The problem of axially-symmetric TM-wave diffraction from the perfectly conducting sphere-conical cavity is analysed. The cavity is formed by a semi-infinite truncated cone; one of the sectors of this cone is covered by the spherical diaphragm. The problem is formulated in terms of scalar potential for spherical coordinate system as a mixed boundary problem for Helmholtz equation. The unknown scalar potential of the diffracted field is sought as expansion in series of eigenfunctions for each region, formed by the sphere-conical cavity. Using the mode matching technique and orthogonality properties of the eigenfunctions, the solution to the problem is reduced to an infinite set of linear algebraic equations (ISLAE). The main part of asymptotic of ISLAE matrix elements determined for large indexes identifies the convolution type operator. The corresponding inverse operator is represented in an explicit form. The convolution type operator and corresponding inverse operator are applied to reduce the problem to the ISLAE of the second kind. This procedure determines the new analytical regularization method for the solution of wave diffraction problems for the sphere-conical cavity. The unknown expansion coefficients, which are determined from the ISLAE by the reduction, belong to the space of sequences that allow obtaining the solution which satisfies all the necessary conditions with the given accuracy. The particular cases, such as transition from sphereconical cavity to the open hemispherical resonator, as well as the low frequency approximation, are analysed. The numerically obtained results are applied to the analysis of TM-waves radiation through the circular hole in the cavity.
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