On the Joint Action of Diffusion and Recombination of Ions

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Abstract
The differential equation which describes the joint action of diffusion and recombination of ions is solved, for the one-dimensional case, by a method previously developed by the author. In Section I, the decay of a given initial distribution of ions is treated. The observable coefficient of recombination, as modified by diffusion, depends strongly in the initial stage on the given distribution. For later times it depends in a simple way on the density of ionization and the distance between the collecting plates. In Section II, the establishment of the steady state, with constant production of ions, is calculated. Diffusion introduces a linear term which may, for sufficiently small values of the ionic density and the electrode distance, mask the usual quadratic term. In Section III, it is shown that anomalies observed by Gardner in the recombination coefficient of oxygen and by Power in the establishment of the steady state in air are explained, without further assumptions, by diffusion to the walls.

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