Skip to main content
SpringerLink
Log in

Kinetics of ions in a neutral gas upon abrupt application of an electric field. I. CEM model

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

Abstract

A new method for calculating matrix elements of the collision integral is used for solving problems of the mobility of ions against the background of atoms and for constructing the distribution functions for ions upon an abrupt application of an electric field. It is shown how the stationary distribution function can be constructed using the nonstationary moments method in the case when the stationary moments method is completely inapplicable. The solution to the nonstationary problem for the CEM model corresponding to resonant charge exchange with a constant collision frequency, which is constructed analytically, is used for analyzing the limits of applicability of the nonstationary moments method.

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. D. Burnett, Proc. London Math. Soc. 40, 382 (1935).

    Article  MATH  Google Scholar 

  2. A. Ya. Ender and I. A. Ender, Phys. Fluids 11, 2720 (1999).

    Article  MATH  MathSciNet  ADS  Google Scholar 

  3. A. Ya. Ender and I. A. Ender, Collision Integral of the Boltzmann Equation and Moment Method (St. Peterb. Gos. Univ., St. Petersburg, 2003) [in Russian].

    Google Scholar 

  4. A. Ya. Ender and I. A. Ender, Transp. Theory Stat. Phys. 56, 563 (2007).

    Article  MathSciNet  ADS  Google Scholar 

  5. L. Sena, Zh. Eksp. Teor. Fiz. 8, 734 (1946).

    Google Scholar 

  6. G. H. Wannier, Bell Syst. Tech. J. 32, 170 (1953).

    Google Scholar 

  7. Yu. M. Kagan and V. I. Perel’, Dokl. Akad. Nauk SSSR 98, 575 (1954).

    Google Scholar 

  8. B. M. Smirnov, Zh. Tekh. Fiz. 36, 1864 (1966) [Sov. Phys. Tech. Phys. 11, (1966)].

    Google Scholar 

  9. E. A. Mason and E. W. McDaniel, The Mobility and Diffusion in Gases (Wiley, New York, 1973).

    Google Scholar 

  10. E. A. Mason and E. W. McDaniel, Transport Properties of Ions in Gases (Wiley, New York, 1988).

    Book  Google Scholar 

  11. R. D. White, K. F. Ness, and R. E. Robson, Appl. Surface Sci. 192, 26 (2002).

    Article  ADS  Google Scholar 

  12. B. Li, R. E. Robson, and R. D. White, Phys. Rev. E 74, 026405 (2006).

    Article  ADS  Google Scholar 

  13. K. Kumar, Ann. Phys. 37, 113 (1966).

    Article  MATH  ADS  Google Scholar 

  14. K. Kumar, H. R. Skullerud, and R. E. Robson, Aust. J. Phys. 33, 343 (1980).

    MathSciNet  ADS  Google Scholar 

  15. R. E. Robson and K. F. Ness, Phys. Rev. A 33, 2068 (1986).

    Article  ADS  Google Scholar 

  16. K. F. Ness, J. Phys. D: Appl. Phys. 27, 1848 (1994).

    Article  ADS  Google Scholar 

  17. R. E. Robson, Aust. J. Phys. 47, 279 (1994).

    ADS  Google Scholar 

  18. J. V. Jovanovic, S. B. Vrhovac, and Z. L. Petrovic, Eur. Phys. J. A 21, 335 (2002).

    Google Scholar 

  19. S. Chapman and T. G. Cowling, Mathematical Theory of Non_Uniform Gases (Cambridge Univ., London, 1939; Inostrannaya Literatura, Moscow, 1960).

    Google Scholar 

  20. J. Ferziger and H. G. Kaper, Mathematical Theory of Transport Processes in Gases (North-Holland, Amsterdam-London, 1972; Mir, Moscow, 1976).

    Google Scholar 

  21. A. Ya. Ender and I. A. Ender, in Aerodynamics: Collection of Scientific Works, Ed. by ed]R. N. Miroshin (Balabanov, Moscow, 2008), pp. 95–157.

    Google Scholar 

  22. A. Ya. Ender and I. A. Ender, Dokl. Akad. Nauk SSSR 193, 61 (1970) [Sov. Phys. Dokl. (1970)].

    Google Scholar 

  23. A. Ya. Ender and I. A. Ender, in Aerodynamics: Collection of Scientific Works, Ed. by ed]R. N. Miroshin (NIIKh SPbGU, St. Petersburg, 2003), pp. 179–203.

    Google Scholar 

  24. A. Ya. Ender, I. A. Ender, and A. B. Gerasimenko, Open Plasma Phys. J. 2, 24 (2009).

    Article  ADS  Google Scholar 

  25. T. Kihara, Rev. Mod. Phys. 25, 844 (1953).

    Article  MATH  ADS  Google Scholar 

  26. P. L. Bhatnagar, E. P. Gross, and M. Krook, Phys. Rev. 94, 511 (1954).

    Article  MATH  ADS  Google Scholar 

  27. R. E. Robson and T. Makabe, Aust. J. Phys. 47, 305 (1994).

    ADS  Google Scholar 

  28. H. Sugawara, H. Tagashira, and Y. Sakay, J. Phys. D: Appl. Phys. 29, 1168 (1996).

    Article  ADS  Google Scholar 

  29. A. Ya. Ender and I. A. Ender, in Proceedings of International Conference on Mechanics “Fourth Polyakhov Readings, ” St. Peterburg, 2006, pp. 455–464.

Download references

Author information

Authors and Affiliations

  1. Ioffe Physicotechnical Institute, Russian Academy of Sciences, Politekhnicheskaya ul. 26, St. Petersburg, 194021, Russia

    A. Ya. Ender

  2. St. Petersburg State University, Universitetskaya nab. 7/9, St. Petersburg, 199164, Russia

    I. A. Ender

Authors
  1. A. Ya. Ender
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. I. A. Ender
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to A. Ya. Ender.

Additional information

Original Russian Text © A.Ya. Ender, I.A. Ender, 2010, published in Zhurnal Tekhnicheskoǐ Fiziki, 2010, Vol. 80, No. 2, pp. 8–17.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Ender, A.Y., Ender, I.A. Kinetics of ions in a neutral gas upon abrupt application of an electric field. I. CEM model. Tech. Phys. 55, 166–175 (2010). https://doi.org/10.1134/S1063784210020027

Download citation

  • Received:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1134/S1063784210020027

Keywords

Search

Navigation