Ion Velocity Distribution of a Weakly Ionized Gas in a Uniform Electric Field of Arbitrary Strength

The velocity-distribution function of ions in a neutral gas is studied. A uniform electric field of arbitrary strength is assumed and only binary-ion-neutral-particle collisions are considered. Under these conditions part of the Boltzmann-equation collision operator is replaced by a kinetic model which enables the ion velocity distribution to be found in compact analytical form if the mean free time between ions and neutrals is independent of velocity. This velocity distribution exhibits the expected properties of drift, elevated ion temperature (as compared to the neutral gas), and skewness in the field direction. In addition, the velocity distribution obtained agrees with the known distributions in the extreme cases of (a) low fields and arbitrary masses and (b) arbitrary fields but extremely disparate ion and gas masses. Other tests are made for this distribution with satisfactory agreement.