Spectral analysis on effects of spreads in energy and momenta in a gyrotron amplifier

The combined effects of the spreads in energy and axial momentum of annular-beam electrons in a gyrotron amplifier are spectrally investigated. A conveniently normalized dispersion relation is found for modes, and analyzed to obtain the growth-rate contours. The spread effects prove to reduce the growth rate near the beam-waveguide synchronous mode, and enhance it for the mode out of synchronization. In particular, the growth rate at the synchronous mode tends to peak when the electron distribution is thermally isotropic. The results will serve as a guideline in the design of a thermal electron gun giving linear gain.