Properties of generalized magnetic polarizability tensors

Ledger, Paul

doi:10.1002/mma.8856

Properties of generalized magnetic polarizability tensors

Ledger, Paul

Authors

Paul Ledger p.d.ledger@keele.ac.uk

Abstract

We present new alternative complete asymptotic expansions for the time harmonic low‐frequency magnetic field perturbation caused by the presence of a conducting permeable object as its size tends to zero for the eddy current approximation of the Maxwell system. Our new alternative formulations enable a natural extension of the well‐known rank 2 magnetic polarizability tensor (MPT) object characterization to higher order tensor descriptions by introducing generalized MPTs (GMPTs) using multi‐indices. In particular, we identify the magnetostatic contribution, provide new results on the symmetries of GMPTs, derive explicit formulae for the real and imaginary parts of GMPT coefficients and also describe the spectral behavior of GMPT coefficients. We also introduce the concept of harmonic GMPTs (HGMPTs) that have fewer coefficients than other GMPT descriptions of the same order. We describe the scaling, translation and rotational properties of HGMPTs and describe an approach for obtaining those HGMPT coefficients that are invariant under the action of a symmetry group. Such an approach is one candidate for selecting features in object classification for hidden object identification using HGMPTs.

Journal Article Type	Article
Acceptance Date	Oct 19, 2022
Online Publication Date	Nov 19, 2022
Publication Date	Mar 30, 2023
Publicly Available Date	May 30, 2023
Journal	Mathematical Methods in the Applied Sciences
Print ISSN	0170-4214
Electronic ISSN	1099-1476
Publisher	Wiley
Peer Reviewed	Peer Reviewed
Volume	46
Issue	5
Pages	5604-5631
DOI	https://doi.org/10.1002/mma.8856
Keywords	asymptotic analysis; eddy current; inverse problems; magnetic polarizability tensor; metal detection; spectral problems
Publisher URL	https://onlinelibrary.wiley.com/doi/10.1002/mma.8856