volume | PIER Journals

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.

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Professor Dozyslav B. Kuryliak

Dr. Oleksiy M. Sharabura