Noise wave excitation at the cathode of a microwave beam amplifier

General equations are derived, giving the amplitudes of noise current and velocity for the many modes of space-charge wave propagation in an electron beam. The properties of the cathode taken into consideration are the current density and the emission velocity distribution as a function of position. Simplified cases are considered which show the order of magnitude of effects due to cathode nonuniformity and magnetic field strength. From present evidence, it can be shown that high noise figure in low noise tubes is almost certainly due to excess noise velocity, brought about by cathode nonuniformities. Suggestions are given for reducing these undesirable effects.