Chandrasekhar theory of electromagnetic scattering from strongly conducting ellipsoidal targets

Abstract: Exactly soluble models in the theory of electromagnetic propagation and scattering are essentially restricted to horizontally stratified or spherically symmetric geometries, with results also available for certain waveguide geometries. However, there are a number of new problems in remote sensing and classification of buried compact metallic targets that require a wider class of solutions that, if not exact, at least support rapid numerical evaluation. Here, the exact Chandrasekhar theory of the electrostatics of heterogeneously charged \emph{ellipsoids} is used to develop a "mean field" perturbation theory of low frequency electrodynamics of highly conducting ellipsoidal targets, in insulating or weakly conducting backgrounds. The theory is based formally on an expansion in the parameter $\eta_s = L_s/\delta_s(\omega)$, where $L_s$ is the characteristic linear size of the scatterer and $\delta_s(\omega)$ is the electromagnetic skin depth. The theory is then extended to a numerically efficient description of the intermediate-to-late-time dynamics following an excitation pulse. As verified via comparisons with experimental data taken using artificial spheroidal targets, when combined with a previously developed theory of the high frequency, early-time regime, these results serve to cover the entire dynamic range encountered in typical measurements.