Wave interaction in relativistic harmonic gyro-traveling-wave devices

In gyro-traveling-wave devices, several waves can be excited at different cyclotron harmonics simultaneously. This paper analyzes the interaction between three waves synchronous with gyrating electrons at different cyclotron harmonics in two relativistic gyro-amplifier configurations; viz., gyro-traveling-wave tubes and gyrotwystrons. Two types of nonlinear interactions are considered: (a) excitation of two waves at cyclotron harmonics by a wave excited at the fundamental resonance, and (b) excitation of a wave at the fundamental resonance and another wave at the third harmonic by a wave excited at the second cyclotron harmonic. The effect of the overlapping of electron cyclotron resonances on the performance of relativistic gyrodevices is investigated as well.