Theory of cusptron microwave tubes

Stability properties of the negative-mass instability in a rotating annular electron beam (E-layer) is investigated, in connection with applications on the cusptron microwave tubes. Analysis is carried out for an infinitely long E-layer propagating through a magnetron-type conducting wall and propagating parallel to an applied axial magnetic field. We assume that the E-layer is thin and very tenuous. A closed algebraic dispersion relation of the negative-mass instability is obtained, including the important influence of conducting boundaries on the mode control in microwave generation and amplification. It is shown that for typical present experimental beam parameters, gain and efficiency of the cusptron can be more than five times those of the gyrotron. Moreover, with an appropriate geometric configuration, perturbations with azimuthal mode number N can be dominantly unstable, thereby optimizing the microwave power output for radiation with high frequency omega = N times omega sub c, where omega sub c is the electron cyclotron frequency and N is the resonator number in the conducting wall.