Modeling surface currents on electrically large impedance cylinders-2D, TM case

Scattering and diffraction from terrain obstacles have a major effect on radio wave propagation in a natural environment. Mountains, ridge lines and hills can exhibit the properties of a long, slowly curving feature essentially infinite in one dimension. The local radius of curvature of these obstacles is large compared to wavelength and therefore diffraction from convex surfaces as opposed to wedge diffraction is the more applicable approach. No GTD field solutions for diffraction from convex surfaces are valid in all regions around the object. The calculation of surface currents will generate the exact fields in all regions through the radiation integrals. If the exact surface current is formulated in terms of a physical optics (PO) term and correction or diffraction term the diffraction current is highly localized to the shadow boundary for a surface with large, slowly varying, radius of curvature. The diffraction current for a circular cross section is therefore applicable to any convex surface where the local radius of curvature is known. Surface diffraction currents can be generated by applying Fock theory, however the formulations are mathematically complex, and in the lit region near the shadow boundary numerical integration must be performed. In Casciato and Sarabandi a heuristic approach was used to develop a macromodel which simply and accurately predicts the asymptotic behavior of the Fock currents for a PEC circular cylinder illuminated by a plane wave at oblique incidence. In this paper a method is developed to extend this method for the TM case, normal incidence, to that of an impedance cylinder which more accurately represents a natural terrain feature.