Analysis of a large-orbit gyrotron in a coaxial waveguide under assistant background fields

The dispersion relation of a large-orbit gyrotron in a coaxial waveguide excited in the transverse-electric mode was developed starting from the beam-present wave equation. The relativistic Vlasov's equation was solved under tenuous beam approximations for the perturbed electron distribution function, hence the required current density to be used in the wave equation was found. The analysis was generalized, with respect to background fields, by considering a dc radial electric field and a dc azimuthal magnetic field, over and above conventional dc axial magnetic field. The dispersion relation was solved for the complex frequency for a given propagation constant and the imaginary part interpreted for the growth rate as well as the saturated efficiency of the device. Similarly, for a given frequency the dispersion relation was solved for the complex propagation constant and the imaginary part interpreted for the gain of the device, if configured as an amplifier. Two peaks were obtained in the gain-frequency response corresponding to two points of intersection between the beam-mode dispersion line and the waveguide-mode dispersion curve. The improvement in the growth rate, gain and saturated efficiency was predicted by the application of the additional background fields. A redistribution of beam kinetic energy between the axial and transverse electron velocities led to a remarkable enhanced saturated efficiency at the second peak. A detailed study of the variation of device performance with respect to the gain and saturated efficiency was presented, for a wide range of the dc background field and electron kinetic energy distribution parameters.