Skip to main content
SpringerLink
Log in

Variational approaches to the problems of plasma stability and of nonlinear plasma dynamics

  • Scientific Summaries
  • Published:
Journal of Experimental and Theoretical Physics Letters Aims and scope Submit manuscript

Abstract

A variational method is developed in order to investigate the nonlinear dynamics and stability of plasma using hydrodynamic plasma models, namely, the one-fluid, Hall, and electron MHD models. The key idea of the method is to adequately take into account variational symmetries and the associated conservation laws inherent in these hydrodynamic models. This approach is applied to derive variational criteria for the stability of a steadily moving plasma and to propose a variational method of the adiabatic separation of fast and slow motions, which makes it possible to simplify (reduce) the basic hydrodynamic models.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. I. B. Bernstein, E. A. Frieman, M. D. Kruskal, and R. M. Kulsrud, Proc. R. Soc. London, Ser. A 244, 17 (1958).

    ADS  MathSciNet  Google Scholar 

  2. R. Courant and D. Hilbert, Methoden der mathematischen Physik (Springer-Verlag, Berlin, 1931; Gostekhizdat, Moscow, 1951).

    Google Scholar 

  3. J. Serrin, Handbuch der Physik, Ed. by S. Flügge (Springer-Verlag, Berlin, 1959), Bd. VIII/1.

    Google Scholar 

  4. T. H. Boyer, Ann. Phys. 42, 445 (1967).

    MATH  Google Scholar 

  5. V. Rosenhaus and G. H. Katzin, J. Math. Phys. 35, 1998 (1994).

    Article  ADS  MathSciNet  Google Scholar 

  6. V. I. Ilgisonis and V. P. Lakhin, Fiz. Plazmy 25, 64 (1999) [Plasma Phys. Rep. 25, 58 (1999)].

    Google Scholar 

  7. W. Newcomb, Nucl. Fusion Suppl. 2, 451 (1962).

    Google Scholar 

  8. N. Padhye and P. Morrison, Fiz. Plazmy 22, 960 (1996) [Plasma Phys. Rep. 22, 869 (1996)].

    Google Scholar 

  9. V. I. Ilgisonis and V. P. Pastukhov, Fiz. Plazmy 22, 228 (1996) [Plasma Phys. Rep. 22, 208 (1996)].

    Google Scholar 

  10. E. Hameiri, J. Math. Phys. 22, 2080 (1981).

    Article  ADS  MATH  MathSciNet  Google Scholar 

  11. A. S. Kingsep, K. V. Chukbar, and V. V. Yan’kov, in Reviews of Plasma Physics, Ed. by B. B. Kadomtsev (Énergoizdat, Moscow, 1987; Consultants Bureau, New York, 1990), Vol. 16.

    Google Scholar 

  12. V. I. Ilgisonis and V. P. Lakhin, Electromagn. Waves Electron. Syst. 3(2–3) (1998).

  13. P. J. Olver, Applications of Lie Groups to Differential Equations (Springer-Verlag, Berlin, 1986).

    Google Scholar 

  14. V. P. Pastukhov, Pis’ma Zh. Éksp. Teor. Fiz. 67, 892 (1998) [JETP Lett. 67, 940 (1998)].

    Google Scholar 

  15. V. P. Pastukhov, Fiz. Plazmy 26, 566 (2000) [Plasma Phys. Rep. 26, 529 (2000)].

    Google Scholar 

  16. B. B. Kadomtsev and O. P. Pogutse, Zh. Éksp. Teor. Fiz. 65, 575 (1973) [Sov. Phys. JETP 38, 283 (1974)].

    ADS  Google Scholar 

  17. B. B. Kadomtsev and O. P. Pogutse, Zh. Éksp. Teor. Fiz. 66, 2067 (1974).

    Google Scholar 

  18. R. White, D. Monticello, et al., in Proceedings of the 5th International Conference on Plasma Physics and Controlled Nuclear Fusion Research, Tokyo, 1974 (IAEA, Vienna, 1975), Vol. 1, p. 495.

    Google Scholar 

  19. H. Strauss, Phys. Fluids 19, 134 (1976).

    ADS  Google Scholar 

  20. H. Strauss, Nucl. Fusion 23, 649 (1983).

    Google Scholar 

  21. R. D. Hazeltine, M. Kotschenreuther, and P. J. Morrison, Phys. Fluids 28, 2466 (1985).

    Article  ADS  Google Scholar 

  22. A. Bernstein, in Basic Plasma Physics, Ed. by A. A. Galeev and R. N. Sudan (Énergoatomizdat, Moscow, 1983; North-Holland, Amsterdam, 1983), Vol. 1.

    Google Scholar 

  23. V. I. Ilgisonis and V. P. Pastukhov, Pis’ma Zh. Éksp. Teor. Fiz. 61, 186 (1995) [JETP Lett. 61, 189 (1995)].

    Google Scholar 

  24. E. Frieman and M. Rotenberg, Rev. Mod. Phys. 32, 898 (1960).

    Article  ADS  MathSciNet  Google Scholar 

  25. D. D. Holm, J. E. Marsden, T. Ratiu, and A. Weinstein, Phys. Rep. 123(1–2), 1 (1985).

    ADS  MathSciNet  Google Scholar 

  26. V. A. Gordin and V. I. Petviashvili, Zh. Éksp. Teor. Fiz. 95, 1711 (1989) [Sov. Phys. JETP 68, 988 (1989)].

    Google Scholar 

  27. V. I. Arnold, J. Appl. Math. Mech. 29, 1002 (1965).

    MATH  Google Scholar 

  28. E. Hameiri and H. A. Holties, Phys. Plasmas 1, 3807 (1994).

    Article  ADS  MathSciNet  Google Scholar 

  29. V. I. Ilgisonis, Trans. Fusion Technol. 35, 170 (1999).

    Google Scholar 

  30. V. I. Ilgisonis, in Proceedings of the 26th EPS Conference on Controlled Fusion and Plasma Physics, Maastricht, 1999 [ESA 23J, 861 (1999)].

  31. V. I. Ilgisonis, Phys. Plasmas 3, 4577 (1996).

    Article  ADS  Google Scholar 

  32. V. P. Pastukhov, in Proceedings of the Joint Varenna-Lausanne International Workshop on Theory of Fusion Plasmas, Varenna, 1998, Ed. by J. W. Connor, E. Sindoni, and J. Vaclavik (Bologna, Compositori, 1998), p. 449.

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Institute of Nuclear Fusion, Russian Research Centre Kurchatov Institute, pl. Kurchatova 1, Moscow, 123182, Russia

    V. I. Ilgisonis & V. P. Pastukhov

Authors
  1. V. I. Ilgisonis
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. V. P. Pastukhov
    View author publications

    You can also search for this author in PubMed Google Scholar

Additional information

__________

Translated from Pis’ma v Zhurnal Éksperimental’no\(\overset{\lower0.5em\hbox{$\smash{\scriptscriptstyle\smile}$}}{l} \) i Teoretichesko\(\overset{\lower0.5em\hbox{$\smash{\scriptscriptstyle\smile}$}}{l} \) Fiziki, Vol. 72, No. 10, 2000, pp. 758–773.

Original Russian Text Copyright © 2000 by Ilgisonis, Pastukhov.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Ilgisonis, V.I., Pastukhov, V.P. Variational approaches to the problems of plasma stability and of nonlinear plasma dynamics. Jetp Lett. 72, 530–540 (2000). https://doi.org/10.1134/1.1343158

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1134/1.1343158

PACS numbers

Search

Navigation