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 surface current. Simple integration of these leading terms of the current expansion yield the leading terms in the low-frequency expansions of the scattered fields. The general low-frequency expressions are confirmed by comparing them to low-frequency results obtained from exact time-harmonic eigenfunction solutions