioned ellipsoids [5,6] is open to accept new and useful analytical results. Indeed, very recently, similar analytical techniques based on differential analysis were adopted for targeting toroidal metallic objects within either a conductive surrounding, for example, Earth [12] or a lossless medium, for example, air [13]. Nevertheless, aspects dealing with integral methods stand in the frontline of the current research, for example, an inverse scheme is used to localize a smooth surface of a three-dimensional perfectly conducting object using a boundary integral formulation in [14], while a numerical implementation via integral equations is illustrated in [15].…”

Semianalytical method for the identification of inclusions by air‐cored coil interaction in ferromagnetic media

“…[12][13][14][15] Besides, two of the authors have been involved the last decade with several cases related to the retrieval of metallic objects of different shapes and sizes with magnetic dipolar excitation. [16][17][18][19][20][21][22][23] On the other hand, near surface phenomena are of theoretical interest and practical importance, particularly, in the domain of optics. The first successful attempt of deriving a general solution for the electromagnetic scattering of a planar monochromatic wave by a homogeneous sphere in a homogeneous infinite medium is in the classical paper of Mie.…”