We solve the problem of diffraction of the field of radial electric dipole on a cone whose surface is formed by finite perfectly magnetically conducting and truncated semiinfinite perfectly electrically conducting conical surfaces. The problem is solved by the Wiener–Hopf technique with the use of the Kontorovich–Lebedev integral transformation. We obtain the exact solution of the problem in the static limit and its approximate solution in the low-frequency case. We deduce an expression for the directional pattern of a cone with perfectly absorbing vertex (within the framework of the Macdonald model). We also clarify the effect of the edge of absorbing fragment of the cone surface on its scattering properties.
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Translated from Matematychni Metody ta Fizyko-Mekhanichni Polya, Vol. 56, No. 2, pp. 191–202, April–June, 2013.
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Kurylyak, D.B. Diffraction of Electric Waves on a Cone Formed of Perfectly Magnetically and Electrically Conducting Surfaces. J Math Sci 203, 239–252 (2014). https://doi.org/10.1007/s10958-014-2104-8
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DOI: https://doi.org/10.1007/s10958-014-2104-8