Theory of Normal Cathode Fall in Glow Discharges

Basis of theory of cathode fall.—From the principle of minimum energy dissipation it is shown that the actual potential distribution in the fall space must be that one which is most favorable to ionization, subject to limitations imposed by Poisson's equation. With the aid of this principle, taking as known quantities the normal cathode fall $V_n$ and Townsend's ionization constants $N$ and $V_0$, expressions are derived for the potential distribution, the thickness of the fall space $d_n$, the distribution of ionization $n_x$ and the current density $j_n$ which agree acceptably with experimental values.