Control of the Space Charge

Author: J.B. Hoag

The effects due to the space charge can be shown in another fashion. Let the temperature of the filament of the tube in Fig. 10 A be held constant and let the voltage on the plate be increased.

Fig. 10 E. The plate voltage V changes the plate current i. Fixed filament temperatures, T2 and T1. (From E. & N. P.)

As shown in Fig. 10 E, the space-charge-limited current increases along the line AD and eventually equals the saturation value shown by the horizontal line, upper right of the figure. With a hotter filament the dotted curve ADT₂ will be obtained. The relationship between the applied voltage V and the resulting current i is expressed by the following equation: i = BV^3/2, where B is a constant. This is variously known as the three-halves-power law, the Child law, and also as the Langmuir law. In actual tubes, the exponent in this equation varies between two-halves and five-halves. This is because of the drop of voltage between one end of the filament and the other, and because of the initial velocities with which the electrons leave the filament.