Potential and Gradient Distributions in Parallel Plane Diodes at Currents below Space-Charge-Limited Values

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Abstract
The equations for electron motion in a plane diode under the influence of space charge are integrated. The solution is expressed in terms of four dimensionless numbers, normalized so that their range is from zero to unity. The gradient at the cathode is expressed as a function of the current density as it varies from zero to space-charge-limited values. Space distributions of potential and gradient are given in terms of the location of the plane of interest between the cathode and the anode for a number of specific current densities.