GENERAL RELATION BETWEEN SURFACE IMPEDANCE AND SURFACE CURVATURE

We relate in a general way the surface impedance of a metal to the loc al curvature of the surface. We obtain the corrections to the flat-sur face impedance formula up to second order in d Delta, where d is the p enetration depth of the electromagnetic field and Delta is the differe nce between maximum and minimum curvature. We give explicit expression s relating to each other the electric and magnetic fields parallel to the surface, E(parallel to) and H-parallel to respectively. We show th at the terms neglected in the surface impedance approximation contain only the second derivatives of these fields in the plane tangent to th e surface.