Plasma Physics Reports

, Volume 36, Issue 1, pp 30–49 | Cite as

Nonquasineutral current equilibria as elementary structures of plasma dynamics

  • A. V. Gordeev
Plasma Dynamics

Abstract

A study is made of the fundamental features of current filaments with a nonzero electron vorticity Ω e B − (c/e) ▿ × p ee ≠ 0 and the corresponding Lagrangian invariant I e . Such current structures can exist on spatial scales of up to ω pi −1 . It is shown that the dissipative stage of the plasma evolution and the violation of Thomson’s theorem on vorticity conservation in an electron fluid are of fundamental importance for the onset of electron current structures. A key role of the screening of electric and magnetic fields at distances on the order of the magnetic Debye radius r B = B/(4πen e )—the main property of such current structures in a Hall medium with σB/(en e c) ≫ 1—is stressed. Since the minimum size of a vortex structure is the London length c pe , the structures under consideration correspond to the condition r B > c pe or B 2 > 4πn e m e c 2, which leads to strong charge separation in the filament and relativistic electron drift. It is demonstrated that the specific energy content in current structures is high at a filament current of 10–15 kA: from 100 J/cm3 at a plasma density of 1014 cm−3 (the parameters of a lightning leader) to 107 J/cm3 for a fully ionized atmospheric-pressure air. Estimates are presented showing that the Earth’s ionosphere, circumsolar space, and interstellar space are all Hall media in which current vortex structures can occur. A localized cylindrical equilibrium with a magnetic field reversal is constructed—an equilibrium that correlates with the magnetic structures observed in intergalactic space. It is shown that a magnetized plasma can be studied by using evolutionary equations for the electron and ion Lagrangian invariants I e and I i . An investigation is carried out of the evolution of a current-carrying plasma in a cylinder with a strong external magnetic field and with a longitudinal electron current turned on in the initial stage—an object that can serve as the simplest electrodynamic model of a tokamak. In this case, it is assumed that the plasma conductivity is low in the initial stage and then increases substantially with time. Based on the conservation of the integral momentum of the charged particles and electromagnetic field in a plasma cylinder within a perfectly conducting wall impenetrable by particles, arguments are presented in support of the generation of a radial electric field in a plasma cylinder and the production of drift ion fluxes along the cylinder axis. A hypothesis is proposed that the ionized intergalactic gas expands under the action of electromagnetic forces.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    S. I. Braginskii, in Reviews of Plasma Physics, Ed. by M. A. Leontovich (Gosatomizdat, Moscow, 1963; Consultants Bureau, New York, 1965), Vol. 1.Google Scholar
  2. 2.
    E. M. Lifshitz and L. P. Pitaevskii, Statistical Physics, Vol. 2: Theory of Condensed State (Fizmatlit, Moscow, 2001; Butterworth-Heinemann, Oxford, 2002).Google Scholar
  3. 3.
    R. Z. Sagdeev, in Plasma Physics and the Problem of Controlled Thermonuclear Reactions, Ed. by M. A. Leontovich (Izd. Akad. Nauk SSSR, Moscow, 1958; Pergamon, New York, 1960), Vol. 4.Google Scholar
  4. 4.
    A. V. Gordeev and T. V. Losseva, Fiz. Plazmy 31, 30 (2005) [Plasma Phys. Rep. 31, 26 (2005)].Google Scholar
  5. 5.
    A. V. Gordeev and S. V. Levchenko, Pis’ma Zh. Éksp. Teor. Fiz. 67, 461 (1998) [JETP Lett. 67, 482 (1998)].Google Scholar
  6. 6.
    M. Tatarakis, A. Gopal, I. Watts, et al., Phys. Plasmas 9, 2244 (2002).CrossRefADSGoogle Scholar
  7. 7.
    U. Wagner, M. Tatarakis, A. Gopal, et al., Phys. Rev. E 70, 021401 (2004).CrossRefGoogle Scholar
  8. 8.
    L. D. Landau and E. M. Lifshitz, Fluid Mechanics (Nauka, Moscow, 1986; Pergamon, Oxford, 1987).Google Scholar
  9. 9.
    H. Ertel, Meteorolog. Z. 59, 277 (1942).Google Scholar
  10. 10.
    T. A. Shelkovenko, S. A. Pikuz, D. B. Sinars, et al., Phys. Plasmas 9, 2165 (2002).CrossRefADSGoogle Scholar
  11. 11.
    T. A. Shelkovenko, S. A. Pikuz, B. M. Song, et al., Phys. Plasmas 12, 033102 (2005).CrossRefADSGoogle Scholar
  12. 12.
    J. Sakai, S. Saito, H. Mae, et al., Phys. Plasmas 9, 2959 (2002).CrossRefADSGoogle Scholar
  13. 13.
    A. V. Gordeev and T. V. Losseva, Fiz. Plazmy 35, 141 (2009) [Plasma Phys. Rep. 35, 118 (2009)].Google Scholar
  14. 14.
    S. S. Anan’ev, Yu. L. Bakshaev, P. L. Blinov, et al., Pis’ma Zh. Éksp. Teor. Fiz. 87, 426 (2008) [JETP Lett. 87, 364 (2008)].Google Scholar
  15. 15.
    A. V. Gordeev, Fiz. Plazmy 32, 999 (2006) [Plasma Phys. Rep. 32, 921 (2006)].Google Scholar
  16. 16.
    A. V. Gordeev and T. V. Losseva, Pis’ma Zh. Éksp. Teor. Fiz. 70, 669 (1999) [JETP Lett. 70, 684 (1999)].Google Scholar
  17. 17.
    A. V. Gordeev and T. V. Losseva, Fiz. Plazmy 29, 809 (2003) [Plasma Phys. Rep. 29, 748 (2003)].Google Scholar
  18. 18.
    L. D. Landau and E. M. Lifshitz, Electrodynamics of Continuous Media (Nauka, Moscow, 1982; Pergamon, New York, 1984).Google Scholar
  19. 19.
    E. W. Weibel, Phys. Rev. Lett. 2, 83 (1959).CrossRefADSGoogle Scholar
  20. 20.
    A. A. Frolov, Fiz. Plazmy 30, 750 (2004) [Plasma Phys. Rep. 30, 698 (2004)].Google Scholar
  21. 21.
    S. V. Bulanov, F. Califano, G. I. Dudnikova, et al., in Reviews of Plasma Physics, Ed. by V. D. Shafranov (Kluver Academic, New York, 2001), Vol. 22, p. 227.Google Scholar
  22. 22.
    L. I. Rudakov, M. V. Babykin, A. V. Gordeev, et al., Generation and Focusing of High-Current Relativistic Electron Beams, Ed. by L. I Rudakov (Énergoatomizdat, Moscow, 1990), p. 112 [in Russian].Google Scholar
  23. 23.
    A. V. Gordeev, Fiz. Plazmy 32, 847 (2006) [Plasma Phys. Rep. 32, 780 (2006)].Google Scholar
  24. 24.
    A. V. Gordeev, XXXV International Zvenigorod Conference on Plasma Physics and Controlled Fusion, Zvenigorod, 2008, Book of Abstracts, p. 115.Google Scholar
  25. 25.
    A. V. Gordeev and T. V. Losseva, XXXV International Zvenigorod Conference on Plasma Physics and Controlled Fusion, Zvenigorod, 2008, Book of Abstracts, p. 167.Google Scholar
  26. 26.
    A. V. Gordeev and T. V. Losseva, 17th International Conference on High-Power Particle Beams, Xi’an, 2008, Conf. Guide and Abstracts, p. 6.Google Scholar
  27. 27.
    A. A. Galeev and R. Z. Sagdeev, Handbook of Plasma Physics, Ed. by A. A. Galeev and R. N. Sudan (North-Holland, Amsterdam, 1984; Énergoatomizdat, Moscow, 1983), Vol. 1.Google Scholar
  28. 28.
    Yu. N. Chekh, A. A. Goncharov, and I. M. Protsenko, Pis’ma Zh. Tekh. Fiz. 32(2), 8 (2006) [Tech. Phys. Lett. 32, 51 (2006)].Google Scholar
  29. 29.
    Yu. N. Chekh, Fiz. Plazmy 34, 473 (2008) [Plasma Phys. Rep. 34, 431 (2008)].ADSGoogle Scholar
  30. 30.
    Encyclopedia of Physics (Sovetskaya Éntsiklopediya, Moscow, 1990), Vol. 2, p. 682 [in Russian].Google Scholar
  31. 31.
    A. V. Gordeev, Fiz. Plazmy 34, 563 (2008) [Plasma Phys. Rep. 34, 515 (2008)].Google Scholar
  32. 32.
    A. V. Olinto, in Proceedings of the 3rd RESCEU International Symposium on Particle Cosmology, Tokyo, 1997, p. 151.Google Scholar
  33. 33.
    P. P. Kronberg, Phys. Plasmas 10, 1985 (2003).CrossRefADSGoogle Scholar
  34. 34.
    D. Grasso and H. R. Rubinstein, Phys. Rep. 348, 163 (2001).CrossRefADSGoogle Scholar
  35. 35.
    A. N. Kapitanov, I. V. Obraztsov, L. A. Sukhanova, et al., Fiz. Plazmy 35, 559 (2009) [Plasma Phys. Rep. 35, 510 (2009)].Google Scholar
  36. 36.
    A. V. Gordeev, Preprint No. 6398/6 (Kurchatov Inst., Moscow, 2006).Google Scholar
  37. 37.
    A. V. Gordeev, Fiz. Plazmy 27, 815 (2001) [Plasma Phys. Rep. 27, 769 (2001)].Google Scholar
  38. 38.
    S. M. Kaye, W. H. Solomon, R. E. Bell, et al., in Proceedings of the 22nd IAEA Fusion Energy Conference, Geneva, 2008, Paper EX/3-2.Google Scholar
  39. 39.
    W. H. Solomon, K. H. Burrell, A. M. Garofalo, et al., in Proceedings of the 22nd IAEA Fusion Energy Conference, Geneva, 2008, Paper EX/3-4.Google Scholar
  40. 40.
    P. H. Diamond, C. McDevitt, O. D. Gurcan, et al., in Proceedings of the 22nd IAEA Fusion Energy Conference, Geneva, 2008, Paper TH/1-1.Google Scholar
  41. 41.
    A. V. Gordeev, XXXVI International Zvenigorod Conference on Plasma Physics and Controlled Fusion, Zvenigorod, 2009, Book of Abstracts, p. 97.Google Scholar
  42. 42.
    A. V. Gordeev, Preprint No. 6578/6 (Kurchatov Inst., Moscow, 2009).Google Scholar
  43. 43.
    A. V. Gordeev, Preprint No. 6589/6 (Kurchatov Inst., Moscow, 2009).Google Scholar

Copyright information

© Pleiades Publishing, Ltd. 2010

Authors and Affiliations

  • A. V. Gordeev
    • 1
  1. 1.Russian Research Centre Kurchatov InstituteMoscowRussia

Personalised recommendations