Theory of relativistic backward wave oscillators operating near cyclotron resonance

A linear and nonlinear, time dependent self-consistent theory for relativistic backward wave oscillator is developed. In this theory the transverse motion of the electrons is taken into account. Analytical and numerical analysis of the model equations near the cyclotron resonance gives a good estimate for the power drop due to the cyclotron absorption observed in many experiments and predicts an increase in the power under some conditions.