Traveling Waves in Relation to the Surface Fields on a Semi‐Infinite Cone

Abstract

For a plane electromagnetic wave at nose-on incidence on a semi-infinite perfectly conducting cone expressions for the surface field components are obtained. These have been programmed for numerical computation and data are presented for the magnitudes and phases as functions of the distance from the tip for three different cone angles. Comparison with results derived from the physical optics approximation and from a simple wedge approximation shows that the differences between the exact and physical optics values are not attributable to a tip-excited wave.

The Zeros of P 1 ν (cosθ) and ∂ ∂θ P 1 μ (cosθ)

“…In the course of a recent study [1] of the scattering of an electromagnetic wave by a semi-infinite, perfectly conducting cone, it became necessary to compute numerically sets of positive zeros of certain associated Legendre functions treated as functions of their degree; that is, to find vi and Ai, i = 1, 2, 3, * * satisfying (1) PVi(cos 0) = 0, and (2) (a/a@) PIi(cos 0) = 0, for a given 0. In the course of a recent study [1] of the scattering of an electromagnetic wave by a semi-infinite, perfectly conducting cone, it became necessary to compute numerically sets of positive zeros of certain associated Legendre functions treated as functions of their degree; that is, to find vi and Ai, i = 1, 2, 3, * * satisfying (1) PVi(cos 0) = 0, and (2) (a/a@) PIi(cos 0) = 0, for a given 0.…”

Further studies of backscattering from a finite cone

“…A possible explanation of the discrepancy is the influence of the conical surface on the effective strength of the rays incident on and backscattered from the edge of the base. Computed data for the fields on the surface of a semi-infinite cone [Senior and Wilcox, 1967] show a behavior which, at large distances from the tip, can be approximated by a Fresnel integral with argument r = [ka tan (•/ 2) ]•/•-. For r >> 1 the computed results agree with physical optics, but for , • 1.5 the results can exceed physical optics by more than 1.5 db.…”

Commission 6: Progress in Radio Waves and Transmission of Information: 1. Radio Waves

“…Such questions as the relative advantages of the different methods and the error estimates of the various solutions remain unanswered, and, in spite of the valuable data obtained for specific (simple) geometries, the approach has so far added little to our knowledge of scattering phenomena. On the other hand, the advent of high-speed computers has made feasible the evaluation of solutions obtained by mode matching [Weiner and Borison, 1966], including those 'canonical' solutions for which only modal expansions are available [Senior, 1966;Liang and Lo, 1967;Senior and Wilcox, 1967].…”