Understanding the magnetic polarizability tensor

• Published in: IEEE transactions on magnetics 2016-05, Vol.52 (5), p.1-16
• Main Authors: Ledger, Paul D., Lionheart, W. R. Bill
• Format: Article
• Language: English
• Subjects: Conductivity; Eddy currents; land mine detection; magnetic induction; Magnetic moments; Magnetic resonance imaging; Magnetism; Mathematical model; metal detectors; polarizability tensors; Shape; Tensile stress
• ISSN: 0018-9464; 1941-0069
• DOI: 10.1109/TMAG.2015.2507169

The aim of this paper is to provide new insights into the properties of the rank 2 polarizability tensor M̆ proposed by Ledger and Lionheart for describing the perturbation in the magnetic field caused by the presence of a conducting object in the eddy-current regime. In particular, we explore its connection with the magnetic polarizability tensor and the Pólya-Szegö tensor and how, by introducing new splittings of M̆, they form a family of rank 2 tensors for describing the response from different categories of conducting (permeable) objects. We include new bounds on the invariants of the Pólya-Szegö tensor and expressions for the low-frequency and high-conductivity limiting coefficients of M̆. We show, for the high-conductivity case (and for frequencies at the limit of the quasi-static approximation), that it is important to consider whether the object is simply or multiply connected but, for the low-frequency case, the coefficients are independent of the connectedness of the object. Furthermore, we explore the frequency response of the coefficients of M̆ for a range of simply and multiply connected objects.