DOI: https://doi.org/10.26089/NumMet.v19r218

Numerical modeling of plasma oscillations with consideration of electron thermal motion

Authors

  • A.A. Frolov
  • E.V. Chizhonkov

Keywords:

numerical simulation
finite-difference method
plasma oscillations
traveling waves
perturbation method

Abstract

The effect of electron thermal motion on plane nonrelativistic nonlinear plasma oscillations is studied. It is shown numerically and analytically that when the thermal motion is taken into account, the oscillations are transformed to a traveling wave. At the same time, the wave amplitude grows with increasing temperature, which promotes the removal of energy from the initial region of oscillation localization. A finite-difference scheme is proposed for the numerical simulation on the basis of Eulerian variables. When using the Lagrangian variables to approximate small perturbations, the distributions of electron density maxima are obtained depending on the plasma temperature. The obtained analytical results are in good agreement with numerical experiments.


Published

2018-05-15

Issue

Section

Section 1. Numerical methods and applications

Author Biographies

A.A. Frolov

E.V. Chizhonkov


References

  1. R. C. Davidson, Methods in Nonlinear Plasma Theory (Academic, New York, 1972).
  2. A. I. Akhiezer and R. V. Polovin, “Theory of Wave Motion of an Electron Plasma,” Zh. Eksp. Teor. Fiz. 30 (5), 915-928 (1956) [J. Exp. Theor. Phys. 3, 696-705 (1956)].
  3. S. V. Bulanov, T. Zh. Esirkepov, M. Kando, et al., “On the Breaking of a Plasma Wave in a Thermal Plasma. I. The Structure of the Density Singularity,” Physics of Plasmas. 19 (2012).
    doi 10.1063/1.4764052
  4. 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)].
  5. S. Yu. Luk’yanov, Hot Plasma and Controlled Nuclear Fusion (Nauka, Moscow, 1975) [in Russian].
  6. H. A. Bethe, Intermediate Quantum Mechanics (Benjamin, New York 1964; Mir, Moscow, 1965).
  7. N. A. Krall and A. W. Trivelpiece, Principles of Plasma Physics (McGraw-Hill, New York, 1973; Mir, Moscow, 1975).
  8. R. W. Hockney and J. W. Eastwood, Computer Simulation Using Particles (McGraw-Hill, New York, 1981).
  9. N. N. Bogoliubov and Y. A. Mitropol’sky, Asymptotic Methods in the Theory of Non-Linear Oscillations (Nauka, Moscow, 1974; Gordon and Breach, New York, 1961).
  10. V. P. Silin, Introduction to Kinetic Theory of Gases (Nauka, Moscow, 1971) [in Russian].
  11. A. F. Aleksandrov, L. S. Bogdankevich, and A. A. Rukhadze, Principles of Plasma Electrodynamics (Springer, New York, 1984; Vysshaya Shkola, Moscow, 1988).
  12. V. L. Ginzburg and A. A. Rukhadze, Waves in Magnetoactive Plasma (Nauka, Moscow, 1975) [in Russian].
  13. V. P. Silin and A. A. Rukhadze, Electromagnetic Properties of Plasma and Plasma-Like Media (Librokom, Moscow, 2012) [in Russian].
  14. A. A. Frolov and E. V. Chizhonkov, “Relativistic Breaking Effect of Electron Oscillations in a Plasma Slab,” Vychisl. Metody Programm. 15, 537-548 (2014).
  15. E. V. Chizhonkov, “Artificial Boundary Conditions for Numerical Modeling of Electron Oscillations in Plasma,” Vychisl. Metody Programm. 18, 65-79 (2017).
  16. A. R. Maikov, “On Approximate Open Boundary Conditions and Their Performance over Long Time Intervals,” Vychisl. Metody Programm. 13, 139-148 (2012).
  17. S. K. Godunov and V. S. Ryaben’kii, Difference Schemes (Nauka, Moscow, 1973; North Holland, Amsterdam, 1987).
  18. D. A. Anderson, J. C. Tannehill, and R. H. Pletcher, Computational Fluid Mechanics and Heat Transfer (Hemisphere, New York, 1984; Mir, Moscow, 1990).
  19. A. G. Kulikovskii, N. V. Pogorelov, and A. Yu. Semenov, Mathematical Aspects of Numerical Solution of Hyperbolic Systems (Fizmatlit, Moscow, 2001; CRC Press, Boca Raton, 2001).
  20. A. A. Frolov and E. V. Chizhonkov, “Influence of Electron Collisions on the Breaking of Plasma Oscillations,” Fiz. Plazmy 44 (4), 347-354 (2018) [Plasma Phys. Rep. 44 (4), 398-404 (2018)].