Space Charge Neutralization by Positive Ions in Diodes

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Abstract
The neutralization of electron space charge in diodes is analyzed on the basis of the assumption that the ion density is proportional to e−eV/kT, where V is the local potential and T is the cathode temperature. The neglect of electron‐ion collisions enables solutions for the potential variation between electrodes to be obtained by a single numerical quadrature. Curves are presented for the potential as a function of position for a series of values of the ratio α of ion to electron density at the potential minimum. It is shown that for a large range of tube parameters, the electron current reaches two‐thirds of its saturated value when the ion density at the cathode is about one‐third the quantity Is/ev0, where Is is the saturation current and v0 = (2kT/πm)½. The electron current saturates completely when the ion density at the cathode is slightly above 0.81 Is/ev0 for large electrode spacing and slightly below Is/ev0 for small spacing. The anomalous behavior of the potential as a function of position when α lies between 0.81 and unity leads to the possibility of more than one mode of operation for a given ion density at the cathode and also causes the tube current to increase rather than decrease with increasing electrode spacing under certain conditions. Since these phenomena occur only over a narrow range of tube parameters, the effect of electron ion collisions may prevent them from being observed experimentally.