Low Frequency Scattering From Two Dimensional Perfect Conductors

Exact expressions are obtained for the leading terms in the low- frequency expansions of the far field scattered by an arbitrarily shaped cylinder with finite cross section, an arbitrarily shaped cylindrical bump on a ground plane, and an arbitrarily shaped cylindrical dent in a ground plane. By inserting the low-frequency expansions of the incident plane wave and Green's function into exact integral equations for the surface current, integral equations are obtained for the leading terms in the low-frequency expansions of the surf ace current. Simple integrations of these leading terms of the current expansion yield the leading terms in the low-frequency expansions of the scattered fields. For the cylinder with finite cross section, the leading term in the low-frequency expansion of the TM scattered far field is explicitly given by an expression that is independent of the shape of the cylinder. The explicit expression for the low-frequency TE scattered far field contains three constants that depend only on the shape of the cylinder. These three constants are found from the solutions to two electrostatic problems. The explicit expressions for the low-frequency diffracted fields of a bump or dent contain one constant that depends only on the shape of the bump or dent. Remarkably, this single constant is the same for both TM and TE polarization and can be found from the solution to either an electrostatic or magnetostatic problem. The general low-frequency expressions are confirmed by comparing them to low-frequency results obtained from exact time-harmonic eigenfunction solutions, and constants an evaluated for a number of geometries. Low-Frequency scattering, Static problems, Two- dimensional perfect conductors, Integral equations.