Approximate calculations of cathode-fall characteristics

Methods of calculating approximate cathode-fall voltages and distances as a function of current density using a number of alternate empirical relations are introduced. It is shown that these calculated characteristics are considerably different for rare and molecular gases, and are also quite different for the two different mobility assumptions used, but are only slightly different if the field distribution near the cathode is assumed to be linear or if it is assumed to be given by an approximation to Poisson's equation. Comparison of these approximations with more exact calculations made on an electronic computer and with experimental data indicate their usefulness for engineering purposes.