Theory of phase-locked gyrotrons operating at cyclotron harmonics

The theory of phase-locked gyrotrons operating at cyclotron harmonics is developed, with particular attention given to the effects of electron velocity spread. Extensive studies are made for operation at the second harmonic in which phase locking is achieved by subharmonic prebunching. One result of these studies is that we are able to predict, for a range of velocity spreads, the parameters that yield the highest efficiency. More important, we find that for electron beams with velocity spread and a finite transit angle in the drift region, the bandwidth of stable operation is drastically reduced. This effect can be mitigated by properly tapering the external magnetic field there. Such tapering is necessary in devices where the bandwidth is required to be a reasonable fraction of 1/Q