Plasma Physics Reports

, Volume 28, Issue 4, pp 286–295 | Cite as

Numerical modeling of the dynamics of a slow Z-pinch

  • A. S. Kingsep
  • V. E. Karpov
  • A. I. Lobanov
  • Y. Maron
  • A. A. Starobinets
  • V. I. Fisher
Plasma Dynamics

Abstract

A study is made of the method for numerical modeling of pulsed plasma systems by simultaneously solving two-temperature MHD equations and the equations of ionization kinetics. As an example, the method is applied to simulate a relatively slow moderate-density Z-pinch, whose dynamics is well studied experimentally. A specially devised two-dimensional computer code makes use of a promising technique of parallel modeling.

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References

  1. 1.
    M. E. Foord, Y. Maron, G. Davara, et al., Phys. Rev. Lett. 72, 3827 (1994).CrossRefADSGoogle Scholar
  2. 2.
    M. E. Foord, Y. Maron, G. Davara, et al., Phys. Rev. Lett. 73, 1190 (1994).CrossRefGoogle Scholar
  3. 3.
    G. Davara, L. Gregorian, E. Kroupp, and Y. Maron, Phys. Plasmas 5, 1068 (1998).CrossRefADSGoogle Scholar
  4. 4.
    Yu. G. Kalinin, A. S. Kingsep, V. I. Kosarev, and A. I. Lobanov, Mat. Model. 12(11), 47 (2000).Google Scholar
  5. 5.
    A. A. Samarskii and Yu. P. Popov, Difference Methods for Solving Gas Dynamics Problems (Nauka, Moscow, 1992, 3rd ed.).Google Scholar
  6. 6.
    A. S. Kingsep, V. I. Kosarev, A. I. Lobanov, and A. A. Sevast’yanov, Fiz. Plazmy 23, 953 (1997) [Plasma Phys. Rep. 23, 879 (1997)].Google Scholar
  7. 7.
    R. P. Fedorenko, Introduction to the Computer Physics (MFTI, Moscow, 1994).Google Scholar
  8. 8.
    L. M. Biberman, B. S. Vorob’ev, and I. T. Yakubov, Kinetics of Nonequilibrium Low-Temperature Plasmas (Nauka, Moscow, 1982; Consultants Bureau, New York, 1987).Google Scholar
  9. 9.
    H. R. Griem, Principles of Plasma Spectroscopy (Cambridge Univ. Press, Cambridge, 1997).Google Scholar
  10. 10.
    V. E. Fortov and I. T. Iakubov, Physics of Nonideal Plasma (Inst. Khim. Fiz., Chernogolovka, 1984; Hemisphere, New York, 1990).Google Scholar
  11. 11.
    R. M. More, Adv. At. Mol. Phys. 21, 305 (1985).Google Scholar
  12. 12.
    D. G. Hummer and D. Michalas, Astrophys. J. 331, 794 (1988).CrossRefADSGoogle Scholar
  13. 13.
    H. R. Griem, Plasma Spectroscopy (McGraw-Hill, New York, 1964; Atomizdat, Moscow, 1969).Google Scholar
  14. 14.
    D. H. Sampson, Phys. Rev. A 34, 986 (1986).CrossRefADSGoogle Scholar
  15. 15.
    M. E. Foord and E. Nardi, J. Appl. Phys. 68, 5028 (1990).ADSGoogle Scholar
  16. 16.
    V. A. Bernshtam, Yu. V. Ralchenko, and Y. Maron, J. Phys. B 33, 5025 (2000).CrossRefADSGoogle Scholar
  17. 17.
    S. M. Younger and T. D. Mark, in Electron Impact Ionization, Ed. by T. D. Mark and G. H. Dunn (Springer-Verlag, New York, 1985).Google Scholar
  18. 18.
    I. I. Sobelman, L. A. Vainshtein, and E. A. Yukov, Excitation of Atoms and Broadening of Spectral Lines (Springer-Verlag, Berlin, 1995).Google Scholar
  19. 19.
    J. Oxenius, Kinetic Theory of Particles and Photons (Springer-Verlag, Berlin, 1986).Google Scholar
  20. 20.
    L. D. Landau and E. M. Lifshitz, Quantum Mechanics: Non-Relativistic Theory (Nauka, Moscow, 1989; Pergamon, New York, 1977).Google Scholar
  21. 21.
    V. I. Fisher, Yu. V. Ralchenko, A. A. Goldgrish, et al., J. Phys. B 28, 3027 (1995).CrossRefADSGoogle Scholar
  22. 22.
    V. P. Shevelko and L. A. Vainshtein, Atomic Physics for Hot Plasmas (Inst. of Physics Press, Bristol, 1993).Google Scholar
  23. 23.
    V. I. Fisher, Yu. V. Ralchenko, V. A. Bernshtam, et al., Phys. Rev. A 55, 329 (1997).CrossRefADSGoogle Scholar
  24. 24.
    D. Kahaner, C. Moler, and S. Nash, Numerical Methods and Software (Prentice-Hall, Englewood Cliffs, 1989; Mir, Moscow, 1998).Google Scholar
  25. 25.
    E. Hairer, S. Norsett, and G. Wanner, Solving Ordinary Differential Equations, Vol. 1: Nonstiff Problems (Springer-Verlag, Berlin, 1987; Mir, Moscow, 1990).Google Scholar
  26. 26.
    E. Hairer and G. Wanner, Solving Ordinary Differential Equations, Vol. 2: Stiff and Differential-Algebraic Problems (Springer-Verlag, Berlin, 1996; Mir, Moscow, 1999).Google Scholar
  27. 27.
    A. Nordsieck, Math. Comput. 16, 22 (1962).ADSMATHMathSciNetGoogle Scholar
  28. 28.
    S. K. Godunov and V. S. Ryaben’kii, Difference Schemes (Nauka, Moscow, 1977).Google Scholar
  29. 29.
    D. A. Anderson, J. C. Tannehill, and R. H. Pletcher, Computational Fluid Mechanics and Heat Transfer (Hemisphere, New York, 1984; Mir, Moscow, 1990), Vols. 1, 2.Google Scholar

Copyright information

© MAIK "Nauka/Interperiodica" 2002

Authors and Affiliations

  • A. S. Kingsep
    • 1
  • V. E. Karpov
    • 2
  • A. I. Lobanov
    • 2
  • Y. Maron
    • 3
  • A. A. Starobinets
    • 3
  • V. I. Fisher
    • 3
  1. 1.Russian Research Centre Kurchatov InstituteMoscowRussia
  2. 2.Moscow Institute of Physics and TechnologyDolgoprudnyi, Moscow oblastRussia
  3. 3.Weizmann Institute of SciencesRehovotIsrael

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