High power 20 GHz RF source based on seventh harmonic co-generation

The TE₇₂ mode in cylindrical waveguide has its group velocity nearly equal to that of the TE₁₁ mode when the operating frequency of the former is seven times of that of the latter. Thus the two modes have almost the same resonant magnetic field, and coherent radiation can be generated at the 7th harmonic when the fundamental energizes a gyrating electron beam by the cyclotron autoresonance interaction. It is shown analytically that the electron´s gyration radius, normalized to waveguide radius, must be less than 0.5431 in the cyclotron autoresonance interaction. This analytical prediction is well confirmed by computer simulations. For a 300 kV, 30 A warm beam driven by 20 MW RF power at 2.856 GHz, simulations indicate that 7th harmonic power of up to 16 MW at 20 GHz can be obtained