The mechanism of excitation of a microwave in a circular waveguide, partially or completely filled with a dense magnetized plasma, by a weak thin annular relativistic electron beam is investigated. In view of the plasma as a weakly dispersive medium, a self-consistent set of coupled nonlinear and relativistic wave-particle equations is derived. The expressions of energy components are presented, and the conservation character of the total energy is proved. Under the linear approximation, the dispersion equation of interaction in the case of a waveguide completely filled with a plasma is obtained both by using a Green's function and by linearizing the derived coupled wave-particle equations. The frequency of the most unstable wave, as well as the frequency shift and the growth rate, is solved. By using the single-wave model, especially in the approach of one-component simulation, the evolution of the wave in both configurations is studied in some detail. The beam energy to microwave conversion efficiency is obtained when the field is saturated. The effects of the beam energy, position, and quality on the efficiency are discussed. For the configuration of plasma completely filling a waveguide, the distribution of the beam electrons is dotted in the phase space at various times. The saturation of instability is shown to be due to the formation of vortices in the phase space as a result of phase trapping and the bunching of beam electrons.