Theory Of Relativistic Backward Wave Oscillator

A linear and nonlinear theory for a vacuum relativistic BWO of a finite length is developed. A set of reduced equations self-consistently describing the slow evolution of the envelope of the radiation field and the relativistic motion of the particles along strong magnetic field are solved. The model takes into account the finite reflectivity of the electromagnetic wave at both boundaries of the interaction region and allows large variation in the longitudinal velocity of the electron beam. The model equations depend on six normalized parameters: the length, koL; the initial beam velocity, β
_z
(0); the value of the radiation group velocity, |β
_g
|; the value of the combined reflection coefficient at the boundaries of the RF structure, |R|, the current Î and the beam AC space charge parameter, ŵ
_sp
. The results of calculations of the starting current and the maximum efficiency as a function of the above parameters will be presented.