The Rate at Which Ions Lose Energy in Elastic Collisions

Abstract

The rate of energy loss of ions (including electrons) moving through a gas is rigorously calculated on the assumption that the ions and molecules are smooth elastic spheres with no attraction at a distance, having Maxwellian velocity distributions corresponding to the temperatures ${T}_{i}$ and ${T}_{m}$ respectively. The result is $f=\frac{8}{3}\frac{\mathrm{mM}}{{(m+M)}^{2}}\left(1\ensuremath{-}\frac{{T}_{m}}{{T}_{i}}\right)$ where $m$ and $M$ are the masses of ion and molecule respectively, ${T}_{i}$ and ${T}_{m}$ are their temperatures, and $f$ is the average energy loss per collision expressed as a fraction of the average ionic energy.