On analytic solutions of the drift equations for many ionic species

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Abstract
The charge-drift equations result from charge continuity considerations when viewed from a frame of reference moving with the gaseous ions. They are simple in form and have already been used to good effect for single-species drift for which references are given in the text. This paper systematically examines the theory for multiple species looking for algebraically expressible solutions, and has met with some success. It has been shown that the charge density of a packet of a particular species of ions can be written in terms of integrals involving the charge densities of other ions that it meets on its way. A power law governing the charge densities has been found for all time-dependent homogeneous ionic movements. Time-independent motions have also been considered and the constant ratios of charge densities and currents confirmed for all points in these flows. Situations with two ionic species are fully investigated, and an analytic solution has been found for homogeneous distributions of positive and negative ions with equal but opposite mobilities. Stable charged clouds with equal but opposite positive and negative ionic distributions are shown to be possible. When disturbed, the variations from equilibrium charge densities within such a cloud are found to be characterized by an exponential law. The destabilizing effect of an externally applied electric field on these clouds is shown to be resisted by the self-field of the resulting ionic displacements. Perturbation solutions and expansions are considered in some detail, and the paper concludes with a section giving explicit solutions for superimposed clouds of ions with either spherical or cylindrical symmetry. Fuller descriptions of the main findings can be found in the conclusions at the end of the text.

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