MODE COMPETITION IN THE QUASI-OPTICAL GYROTRON

A set of equations describing the nonlinear multimode dynamics in the quasioptical gyrotron is derived. These equations, involving the slow amplitude and phase variation for each mode, result from an expansion of the nonlinear induced current up to fifth order in the wave amplitude. The interaction among various modes is mediated by coupling coefficients, of known analytic dependence on the normalized current I, the interaction length μ, and the frequency detunings Δi corresponding to the competing frequencies ωi. The particular case when the modes form triads with frequencies ω1 + ω3 - 2ω 2≃0 is examined in more detail. The equations are quite general and can be used to study mode competition, the existence of a final steady state, its stability, as well as its accessibility from given initial conditions. It is shown that when μ/β⊥ ≫ 1, μ can be eliminated as an independent parameter. The control space is then reduced to a new normalized current Î and the desynchronism parameters νi = Δiμ for the interacting frequencies. Each coupling coefficient Gij is written as Gij = ÎSijĜij(νi,νj), where the nonlinear filling factor Sij, carrying the information of the beam current spatial profile, can be computed independently. Therefore, it suffices to compute tables of Ĝij as functions of ν1, ν2, and ν3 once to cover the parameter space. Results for a cold beam are presented here. © 1990 American Institute of Physics.