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Spectral representation of the isotropic Coulomb collisional operator

Published online by Cambridge University Press:  01 October 1997

I. K. KHABIBRAKHMANOV  and
D. SUMMERS
I. K. KHABIBRAKHMANOV
Affiliation:
Present address: Institute of Space and Atmospheric Studies, Department of Physics, University of Saskatchewan, Saskatoon, Saskatchewan, Canada, S7N 5E2. Department of Mathematics and Statistics, Memorial University of Newfoundland, St John's, Newfoundland, Canada, A1C 5S7
D. SUMMERS
Affiliation:
Department of Mathematics and Statistics, Memorial University of Newfoundland, St John's, Newfoundland, Canada, A1C 5S7
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Abstract

A spectral representation for the isotropic part of the Coulomb collisional operator is given. The particle distribution function is expanded in a series of generalized Laguerre polynomials, and the Coulomb collisional operator is expressed in terms of the spectral amplitudes. When the spectral representation is applied to the Fokker–Planck equation, a system of coupled ordinary differential equations for the spectral amplitudes is obtained. The spectral coefficients related to the Coulomb operator are defined through recurrence relations, which we reduce to simplified form. This makes possible accurate and efficient analytical and numerical evaluations of the interaction matrices. The results presented can be used in analytical investigations of the properties of the Coulomb collisional operator as well as in numerical calculations for plasmas far from thermal equilibrium. The method can also be generalized to include angular dependencies for non-isotropic particle distributions.

Type
Research Article
Information
Journal of Plasma Physics , Volume 58 , Issue 3 , October 1997 , pp. 475 - 484
Copyright
1997 Cambridge University Press

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