Axially symmetric TM-wave diffraction from bi-cone formed by semi-infinite and truncated semi-infinite cones

Abstract

The problem of axially symmetric TM-wave diffraction from the perfectly conducting bi-cone formed by the semi-infinite and truncated semi-infinite cones is considered. The bi-cone is excited by the ring magnetic source. The problem is formulated in spherical coordinate system as a mixed boundary value problem for Helmholtz equation with respect of the unknown diffracted field. The solution of the problem is reduced to the infinite set of linear algebraic equations (ISLAE) of the second kind by means of the mode matching technique and the analytical regularization procedure. Two sorts of the second kind ISLAE are obtained based on the left- and right-side regularizations. The unknown expansion coefficients can be determined from each of the ISLAE with the given accuracy by the reduction method. The correlations between the ISLAE of our problem and of the supplementary problem of wave diffraction by the bi-cone formed with finite and semi-infinite shoulders are found. The approximate solution is obtained in the analytical form for the small aperture of the truncated shoulder. The numerically obtained results are focused on the practically important diffraction from the bi-cone formed by an infinite plane with circular hole and the semi-infinite conical probe.

Keywords:

• Magnetic ring source
• bi-conical waveguide
• analytical regularization
• rigorous solution

Notes

No potential conflict of interest was reported by the authors.