Abstract
The self-consistent nonlinear analysis is presented for an overmoded gyrotron, in which the gyrotropic beam interacts with more than one cavity eigenmodes. The nonlinear equations are obtained in the slow time scale for the motion of each individual particle and for the evolution of the amplitude and frequency of each individual cavity eigenmode. A numerically efficient algebraic longtime-step algorithm is developed, which includes magnetostatic field tapering and time transients. Numerical examples are presented for the excitation and competition of the cavity eigenmodes.
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