A method of reducing the effects of anode aperture in high-perveance convergent electron guns

A new theoretical method of designing convergent electron guns of high perveance for use in microwave tubes is presented here. A differential equation which represents electron trajectories in a convergent electron stream has been deduced under certain approximations. Electron trajectories in an electron stream and boundary values along its boundary were numerically calculated by solving the differential equation by means of an electronic computer. Boundary values on the virtual anode surface under space-charge-limited conditions were used as the initial values for the calculations. Focusing electrodes were determined to satisfy the boundary conditions on the stream boundary. The design procedure is also shown. The electron guns designed by this method are somewhat different in structure from the conventional ones which are usually designed experimentally rather than theoretically. In these new electron guns, nearly uniform current densities will be obtained over the whole cathode area, while in conventional convergent guns of high perveance, electron emission density near the center of the cathodes is usually reduced due to the influence of the anode aperture. Laminar flow will be obtained at points near the minimum stream diameter also in guns designed by this method. Digital computer experiments were performed and the results proved this hypothesis to be reasonable. An electron gun of 1.72 × 10^-6perveance and area convergence ratio of 70:1 is shown as an example.