Abstract:The dispersion equation of TM mode slow wave in a cylindrical waveguide having a annular plasma sheet is derived under the condition of plasma thickness effect. By means of the relativistic space charge wave theory, the space charge wave equation is obtained when the relativistic electron beam is moving along the inner surface of the plasma sheet guided by a axial magnetic field. The interaction growth rate between the electron beam and slow space wave and the frequency shifting are obtained. The influence of plasma thickness on dispersive characteristics and interaction growth rate are discussed. Someuseful results are obtained.