Kinetic Description of Low Frequency Modes in Inhomogeneous Plasma

  • Jan Weiland
Part of the Springer Series on Atomic, Optical, and Plasma Physics book series (SSAOPP, volume 71)


In the previous chapter we derived simple dispersion relations for some of the most dangerous low frequency instabilities using a fluid description. We will now show how this can be done by kinetic theory, [1–4], from the Vlasov equation in a simple slab geometry. We will start by using the method of integration along unperturbed orbits [1–5], which gives the most general result, i.e. including also modes with \( \omega \geqslant {{\Omega }_{\rm{c}}} \), full finite Larmor radius effects and wave particle resonances. We will, however, restrict attention to modes with \( \omega < < {{\Omega }_{\rm{c}}} \). We will show how wave-particle resonances may impede the free electron motion along the field lines, thus causing drift instability and how the lowest order finite Larmor radius (FLR) effect agrees with that obtained from the stress tensor in  Chap. 2. After the more general treatment we will show how the wave-particle resonances can be described by a simpler drift-kinetic equation that does not contain FLR effects and how the lowest order FLR effect can be obtained by a simple orbit averaging.


Dispersion Relation Drift Wave Finite Larmor Radius Polarisation Drift Diamagnetic Drift 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


  1. 1.
    M.N. Rosenbluth and C. Longmire, Ann. Phys. (N.Y.) 1, 120 (1957).Google Scholar
  2. 2.
    M.N. Rosenbluth and N. Rostoker, Phys. Fluids 2, 23 (1959).ADSCrossRefMATHGoogle Scholar
  3. 3.
    L.I. Rudakov and R.Z. Sagdeev Sov. Phys. JETP 37, 952 (1960).Google Scholar
  4. 4.
    M.N. Rosenbluth, N.A. Krall and N.Rostoker, Nucl. Fusion Suppl. Pt. 1 143 (1962).Google Scholar
  5. 5.
    N. A. Krall and M.N. Rosenbluth, Phys. Fluids 5, 1435 (1962).ADSCrossRefGoogle Scholar
  6. 6.
    B. B. Kadomtsev, Plasma Turbulence, Academic Press, New York 1965Google Scholar
  7. 7.
    A.G. Sitenko, Electromagnetic Fluctuations in a Plasma, Academic Press, N.Y. 1967.Google Scholar
  8. 8.
    N. A. Krall in Advances in Plasma Physics (Ed. A. Simon and W. Thompson), Wiley, New York Vol. 1, p. 153 (1968)Google Scholar
  9. 9.
    B. Coppi, G. Laval, R. Pellat and M.N. Rosenbluth, Plasma Physics 10 1 (1968).ADSCrossRefGoogle Scholar
  10. 10.
    L.I. Rukhadze and V.P. Silin, Soviet Physics Usp. 2, 659 (1969).ADSCrossRefGoogle Scholar
  11. 11.
    B. B. Kadomtsev and O.P. Pogutse, in Reviews of Plasma Physics (Ed. M.A. Leontovitch) Consultant Bureau, New York, Vol. 5, p. 249 (1970).CrossRefGoogle Scholar
  12. 12.
    S. Ichimaru, Basic Principles of Plasma Physics, Mc Graw Hill 1973.Google Scholar
  13. 13.
    N. A. Krall and Trivelpiece, Principle of Plasma Physics, McGraw Hill 1973.Google Scholar
  14. 14.
    A.B. Mikhailovskii, Theory of Plasma Instabilities, Vol. 2, Consultant Bureau, New York 1974.Google Scholar
  15. 15.
    A. Hasagawa, Plasma Instabilities and Nonlinear effects, Springer 1975, Chapter 3.Google Scholar
  16. 16.
    W.M. Manheimer, An Introduction to trapped Particle Instabilities in Tokamak, ERDA Crit. Rev. Series 1977.Google Scholar
  17. 17.
    S.P. Gary and J.J. Sanderson, Phys. Fluids 21, 1181 (1978).ADSCrossRefMATHGoogle Scholar
  18. 18.
    A. Hasegawa, Phys. Fluids 22, 1988 (1979).ADSCrossRefMATHGoogle Scholar
  19. 19.
    C.Z. Cheng, Phys. Fluids 25, 1020 (1982)ADSCrossRefMATHGoogle Scholar

Copyright information

© Springer Science+Business Media New York 2012

Authors and Affiliations

  • Jan Weiland
    • 1
  1. 1.Chalmers University of Technology and EURATOM VR AssociationGothenburgSweden

Personalised recommendations