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The dispersion relation of electromagnetic waves in a rippled-wall waveguide with a degenerate plasma column protected by an annular dielectric layer is theoretically investigated. By injecting a thin annular relativistic electron beam (TAREB) in the region between dielectric and metallic cylinders in the aforementioned configuration as an energy source, the excitation of terahertz (THz) electromagnetic waves is investigated. Also, the dependence of dispersion relation and time growth rate on the radius of the dielectric, the corrugation amplitude, and period is studied. Furthermore, it is found that the presence of the degenerate plasma rod in the rippled-wall waveguide leads to obtain high-frequency modes in the THz frequency region. Finally, the electric-field profiles in this waveguide are plotted.