Extension of Langmuir space-charge theory into the accelerating field range

The paper takes the space-charge theory developed by Langmuir and applies it to the accelerating-field range along with the image-potential theory suggested by Schottky. The combined theory produces a current-voltage curve which begins at the zero-field current and voltage calculated from space-charge theory, and then gradually approaches the curve generated by Schottky theory. The paper summarizes in a single equation the solution procedure outlined by Langmuir. Based on this equation, the paper discusses the behavior of the current-voltage curve at the transition points from the exponential range into the space-charge range and from the space-charge range into the accelerating field range.