An Asymptotic Solution for Boundary - Layer Fields Near a Convex Impedance Surface

Abstract

—An analytic representation for fields (E, H) that, for wavenumber k, satisfies the Maxwell equations to order k ^-2/3 within a suitably-defined boundary-layer neighborhood is provided for the case of a general doubly-curved convex impedance surface. This solution is an ansatz construct obtained via heuristic modification of a residue-series solution to a corresponding circular-cylinder canonical problem with an infinitesimal axial magnetic dipole excitation. The field components are in the form of creeping-ray modal series written as functions of geodesic-polar and normal coordinates (s, , n) appropriate to the vicinity of a general convex surface. Adaptation of the canonical solution to the general case begins with a transformation from the native cylindrical (p, φ, z) coordinates of the canonical solution to a system ( p, _c, s) defined by cylinder-surface geodesics. The transformed canonical solution is further modified by replacement of corresponding factors deriving from the metric and curl operators in the (p, _c, s) and (s, , n) systems, and by pervasive application of a substitution previously employed in a more limited way by Pathak and Wang. The physical content of the substitution process is that the creeping-ray attenuation along the geodesics occurs independently of the surface normal curvature transverse to the geodesic direction.