Hostname: page-component-54dcc4c588-5q6g5 Total loading time: 0 Render date: 2025-09-19T18:14:08.171Z Has data issue: false hasContentIssue false
  • English
  • Français

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 (alexey.mishchenko@ipp.mpg.de)
AXEL KÖNIES
Affiliation:
Max-Planck-Institut für Plasmaphysik, EURATOM-Association, D-17491 Greifswald, Germany (alexey.mishchenko@ipp.mpg.de)
Get access Rights & Permissions [Opens in a new window]

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.

Information

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

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

[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