The theory of the drift of ions in a gas

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This paper considers the general theory of the time-dependent drift of ions in a gas under the action of their own electric field together with any externally imposed electric field. The mean free path is taken as small enough for the macroscopic movement of the ions to be in the direction of the field. Diffusion is ignored and the currents are quantified by the use of mobility coefficients. A charge-drift equation originally given by Waters (1970) is generalised for multiple ionic species, and it is shown how ionisation can be taken into account. Characteristic times of approach to the asymptotic state when the charge density varies inversely with time are considered. The problem of the general motion of a charged cloud of many species of ions has been formulated. This gives rise to simultaneous integro-differential equations with moving boundaries. An alternative approach using field theory is shown to give a simple linear law of volumar expansion with time. This holds for all cases when a single mobility coefficient is appropriate. The asymptotic shape of a simple cloud of ionic charge is proved to be a sphere. Modifications to this when the volume is multiply connected and when many ionic species are present are discussed. The rate of transfer of the electrical field energy (power loss) to the thermodynamic energy of the gas is considered. This results in a variational principle being identified from a physical basis which is equivalent to the charge-drift equation. The movement of either single or multiple ionic species can be treated by this approach which could form the basis of a new finite-element method for problems involving the drift of gaseous ions.