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Covariant form for the collision integral

Published online by Cambridge University Press:  01 August 2007

D. B. MELROSE
D. B. MELROSE*
Affiliation:
School of Physics, University of Sydney, NSW 2006, Australia ([email protected])
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Abstract

The collision integral that describes the evolution of a distribution of particles in a plasma due to Coulomb interactions between themselves or with other particles is generalized to include relativistic effects and the current–current interaction (in addition to the charge–charge interaction). This is achieved through a covariant version of a conventional derivation based on correlation functions for fluctuations in the plasma. The covariant theory is used to distinguish between longitudinal (charge–charge) and transverse (current–current) interactions. For highly relativistic particles, the current–current contribution is half the charge–charge contribution when Debye screening is unimportant, and is unaffected by Debye screening. It is shown that the classical theory is reproduced by a quantum electrodynamics calculation for electron–electron (Møller) scattering in the limit of small momentum transfer.

Type
Papers
Information
Journal of Plasma Physics , Volume 73 , Issue 4 , August 2007 , pp. 599 - 611
Copyright
Copyright © Cambridge University Press 2006

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References

Balescu, R. 1963 Statistical Mechanics of Charged Particles. London: Interscience.Google Scholar
Baral, K. C. and Mohanty, J. N. 2000 Phys. Plasmas 7, 1103.CrossRefGoogle Scholar
Baral, K. C. and Mohanty, J. N. 2002 Phys. Plasmas 9, 4507.CrossRefGoogle Scholar
Beliaev, S. T. and Budker, G. I. 1956 Dokl. Akad. Nauk. SSSR 107, 807 (Engl. transl. 1957 Sov. Phys. Dokl. 1, 218).Google Scholar
Berestetskii, V. B., Lifshitz, E. M. and Pitaevskii, L. P. 1971 Relativistic Quantum Theory. Oxford: Pergamon Press.Google Scholar
Braams, B. J. and Karney, C. F. F. 1987 Phys. Rev. Lett. 59, 1817.CrossRefGoogle Scholar
Dewar, R. L. 1977 Aust. J. Phys. 30, 533.CrossRefGoogle Scholar
Godfrey, B. B., Newberger, B. S. and Taggart, K. A. 1975 IEEE Trans. Plasma Sci. 3, 60, 68.CrossRefGoogle Scholar
Heiselberg, H. and Pethick, C. J. 1993 Phys. Rev. D 48, 2916.Google Scholar
Klimontovich, Yu. L. 1967 Statistical Theory of Non-equilibrium Processes in a Plasma. New York: Pergamon Press.Google Scholar
Lehmann, E. 2006 J. Math. Phys. 47, 023303.CrossRefGoogle Scholar
Lifshitz, E. M. and Pitaevskii, L. P. 1981 Physical Kinetics. Oxford: Pergamon Press.Google Scholar
Prentice, A. J. R. 1967 Plasma Phys. 9, 433.CrossRefGoogle Scholar
Rosenbluth, M. N.MacDonald, W. M. and Judd, D. L. 1957 Phys. Rev. 107, 1.CrossRefGoogle Scholar
Saveiev, V. L. and Nanbu, K. 2002 Phys. Rev. E 65, 051205.Google Scholar
Trubnikov, B. A. 1958 Zh. Eksp. Teor. Fiz. 34, 1341 (Engl. transl. 1958 Sov. Phys. JETP 7, 926).Google Scholar