Skip to main content
SpringerLink
Log in

Role of the mean curvature in the geometry of magnetic confinement configurations

Plasma Physics Reports Aims and scope Submit manuscript

Abstract

Examples are presented of how the geometric notion of the mean curvature is applied to the vector of a general magnetic field and to magnetic surfaces. It is shown that the mean curvature is related to the variation of the absolute value of the magnetic field along its lines. Magnetic surfaces of constant mean curvature are optimum for plasma confinement in multimirror open confinement systems and rippled tori.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price includes VAT (Canada)

Instant access to the full article PDF.

Institutional subscriptions

References

  1. S. P. Novikov and I. A. Taimanov, Contemporary Geometrical Structures and Fields(MTsNMO, Moscow, 2005) [in Russian].

    Google Scholar 

  2. Yu. A. Aminov, Vector Field Geometry(Nauka, Moscow, 1990) [in Russian].

    MATH  Google Scholar 

  3. A. I. Morozov and L. S. Solov’ev, in Reviews of Plasma Physics, Ed. by M. A. Leontovich (Gosatomizdat, Moscow, 1963; Consultants Bureau, New York, 1966), Vol. 2.

    Google Scholar 

  4. A. D. Aleksandrov, Vestn. Leningr. Univ. 11, 5 (1956).

    Google Scholar 

  5. A. A. Skovoroda, Fiz. Plazmy 35, 675 (2009) [Plasma Phys. Rep. 35, 619 (2009)].

    Google Scholar 

  6. K. Kenmotsu, Surfaces with Constant Mean Curvature (Translations of Mathematical Monographs, Vol. 221)(American Mathematical Society, Providence, 2003).

    Google Scholar 

  7. I. A. Taimanov, Usp. Mat. Nauk 61(1), 85 (2006).

    MathSciNet  Google Scholar 

  8. W. Helfrich, Z. Naturforsch. 23, 693 (1973).

    Google Scholar 

  9. A. A. Skovoroda, Magnetic Confinement Systems (Fizmatlit, Moscow, 2009) [in Russian].

    Google Scholar 

  10. D. Palumbo, Nuovo Cimento 53, 507 (1968).

    Article  Google Scholar 

  11. D. Palumbo, Atti Accad. Sci. Lett. Arti Palermo 4, 475 (1983–1984).

    Google Scholar 

  12. B. B. Kadomtsev, Selected Articles (Fizmatlit, Moscow, 2003), Vol. 1, p. 35 [in Russian].

    Google Scholar 

  13. A. Boozer, Phys. Plasmas 9, 3762 (2002).

    Article  MathSciNet  ADS  Google Scholar 

  14. A. A. Skovoroda, Fiz. Plazmy 32, 1059 (2006) [Plasma Phys. Rep. 32, 977 (2006)].

    Google Scholar 

  15. A. A. Skovoroda, Fiz. Plazmy 35, 121 (2009) [Plasma Phys. Rep. 35, 99 (2009)].

    Google Scholar 

Download references

Author information

Authors and Affiliations

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

    A. A. Skovoroda

  2. Sobolev Institute of Mathematics, Siberian Branch, Russian Academy of Sciences, pr. Akademika Koptyuga 4, Novosibirsk, 630090, Russia

    I. A. Taimanov

Authors
  1. A. A. Skovoroda
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. I. A. Taimanov
    View author publications

    You can also search for this author in PubMed Google Scholar

Additional information

Original Russian Text © A.A. Skovoroda, I.A. Taimanov, 2010, published in Fizika Plazmy, 2010, Vol. 36, No. 9, pp. 874–878.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Skovoroda, A.A., Taimanov, I.A. Role of the mean curvature in the geometry of magnetic confinement configurations. Plasma Phys. Rep. 36, 819–823 (2010). https://doi.org/10.1134/S1063780X10090096

Download citation

  • Received:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1134/S1063780X10090096

Keywords

search

Navigation