ASYMPTOTIC EXPRESSIONS FOR THE SURFACE CURRENTS INDUCED ON A CYLINDRICALLY CURVED IMPEDANCE STRIP

The present paper is concerned with the derivation of the electric and magnetic surface currents induced on a cylindrically curved impedance strip. By considering the locality of the high-frequency diffraction phenomena the physical (-pi,pi) interval for the usual cylindrical pol ar angle is replaced by an abstract infinite interval (-infinity,infin ity) whereby the related mixed boundary value problem is formulated as a ''modified matrix Hilbert'' problem. By using the Debye approximati ons for the Hankel and Bessel functions involved, the modified matrix Hilbert problem is first decoupled and then reduced to two pairs of si multaneous Fredholm integral equations of the second kind which are so lved by iterations. The explicit expressions for the electric and magn etic surface current components attributable to the reflection, edge o r surface diffractions of the incident field as well as to the edge re flections of these components themselves are obtained by evaluating th e current integrals asymptotically. The results derived in this paper constitute also a rigorous proof for a conjecture made by Idemen on th e reflections of the surface currents at the edges.