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

Abstract

The magnetostatic harmonic fields scattered by a near‐surface air inclusion of arbitrary shape, embedded in a conductive ferromagnetic medium and illuminated by a current‐carrying coil, are investigated. The scattering domain is separated into homogeneous subdomains under the assumption of a suitable truncation at a long distance from the incident source, whereas a perfect magnetic boundary condition is implied. The introduced methodology addresses the full coupling between the two interfaces, ie, the plane that distinguishes the half‐space ferromagnetic material from the open air and the arbitrary surface among the inclusion and the ferromagnetic region. Therein, continuity conditions are applied in a rigorous way, while the expected behavior of the fields, either as ascending or as descending, are taken into account. The potentials associated with the half‐space are expanded via cylindrical harmonic eigenfunctions, while those related with the inclusion's arbitrary geometry admit generalized‐type formalism. However, since the transmission conditions involve potentials with different eigenexpansions, we are obliged to rewrite cylindrical to generalized functions and vice versa, obtaining handy relationships in terms of easy‐to‐handle integrals, where orthogonality then is feasible. Once done, the calculation of the exact solutions leads to infinite linear algebraic systems, manipulated through standard cut‐off techniques. Thus, we obtain the implicated fields in a general analytical and compact fashion, independent of the inclusion's geometry. We demonstrate the efficiency of the analytical model approach, assuming the degenerate case of a spherical inclusion, whereas the air‐cored coil simulation via a numerical procedure validates our method. The calculation is very fast, rendering it suitable for use with parametric inversion algorithms.