A linear theory and design study for a gyrotron backward-wave oscillator†

A linear theory for a gyrotron backward-wave oscillator (gyro-BWO) is developed. The theory solves a reduced one-dimensional Maxwell-Vlasov equation in the form of a linear integro-differential equation using the Laplace transformation. The relative amplitudes among the waveguide modes and beam modes are completely determined and enable one to calculate gyro-BWO start-oscillation conditions. Using this analysis and including velocity spread effects, a design of a millimetre-wave gyro-BWO has been carried out based on the operating parameters of an existing electron gun. Tunability over a range of 86 GHz to 103 GHz is predicted with output power estimated to be ∼ 1 kW.