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A many-particle approach to the gyro-kinetic theory

Published online by Cambridge University Press:  01 October 2007

ALEXEY MISHCHENKO  and
AXEL KÖNIES
ALEXEY MISHCHENKO
Affiliation:
Max-Planck-Institut für Plasmaphysik, EURATOM-Association, D-17491 Greifswald, Germany ([email protected])
AXEL KÖNIES
Affiliation:
Max-Planck-Institut für Plasmaphysik, EURATOM-Association, D-17491 Greifswald, Germany ([email protected])
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Abstract

A systematic first-principles approach to the many-particle formulation of the gyro-kinetic theory is suggested. The gyro-kinetic many-particle Hamiltonian is derived using the Lie transform technique. The generalized gyro-kinetic equation is obtained following the Born–Bogoliubov–Green–Kirkwood–Yvon approach. The microscopic expression for the self-consistent potential and the polarization density is obtained. It is shown that new terms appear in the gyro-kinetic polarization that can not be derived in the conventional approach. An expression for the collision term is obtained in the Landau approximation.

Type
Papers
Information
Journal of Plasma Physics , Volume 73 , Issue 5 , October 2007 , pp. 757 - 772
Copyright
Copyright © Cambridge University Press 2006

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References

[1]Hahm, T. S. 1988 Phys. Fluids 31, 2670.CrossRefGoogle Scholar
[2]Hahm, T. S., Lee, W. W. and Brizard, A. J. 1988 Phys. Fluids 31, 1940.CrossRefGoogle Scholar
[3]Brizard, A. J. 1989 J. Plasma Phys. 41, 541.CrossRefGoogle Scholar
[4]Sugama, H. 2000 Phys. Plasmas 7, 466.CrossRefGoogle Scholar
[5]Brizard, A. J. 2000 Phys. Plasmas 7, 4816.CrossRefGoogle Scholar
[6]Klimontovich, Y. L. 1967 The Statistical Theory of Non-equilibrium Processes in a Plasma. Oxford: Pergamon Press.Google Scholar
[7]Littlejohn, R. G. 1983 J. Plasma Physics 29, 111.CrossRefGoogle Scholar
[8]Cary, J. R. 1981 Phys. Rep. 79, 131.CrossRefGoogle Scholar
[9]Zubarev, D., Morozov, V. and Röpke, G. 1996 Statistical Mechanics of Nonequilibrium Processes. Berlin: Akademic Verlag.Google Scholar
[10]Mishchenko, A. 2005 PhD thesis, Ernst-Moritz-Arndt-Universität Greifswald.Google Scholar
[11]Rostoker, N. 1960 Phys. Fluids 3, 922.CrossRefGoogle Scholar
[12]O'Neil, T. M. 1983 Phys. Fluids 26, 2128.CrossRefGoogle Scholar
[13]Hübner, G. PhD thesis, University of Bayreuth, 1994.Google Scholar
[14]O'Neil, T. M. and Hjorth, P. G. 1985 Phys. Fluids 28, 3241.CrossRefGoogle Scholar
[15]Glinsky, M. E. and O'Neil, T. M. 1991 Phys. Fluids 3, 1279.CrossRefGoogle Scholar