The problem of excitation and radiation of the array of narrow circumferential or arc transverse slots cut in the infinitely thin and perfectly conducting coaxial line screen has been solved by the magnetomotive forces method (MMF) in this paper. The frequency-energy and spatial characteristics of these systems are calculated taking into account the internal and external space interconnections between the radiators on conditions of arbitrary location of the slot elements when internal and external spaces have been filled by the dielectric for any values of permittivity. The results of calculation and analysis of the amplitude and phase distributions in the slot arrays, directional and energy antenna characteristics depending on the working wavelength in cases of the slot element location on the infinite or semi-infinite coaxial lines have been proposed.