Skip to main content
SpringerLink
Log in

Distribution of Electrons and Ions Near an Absorbing Spherical Body in a Nonequilibrium Plasma

  • STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS
  • Published:
Journal of Experimental and Theoretical Physics Aims and scope Submit manuscript

Abstract

The applicability of the collision kinetic model of point sinks, viz., the linearized theory of screening of the electric field produced by a charged dust particle, based on the Vlasov equations for electrons and ions in a nonequilibrium plasma, which are supplemented with collision terms in the Bhatnagar–Gross–Crook form and effective point sinks to dust particle, is analyzed. The criterion for the applicability of the collision kinetic model of point sinks is the smallness of the deviation of the electron and ion number densities near an absorbing spherical body from unperturbed values. The distributions of electron and ion number densities obtained using the collision kinetic model of point sinks and the orbit motion limited approach are compared. It is shown that the latter approach is applicable only in the low-pressure limit, and upon an increase in pressure, the Coulomb asymptotics of the potential, which is proportional to the frequency electron and ion collisions with neutral atoms (molecules), renders the orbit motion limited approach inapplicable for calculating the ion distribution. It is established that the domain of applicability of the collision kinetic model of point sinks is close to the applicability domain of the Debye–Hückel theory.

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

Fig. 1.
Fig. 2.
Fig. 3.
Fig. 4.

Similar content being viewed by others

REFERENCES

  1. A. A. Vlasov, Zh. Eksp. Teor. Fiz. 8, 291 (1938);

    Google Scholar 

  2. Sov. Phys. Usp. 10, 721 (1967).

  3. L. D. Landau, Zh. Eksp. Teor. Fiz. 16, 574 (1946);

    Google Scholar 

  4. J. Phys. USSR 10, 25 (1946).

  5. N. S. Van Kampen, Physica (Amsterdam, Neth.) 21, 949 (1955).

  6. A. F. Aleksandrov, L. S. Bogdankevich, and A. A. Rukhadze, Principles of Plasma Electrodynamics (Vyssh. Shkola, Moscow, 1988; Springer, Berlin, 1984).

  7. B. B. Kadomtsev, Collective Phenomena in Plasma (Nauka, Moscow, 1988; Elsevier Science, Amsterdam, 1982).

  8. A. V. Timofeev, Resonanse Phenomena in Plasma Oscillations (Fizmatlit, Moscow, 2009) [in Russian].

    Google Scholar 

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

    Article  ADS  Google Scholar 

  10. A. V. Filippov, A. G. Zagorodny, A. I. Momot, A. F. Pal, and A. N. Starostin, J. Exp. Theor. Phys. 104, 147 (2007).

    Article  ADS  Google Scholar 

  11. A. G. Zagorodny, Theor. Math. Phys. 160, 1100 (2009).

    Article  Google Scholar 

  12. A. V. Filippov, A. G. Zagorodny, A. I. Momot, A. F. Pal’, and A. N. Starostin, J. Exp. Theor. Phys. 125, 926 (2017).

    Article  ADS  Google Scholar 

  13. S. A. Khrapak, B. A. Klumov, and G. E. Morfill, Phys. Rev. Lett. 100, 225003 (2008).

    Article  ADS  Google Scholar 

  14. S. Khrapak and G. Morfill, Contrib. Plasma Phys. 49, 148 (2009).

    Article  ADS  Google Scholar 

  15. O. V. Kozlov, Electrical Probe in Plasma (Atomizdat, Moscow, 1969) [in Russian].

    Google Scholar 

  16. P. Chung, L. Talbot, and K. Touryan, Electric Probes in Stationary and Flowing Plasmas: Theory and Application (Springer, Berlin, Heidelberg, 1975).

    Book  Google Scholar 

  17. B. V. Alekseev and V. A. Kotel’nikov, Probe Method of Plasma Diagnostics (Energoatomizdat, Moscow, 1988) [in Russian].

    Google Scholar 

  18. M. S. Benilov, in Diagnostics of Low-Temperature Plasma, Collection of Articles, Ed. by M. F. Zhukov and A. A. Ovsyannikov (Nauka, Novosibirsk, 1994), p. 214 [in Russian].

    Google Scholar 

  19. M. S. Benilov, J. Phys. D: Appl. Phys. 33, 1683 (2000).

    Article  ADS  Google Scholar 

  20. V. I. Demidov, S. V. Ratynskaia, and K. Rypdal, Rev. Sci. Instrum. 73, 3409 (2002).

    Article  ADS  Google Scholar 

  21. A. Autricque, S. A. Khrapak, L. Couldel, N. Fedorczak, C. Arnas, J.-M. Layet, and C. Grisolia, Phys. Plasmas 25, 063701 (2018).

    Article  ADS  Google Scholar 

  22. D. Darian, S. Marholm, M. Mortensen, and W. J. Miloch, Plasma Phys. Control. Fusion 61, 085025 (2019).

    Article  ADS  Google Scholar 

  23. H. M. Mott-Smith and I. Langmuir, Phys. Rev. 28, 727 (1926).

    Article  ADS  Google Scholar 

  24. Ya. L. Al’pert, A. V. Gurevich, and L. P. Pitaevskii, Space Physics with Artificial Satellites (Plenum, New York, 1965).

    Google Scholar 

  25. J. Allen, B. Annaratone, and U. de Angelis, J. Plasma Phys. 63, 299 (2000).

    Article  ADS  Google Scholar 

  26. X.-Z. Tang and G. L. Delzanno, Phys. Plasmas 21, 123708 (2014).

    Article  ADS  Google Scholar 

  27. V. N. Tsytovich, Phys. Usp. 40, 53 (1997).

    Article  ADS  Google Scholar 

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

    Article  ADS  Google Scholar 

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

    Article  ADS  MathSciNet  Google Scholar 

  30. A. Ivlev, H. Löwen, G. Morfill, and C. P. Royall, Series in Soft Condensed Matter (World Sci., Singapore, 2012), Vol. 5.

    Google Scholar 

  31. I. Mann, N. Meyer-Vernet, and A. Czechowski, Phys. Rep. 536, 1 (2014).

    Article  ADS  Google Scholar 

  32. A. V. Ivlev, S. A. Khrapak, V. I. Molotkov, and A. G. Khrapak, Introduction to the Physics of Dusty and Complex Plasma (Intellekt, Moscow, 2017) [in Russian].

    Google Scholar 

  33. F. Greiner, A. Melzer, B.Tadsen, S. Groth, C. Killer, F. Kirchschlager, F. Wieben, I. Pilch, H. Krüger, D. Block, A. Piel, and S. Wolf, Eur. Phys. J. D 72, 81 (2018).

    Article  ADS  Google Scholar 

  34. L. Couedel, V. M. Nosenko, S. Zhdanov, A. V. Ivlev, I. Laut, E. V. Yakovlev, N. P. Kryuchkov, P. V. Ovcharov, A. M. Lipaev, and S. O. Yurchenko, Phys. Usp. 62, 1000 (2019).

    Article  ADS  Google Scholar 

  35. A. A. Samarian and B. W. James, Plasma Phys. Control. Fusion 47, B629 (2005).

    Article  Google Scholar 

  36. I. S. Gradshtein and I. M. Ryzhik, Table of Integrals, Series, and Products (Academic, New York, 1980; Fizmatlit, Moscow, 1963).

  37. E. Jahnke, F. Emde, and F. Lösch, Tables of Higher Functions (McGraw-Hill, New York, 1960).

    MATH  Google Scholar 

  38. Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables, Ed. by M. Abramowitz and I. A. Stegun, Vol. 55 of Applied Mathematics Series (Nature Bureau of Standards, Washington, DC, 1972).

    Google Scholar 

  39. M. Lampe, V. Gavrishchaka, G. Ganguli, and G. Joyce, Phys. Rev. Lett. 86, 5278 (2001).

    Article  ADS  Google Scholar 

  40. M. Lampe, R. Goswami, Z. Sternovsky, S. Robertson, V. Gavrishchaka, G. Ganguli, and G. Joyce, Phys. Plasmas 10, 1500 (2003).

    Article  ADS  Google Scholar 

  41. T. Bystrenko and A. Zagorodny, Phys. Lett. A 299, 383 (2002).

    Article  ADS  Google Scholar 

  42. S. A. Maiorov, Plasma Phys. Rep. 31, 690 (2005).

    Article  ADS  Google Scholar 

  43. I. L. Semenov, A. G. Zagorodny, and I. V. Krivtsun, Phys. Plasmas 19, 043703 (2012).

    Article  ADS  Google Scholar 

  44. A. V. Zobnin, A. D. Usachev, O. F. Petrov, and V. E. Fortov, Phys. Plasmas 15, 043705 (2008).

    Article  ADS  Google Scholar 

  45. A. V. Zobnin, A. P. Nefedov, V. A. Sinel’shchikov, and V. E. Fortov, J. Exp. Theor. Phys. 91, 483 (2000).

    Article  ADS  Google Scholar 

  46. O. S. Vaulina, A. Yu. Repin, O. F. Petrov, and K. G. Adamovich, J. Exp. Theor. Phys. 102, 986 (2006).

    Article  ADS  Google Scholar 

  47. L. G. D’yachkov, A. G. Khrapak, S. A. Khrapak, and G. E. Morfill, Phys. Plasmas 14, 042102 (2007).

    Article  ADS  Google Scholar 

  48. I. H. Hutchinson and L. Patacchini, Phys. Plasmas 14, 013505 (2007).

    Article  ADS  Google Scholar 

  49. S. A. Khrapak and G. E. Morfill, Phys. Plasmas 15, 114503 (2008).

    Article  ADS  Google Scholar 

  50. I. Pilch, L. Caillault, T. Minea, U. Helmersson, A. A. Tal, I. A. Abrikosov, E. P. Münger, and N. Brenning, J. Phys. D: Appl. Phys. 49, 395208 (2016).

    Article  Google Scholar 

  51. I. L. Semenov, A. G. Zagorodny, and I. V. Krivtsun, Phys. Plasmas 18, 103707 (2011).

    Article  ADS  Google Scholar 

  52. G. L. Delzanno and X.-Z. Tang, Phys. Plasmas 22, 113703 (2015).

    Article  ADS  Google Scholar 

Download references

Funding

This study was supported by the Russian Science Foundation (project no. 16-12-10424).

Author information

Authors and Affiliations

  1. Joint Institute for High Temperatures, Russian Academy of Sciences, 125412, Moscow, Russia

    A. V. Filippov

  2. State Research Center of the Russian Federation “Troitsk Institute for Innovation and Fusion Research”, 108840, Troitsk, Moscow, Russia

    A. V. Filippov

Authors
  1. A. V. Filippov
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to A. V. Filippov.

Additional information

Translated by N. Wadhwa

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Filippov, A.V. Distribution of Electrons and Ions Near an Absorbing Spherical Body in a Nonequilibrium Plasma. J. Exp. Theor. Phys. 132, 148–158 (2021). https://doi.org/10.1134/S1063776121010118

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1134/S1063776121010118

Search

Navigation