Near field of a loaded circular toroidal antenna

In this paper a special toroidal coordinate system is introduced in order to derive general solutions for the electric and magnetic fields from a toroidal antenna. These solutions depend on the current distribution on the toroid and are in integral forms. Some Fourier expansion techniques have been used in order to simplify these integral equations. The surface current is found under the assumption that the thickness of the toroid is thin compared to the wavelength, which leads to an analytic solution for the fields at the center. Many uniform loading impedances are used with the purpose of producing a plane-wave-like field at the center of the toroid.