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Properties of the Collision Operators of the Electron Boltzmann Equation for a Weakly Ionized Plasma. I. Representation and General Properties
Author(s) -
Bartolomäus G.,
Wilhelm J.
Publication year - 1982
Publication title -
beiträge aus der plasmaphysik
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.531
H-Index - 47
eISSN - 1521-3986
pISSN - 0005-8025
DOI - 10.1002/ctpp.19820220105
Subject(s) - boltzmann equation , eigenvalues and eigenvectors , boltzmann constant , collision , eigenfunction , physics , operator (biology) , representation (politics) , plasma , electron , statistical physics , quantum mechanics , computer science , chemistry , biochemistry , computer security , repressor , politics , transcription factor , political science , law , gene
In the kinetic theory a great variety of physical systems is investigated by means of Boltzmann‐like equations. This approach is used for neutral gases, neutron as well as radiation transport, plasmas etc. For many problems the knowledge of the properties of the collision operators is of great importance, especially if eigenvalue problems occur. The paper presents an investigation of the properties of the collision operators of the Boltzmann equation covering elastic, exciting and deexciting processes in a weakly ionized plasma. First, a short survey of the importance of eigenfunctions and eigenvalues in the kinetic theory of various systems is given. Then, properties of the outscattering operator as dependent on the course of the differential cross section are considered. Finally, for the inscattering operator such properties as selfadjointness and rotational invariance are investigated in detail. These considerations provide the basis for the proof of compactness and for first conclusions on the spectral properties of the collision operators in the second part of this paper.