The azimuthally invariant fluid equilibrium is obtained for a periodic strongly bunched charged annular beam with arbitrary radial density profile inside of a perfectly conducting cylinder and an external constant magnetic field. The electric and magnetic fields, which are utilized in the equilibrium solution, are computed self-consistently using an electrostatic Green's function technique in the longitudinal rest frame of the beam. An upper bound on the maximum self-field parameter, which allows beam equilibrium is obtained. As an application of the model, we find annular beam equilibrium for the Relativistic Klystron Oscillator experiment at Phillips Laboratory and the Backward Wave Oscillator experiment at the University of New Mexico. In addition, we compare the self-field parameters of these with the maximum theoretical values.