Skip to main content
Log in

Bogoliubov-Born-Green-Kirkwood-Yvon hierarchy and the kinetic theory of dusty plasmas

  • Published:
Theoretical and Mathematical Physics Aims and scope Submit manuscript

Abstract

We consider the modern state of a consistent kinetic theory of dusty plasmas. We present the derivation of equations for microscopic phase densities of plasma particles and grains. Such equations are suitable for extending the Bogoliubov-Born-Green-Kirkwood-Yvon hierarchy to the case of dusty plasmas and for deriving the kinetic equations with regard for both elastic and inelastic particle collisions. Moreover, we describe the effective grain-grain potentials kinetically.

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

Access this article

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

Instant access to the full article PDF.

Similar content being viewed by others

References

  1. N. N. Bogoliubov, Problems of a Dynamical Theory in Statistical Physics [in Russian], Gostekhizdat, Moscow (1946); English transl. (Stud. Statist. Mech., Vol. 1), North-Holland, Amsterdam (1962).

    Google Scholar 

  2. Yu. L. Klimontovich and V. P. Silin, Zh. Ehksper. Teor. Fiz., 23, 151–160 (1952).

    Google Scholar 

  3. Yu. L. Klimontovich, The Statistical Theory of Non-Equilibrium Processes in a Plasma [in Russian], Moscow State Univ., Moscow (1967); English transl., Pergamon, Oxford (1967).

    Google Scholar 

  4. S. Ichimaru, Ann. Phys., 20, 78–118 (1962).

    Article  MATH  ADS  MathSciNet  Google Scholar 

  5. A. G. Sitenko, Fluctuations and Nonlinear Wave Interactions in Plasmas [in Russian], Naukova Dumka, Kiev (1977); (Internat. Ser. Natural Philos., Vol. 107), Pergamon, Oxford (1982).

    Google Scholar 

  6. S. Ichimaru, Statistical Plasma Physics, Addison-Wesley, Redwood City, Calif. (1992).

    Google Scholar 

  7. Yu. L. Klimontovich, H. Wilhelmsson, I. P. Yakimenko, and A. G. Zagorodny, Phys. Rep., 175, 263–401 (1989).

    Article  ADS  Google Scholar 

  8. Yu. L. Klimontovich, Statistical Theory of Open Systems [in Russian], Vol. 2, Kinetic Theory of Plasma. Kinetic Theory of Phase Transitions of Second Order, Yanus-K, Moscow (1999).

    Google Scholar 

  9. V. E. Fortov, A. V. Ivlev, S. A. Khrapak, A. G. Khrapak, and G. E. Morfill, Phys. Rep., 421, 1–103 (2005).

    Article  ADS  MathSciNet  Google Scholar 

  10. V. E. Fortov, A. G. Khrapak, S. A. Khrapak, V. I. Molotkov, and O. F. Petrov, Phys. Usp., 47, 447–492 (2004).

    Article  ADS  Google Scholar 

  11. P. P. J. M. Schram, A. G. Sitenko, S. A. Trigger, and A. G. Zagorodny, Contrib. Plasma Phys., 41, 211–214 (2001).

    Article  ADS  Google Scholar 

  12. P. P. J. M. Schram, A. G. Sitenko, S. A. Trigger, and A. G. Zagorodny, Phys. Rev. E, 63, 016403 (2000).

    Google Scholar 

  13. A. V. Filippov, A. G. Zagorodny, A. F. Pal’, A. N. Starostin, and A. I. Momot, JETP Lett., 86, 761–766 (2007).

    Article  ADS  Google Scholar 

  14. A. V. Filippov, A. G. Zagorodny, and A. I. Momot, JETP Lett., 88, 24–30 (2008).

    Article  ADS  Google Scholar 

  15. N. N. Bogoliubov, Theor. Math. Phys., 24, 804–807 (1975).

    Article  Google Scholar 

  16. D. Ya. Petrina and K. D. Petrina, Ukrainian Math. J., 50, 224–240 (1998).

    Article  MathSciNet  Google Scholar 

  17. P. L. Bhatnagar, E. P. Gross, and M. Krook, Phys. Rev., 54, 511–525 (1954).

    Article  ADS  Google Scholar 

  18. A. G. Zagorodny, A. V. Filippov, A. F. Pal’, A. N. Starostin, and A. I. Momot, Probl. Atomic Sci. and Technology, No. 6, 99–103 (2006).

  19. A. V. Filippov, A. G. Zagorodny, A. I. Momot, A. F. Pal, and A. N. Starostin, JETP, 104, 147–161 (2007).

    Article  ADS  Google Scholar 

  20. S. A. Khrapak, S. K. Zhdanov, A. V. Ivlev, and G. E. Morfill, J. Appl. Phys., 101, 033307 (2007).

    Google Scholar 

  21. M. Chandhuri, S. A. Khrapak, and G. E. Morfill, Phys. Plasmas, 14, 022102 (2007).

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to A. G. Zagorodny.

Additional information

Prepared from an English manuscript submitted by the author; for the Russian version, see Teoreticheskaya i Matematicheskaya Fizika, Vol. 160, No. 2, pp. 276–289, August, 2009.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Zagorodny, A.G. Bogoliubov-Born-Green-Kirkwood-Yvon hierarchy and the kinetic theory of dusty plasmas. Theor Math Phys 160, 1101–1112 (2009). https://doi.org/10.1007/s11232-009-0103-6

Download citation

  • Received:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11232-009-0103-6

Keywords

Navigation