Abstract: Making use of the self-consistent linear field theory, the three-dimensional perturbation of electrons affected by the perturbed electromagnetic fields is generally discussed. The interactions of wave to the two conventional relativistic electron beams in the dielectric Cherenkov maser, i.e., annular electron beam and solid electron beam, are analyzed in detail. The dispersion equations and the wave growth rates corresponding to the two relativistic electron beams are derived.The effects of the radii of the two electron beams on the wave growth rates are calculated, and the discussions are presented.

Key words: relativistic electron beam, three-dimensional pertu rbation of electron, wave growth rate, dielectric Cherenkov maser, annular, solid