A hybrid procedure to solve Hallen's problem

The knowledge of the electromagnetic fields in the neighborhood of an antenna needs the accurate evaluation of the current distribution on it. This is a subject which deserves particular attention mainly for sensors. It is called Hallen's problem and is relevant to the current distribution on a cylindrical antenna, two hollow cylinders separated by an infinitesimal gap. In this paper, we show that it is possible to extract the singular part of the current, and to obtain a reasonable precision with a finite number of terms regardless of the distance from the gap. The method seems to be suitable for thick dipole antennas. The procedure has been defined hybrid because we first resort to a finite number of steps of the iterative solution, and then the nth integral equation is solved by the Bubnov-Galerkin projection method.