A New Analysis of Space-Charge-Limited Emission between Concentric Spheres and Concentric Cylinders

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Abstract
Space‐charge‐limited current flow between a small spherical cathode and a concentric spherical anode has been reexamined, taking into account the full energy and angle distribution of the emitted thermoelectrons. A similar analysis has been carried out for concentric cylindrical electrodes. On the basis of the theory thus developed, self‐consistent iterative computations have been carried out to determine the variation of the potential and the space charge with radius at various cathode temperatures and fixed anode potential. The important effect of the initial angular motion of the thermoelectrons is demonstrated, and a comparison with other calculations is presented.