Space Charge Currents between Coaxial Cylinders in the Presence of a Gas

Approximate theoretical equation for space charge currents between coaxial cylinders with gas present.—Langmuir has derived an equation for the space charge limited current between coaxial cylindrical electrodes in high vacuum. In this paper Compton's equation for the terminal velocity of an ion suffering elastic collisions in an electric field, is applied to the case of space charge currents with gas present. Assuming the pressure sufficient so that the ions reach nearly the terminal velocity and neglecting the contribution of thermal agitation to the velocities of the ions, the following approximate equation is derived: $i=A\sqrt{\frac{l{V}^3}{{\mathrm{}\left(\mathrm{aB}\right)\mathrm{}}^3}}$, where $l$ is the mean free path, $V$ is the voltage, $a$ is the radius of the outer cylinder, $B$ is a function of the ratio of the two radii (values are given in a table), and $A$ is a constant depending on the charge and mass of the ions.