Excitation of Electromagnetic Waves by an Electron Ring Beam in a Magnetized Plasma Waveguide

We study the resonant interactions between an electron ring beam and plasma waveguide modes,This is motivated by the research of radio emission in low solar corona.We consider a density-depleted duct(above an active region near a flare site)that may be treated as a magnetized plasma waveguide.The electromagnetic waves excited in the wveguide are classified into the so-called E-type and B-type waves.The results show that there are two unstable modes of B-type waves propagating parallel and anti-parallel to the direction of the electron beam.The effect of the finite radius and boundary conditions of the waveguide on the excitation of the electron beam.The effect of the finite radius and oundary conditions of the waveguide on the excitation of waveguide modes is important.For a given B-type mode,the smaller the radius R,the larger the temporal and spatial amplification important.For a given B-type mode.the smaller the radius R ,the larger the temporal and spatial amplification rate,we suggest that these excited waveguide modes could be one of the processes respondsible for the observed solar radio emission.