Non-Local Descriptions of Electron Swarms in Space-Time

Abstract

The behavior of a group of electrons moving in a neutral gas under the influence of a space-time dependent force can be described by the velocity distribution function f(v,r,t). In the following discussion it will be assumed that space-charge fields are negligible and only an external electric field E(r,t) is considered. The distribution function can be obtained from the Boltzmann equation

$$ \frac{{\partial f}}{{\partial f}} + {\underset{\raise0.3em\hbox{$\smash{\scriptscriptstyle-}$}}{v} ^.}{\nabla _r}f + \frac{q}{m}{\underset{\raise0.3em\hbox{$\smash{\scriptscriptstyle-}$}}{E} ^.}{\nabla _v}f = (\frac{{\partial f}}{{\partial f}})coll. $$

(1)