Hostname: page-component-7dd5485656-frp75 Total loading time: 0 Render date: 2025-10-30T22:19:48.168Z Has data issue: false hasContentIssue false
  • English
  • Français

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
Get access Rights & Permissions [Opens in a new window]

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.

Information

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

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

Article purchase

Temporarily unavailable

References

REFERENCES

Ashby, N. 1961 Applications of Field Theory to Electrical Conductivity, Ph.D. dissertation, University of Colorado.Google Scholar
Balescu, R. 1968 Acta Phys. Austriaca, 28, 336.Google Scholar
Balescu, R. 1975 Equilibrium and Nonequilibrium Statistical Mechanics. Wiley.Google Scholar
Balescu, R. & Poulain, M. 1974 Physica, 76, 421.CrossRefGoogle Scholar
Balescu, R. & Zhang, W. Y. 1988 J. Plasma Phys. 40, 215.CrossRefGoogle Scholar
Bialynicki-Birula, I. & Iwinski, Z. 1973 Rep. Math. Phys. 4, 139.CrossRefGoogle Scholar
Brunelli, B. et al. (eds) 1988 Muon-Catalyzed Fusion and Fusion with Polarized Nuclei: Erice, April 1987. Plenum (to appear).Google Scholar
Carruthers, P. & Zachariasen, F. 1983 Rev. Mod. Phys. 55, 245.CrossRefGoogle Scholar
Connor, J. P., Bonnor, T. W. & Smith, J. R. 1952 Phys. Rev. Lett. 88, 468.Google Scholar
Cowley, S. C., Kulsrud, R. M. & Valeo, E. J. 1986 Phys. Fluids, 29, 430.CrossRefGoogle Scholar
De Groot, S. R. & Suttorp, L. G. 1972 Foundations of Electrodynamics. North-Holland.Google Scholar
Goldhaber, M. 1934 Proc. Camb. Phil. Soc. 30, 561.CrossRefGoogle Scholar
Kulsrud, R. M. 1987 Muon-Catalyzed Fusion and Fusion with Polarized Nuclei: Erice, April 1987 (ed. Brunelli, B. et al. ). Plenum.Google Scholar
Kulsrud, R. M., Furth, H. P., Valeo, E. J. & Goldhaber, M. 1982 Phys. Rev. Lett. 49, 1248.CrossRefGoogle Scholar
Kulsrud, R. M., Valeo, E. J. & Cowley, S. C. 1986 Nucl. Fusion, 26, 1443.CrossRefGoogle Scholar
Littlejohn, R. 1981 Phys. Fluids, 24, 1730.CrossRefGoogle Scholar
Mori, H., Oppenheim, I. & Ross, J. 1962 Studies in Statistical Mechanics, vol. 1, p. 217 (ed. de Boer, J. & Uhlenbeck, G.). North-Holland.Google Scholar
Moyal, J. E. 1949 Proc. Camb. Phil. Soc. 45, 99.CrossRefGoogle Scholar
Rukhadze, A. A. & Silin, V. P. 1960 Soviet Phys. JETP, 11, 463.Google Scholar
Silin, V. P. 1956 Zh. Teor. Eksp. Fiz. 30, 421.Google Scholar
Weyssow, B. & Balescu, R. 1986 J. Plasma Phys. 35, 449.CrossRefGoogle Scholar
Weyssow, R. & Balescu, R. 1987 J. Plasma Phys. 37, 467.CrossRefGoogle Scholar