Gyrotron backward-wave oscillator

A linear theory for a gyrotron backward wave oscillator (BWO) has been developed and is presented in this report. The theory solves a reduced one-dimensional Maxwell-Vlasov equation in the form of a linear integro-differential equation using Laplace transformation. The relative amplitudes among the waveguide modes and beam modes are completely determined and enable us to determine BWO oscillation conditions. A design is made based upon this analysis including velocity spread effects. A several tens kilowatt power level gyrotron BWO may be possible and find useful applications as RF heating sources in fusion devices and as driving sources in high power gyrotron amplifiers.