Some fundamental questions concerning the kinetic theory of electrons in molecular gases and thee–H2 vibrational cross section controversy

Abstract

We commence a fundamental re-examination of the kinetic theory of charged particleswarms in molecular gases, focusing on collisional excitation of molecular rotational andro-vibrational states by electrons. Modern day analysis of electron swarms has been basedupon the kinetic equation of Wang-Chang et al, which simply treats all processes as scalarenergy excitations, and ignores angular momentum conservation and the vector dynamicsassociated with rotational excitation. It is pointed out that there is no alternative, moreexact kinetic equation readily available for electrons which enables one to directly ascertainthe degree of error introduced by this approximation. Thus in this preliminarystudy, we approach the problem indirectly, from the standpoint of the neutralmolecules, using the Waldmann–Snider quantum kinetic equation, and insistthat an electron–molecule collision must look the same from the perspective ofboth electron and molecule. We give a formula for quantitatively assessing theimportance of scalar versus vectorial treatments of rotational excitation by looking atthe post-collisional ‘echo’ produced by an electron swarm as it passes throughthe gas. It is then pointed out that in order to remedy any deficiency, it will benecessary to introduce a kinetic collisional operator non-local in space to properlyaccount for angular momentum conservation, as has long been established in theliterature. This is a major exercise and given the preliminary nature of this study,we consider the inclusion of such effects from a formal point of view only. Inparticular we show how non-local effects lead to a spatially dependent ‘source’ term inthe equation of continuity, and hence to corrections for both drift velocity anddiffusion coefficients. The magnitude of these corrections has yet to be established.