Abstract
Diocotron instability and drift-beam instability of an annular relativistic electron beam are studied concurrently. It is shown that the conditions for the appearance of both instabilities can be satisfied simultaneously, but that diocotron instability is predominant, because its growth increment is larger. The ion coat protruding beyond the beam increases the growth increment of drift-beam instability and has practically no effect on the conditions of its development. The presence of ions inside the cavity of the annular electron beam increases the growth increment of diocotron instability and makes the conditions for its appearance more favorable. Perturbations with an azimuthal wave number absolute value l = 1 can then become unstable.
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