Theory of gyro-backward wave oscillators with tapered magneticfield and waveguide cross section

A theory is developed which describes gyro-backward wave oscillators (gyro-BWO's) with arbitrarily relativistic electron beams and tapered external magnetic field and waveguide wall radius. For the case of linear tapering the optimal parameters are found that correspond to highly efficient operation. The frequency tunability as the function of magnetic field and voltage deviations has been analyzed. It is shown how to use the results given in terms of normalized parameters for designing concrete gyro-BWO's. For one concrete design the effect of electron velocity spread on the efficiency has been studied