Axial‐Radar Cross Section of Finite Cones by the Equivalent‐Current Concept with Higher‐Order Diffraction

In a recent paper, Senior and Uslenghi [1971] further developed the radar cross section of a finite cone. For the axial radar cross section, they evaluated the fields on the axial caustic using the first‐ and second‐order solution of Keller [1960]. It is the intent of this paper to show that the equivalent‐current method of Ryan and Peters [1969, 1970] yields the same results as those of Senior and Uslenghi. The equivalent‐current technique is, however, a more straightforward procedure to implement for the treatment of the scattered fields in the vicinity of the caustic and should be included in the collection of diffraction solutions. The equivalent‐current technique is required only in the vicinity of the axial caustic. The results merge with the more conventional procedures as the observation point moves away from the axial caustic region. Thus, the numerical results discussed in this paper are concerned with the axial backscattered fields. In our development, the second‐order diffracted ray across the base of the cone includes a factor of one‐half not included in the Senior‐Uslenghi solution. The reason for this factor is discussed in detail. The solution to a simpler wedge problem with and without this factor is compared to an integral equation solution in the Appendix. The experimental and theoretical results for the cone differ consistently by approximately 2 db for a wide range of cone‐base radii and indicate that an additional mechanism contributes significantly to the scattered fields. One is suggested and indeed is required in the similar wedge solution of the Appendix. The equivalent‐current technique is seen to be applicable to cones which have base radii as small as 0.3λ.