Computing the magnetic polarizability of thin conducting sheets using an eigenvalue decomposition

The ability to detect and dispose of buried mines requires effective means by which to discriminate between hazardous targets and benign clutter. In that regard, wide-band electromagnetic induction (EMI) sensors have shown significant promise in their ability to classify buried metallic objects based on their response to illumination by a time-varying magnetic field. A target´s scattered response may be expressed compactly in its magnetic polarizability dyadic, a form that describes the reaction of the scatterer to an arbitrary magnetic field. The magnetic polarizability dyadic may be written in terms of the eddy currents that are induced in the target. The method described in this paper uses a scalar stream function as a basis for the eddy currents that are induced in the target. This approach is powerful since the solenoidality of the current density is enforced trivially and its boundary conditions may be enforced elegantly. By setting up the eddy current equation as a generalized eigenvalue problem we arrive at a modal decomposition of the polarizability dyadic. Distribution A: Approved for public release.