A new method of solution of Hallén’s problem

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Abstract
A wide class of electromagnetic scattering problems can be expressed as a system of dual integral equations. This kind of integral equation, occurring in boundary value problems wherein there is one equation for a certain region and another for the dual domain, is usual in diffraction problems. Considerable attention has been drawn by many researchers in the field of optics, acoustics, scattering of elastic waves, accelerator physics, and antenna theory. Wiener–Hopf techniques enable us to solve such kinds of integral equations when the two regions are contiguous and semi-infinite. Unfortunately Wiener–Hopf techniques do not apply if one of the regions is finite; this is the case for realistic scatterers, such as irises, antennas, and drift tubes in accelerators. In this article a general method for solving such dual integral equations is discussed and applied to a particular case: Hallén’s equation of cylindrical antennas. This method consists of a transformation of the dual integral equations into a Fredholm integral equation of the second kind and then into a linear system of algebraic equations. Comparisons with results obtained by other methods for a wide range of frequencies show the accuracy and the robustness of the proposed one.

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