The near field and aperture admittance of a circumferential slot in a circular cylinder

Consider a circumferential slot in an infinitely long perfectly conducting circular cylindrical surface. The slot is driven by an electric field provided by either a microwave network (antenna problem) or an incident wave (scattering problem). The electric field in a slot less than one wavelength long is approximately half a cycle of a sinusoid. Assuming this approximate electric field, the authors compute the near field and the external aperture admittance of the slot. The electromagnetic field outside the cylinder is expressed as a continuous spectrum of cylindrical waves with z dependence e^jwz. Special treatment is given to the singularity that occurs when the phase constant is equal to the wavenumber. Ratios of Hankel functions that appear in the solution are replaced by simple approximations whenever possible