A kinetic cyclotron maser instability associated with a hollow beam of electrons

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.