Effect of space charge and the initial electron velocity on the potential distribution in a plane diode

The problem of the potential distribution in a plane vacuum diode is solved for arbitrary values of the space charge density and the initial electron velocity. The resultant solution makes it possible to study the conditions for the potential minimum appearing near the cathode, to determine the position and depth of this minimum, to derive analytic formulas for the potential distribution in the entire space between the cathode and the anode, and to analyze the problem of an infinitely high space charge density.