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Statistical mechanics of a spin-polarized plasma

Published online by Cambridge University Press:  13 March 2009

W. Y. Zhang  and
R. Balescu
W. Y. Zhang
Affiliation:
Association Euratom-Etat Belge, Faculté des Sciences CP 231, Campus Plaine, Université Libre de Bruxelles, 1050 Bruxelles, Belgium
R. Balescu
Affiliation:
Association Euratom-Etat Belge, Faculté des Sciences CP 231, Campus Plaine, Université Libre de Bruxelles, 1050 Bruxelles, Belgium
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Abstract

The statistical mechanics of a spin-polarized plasma is investigated in detail. A rigorous quantum-mechanical description is constructed in terms of a generalized matrix Wigner function. In order to ensure the manifest gauge invariance of the theory, the non-canonical variables q (position) and π (mechanical momentum) are used for the particles. The evolution equation for the phase-space Wigner function, as well as the BBGKY hierarchy for the reduced distribution functions, are derived. A general expression is found for the quantum-mechanical realization of the Lie bracket of any pair of dynamical functions. In the quasi-classical limit, the equations of evolution and the Lie bracket reduce to a simple form. Our approach is compared with the previous semi-phenomenological theory of Cowley, Kulsrud and Valeo.

Type
Research Article
Information
Journal of Plasma Physics , Volume 40 , Issue 2 , October 1988 , pp. 199 - 213
Copyright
Copyright © Cambridge University Press 1988

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References

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