Linear and nonlinear behaviors of gyrotron backward wave oscillators

Linear and nonlinear behaviors of gyrotron backward wave oscillators (gyro-BWO) were investigated by both analytical theories and direct numerical calculations. Employing two-scale-length expansion, an analytical linear dispersion relation corresponding to absolute instabilities in a finite-length system has been derived. Detuning from the beam-wave resonance condition due to the finite amplitude radiation fields, meanwhile, was found to play the crucial roles in the nonlinear physics. Near the start oscillation of the gyro-BWO, the radiation field amplitude saturates when the resonance broadening is comparable to the linear growth rate. Far beyond the start oscillation threshold, the beam-wave resonance detuning effectively shortens the interaction length toward that corresponding to the critical oscillation length for the given beam current. The theoretically predicted scaling laws for the linear stability properties and nonlinear stationary states of the gyro-BWO are in good agreement with numerical results.