SURFACE IMPEDANCE OF CONDUCTING CYLINDERS Luc Knockaert and Daniel De Zutter 1 Abstract Asymptotic developments for electromagnetic field problems involving imperfectly con- ducting cylinders are presented. It is shown that a judiciously chosen partial integration scheme, based on a theorem of Darboux, leads to an asymptotic series which takes into account both local curvature and global diameter of the cylinder. As a byproduct of the asymptotic series, new formulas are obtained for the surface impedance of cylinders with boundaries with continuous curvature and cylinders with polygonal boundaries. 1 INTRODUCTION The concept of surface impedance [1], [2] is of utmost importance in electromagnetic scattering in the presence of penetrable bodies, since it allows one to deal immediately with the scattering (exterior) problem, without having to solve concurrently for the interior fields. To these author’s knowledge, no rigorous asymptotic treatment concerning surface impedance and its range of validity has appeared in the literature since Senior [2] presented the first validity results in 1960, except for a numerical validation [3] in the case of simple shapes and an interesting result in the limited context of scattering by periodic gratings [4]. The main problem in this context is that surface impedance is in reality an integral operator. What is usually called surface impedance is a constant operator which asymptotically approximates the exact surface impedance operator. In this paper we tackle the surface impedance problem for cylinders in an indirect way. We present asymptotic developments for two relevant integrals pertaining to electromagnetic time-harmonic scattering by imperfectly conducting cylinders. The asymptotic evaluations are obtained through pertinently chosen partial integration schemes and by invoking a theorem of Darboux [5], [6]. The important features of the asymptotic developments thus obtained is that both local aspects of the boundary curve, such as the curvature, and global aspects, such as the diameter of the curve, come into action. The calculations lead straightforwardly to the determination of the surface impedance of conducting cylinders in the cases of E and H-wave 1 Dept. of Information Technology INTEC, St. Pietersnieuwstraat 41, B-9000 Gent, Belgium. Tel: +32 9 264 33 16, Fax: +32 9 264 42 99, e-mail: knokaert@intec.rug.ac.be