Properties of the Collision Operators of the Electron Boltzmann Equation for a Weakly Ionized Plasma. I. Representation and General Properties
作者:
G. Bartolomäus,
J. Wilhelm,
期刊:
Beiträge aus der Plasmaphysik
(WILEY Available online 1982)
卷期:
Volume 22,
issue 1
页码: 15-28
ISSN:0005-8025
年代: 1982
DOI:10.1002/ctpp.19820220105
出版商: WILEY‐VCH Verlag
数据来源: WILEY
摘要:
AbstractIn 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 pape
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