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Exactly soluble models in the theory of electromagnetic propagation andscattering are essentially restricted to horizontally stratified or sphericallysymmetric geometries, with results also available for certain waveguidegeometries. However, there are a number of new problems in remote sensing andclassification of buried compact metallic targets that require a wider class ofsolutions that, if not exact, at least support rapid numerical evaluation.Here, the exact Chandrasekhar theory of the electrostatics of heterogeneouslycharged \emph{ellipsoids} is used to develop a "mean field" perturbation theoryof low frequency electrodynamics of highly conducting ellipsoidal targets, ininsulating or weakly conducting backgrounds. The theory is based formally on anexpansion in the parameter $\eta_s = L_s/\delta_s(\omega)$, where $L_s$ is thecharacteristic linear size of the scatterer and $\delta_s(\omega)$ is theelectromagnetic skin depth. The theory is then extended to a numericallyefficient description of the intermediate-to-late-time dynamics following anexcitation pulse. As verified via comparisons with experimental data takenusing artificial spheroidal targets, when combined with a previously developedtheory of the high frequency, early-time regime, these results serve to coverthe entire dynamic range encountered in typical measurements.

Chandrasekhar theory of electromagnetic scattering from strongly conducting ellipsoidal targets