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We study the resonant interactions between an electron ring beam and plasma waveguide modes. This is motivatedby the research of radio emission in low solar corona. We consider a density-depleted duct (above an active regionnear a flare site) that may be treated as a magnetized plasma waveguide. The electromagnetic waves excited inthe waveguide are classified into the so-called E-type and B-type waves. The results show that there are twounstable modes of B-type waves propagating parallel and anti-parallel to the direction of the electron beam. Theeffect of the finite radius and boundary conditions of the waveguide on the excitation of waveguide modes isimportant. For a given B-type mode, the smaller the radius R, the larger the temporal and spatial amplificationrate. We suggest that these excited waveguide modes could be one of the processes responsible for the observedsolar radio emission.