Theory of High Frequency Gas Discharges. I. Methods for Calculating Electron Distribution Functions

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Abstract
After a brief summary of the "free-electron" theory of a.c. currents in gases, which is shown to be inadequate for microwaves, methods for calculating distribution functions for electrons with consideration of all types of collisions are developed and discussed. Conditions are specified under which non-elastic collisions may be introduced as integral and as differential expressions in the Boltzmann transfer equation. In Section VI this equation is solved approximately and the differences between direct current and h.f. current discharges are pointed out. Finally, Section VIII is concerned with an aspect of what is usually called Paschen's law; it indicates that a minimum should exist in the graph of voltage vs. pressure, and of voltage vs. frequency, both at constant current. This minimum comes when the frequency of the field is of the order of magnitude of the collision frequency of the electrons.