Excitation of extraordinarily polarized azimuthal surface eigenwaves is shown to be possible in the electron cyclotron frequency range in waveguides with metal walls that are partially filled with cold magnetoactive plasma. Interaction of these waves with electron beams, which rotate around the plasma column in a narrow layer separating the plasma from the wall of the waveguide, is studied. Dependences of the beam instability growth rate on the waveguide parameters (plasma and beam density; value of the external steady axial magnetic field; radius of the plasma cylinder and width of the vacuum layer; magnitude and sign of azimuthal wave number) are studied numerically. Two regimes of beam instability are demonstrated: separate resonance and resonance overlapping.
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