The dispersion equation for the gyrotron amplifier

Abstract

The dispersion equation For the gyrotron amplifier has been derived by uso of a general expression for the perturbed propagation constant of a waveguide containing r.f. current. The derivation is valid for all guide modes and cyclotron harmonica and shown that space–charge dose not affect TE^° _on modes. The distribution of the unmodulated beam can be simply expressed as a function of the coordinates of guiding centres, showing that power transfer can occur' through radial drift of electrons' orbits. For a univeloeily beam, growing–wave gain is found over a bandwidth of about 20%, but the same bandwidth is unlikely to be obtained with a quasi–max–wcllian beam unless the spread in axial momentum lies within stringent limits.