Skip to main content
SpringerLink
Log in

Electric Field on the Surface of a Metal Electrode Immersed in Plasma at a High Negative Potential

  • APPLIED PHYSICS
  • Published:
Plasma Physics Reports Aims and scope Submit manuscript

Abstract

An analytical solution of the Poisson’s equation is found for the electric field on the surface of the electrode immersed in a homogeneous non-isothermal collisionless plasma consisting of electrons and single-charged ions with charge e, with electron temperature Te and high values of negative electric potential Ψ when the parameter |eΨ|/Te ≫ 1. It is found that the plasma layer L with violated quasi neutrality near the high-potential electrode increases compared to the Debye length rD proportionally to the parameter [eΨ/2Te]3/4, as L = rD[eΨ/2Te]3/4. The electric field was calculated on the surface of the negative electrode in plasma. It is shown that in a laboratory plasma with density in the range 1010–1013 cm–3 and electron temperature from 1 to 10 eV, at high potential for the parameter eΨ/Te ≫ 1, the electric field calculated by the obtained formula E = Ψ/L near the surface of the electrode up to 200 times lower than the fields calculated by the classical formula E = Ψ/rD, which was obtained at low potential and for the parameter eΨ/Te ≪ 1.

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.

REFERENCES

  1. Yu. P. Raizer, Gas Discharge Physics (ID Intellekt, Dolgoprudnyi, 2009; Springer, Berlin, 1997).

  2. E. D. Lozanskii and O. B. Firsov, Theory of Spark (Atomizdat, Moscow, 1975) [in Russian].

    Google Scholar 

  3. Yu. D. Korolev and G. A. Mesyats, Field-Emission and Explosive Processes in Gas Discharges (Nauka, Novosibirsk, 1982) [in Russian].

    Google Scholar 

  4. G. A. Mesyats and D. I. Proskurovsky, Pulsed Electrical Discharge in Vacuum (Nauka, Novosibirsk, 1984; Springer-Verlag, Berlin, 1989).

  5. A. Von Engel, Ionized Gases (Clarendon, Oxford, 1955).

    MATH  Google Scholar 

  6. A. D. MacDonald, Microwave Breakdown in Gases (Wiley, New York, 1966

    Google Scholar 

  7. Vacuum Arcs: Theory and Application, Ed. by J. M. Lafferty and J. D. Cobine (Wiley, New York, 1980, 1980).

    Google Scholar 

  8. G. A. Mesyats, Ectons in Vacuum Discharges: Breakdown, Spark, and Arc (Nauka, Moscow, 2000) [in Russian].

    Google Scholar 

  9. V. A. Ivanov, Plasma Dynamics in Strong Microwave Fields (NIYaU MIFI, Moscow, 2019) [in Russian].

  10. V. A. Ivanov, A. S. Sakharov, and M. E. Konyzhev, Plasma Phys. Rep 34, 150 (2008).

    Article  ADS  Google Scholar 

  11. V. A. Ivanov, A. S. Sakharov, and M. E. Konyzhev, Plasma Phys. Rep. 42, 619 (2016).

    Article  ADS  Google Scholar 

  12. V. A. Ivanov, M. E. Konyzhev, A. A. Dorofeyuk, and T. I. Kamolova, J. Phys.: Conf. Ser. 1647, 012018 (2020). https://doi.org/10.1088/1742-6596/1647/1/012018

  13. V. A. Ivanov, M. E. Konyzhev, L. I. Kuksenova, V. G. Lapteva, A. S. Sakharov, T. I. Kamolova, A. A. Dorofeyuk, and S. N. Satunin, Plasma Phys. Rep. 36, 1241 (2010).

    Article  ADS  Google Scholar 

  14. L. I. Kuksenova, V. G. Lapteva, V. A. Ivanov, and M. E. Konyzhev, Trenie Smazka Mash. Mekh., No. 5, 10 (2009).

  15. V. A. Ivanov, M. E. Konyzhev, L. I. Kuksenova, V. G. Lapteva, and I. A. Khrennikova, Trenie Iznos 30, 396 (2009).

    Google Scholar 

  16. D. A. Dimitrovich, A. I. Bychkov, and V. A. Ivanov, Prikl. Fiz., No. 2, 35 (2009).

  17. V. A. Ivanov, M. E. Konyzhev, L. I. Kuksenova, V. G. Lapteva, and I. A. Khrennikova, J. Mach. Manuf. Reliab. 44, 384 (2015).

    Article  Google Scholar 

  18. V. A. Ivanov, A. S. Sakharov, M. E. Konyzhev, T. I. Kamolova, A. A. Dorofeyuk, and L. I. Kuksenova, J. Phys.: Conf. Ser. 907, 012023 (2017). https://doi.org/10.1088/1742-6596/907/1/012023

  19. V. A. Ivanov, M. E. Konyzhev, T. I. Kamolova, and A. A. Dorofeyuk, Plasma Phys. Rep. 47, 603 (2021). https://doi.org/10.1134/S1063780X21060076

    Article  ADS  Google Scholar 

  20. M. D. Gabovich, N. V. Pleshivtsev, and N. N. Semashko, Ion and Atomic Beams for Controlled Nuclear Fusion and Technology (Energoatomizdat, Moscow, 1986; Consultants Bureau, New York, 1989).

  21. D. Smith, W. Daenner, Y. Gohar, T. Kuroda, G. E. Shatalov, A. B. Antipenkov, H. Attaya, C. Baker, M. Billone, I. V. Danilov, L. El Guebaly, M. Ferrari, P. Gierszewski, V. I. Khripunov, V. G. Kovalenko, et al., Preprint INIS-MF-13018 (IAEA, Vienna, 1991), p. 247–266. https://inis.iaea.org/collection/NCLCollectionStore/_Public/23/003/23003898.pdf.

    Google Scholar 

  22. R. Behrich and J. Ehrenberg, J. Nucl. Mater. 155–157, 95 (1988).

    Article  ADS  Google Scholar 

  23. N. V. Pleshivtsev and A. I. Bazhin, Physics of Action of Ion Beams on Materials (Vuzovskaya Kniga, Moscow, 1998) [in Russian].

    Google Scholar 

  24. A. I. Morozov, Introduction to Plasma Dynamics (Fizmatlit, Moscow, 2006; CRC, Boca Raton, FL, 2012).

  25. V. E. Golant, A. P. Zhilinskii, and I. E. Sakharov, Fundamentals of Plasma Physics (Atomizdat, Moscow, 1977; Wiley, New York, 1980).

  26. J. A. Bittencourt, Fundamentals of Plasma Physics (Springer-Verlag, New York, 2004).

    Book  MATH  Google Scholar 

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

    Google Scholar 

  28. Plasma Diagnostics, Ed. by W. Lochte-Holtgreven, Kiel University (North-Holland Publishing Company, Amsterdam, 1968).

  29. Plasma Diagnostic Techniques, Ed. by R. H. Huddlestone and S. L. Leonard (Academic, New York, 1965).

    Google Scholar 

  30. D. I. Bohm, in The Characteristics of the Electrical Discharges in Magnetic Fields, Ed. by R. K. Guthrie and A. Wakerling (McGraw-Hill, New York, 1949), p. 77.

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Prokhorov General Physics Institute of the Russian Academy of Sciences, 119991, Moscow, Russia

    V. A. Ivanov

Authors
  1. V. A. Ivanov
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to V. A. Ivanov.

Ethics declarations

The author declares no conflict of interest.

Additional information

Translated by E. Voronova

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Ivanov, V.A. Electric Field on the Surface of a Metal Electrode Immersed in Plasma at a High Negative Potential. Plasma Phys. Rep. 49, 284–289 (2023). https://doi.org/10.1134/S1063780X22601365

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1134/S1063780X22601365

Keywords:

Search

Navigation