Plasma Physics Reports

, Volume 45, Issue 7, pp 685–698 | Cite as

MHD Waves and Instabilities in Two-Component Anisotropic Plasma

  • N. S. Dzhalilov
  • S. Sh. HuseinovEmail author


Based on the 16-moment MHD transport equations, the propagation of linear waves in an anisotropic homogeneous cosmic plasma is considered. A general dispersion relation is derived with allowance for two plasma components (electrons and protons) and heat flux along the magnetic field. This dispersion relation is a generalization of the previously studied cases of one-component (ion) plasma. The case in which the effects associated with the heat flux are ignored is analyzed in more detail. In the limit of longitudinal propagation, the wave modes fully consistent with the modes known in the low-frequency kinetic theory of collisionless plasma are classified. Firehose and mirror instabilities are analyzed. It is shown that taking into account the electron component modifies the growth rates and thresholds of instabilities.



We are grateful to the anonymous referee for useful comments and recommendations, which were taken into account when revising the manuscript.


This work was supported by the Foundation for the Development of Science under the President of the Republic of Azerbaijan, project nos. EIF-KETPL-2-2015-1(25)-56/11/1 and EIF-BGM-4-RFTF-1/2017-21/06/1 (joint Russian–Azerbaijan grant).


  1. 1.
    G. F. Chew, M. L. Goldberger, and F. E. Low, Proc. Roy. Soc. London A 236, 112 (1956).ADSCrossRefGoogle Scholar
  2. 2.
    V. N. Oraevskii, Y. V. Konikov, and G. V. Khazanov, Transport Processes in Anisotropic Near-Earth Plasma (Nauka, Moscow, 1985) [in Russian].Google Scholar
  3. 3.
    J. J. Ramos, Phys. Plasmas 10, 3601 (2003).ADSCrossRefGoogle Scholar
  4. 4.
    N. S. Dzhalilov, V. D. Kuznetsov, and J. Staude, Contrib. Plasma Phys. 51, 621 (2011).ADSCrossRefGoogle Scholar
  5. 5.
    N. S. Dzhalilov and V. D. Kuznetsov, Plasma Phys. Rep. 39, 1026 (2013).ADSCrossRefGoogle Scholar
  6. 6.
    A. N. Hall, J. Plasma Phys. 21, 431 (1979).ADSCrossRefGoogle Scholar
  7. 7.
    E. A. Kuznetsov, T. Passot, and P. L. Sulem, Phys. Plasmas 19, 090701 (2012).ADSCrossRefGoogle Scholar
  8. 8.
    V. D. Kuznetsov and N. S. Dzhalilov, Geomagn. Aeron. 54, 886 (2014).ADSCrossRefGoogle Scholar
  9. 9.
    N. S. Dzhalilov, V. D. Kuznetsov, and J. Staude, Astron. Astrophys. 489, 769 (2008).ADSCrossRefGoogle Scholar
  10. 10.
    N. S. Dzhalilov and S. Sh. Huseynov, Azerbaijan Astron. J., No. 1, 1 (2016).Google Scholar
  11. 11.
    P. Travnicek, S. Stverak, and M. Maksimovic, J. Geophys. Res. 113, A03103 (2008).ADSGoogle Scholar
  12. 12.
    P. Hellinger, P. Travnicek, and J. C. Kasper, Geophys. Rev. Lett. 33, L09101 (2006).Google Scholar
  13. 13.
    L. I. Rudakov and R. Z. Sagdeev, in Plasma Physics and the Problem of Controlled Thermonuclear Reactions, Ed. by M. A. Leontovich (Pergamon, New York, 1959), Vol. 3, p. 321.Google Scholar
  14. 14.
    S. A. Chandrasekhar, A. N. Kaufman, and K. M. Watson, Proc. R. Soc. London A 245, 435 (1958).ADSCrossRefGoogle Scholar
  15. 15.
    T. Stix, The Theory of Plasma Waves (Mc Graw-Hill, New York, 1962).zbMATHGoogle Scholar
  16. 16.
    A. Barnes, Phys. Fluids 9, 1483 (1966).ADSCrossRefGoogle Scholar
  17. 17.
    O. A. Pokhotelov, R. Z. Sagdeev, M. A. Balikhin, and R. A. Treumann, J. Geophys. Res. 109, A09213 (2004).ADSGoogle Scholar
  18. 18.
    C. Califano, P. Hellinger, E. Kuznetsov, T. Passot, P. L. Sulem, and P. M. Trávnicek, J. Geophys. Res. 113, A08219 (2008).ADSGoogle Scholar
  19. 19.
    F. G. E. Pantellini and S. J. Schwartz, J. Geophys. Res. 100, 3539 (1995).ADSCrossRefGoogle Scholar
  20. 20.
    V. Ge’not, S. J. Schwartz, C. Mazelle, M. Balikhin, M. Dunlop, and T. M. Bauer, J. Geophys. Res. 106, 21611 (2001).ADSCrossRefGoogle Scholar
  21. 21.
    O. A. Pokhotelov, M. A. Balikhin, and H. St.-C. K. Alleyne, and O. G. Onishchenko, J. Geophys. Res. 105, 2393 (2000).ADSCrossRefGoogle Scholar
  22. 22.
    S. P. Gary and H. Karimabadi, J. Geophys. Res. 111, A11224 (2006).ADSCrossRefGoogle Scholar
  23. 23.
    P. Hellinger, Phys. Plasmas 14, 082105 (2007).ADSCrossRefGoogle Scholar
  24. 24.
    Y. N. Istomin, O. A. Pokhotelov, and M. A. Balikhin, Phys. Plasmas 16, 122901 (2009).ADSCrossRefGoogle Scholar
  25. 25.
    R. C. Davidson and H. J. Völk, Phys. Fluids 11, 2259 (1968).ADSCrossRefGoogle Scholar
  26. 26.
    A. Achterberg, Monthly Notices Roy. Soc. 436, 705 (2013).ADSCrossRefGoogle Scholar
  27. 27.
    J. V. Hollweg and H. J. Völk, J. Geophys. Res. 75, 5297 (1970).ADSCrossRefGoogle Scholar
  28. 28.
    S. P. Gary and C. D. Madland, J. Geophys. Res. 90, 7607 (1985).ADSCrossRefGoogle Scholar
  29. 29.
    P. H. Yoon, C. S. Wu, and A. S. de Assis, Phys. Fluids 5, 1971 (1993).CrossRefGoogle Scholar
  30. 30.
    X. Li and S. R. Habbal, J. Geophys. Res. A105, 27377 (2000).ADSCrossRefGoogle Scholar
  31. 31.
    P. Hunana and G. P. Zank, Astrophys. J. 839, 13 (2017).ADSCrossRefGoogle Scholar
  32. 32.
    J. J. Ramos, Phys. Plasmas 12, 052102 (2005).ADSMathSciNetCrossRefGoogle Scholar
  33. 33.
    J. J. Ramos, Phys. Plasmas 14, 052506 (2007).ADSCrossRefGoogle Scholar

Copyright information

© Pleiades Publishing, Ltd. 2019

Authors and Affiliations

  1. 1.Shamakhy Astrophysical Observatory, Azerbaijan National Academy of SciencesPirkuluAzerbaijan

Personalised recommendations