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Equations for nonlinear MHD convection in shearless magnetic systems

  • Nonlinear Phenomena
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Abstract

A closed set of reduced dynamic equations is derived that describe nonlinear low-frequency flute MHD convection and resulting nondiffusive transport processes in weakly dissipative plasmas with closed or open magnetic field lines. The equations obtained make it possible to self-consistently simulate transport processes and the establishment of the self-consistent plasma temperature and density profiles for a large class of axisymmetric nonparaxial shearless magnetic devices: levitated dipole configurations, mirror systems, compact tori, etc. Reduced equations that are suitable for modeling the long-term evolution of the plasma on time scales comparable to the plasma lifetime are derived by the method of the adiabatic separation of fast and slow motions.

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References

  1. B. B. Kadomtsev and O. P. Pogutse, in Reviews of Plasma Physics, Ed. by M. A. Leontovich (Atomizdat, Moscow, 1967; Consultants Bureau, New York, 1970), Vol. 5.

    Google Scholar 

  2. W. Horton, in Basic Plasma Physics, Ed. by A. A. Galeev and R. N. Sudan (North-Holland, Amsterdam, 1984; Énergoatomizdat, Moscow, 1984), Vol. 2.

    Google Scholar 

  3. J. W. Connor, P. Buratti, J. D. Cordey, et al., Plasma Phys. Controlled Fusion 41, 693 (1999).

    ADS  Google Scholar 

  4. M. V. Ossipenko and T-10 Team, in Proceedings of the 19th IAEA Fusion Energy Conference, Lyon, 2002 (IAEA, Vienna, 2003), Report OV/5-2.

    Google Scholar 

  5. G. M. Batanov, L. V. Kolik, A. E. Petrov, et al., Fiz. Plazmy 29, 395 (2003) [Plasma Phys. Rep. 29, 363 (2003)].

    Google Scholar 

  6. G. M. Batanov, V. E. Bening, V. Yu. Korolev, et al., Pis’ma Zh. Éksp. Teor. Fiz. 78, 974 (2003) [JETP Lett. 78, 502 (2003)].

    Google Scholar 

  7. T. Cho, M. Yoshida, H. Higaki, et al., J. Plasma Fusion Res. 80, 81 (2004).

    Article  Google Scholar 

  8. V. V. Abrakov, A. E. Petrov, K. A. Sarksyan, and N. N. Skvortsova, Fiz. Plazmy 20, 1069 (1994) [Plasma Phys. Rep. 20, 959 (1994)].

    Google Scholar 

  9. G. Y. Antar, S. I. Krasheninnikov, P. Devynck, et al., Phys. Rev. Lett. 87, 065001 (2001).

    Google Scholar 

  10. N. Ohno, D. Nishijima, S. Takamura, et al., Nucl. Fusion 41, 1055 (2001).

    Article  Google Scholar 

  11. J. A. Boedo, D. L. Rudakov, R. Moyer, et al., Phys. Plasmas 8, 4826 (2001).

    Article  ADS  Google Scholar 

  12. B. B. Kadomtsev and O. P. Pogutse, Zh. Éksp. Teor. Fiz. 65, 575 (1973) [Sov. Phys. JETP 38, 283 (1974)].

    ADS  Google Scholar 

  13. B. B. Kadomtsev and O. P. Pogutse, Zh. Éksp. Teor. Fiz. 66, 2067 (1974) [Sov. Phys. JETP 39, 1017 (1974)].

    Google Scholar 

  14. R. White, D. Monticello, M. N. Rosenbluth, et al., in Proceedings of the 5th International Conference on Plasma Physics and Controlled Nuclear Fusion Research, Tokyo, 1974 (IAEA, Vienna, 1975), Vol. 1, p. 495.

    Google Scholar 

  15. H. Strauss, Phys. Fluids 19, 134 (1976).

    ADS  Google Scholar 

  16. H. Strauss, Phys. Fluids 20, 1354 (1977).

    ADS  Google Scholar 

  17. V. P. Pastukhov, Pis’ma Zh. Éksp. Teor. Fiz. 67, 892 (1998) [JETP Lett. 67, 940 (1998)].

    Google Scholar 

  18. V. P. Pastukhov, Fiz. Plazmy 26, 566 (2000) [Plasma Phys. Rep. 26, 529 (2000)].

    Google Scholar 

  19. V. P. Pastukhov and N. V. Chudin, Fiz. Plazmy 27, 963 (2001) [Plasma Phys. Rep. 27, 907 (2001)].

    Google Scholar 

  20. V. P. Pastukhov and N. V. Chudin, in Proceedings of the 19th IAEA Fusion Energy Conference, Lyon, 2002 (IAEA, Vienna, 2003), Report TH/2-5.

  21. A. Hasegava, L. Chen, and M. E. Mauel, Nucl. Fusion 30, 2405 (1990).

    Google Scholar 

  22. A. I. Morozov, V. P. Pastukhov, and A. Yu. Sokolov, in Proceedings of the Workshop on D-3He-Based Reactor Studies, Moscow, 1991, p. 1C1.

  23. J. Kesner, L. Bromberg, D. T. Garnier, and M. E. Mauel, in Proceedings of the 17th IAEA Fusion Energy Conference, Yokohama, 1998 (IAEA, Vienna, 1999), Vol. 3, p. 1165.

  24. V. P. Pastukhov and A. Yu. Sokolov, Fiz. Plazmy 17, 1043 (1991) [Sov. J. Plasma Phys. 17, 603 (1991)].

    Google Scholar 

  25. V. V. Arsenin, E. D. Dlougach, V. M. Kulygin, et al., Nucl. Fusion 41, 945 (2001).

    Article  Google Scholar 

  26. A. Yu. Sokolov, Fiz. Plazmy 18, 657 (1992) [Sov. J. Plasma Phys. 18, 343 (1992)].

    Google Scholar 

  27. V. V. Arsenin and A. Yu. Kuyanov, Fiz. Plazmy 27, 675 (2001) [Plasma Phys. Rep. 27, 635 (2001)].

    Google Scholar 

  28. P. A. Popovich and V. D. Shafranov, Fiz. Plazmy 26, 519 (2000) [Plasma Phys. Rep. 26, 484 (2000)].

    Google Scholar 

  29. V. V. Arsenin and A. Yu. Kuyanov, Fiz. Plazmy 26, 793 (2000) [Plasma Phys. Rep. 26, 741 (2000)].

    Google Scholar 

  30. A. Bernstein, in Basic Plasma Physics, Ed. by A. A. Galeev and R. N. Sudan (North-Holland, Amsterdam, 1984; Énergoatomizdat, Moscow, 1983), Vol. 1.

    Google Scholar 

  31. B. B. Kadomtsev, in Reviews of Plasma Physics, Ed. by M. A. Leontovich (Gosatomizdat, Moscow, 1963; Consultants Bureau, New York, 1966), Vol. 2.

    Google Scholar 

  32. S. Krasheninnikov, P. Catto, and R. D. Hazeltine, Phys. Rev. Lett. 82, 2689 (1999).

    Article  ADS  Google Scholar 

  33. D. T. Garnier, J. Kesner, and M. E. Mauel, Phys. Plasmas 6, 3431 (1999).

    ADS  Google Scholar 

  34. V. V. Arsenin, Fiz. Plazmy 28, 843 (2002) [Plasma Phys. Rep. 28, 776 (2002)].

    Google Scholar 

  35. V. P. Pastukhov, in Reviews of Plasma Physics, Ed. by B. B. Kadomtsev (Énergoatomizdat, Moscow, 1984; Consultants Bureau, New York, 1987), Vol. 13.

    Google Scholar 

  36. 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 

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Authors and Affiliations

  1. Russian Research Centre Kurchatov Institute, pl. Kurchatova 1, Moscow, 123182, Russia

    V. P. Pastukhov

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  1. V. P. Pastukhov
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__________

Translated from Fizika Plazmy, Vol. 31, No. 7, 2005, pp. 628–641.

Original Russian Text Copyright © 2005 by Pastukhov.

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Pastukhov, V.P. Equations for nonlinear MHD convection in shearless magnetic systems. Plasma Phys. Rep. 31, 577–590 (2005). https://doi.org/10.1134/1.1992585

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  • DOI: https://doi.org/10.1134/1.1992585

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