Advertisement

Plasma Physics Reports

, Volume 45, Issue 2, pp 108–120 | Cite as

MHD Stability and Energy Principle for Two-Dimensional Equilibria without Assumption of Nested Magnetic Surfaces

  • S. Yu. MedvedevEmail author
  • A. A. Martynov
  • V. V. Drozdov
  • A. A. Ivanov
  • Yu. Yu. Poshekhonov
  • S. V. Konovalov
  • L. Villard
TOKAMAKS
  • 7 Downloads

Abstract

Abandoning the assumption of nested magnetic surfaces in tokamak plasma expands the field of research and opens up new approaches for both theoretical and experimental plasma physics. The computer code KINX for calculations of the ideal MHD stability was developed for studies of doublet plasmas with two magnetic axes and using block-structured grids in each subdomain with nested magnetic surfaces. Then, the MHD_NX code on unstructured grids was developed to calculate the stability of two-dimensional equilibria with an arbitrary topology of magnetic surfaces. The study of equilibrium and stability of equilibrium configurations with toroidal current density reversal and axisymmetric n = 0 islands, which are associated with internal transport barrier and low current density at the magnetic axis, as well as with the operation of tokamaks in the alternating current regime, leads to more general issues of MHD stability of two-dimensional solutions of the Grad−Shafranov equations with islands under other types of symmetry—chain of islands in helical symmetry and cylindrically symmetric m = 0 islands in configurations with the longitudinal field reversal. New ideal MHD unstable modes have been discovered for various types of two-dimensional island configurations. The energy principle with MHD-compatible boundary conditions at open magnetic field lines is necessary for the self-consistent stability analysis of divertor configurations in tokamaks with a finite current density at the separatrix, taking into account the plasma outside the separatrix. Several codes have been developed for calculations of plasma equilibrium and stability, taking into account the influence of currents outside the separatrix, which are ready for integration with other codes for edge plasma modeling.

Notes

ACKNOWLEDGMENTS

This work was supported by the Russian Science Foundation (grant no. 16-11-10278).

REFERENCES

  1. 1.
    A. I. Morozov and L. S. Solov’ev, in Reviews of Plasma Physics, Ed. by M. A. Leontovich (Consultants Bureau, New York, 1966), Vol. 2, p. 201.Google Scholar
  2. 2.
    V. D. Pustovitov, Nucl. Fusion 30, 1079 (1990).CrossRefGoogle Scholar
  3. 3.
    K. V. Brushlinskii and A. S. Goldich, Diff. Equat. 52, 845 (2016).CrossRefGoogle Scholar
  4. 4.
    L. Degtyarev, A. Martynov, S. Medvedev, F. Troyon, L. Villard, and R. Gruber, Comput. Phys. Commun. 103, 10 (1997).ADSCrossRefGoogle Scholar
  5. 5.
    A. A. Martynov, S. Yu. Medvedev, and L. Villard, Phys. Rev. Lett. 91, 85004 (2003).ADSCrossRefGoogle Scholar
  6. 6.
    Y. Hu, Phys. Plasmas 15, 022505 (2008).ADSCrossRefGoogle Scholar
  7. 7.
    W. Guo, S. Wang, and J. Li, Plasma Sci. Technol. 12, 657 (2010).ADSCrossRefGoogle Scholar
  8. 8.
    T. Fujita, Nucl. Fusion 50, 113001 (2010).ADSCrossRefGoogle Scholar
  9. 9.
    S. Yu. Medvedev, A. A. Martynov, and L. Villard, in Proceedings of the 35th EPS Conference on Plasma Physics, Hersonissos, 2008, ECA 32D, P2.063 (2008).Google Scholar
  10. 10.
    S. Yu. Medvedev, A. A. Martynov, V. V. Drozdov, A. A. Ivanov, and Yu. Yu. Poshekhonov, Plasma Phys. Controlled Fusion 59, 025018 (2017).ADSCrossRefGoogle Scholar
  11. 11.
    I. B. Bernstein, E. A. Frieman, M. D. Kruskal, and R. M. Kulsrud, Proc. Roy. Soc. A 244, 17 (1958).ADSGoogle Scholar
  12. 12.
    B. B. Kadomtsev, in Reviews of Plasma Physics, Ed. by M. A. Leontovich (Consultants Bureau, New York, 1966), Vol. 2, p. 153.Google Scholar
  13. 13.
    H. R. Strauss, Phys. Plasmas 21, 032506 (2014).ADSCrossRefGoogle Scholar
  14. 14.
    S. Yu. Medvedev, A. A. Martynov, and L. Villard, in Proceedings of the 33rd EPS Conference on Plasma Physics, Rome, 2006, ECA 30I, P1.167 (2006).Google Scholar
  15. 15.
    S. Yu. Medvedev, A. A. Martynov, and L. Villard, in Proceedings of the 34th EPS Conference on Plasma Physics, Warsaw, 2007, ECA 31F, P4.087 (2007).Google Scholar
  16. 16.
    S. Yu. Medvedev, A. A. Martynov, and L. Villard, in Proceedings of the 36th EPS Conference on Plasma Physics, Sofia, 2009, ECA 33E, P1.130 (2009).Google Scholar
  17. 17.
    S. Yu. Medvedev, A. A. Martynov, and L. Villard, in Proceedings of the 41st EPS Conference. on Plasma Physics, Berlin, 2014, ECA 38F, P4.042 (2014).Google Scholar
  18. 18.
    S. Yu. Medvedev, A. A. Martynov, and L. Villard, in Proceedings of the 39th EPS Conference on Plasma Physics, Stockholm, 2012, ECA 36F, P1.082 (2012).Google Scholar
  19. 19.
    S. Yu. Medvedev, A. A. Martynov, and L. Villard, in Proceedings of the 40th EPS Conference on Plasma Physics, Espoo, 2013, ECA 37D, P5.145 (2013).Google Scholar
  20. 20.
    A. A. Martynov and S. Yu. Medvedev, in Proceedings of the 44th EPS Conference on Plasma Physics and Controlled Fusion, Belfast, 2017, ECA 41F, P4.135 (2017).Google Scholar
  21. 21.
    S. Yu. Medvedev, A. A. Martynov, V. V. Drozdov, A. A. Ivanov, Yu. Yu. Poshekhonov, S. V. Konovalov, and L. Villard, in Proceedings of the 44th EPS Conference on Plasma Physics and Controlled Fusion, Belfast, 2017, ECA 41F, O4.125 (2017).Google Scholar
  22. 22.
    A. Loarte, F. Liu, G. T. A. Huysmans, A. S. Kukushkin, and R. A. Pitts, J. Nucl. Mater. 463, 401 (2014).ADSCrossRefGoogle Scholar

Copyright information

© Pleiades Publishing, Ltd. 2019

Authors and Affiliations

  • S. Yu. Medvedev
    • 1
    • 2
    • 3
    Email author
  • A. A. Martynov
    • 1
    • 2
  • V. V. Drozdov
    • 1
  • A. A. Ivanov
    • 1
  • Yu. Yu. Poshekhonov
    • 1
  • S. V. Konovalov
    • 2
  • L. Villard
    • 4
  1. 1.Keldysh Institute of Applied Mathematics, Russian Academy of SciencesMoscowRussia
  2. 2.National Research Center “Kurchatov Institute”MoscowRussia
  3. 3.National Research Nuclear University “MEPhI”MoscowRussia
  4. 4.Swiss Plasma Center, EPFL-SB-SPCLausanneSwitzerland

Personalised recommendations