Abstract
The electromagnetic vector fields, which are scattered off a highly conductive spheroid that is embedded within an otherwise lossless medium, are investigated in this contribution. A time-harmonic magnetic dipolar source, located nearby and operating at low frequencies, serves as the excitation primary field, being arbitrarily orientated in the three-dimensional space. The main idea is to obtain an analytical solution of this scattering problem, using the appropriate system of spheroidal coordinates, such that a possibly fast numerical estimation of the scattered fields could be useful for real data inversion. To this end, incident and scattered as well as total fields are written in a rigorous low-frequency manner in terms of positive integral powers of the real-valued wave number of the exterior environment. Then, the Maxwell-type problem is converted to interconnected Laplace’s or Poisson’s equations, complemented by the perfectly conducting boundary conditions on the spheroidal object and the necessary radiation behavior at infinity. The static approximation and the three first dynamic contributors are sufficient for the present study, while terms of higher orders are neglected at the low-frequency regime. Henceforth, the 3D scattering boundary value problems are solved incrementally, whereas the determination of the unknown constant coefficients leads either to concrete expressions or to infinite linear algebraic systems, which can be readily solved by implementing standard cut-off techniques. The nonaxisymmetric scattered magnetic and electric fields follow and they are obtained in an analytical compact fashion via infinite series expansions in spheroidal eigenfunctions. In order to demonstrate the efficiency of our analytical approach, the results are degenerated so as to recover the spherical case, which validates this approach.
Highlights
The fundamental principles of classical electromagnetism [1], initially introduced by the pioneer in the field James Clerk Maxwell, represent the basic foundation of the low-frequency scattering theory [2]
By deciphering the implicated fields to each case, information about main parameters like orientations, sizes, shapes, and magnetic and electric properties of the anomalies brings insight into the field behavior. This is not at all an easy task, since the situation of an inversion scheme [3] cannot be tackled in a robust-like manner, unless efficient models of the field distribution and strong effective mathematical tools [4] are available, since in practice the measurement and the identification of the scatterer are needed simultaneously
An analytical method to the electromagnetic low-frequency scattering problem for a perfectly electrically conducting spheroidal body in a conductive surrounding, which is illuminated by a magnetic dipole with arbitrary close to the object location and orientation, is developed
Summary
The fundamental principles of classical electromagnetism [1], initially introduced by the pioneer in the field James Clerk Maxwell, represent the basic foundation of the low-frequency scattering theory [2]. High-contrast cases, where the target has an extremely large conductivity with respect to the surrounding host environment and is considered to be impenetrable, motivated researchers to embark upon much more complex patterns, such as the two-sphere case for two closely adjacent metallic objects [10] or the circumstance of a nonpenetrable, that is, perfect conductor, ring torus [11], both articles presuming a conductive occupied medium These reports, each one containing a sufficient reference list, are a small but representative sample of displaying the inconvenience induced in performing analytical techniques when incorporating with different geometrical models [12, 13]. A short conclusion and discussion, containing an outline of our work and future steps, follow in Section 5, while an updated reference list is displayed immediately after
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call
