Motion of Gaseous Ions in Strong Electric Fields

TLDR

The paper applies the Boltzmann method of gaseous kinetics to study the motion of charged particles in a gas under a strong static, uniform electric field and discusses extending the results beyond their original range. The authors develop a Boltzmann‑based kinetic theory for ions in a strong uniform electric field, assuming low density and elastic collisions, deriving drift‑velocity and anisotropic diffusion equations, solving analytically for the high‑field regime with speed‑independent mean free time and extreme mass ratios, and treating intermediate fields via convolution and numerical methods. They obtain complete analytical solutions for the high‑field case—including extreme mass ratios and numerical treatment of equal masses—and provide numerical results for the diffusion process, demonstrating the theory’s applicability and potential for semiquantitative extension.

Abstract

This paper applies the Boltzmann method of gaseous kinetics to the problem of charged particles moving through a gas under the influence of a static, uniform electric field. The particle density is assumed to be vanishing low, and the ion-atom collisions are assumed elastic, but the field is taken to be strong; that is the energy which it imparts to the charges is not assumed negligible in comparison to thermal energy. In Part I, the formal framework of such a theory is built up; the motion in the field is describable by the drift velocity concept, and the smoothing out of density variations as an anisotropic diffusion process. In Part II, the “high field” case is treated in detail; this is the case, for which thermal motion of the gas molecules is negligible; the equation is solved completely for the case that the mean free time between collisions may be treated as independent of speed; complete solutions are also presented for extreme mass ratios of the ions and the molecules; special attention is given to the case of equal masses, which has to be handled by numerical methods. In Part III, information about the “intermediate field” case is collected; with the help of a convolution theorem the case of constant mean free time is solved; beyond this, only the case of small ion mass (electrons) is available. In Part IV, the diffusion process, whose existence was proved in Part I, is pushed through to numerical results. Part V discusses the scope of the results achieved and demonstrates the possibility of extending them semiquantitatively beyond their original range.