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A kinetic cyclotron maser instability associated with a hollow-beam distribution function is studied. The instability differs from that discussed for the gyrotron device in two respects: in the present case the momentum dispersion is substantial, and furthermore there exists a low-energy background plasma. On the basis of physical arguments we can demonstrate that the hollow-beam distribution is far more unstable than the loss cone distribution which has been extensively investigated in recent years. A criterion for maximum growth rate is established on the basis of consideration of the resonance ellipse. The validity of this criterion is supported by the results of numerical calculation.