Diffraction of Axially-Symmetric Tm-Wave From Bi-Cone Formed by Finite and Semi-Infinite Shoulders

Abstract

The problem of axially-symmetric TM-wave diffraction from a perfectly conducting bi-cone is analyzed. Bi-cone is formed by finite and semi-infinite conical shoulders and illuminated by ring magnetic source. The problem is formulated in a spherical coordinate system as a mixed boundary problem for Helmholtz equation. The unknown H ϕ-diffracted field is sought as expansion in series of eigenfunctions for each region, formed by the bi-cone. The solution of the problem then is reduced to the infinite set of linear algebraic equations (ISLAE) of the first kind by means of mode matching technique and orthogonality properties of the eigen functions. The main parts of the asymptotic expressions of ISLAE matrix elements, determined for large indexes, identify the convolution type operator. The corresponding inversed operator is represented in an explicit form. Two of these operators are applied to reduce the problem to the ISLAE of the second kind and to determine the new analytical regularization method for the solution of wave diffraction problems for bi-conical scatterers. The unknown expansion coefficients can be determined from the ISLAE with the given accuracy by the reduction method. The particular cases such as low frequency approximation and transition from bi-cone to conical monopole and disc-cone scatterer are analyzed. The numerically obtained results are applied to the analysis of scattering properties of hollow conical monopoles and disc-conical scatterers.

Wave diffraction from the Biconical Section in the semi‐infinite conical region

“…are known. Making use of the orthogonality of Legendre functions, the next representation can be written as in the previous studies 16,24…”

“…[16][17][18][19][20][21][22][23] The particular case of this problem, when the two cones form a biconical structure with only one edge, was considered in the previous studies. 24,25 The presence of the shoulder with more than one circular edge in the bicone greatly complicates the problem, because this presence creates the interaction of waves between the edges, which needs to be taken into account. But such a minor geometric complication substantially expands the range of practical applicability of this structure.…”

Axially-Symmetric Tm-Waves Diffraction by Sphere-Conical Cavity

“…Let us simplify Equation (38). For this purpose we take into account the small dimensions of the hole (|sc 1 /2| 1).…”

“…For this purpose we take into account the small dimensions of the hole (|sc 1 /2| 1). Thus, we apply the appropriate asymptotic expressions for modified Bessel and Macdonald functions [41] to estimate the known coefficients in Equation (38) and, neglecting the terms of order |ρ 1 /2| 2 in the first double series, we immediately derive the approximate equation as…”

“…The proposed approach is called the method of analytical regularization or semi-inversion method. This approach was used earlier for the studies of the diffraction of acoustic and electromagnetic waves from conical, bi-conical, and wedge structures [21][22][23][32][33][34][35][36][37][38][39][40].…”