This paper applies the Boltzmann method of gaseous kinetics to the problem of positive ions moving through a gas under the influence of a static, uniform electric field. The ion density is assumed to be vanishingly low, but the field is taken to be strong; that is, the energy which it imparts to the ions is not assumed negligible in comparison to thermal energy. Attention is focused upon the computation of velocity averages, and the drift velocity in particular, rather than a complete knowledge of the entire velocity distribution. It is shown in Secs. C and E that the problem so formulated is completely soluble if the mean free time between collisions of ions and molecules is a constant; this is the casee for the so-called polarization force between ions and molecules which predominates over other forces at low temperature. A method for obtaining averages to any desired accuracy in the general case is developed in Sec. D. The method is applied to the hard sphere model for the high field range and mass ratio 1. An application of the resulting formula (43) to experimental material has been published earlier.

• Received 12 March 1951

DOI:https://doi.org/10.1103/PhysRev.83.281