Plasma Physics Reports

, Volume 43, Issue 10, pp 969–980 | Cite as

Local synthesis of 3D magnetic surfaces

  • A. A. Skovoroda
Magnetic Confinement Systems


Local synthesis of nested 3D toroidal magnetic surfaces is carried out on the basis of the general theory of surfaces by using magnetic coordinates (generally unknown a priori). An equilibrium magnetic surface is calculated by specifying two functions on the surface (the absolute value of the magnetic field and the distance to the nearest magnetic surface) and three parameters (the rotational transform, pressure gradient, and poloidal current). The choice of the parameters is restricted by the requirement that the surface should be closed toroidally. A method of synthesis of a closed magnetic surface is proposed when two functions—the absolute value of the magnetic field and the major radius—are specified. A set of harmonics of a new type of poloidally preudosymmetric configuration (a toroidal mirror with a large mirror ratio and small rotational transform) is obtained.


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  1. 1.
    A. A. Skovoroda, Magnetic Systems for Plasma Confinement (Fizmatlit, Moscow, 2009) [in Russian].Google Scholar
  2. 2.
    A. A. Subbotin, M. I. Mikhailov, V. D. Shafranov, M. Yu. Isaev, C. Nührenberg, J. Nührenberg, R. Zille, V. V. Nemov, S. V. Kasilov, V. N. Kalyuzhnyj, and W. A. Cooper, Nucl. Fusion 46, 921 (2006).ADSCrossRefGoogle Scholar
  3. 3.
    A. H. Boozer, Phys. Plasmas 9, 3762 (2002).ADSMathSciNetCrossRefGoogle Scholar
  4. 4.
    A. A. Skovoroda, JETP 117, 153 (2013).ADSCrossRefGoogle Scholar
  5. 5.
    A. A. Skovoroda, Plasma Phys. Rep. 32, 977 (2006).ADSCrossRefGoogle Scholar
  6. 6.
    M. I. Mikhailov, V. D. Shafranov, and D. Zyunder, Plasma Phys. Rep. 24, 653 (1998).ADSGoogle Scholar
  7. 7.
    A. A. Skovoroda and V. D. Shafranov, Plasma Phys. Rep. 21, 887 (1995).ADSGoogle Scholar
  8. 8.
    A. H. Boozer, Phys. Fluids 26, 496 (1983).ADSCrossRefGoogle Scholar
  9. 9.
    V. D. Shafranov, Plasma Phys. Controlled Fusion 43, A1 (2001).ADSCrossRefGoogle Scholar
  10. 10.
    D. A. Panov, Plasma Phys. Rep. 9, 112 (1983).Google Scholar
  11. 11.
    A. A. Skovoroda, Plasma Phys. Controlled Fusion 47, 1911 (2005).ADSCrossRefGoogle Scholar
  12. 12.
    S. Gori, W. Lotz, and J. Nührenberg, in Proceedings of the ISPP-17 Joint Varenna–Lausanne International Workshop on Theory of Fusion Plasmas, Varenna, 1996, Ed. by. J. W. Connor, E. Sindoni, and J. Vaclavik (Società Italiana di Fisica, Bologna, 1996), p. 335.Google Scholar
  13. 13.
    W. A. Cooper, M. Yu. Isaev, M. F. Heyn, V. N. Kalyuzhnyj, S. V. Kasilov, W. Kerbichler, A. Yu. Kuyanov, M. I. Mikhailov, V. V. Nemov, J. Nührenberg, M. A. Samitov, V. D. Shafranov, A. A. Skovoroda, A. A. Subbotin, R. Zille, et al., in Proceedings of the 19th International Conference on Fusion Energy, Lyon, 2002, Paper IC/P-06. Scholar
  14. 14.
    A. A. Skovoroda, Plasma Phys. Rep. 26, 550 (2000).ADSCrossRefGoogle Scholar
  15. 15.
    S. P. Novikov and I. A. Taimanov, Contemporary Geometrical Structures and Fields (MTsNMO, Moscow, 2005) [in Russian].Google Scholar
  16. 16.
    C. Nührenberg, M. I. Mikhailov, J. Nührenberg, and V. D. Shafranov, Plasma Phys. Rep. 36, 558 (2010).ADSCrossRefGoogle Scholar

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© Pleiades Publishing, Ltd. 2017

Authors and Affiliations

  1. 1.National Research Center “Kurchatov Institute,”MoscowRussia

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