Singular Integral Equations in the Problem of Diffraction of an Electromagnetic Plane Wave by a Perfectly Conducting Finite Hollow Cylinder

摘要

The problem of diffraction of a plane electromagnetic wave by a finite metallic cylinder (linear electric vibrator) is one of the key problems in the theory of receiving antennas, and it is most difficult to determine the electric-current distribution over the cylinder. The method of calculating the electric-current distribution in a system of thin linear vibrators excited by a plane wave was developed in [1 ]. In that paper, the diffraction problem (in the thin-vibrator approximation) was reduced to an ill-posed problem [2] that was represented by a set of Fredholm integral equations of the first kind with logarithmic singularities in their kernels and was solved by the self-regularization method [3], Symmetric vibrations (independent of the azimuth coordinate) of a perfectly conducting finite hollow cylinder were considered in [4]. However, Tikhonov and Dmitriev [3] stated that the solution obtained in [4] is incorrect. On the other hand, the two-dimensional problem of diffraction of a plane electromagnetic wave by an infinite perfectly conducting circular cylinder was solved long ago in [5] under the assumption of the absence of field variations along the axial cylindrical coordinate. In [6-8], the theory of singular equations was applied to develop the theory of a thin electric vibrator in the approximation of a perfectly conducting finite hollow circular cylinder by ignoring the azimuthal electric-current component. In the present study, the problem of the diffraction of a plane electromagnetic wave by a perfectly conducting finite hollow circular cylinder is analyzed with allowance for the azimuthal component of the electric current arising on the cylinder surface.