Ion Energies at the Cathode for Conduction Through Rarefield Gases

Abstract

The characteristics of ion energies at the cathode are derived from collisional ionization cross sections for conduction between plane, parallel electrodes in rarefield gases, where the mean-free path is much greater than the cathode-anode separation. Expressions are given for the electron ionization efficiency, the ion particle-current density striking the cathode, the power density transferred to the cathode by the ions, and the average impacting ion energy. These expressions are given both for a homogeneous (single species) gas and for a heterogeneous mixture of gases. The latter can be obtained additively from the results obtained by treating each of the constituent gases individually. The maximum impacting ion energy is equivalent to the potential applied across the cathode and the anode; the minimum impacting ion energy is equivalent to the smallest first ionization potential of the gases present in the cathode-anode space.The amount of ionization is discussed in terms of an "ionization volume" swept out by each of the bombarding electrons. By maximizing this volume with respect to the applied potential, the maximum amount of collisional ionization occurs in the cathode-anode space (a potential of approximately 200 V for most gases). Drawings of the typical shape of the ionization volume are given for applied potentials much less than, equal to, and much greater than, the applied potential which yields maximum ionization. A specific example demonstrating an application of the derivations is given, using argon as a model.