Theory of relativistic Backward Wave Oscillators operating near cutoff

Backward-Wave Oscillators utilize a high-current electron beam to produce high-power, coherent radiation in the centimeter and millimeter wavelength regime. Under certain voltage and beam current operating conditions, a Backward-Wave Oscillator (BWO) can operate near the upper edge of the transmission band where the group velocity of the electromagnetic wave goes to zero. In this regime, the cold structure dispersion relation can be approximated as a quadratic function of the wavenumber. A theoretical model similar to those presented in [1–3] has been developed to describe the operation of the device in this regime. We solve a self-consistent set of equations to describe the slow evolution of the envelope of the radiation field and the relativistic motion of the particles along a strong magnetic field. Included in the theoretical model are the effects of D.C. and A.C. space charge, and velocity spread in the beam. Numerical calculations of the starting current are performed and compared with an analytic expression for the starting current derived by assuming a fixed field profile.