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Semi–analytical method for the identification of inclusions by air–cored coil interaction in ferromagnetic media

Abstract : The magnetostatic vector fields in terms of harmonic scalar potentials scattered by near–surface air inclusion of arbitrary shape, embedded in a conductive ferromagnetic medium, are investigated. The hollow inclusion is illuminated by a current–carrying coil, which serves as the primary field. The do-main of interest is separated into homogeneous subdomains under the assumption of a suitable truncation of the region of magnetostatic activity at a long distance from the incident source. Therein, the field is considered negligible and consequently a perfect magnetic boundary condition is implied. On the other hand, the introduced methodology addresses the full coupling between the two interfaces, i.e. the plane that distinguishes the half–space ferromagnetic material from the open air and the arbitrary surface among the inclusion and the ferromagnetic region. To this end, 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 scattering problem is solved by means of a modal approach, where potentials associated with the half–space are expanded via cylindrical harmonic eigenfunctions, while those related with the inclusion’s arbitrary geometry admit a generalized–type formalism, being the key to our method. 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 would be feasible. Once done, the calculation of the exact solutions leads to infinite linear algebraic systems, whose solution is achieved trivially through standard cut–off techniques. Thus, we obtain the implicated fields in a general analytical and compact fashion, independent of the inclusion’s geometry. In order to demonstrate the efficiency of the analytical model approach, we assume the degenerate case of a spherical inclusion, whereas the air–cored coil simulation via a numerical procedure validates our generalized method. The calculation is very fast, rendering it suitable for use with parametric inversion algorithms.
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Contributor : Dominique Lesselier Connect in order to contact the contributor
Submitted on : Monday, November 13, 2017 - 4:41:08 PM
Last modification on : Saturday, June 25, 2022 - 10:27:28 PM



Panayiotis Vafeas, Anastassios Skarlatos, Theodoros Theodoulidis, Dominique Lesselier. Semi–analytical method for the identification of inclusions by air–cored coil interaction in ferromagnetic media. Mathematical Methods in the Applied Sciences, Wiley, 2018, 41, pp.6422-6442. ⟨10.1002/mma.5168⟩. ⟨hal-01634075⟩



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