The interaction of transverse eigenmodes with a relativistic electron beam in an overmoded cyclotron autoresonance maser amplifier is analyzed using a nonlinear self-consistent model and kinetic theory. It is shown that all of the coupled modes grow with the dominant unstable mode at the same growth rate, but suffer different launching losses. The phases of coupled modes are locked in the linear and nonlinear regimes. Simulations indicate that the rf power distribution among the interacting modes at saturation is insensitive to input power distribution but sensitive to detuning.
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