On the Theory of Space Charge Between Parallel Plane Electrodes

The problem of the potential distribution, current, and electron transit time resulting from the perpendicular injection of electrons into the space between parallel planes is considered. The electrons are assumed to be injected uniformly with velocities corresponding to the potential of the plane through which they are injected. Consideration of all possible solutions of the basic equation shows that four general types of potential distribution are possible. Curves are given which enable the easy calculation of transmitted current and transit time and show the complete potential distribution for any concrete example. The case for current injected through both planes is also considered. The complete mathematical treatment is given in the appendix.