Theory of the temporal growth of ionization in gases, involving the action of metastable atoms and trapped radiation

Abstract

There exists no accurate mathematical treatment of the temporal growth of ionization current in a gas due to the primary a ionization process, together with the action of metastable atoms liberating electrons from the cathode as the significant secondary process. The present paper supplies such a treatment. The continuity equation and boundary conditions are derived, and first the solution for the steady state is obtained, showing how the Townsend steady-state formula is modified when this process involving metastable atoms, with some internal destruction in the gas, is present. To derive formulae for temporal growth a contour integral is introduced, from which the required solution is obtained in various exact forms. Approximate formulae are also obtained, convenient for calculating both the initial and later stages of the current growth in various practical cases. Another well-known secondary cathode process is that due to fluorescent light, that is, to photons which have been repeatedly absorbed by atom s and re-emitted. Thus, like metastable atoms, they move through the gas by a process of diffusion. Formulae for the resulting current growth are derived. The general case in which, in addition to these diffusion processes, there is secondary cathode action due to unscattered photons and positive ions, is also treated.