Linear Theory of Beam-Wave Interaction in Gyrotron Cavities with Mode Conversion

Self-consistent linear theory of beam-wave interaction is developed for gyrotron cavities with mode conversion and ohmic losses. The system of linearized integrodifferential equations is derived to evaluate the oscillation threshold (starting current). As a numerical example, beam-wave interaction in cylindrical cavity of the FU CW III gyrotron is considered. This cavity exhibits strong mode conversion in output section. It is found that this mode conversion materially affects the output radiation pattern of the operating mode, but has only a slight effect on the frequency and starting current of the FU CW III gyrotron.