The electromagnetic wave diffraction from the modified cone formed by a circular truncated cone whose aperture is closed by a spherical cap is considered. The problem is reduced to the solution of the mixed boundary value problem for the Helmholtz equation. The axially symmetric version of the problem, where the cone is excited by a radial electric dipole (E-polarization wave diffraction problem), is analyzed. A new approach to the solution is proposed. The solution includes the application of the Kontorovich-Lebedev integral transformation, the nonstandard procedure for derivation of the Wiener-Hopf equation and its reduction to the set of linear algebraic equations of the second kind. Their solution ensures the fulfillment of all the necessary conditions including the edge condition. The approximate equation for the sharp truncated cone terminated by the spherical cap is analyzed. The low frequency approximation as well as the transition to the plane which incorporates the hemispheric cavity is analysed. The numerical calculation results are presented.
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