Properties of the Collision Operators of the Electron Boltzmann Equation for a Weakly Ionized Plasma. II. Compactness Proof and Statements on the Spectrum

Abstract

AbstractThe compactness has been proved of the inscattering operator covering elastic, exciting and deexciting processes between electrons and heavy neutral particles. Starting point is the proof of the boundedness of the different inscattering operators for the individual collision processes using certain assumptions on the structure of the corresponding differential cross sections. Then, under somewhat more confined conditions the proff of compactness could be performed with the aid of the square integrability of an eightfold iterated kernel. On the basis of this property it was possible to draw conclusions with regard to the spectrum of the total collision operator. They are related to the continuous as well as the discrete part of the spectrum and are discussed in detail. For elastic collisions additional statements can be deduced from our investigation.