A perturbation technique for solving boundary value problems arising in the electrodynamics of conducting bodies

Abstract

The electrodynamics of wave reflection from conducting media lead to difficult mathematical problems because of the matching conditions which must be met at the interface between conductors and nonconductors. Simplified boundary conditions have been proposed by Leontovitch and others which considerably simplify certain of the mathematical problems. We discuss the Leontovitch condition together with certain of its shortcomings and present a new method which overcomes some of the difficulties of the Leontovitch condition. The new method is a perturbation away from infinite conductivity which allows the solution of electrodynamics problems to be calculated to any order of accuracy in the quantity (ωε/σ)^1/2 for some important cases. An instance in which the perturbation method fails is also discussed.