ANALYSIS OF CATHODE FALL FROM A PLANAR ELECTRODE IN GAS-DISCHARGES AT LOW E/P LOW-PRESSURE

An analytic investigation is reported of cathode fall from a planar electrode in a gas discharge at low electric field to pressure and low gas pressure. In order to avoid complex calculations, a simple function is used to fit the experimental data on Townsend's first ionization coefficient. Analytic expressions of variation of electric field, cathode fall, and length of the cathode dark space with the ratio of current density to pressures squared are obtained using a first-order approximation. The results show the characteristic current-voltage relation for subnormal and abnormal discharge. The cathode fall, the length of cathode dark space, and the ratio of current density to pressure squared are also estimated for the normal discharge. It is also shown that the length of cathode dark space is a function of the cathode fall. Numerical calculations for several gases are made to demonstrate the model.