A Field Analysis of the M-Type Backward Wave Oscillator

A field theory of electron beams focused by crossed electric and magnetic fields is given. The theory is basic to the understanding of the small signal behavior of crossed field electron devices. It is applied to explain the slipping stream, or diocotron, effect as a coupling of two surface waves of the electron beam, and to derive the start oscillation conditions of the M-type backward wave oscillator. It is found that the slipping stream effect can reduce the starting current by an appreciable factor. The results are compared with the thin beam theory which neglects space charge effects. An analysis of a loaded strip transmission line is given, from which a method of representing space harmonic slow wave circuits by a surface admittance boundary condition is obtained. Forward and backward space harmonic interaction may be treated equally well.