DOI: https://doi.org/10.26089/NumMet.v18r106

Artificial boundary conditions for numerical modeling of electron oscillations in plasma

Authors

  • E.V. Chizhonkov

Keywords:

numerical modeling
plasma oscillations
breaking effect
artificial boundary conditions

Abstract

The behavior of the functions describing the relativistic breaking effect of plane one-dimensional electron plasma oscillations is studied by asymptotic methods. The obtained formulas generate various forms of artificial boundary conditions which analyzed by numerical experiments. A special combination of the proposed boundary conditions is used to simulate the breaking effect in the spatially two-dimensional case. A part of computation was performed on the «Chebyshev» Moscow University supercomputer system.


Published

2017-02-26

Issue

Section

Section 1. Numerical methods and applications

Author Biography

E.V. Chizhonkov


References

  1. M. A. Il’gamov and A. N. Gil’manov, Nonreflecting Conditions at Boundaries of the Calculation Region (Fizmatlit, Moscow, 2003) [in Russian].
  2. Ya. B. Zel’dovich and A. D. Myshkis, Elements of Mathematical Physics (Nauka, Moscow, 1973) [in Russian].
  3. L. M. Gorbunov, A. A. Frolov, E. V. Chizhonkov, and N. E. Andreev, “Breaking of Nonlinear Cylindrical Plasma Oscillations,” Fiz. Plazmy 36 (4), 375-386 (2010) [Plasma Phys. Rep. 36 (4), 345-356 (2010)].
  4. J. M. Dawson, “Nonlinear Electron Oscillations in a Cold Plasma,” Phys. Rev. 113 (2), 383-387 (1959).
  5. E. V. Chizhonkov, A. A. Frolov, and L. M. Gorbunov, “Modelling of Relativistic Cylindrical Oscillations in Plasma,” Russ. J. Numer. Anal. Math. Model. 23 (5), 455-467 (2008).
  6. L. M. Gorbunov, A. A. Frolov, and E. V. Chizhonkov, “On Modeling of Nonrelativistic Cylindrical Oscillations in Plasma,” Vychisl. Metody Programm. 9, 58-65 (2008).
  7. A. A. Frolov and E. V. Chizhonkov, “Relativistic Breaking Effect of Electron Oscillations in a Plasma Slab,” Vychisl. Metody Programm. 15, 537-548 (2014).
  8. B. L. Rozhdestvenskii and N. N. Janenko, Systems of Quasilinear Equations and Their Applications to Gas Dynamics (Nauka, Moscow, 1978; Am. Math. Soc., Providence, 1983).
  9. N. N. Bogolyubov and Y. A. Mitropol’sky, Asymptotic Methods in the Theory of Non-Linear Oscillations (Nauka, Moscow, 1974; Gordon and Breach, New York, 1961).
  10. E. V. Chizhonkov, “To the Question of Large-Amplitude Electron Oscillations in a Plasma Slab,” Zh. Vychisl. Mat. Mat. Fiz. 51 (3), 456-469 (2011) [Comput. Math. Math. Phys. 51 (3), 423-434 (2011)].
  11. N. S. Bakhvalov, A. A. Kornev, and E. V. Chizhonkov, Numerical Methods. Problems and Exercises with Solutions (Laboratory of Knowledge, Moscow, 2016) [in Russian].
  12. A. V. Popov and E. V. Chizhonkov, “A Finite-Difference Scheme for Computing Axisymmetric Plasma Oscillations,” Vychisl. Metody Programm. 13, 1-13 (2012).
  13. E. V. Chizhonkov, A. A. Frolov, and S. V. Milyutin, “On Overturn of Two-Dimensional Nonlinear Plasma Oscillations,” Russ. J. Numer. Anal. Math. Model. 30 (4), 213-226 (2015).
  14. A. F. Alexandrov, L. S. Bogdankevich, and A. A. Rukhadze, Principles of Plasma Electrodynamics (Vysshaya Shkola, Moscow, 1978; Springer, Heidelberg, 1984).
  15. V. L. Ginzburg and A. A. Rukhadze, Waves in Magnetoactive Plasma (Nauka, Moscow, 1975) [in Russian].
  16. V. P. Silin, Introduction to the Kinetic Theory of Gases (Nauka, Moscow, 1971) [in Russian].
  17. V. P. Silin and A. A. Rukhadze, Electromagnetic Properties of Plasma and Plasma-like Media (Librokom, Moscow, 2012; Gordon and Breach, New York, 1965).
  18. Yu. N. Dnestrovskii and D. P. Kostomarov, Numerical Simulation of Plasmas (Nauka, Moscow, 1982; Springer, Berlin, 1986).
  19. A. B. Vatazhin, G. A. Lyubimov, and S. A. Regirer, Magnetohydrodynamic Flows in Channels (Nauka, Moscow, 1970) [in Russian].
  20. A. I. Morozov and L. S. Solov’ev, “Steady-State Plasma Flow in a Magnetic Field,” in Reviews of Plasma Physics (Springer, New York, 1980), Vol. 8, pp. 1-102.
  21. A. Sh. Abdullaev, Yu. M. Aliev, and A. A. Frolov, “Generation of Quasi-Static Magnetic Fields by Strong Circularly Polarized Electromagnetic Radiation in a Relativistic Magnetoactive Plasma,” Fiz. Plasmy 12 (7), 827-835 (1986).
  22. E. V. Chizhonkov and A. A. Frolov, “Numerical Simulation of the Breaking Effect in Nonlinear Axially-Symmetric Plasma Oscillations,” Russ. J. Numer. Anal. Math. Model. 26 (4), 379-396 (2011).
  23. S. V. Milyutin, A. A. Frolov, and E. V. Chizhonkov, “Spatial Modeling of Breaking Effects in Nonlinear Plasma Oscillations,” Vychisl. Metody Programm. 14, 295-305 (2013).