Modeling of a cylindrical wire antenna with flat end caps using a rigorous moment method technique

It is usually assumed in the modeling of a thin wire antenna that the current distribution vanishes at the ends. This is a true condition in the limit as the wire radius approaches zero. With finite dimensions, however, charges can accumulate on the ends of the dipole which can have an effect on the current distribution of the wire. Modeling the dipole with flat end caps effectively isolates the inside of the cylinder from the outside and allows finite charge to exist on the end surface. An investigation is conducted in order to determine an accurate model for the charge density on the flat end faces of a cylindrical dipole. A moment method technique is applied to the problem in which trigonometric basis functions are assumed for the current on the wire and pulse basis functions are assumed for the charge distribution on the end caps. In addition, the edge discontinuity is taken into account by including a ring charge. The moment method technique involves the theory of extrapolated continuity [Yeh and Mei, 1967] and point matching. The solution is very general in terms of dipole length, radius and wavelength, since no simplifying assumptions or approximations were made. This rigorous analysis of a closed dipole should provide an accurate model for the charge density and its associated current distribution on the flat end cap.