Abstract
Three general differential equations are set up which determine the average behavior of a discharge of electricity through a gas. Approximate solutions, giving the electric field and the concentration of electrons and positive ions, and , at any distance from the cathode, are found for several ranges of value of .
When is large, the solution corresponds to the conditions in the cathode and anode fall spaces in a glow discharge. Equations are obtained for the potential drop across the fall space; the current density at the electrode divided by the square of the gas pressure, ; and the thickness of the fall space times the pressure, .
These equations indicate that for the cathode fall space there is a certain minimum value of , called ; and for , called ; and a corresponding maximum value of , , beyond which values the discharge ceases. These stationary values are shown to be constants, dependent only on the nature of the gas used and of the cathode material, and correspond to the normal cathode fall space. The equation determining is shown to be of the right from by comparison with the experimentally determined values. From these values of , values of and of are calculated for four gases and four cathode materials, and the calculated values check with the experimental data. The corresponding equations for the anode fall space show why there is no corresponding normal anode fall.
A consideration of the discharge when is large throughout the distance between electrodes indicates that there is another stationary value of the cathode fall space when the current density at the cathode reaches its maximum possible value. The in this case is much smaller than the for the glow discharge, and the form of the equations indicate that they describe the conditions in an electric arc.
Another approximate equation is obtained when is constant, which is the case in the positive column of a glow discharge. This solution indicates that within certain limits of pressure and current density, small sinusoidal variations about the average value , are possible in . These correspond to the striations sometimes observed in the positive column. The equations determining and those determining the distance between striations check with the known empirical laws relating these amounts to the pressure, the radius of the discharge tube and the critical potentials of the gas used. A general discussion is given of the Faraday dark space and reasons are given why it should be near the cathode rather than the anode.
- Received 1 March 1928
DOI:https://doi.org/10.1103/PhysRev.31.1003
©1928 American Physical Society