Skip to main content
SpringerLink
Log in

Simulation of a Cylindrical Slow Extraordinary Wave in Cold Magnetoactive Plasma

  • MATHEMATICAL PHYSICS
  • Published:
Computational Mathematics and Mathematical Physics Aims and scope Submit manuscript

Abstract

The influence exerted by an external magnetic field on nonrelativistic cylindrical plasma oscillations is studied. To initialize a slow extraordinary wave in a magnetoactive plasma, the missing initial conditions are constructed using the solution of a linear problem in terms of Fourier–Bessel series. A second-order accurate finite-difference scheme of the MacCormack type is constructed for the numerical simulation of a nonlinear wave. It is shown that, when the external magnetic field is taken into account, the Langmuir oscillations are transformed into a slow extraordinary wave. The velocity of the wave grows with increasing external constant field, which facilitates energy transfer out of the initial localization domain of oscillations. As a result, the well-known effect of off-axial breaking is observed with a time delay and, starting at some critical value of external field, is not observed at all, i.e., a global-in-time smooth solution is formed.

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.
Fig. 5.
Fig. 6.
Fig. 7.
Fig. 8.
Fig. 9.
Fig. 10.
Fig. 11.
Fig. 12.

Similar content being viewed by others

REFERENCES

  1. R. C. Davidson, Methods in Nonlinear Plasma Theory (Academic, New York, 1972), pp. 33–53.

    Google Scholar 

  2. E. V. Chizhonkov, Mathematical Aspects of Modelling Oscillations and Wake Waves in Plasma (Fizmatlit, Moscow, 2018; CRC, Boca Raton, 2019).

  3. A. F. Alexandrov, L. S. Bogdankevich, and A. A. Rukhadze, Principles of Plasma Electrodynamics (Springer, Berlin, 1984).

    Book  Google Scholar 

  4. V. L. Ginzburg and A. A. Rukhadze, Waves in Magnetoactive Plasma (Nauka, Moscow, 1975), pp. 112–124 [in Russian].

    Google Scholar 

  5. A. A. Frolov and E. V. Chizhonkov, “Numerical simulation of a slow extraordinary wave in magnetoactive plasma,” Vychisl. Metody Program. 21, 420 (2020).

    Google Scholar 

  6. D. Jackson, Fourier Series and Orthogonal Polynomials (Dover, New York, 2004).

    MATH  Google Scholar 

  7. E. V. Chizhonkov, “On second-order accuracy schemes for modeling of plasma oscillations,” Vychisl. Metody Program. 21, 115 (2020).

    Google Scholar 

  8. L. M. Gorbunov, A. A. Frolov, E. V. Chizhonkov, and N. E. Andreev, “Breaking of nonlinear cylindrical plasma oscillations,” Plasma Phys. Rep. 36 (4), 345 (2010).

    Article  Google Scholar 

  9. J. Borhanian, “Extraordinary electromagnetic localized structures in plasmas: Modulational instability, envelope solitons, and rogue waves,” Phys. Lett. A 379 (6), 595 (2015).

    Article  Google Scholar 

  10. A. Moradi, “Energy behavior of extraordinary waves in magnetized quantum plasmas,” Phys. Plasmas 25, 052123 (2018).

  11. V. P. Silin, Introduction to Kinetic Gas Theory (Nauka, Moscow, 1971), p. 119 [in Russian].

    Google Scholar 

  12. V. P. Silin and A. A. Rukhadze, Electromagnetic Properties of Plasmas and Plasmalike Media, 2nd ed. (Librokom, Moscow, 2012), pp. 104–110 [in Russian].

    Google Scholar 

  13. A. A. Frolov and E. V. Chizhonkov, “Application of the energy conservation law in the cold plasma model,” Comput. Math. Math. Phys. 60 (3), 498–513 (2020).

    Article  MathSciNet  Google Scholar 

  14. R. W. MacCormack, “The effect of viscosity in hypervelocity impact cratering,” J. Spacecr. Rockets 40 (5), 757 (2003).

    Article  Google Scholar 

  15. Yu. I. Shokin and N. N. Yanenko, Method of Differential Approximation: Application to Gas Dynamics (Nauka, Novosibirsk, 1985), pp. 251–252 [in Russian].

    MATH  Google Scholar 

  16. D. A. Anderson, J. C. Tannehill, and R. H. Pletcher, Computational Fluid Mechanics and Heat Transfer (McGraw-Hill, New York, 1984).

    MATH  Google Scholar 

  17. A. A. Frolov and E. V. Chizhonkov, “On breaking of a slow extraordinary wave in a cold magnetoactive plasma,” Mat. Model. 33 (6), 3–16 (2021).

    MathSciNet  MATH  Google Scholar 

  18. A. A. Frolov and E. V. Chizhonkov, “The effect of electron-ion collisions on breaking cylindrical plasma oscillations,” Math. Models Comput. Simul. 11 (3), 438–450 (2019).

    Article  MathSciNet  Google Scholar 

  19. C. Maity, PhD Thesis (Saha Institute of Nuclear Physics, Kolkata, India, 2013).

  20. E. de Doncker, “An adaptive extrapolation algorithm for automatic integration,” SIGNUM Newslett., No. 13, 12 (1978).

  21. W. J. Cody, “The FUNPACK package of special function subroutines,” ACM Trans. Math. Software, No. 1, 13 (1975).

  22. E. V. Chizhonkov and A. A. Frolov, “Influence of electron temperature on breaking of plasma oscillations,” Russ. J. Numer. Anal. Math. Model. 34 (2), 71 (2019).

    Article  MathSciNet  Google Scholar 

Download references

Funding

This paper was published with the financial support of the Ministry of Science and Higher Education of the Russian Federation as part of the program of the Moscow Center for Fundamental and Applied Mathematics under agreement no. 075-15-2019-1621.

Author information

Authors and Affiliations

  1. Lebedev Physical Institute, Russian Academy of Sciences, 119991, Moscow, Russia

    A. A. Frolov

  2. Faculty of Mechanics and Mathematics, Lomonosov Moscow State University, 119899, Moscow, Russia

    E. V. Chizhonkov

Authors
  1. A. A. Frolov
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. E. V. Chizhonkov
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding authors

Correspondence to A. A. Frolov or E. V. Chizhonkov.

Ethics declarations

The authors declare that they have no conflicts of interest.

Additional information

Translated by I. Ruzanova

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Frolov, A.A., Chizhonkov, E.V. Simulation of a Cylindrical Slow Extraordinary Wave in Cold Magnetoactive Plasma. Comput. Math. and Math. Phys. 62, 845–860 (2022). https://doi.org/10.1134/S0965542522050049

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1134/S0965542522050049

Keywords:

Search

Navigation