Mathematical and numerical analysis of low-frequency scattering from a PEC ring torus in a conductive medium

International audienceThe electric and magnetic fields scattered offa non-penetrable ring torus, being characterized as perfect conductor, embedded in a homogeneous conductive medium and illu- minated by a low-frequency magnetic dipole of arbitrary orientation and harmonic time-dependence are investigated herein. Upon definition of the complex wave number of the exterior medium k via its skin-depth, the 3-D scattering boundary value problem is handled via convenient low-frequency expansions in terms of powers of (ik ) to n, n ≥ 0 for the fields. A Maxwell-type problem is transformed into intertwined Laplace’s or Poisson’s potential-type boundary value problems with impenetrable boundary conditions. Using a toroidal coordinate system attached to the torus, they are solved as infinite series expansions for the fields in terms of toroidal eigenfunctions. In practice, what is accessible to the measurement is the scattered magnetic field. The static term (n = 0) provides most of its real (or in-phase) part and the second-order term (n = 2) consists of most of its imaginary part (quadrature), where in both cases a small contribution of the third-order term (n = 3) is being calculated. For n = 1, there exists no field, while the terms for n ≥ 4 and for such kind of applications have been proved to be of minor significance, hence they are neglected. The resulting infinite linear systems can be solved at any accuracy level through a cut-offprocess or via an analytical technique based on the method of finite continuous fraction solutions. Basics of the far-field approximation and the magnetic po- larizability tensor are also included. At implementation stage, simulations are proposed in various situations, where a full-wave, finite-element approach is discussed