Linear and nonlinear theory of cyclotron autoresonance masers with multiple waveguide modes

The interaction of multiple waveguide modes with a relativistic electron beam in an overmoded, single-frequency, cyclotron autoresonance maser amplifier is analyzed using a nonlinear self-consistent model and kinetic theory. It is shown analytically, and confirmed by simulation, that all of the coupled waveguide modes grow at the spatial growth rate of the dominant unstable mode, but suffer different launching losses which depend upon detuning. The phases of coupled modes are locked in the exponential gain regime, and remain approximately locked for some finite interaction length beyond saturation. The saturated power in each mode is found to be insensitive to the input modal radio-frequency (rf) power distribution, but sensitive to detuning. Simulations indicate that the saturated fractional rf power in a given mode reaches a maximum at its resonant magnetic field, and then decreases rapidly off resonance. Good agreement is found between the simulations and the kinetic theory in the linear regime.