Springer Nature is making SARS-CoV-2 and COVID-19 research free. View research | View latest news | Sign up for updates

Suppression of Small-Scale Magnetic Field Generation by Transformation of the Kinetic Energy Spectrum

  • 2 Accesses

Abstract

The stabilization of a small-scale dynamo caused by a change in the energy spectrum of a conducting plasma flow is investigated. Such a change in kinetic properties can be due to the reverse conversion of generated magnetic energy into kinetic energy. We model the reverse conversion process using the classical Kazantsev model, which describes the operation of a small-scale dynamo in a mirror-symmetric turbulent flow. Our results suggest that the appearance of magnetic energy at small scales in the kinetic spectrum can stop the generation process. This stabilization turns out to be no less efficient than the braking of a turbulent dynamo through the conservation of total magnetic and kinetic energies. However, it looks more realistic, because for most dynamo systems the observed magnetic energy is lower than the kinetic one by several orders of magnitude. We show that in this method of nonlinear suppression just the appearance of energy at small scales is often not enough; in particular, a simple shift of the Gaussian spectrum toward small scales only amplifies the generation. In this paper, we describe a reasonable spectrum transformation method that allows the generation in both critical and supercritical regimes of small-scale dynamo operation to be stabilized. The fact that the described spectrum transformation can be directly recorded in an experimental test is equally important.

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

Fig. 1.
Fig. 2.
Fig. 3.
Fig. 4.

REFERENCES

  1. 1

    F. Krause and K.-H. Rädler, Mean-Field Magnetohydrodynamics and Dinamo Theory (Pergamon, Oxford, 1980).

  2. 2

    Ya. B. Zeldovich, A. A. Ruzmaikin, and D. D. Sokoloff, Magnetic Fields in Astrophysics (G&B, New York, 1983).

  3. 3

    R. Beck, A. Brandenburg, D. Moss, A. Shukurov, and D. Sokoloff, Ann. Rev. Astron. Astrophys. 34, 155 (1996).

  4. 4

    S. A. Molchanov, A. A. Ruzmaikin, and D. D. Sokolov, Sov. Phys. Usp. 28, 307 (1985).

  5. 5

    A. P. Kazantsev, Sov. Phys. JETP 26, 1031 (1967).

  6. 6

    A. Brandenburg and K. Subramanian, Phys. Rep. 417, 1 (2005).

  7. 7

    A. Ruzmaikin, D. Sokoloff, and A. Shukurov, Mon. Not. R. Astron. Soc. 241, 1 (1989).

  8. 8

    D. Sokoloff, A. Khlystova, and V. Abramenko, Mon. Not. R. Astron. Soc. 451, 6040 (2015).

  9. 9

    D. D. Sokoloff, E. V. Yushkov, and A. S. Lukin, Geomagn. Aeron. 57, 844 (2017).

  10. 10

    V. G. Novikov, A. A. Ruzmaikin, and D. D. Sokolov, Sov. Phys. JETP 58, 527 (1983).

  11. 11

    K. Subramanian, Mon. Not. R. Astron. Soc. 294, 718 (1998).

  12. 12

    E. Yushkov, A. Lukin, and D. Sokoloff, Phys. Rev. E 97, 063108 (2018).

  13. 13

    E. V. Yushkov, A. S. Lukin, and D. D. Sokoloff, J. Exp. Theor. Phys. 128, 952 (2019).

  14. 14

    O. Artamonova and D. Sokolov, Vestn. Mosk. Univ. 27, 8 (1986).

  15. 15

    E. V. Yushkov, Geophys. Astrophys. Fluid Dyn. 109, 450 (2015).

  16. 16

    R. Kraichnan and S. Nagarajan, Phys. Fluids 10, 853 (1967).

  17. 17

    I. V. Kolokolov, V. V. Lebedev, and G. A. Sizov, J. Exp. Theor. Phys. 113, 339 (2011).

  18. 18

    D. D. Sokolov, R. A. Stepanov, and P. G. Frik, Phys. Usp. 57, 292 (2014).

  19. 19

    E. Yushkov, A. Lukin, D. Sokoloff, and P. Frick, Geophys. Astrophys. Fluid Dyn. 113, 184 (2018).

  20. 20

    F. Plunian, R. Stepanov, and P. Frick, Phys. Rep. 523, 1 (2013).

  21. 21

    D. Sokoloff and N. Yokoi, J. Plasma Phys. 84, 735840307 (2018).

Download references

Funding

The work of D.D.S. and A.S.L. on the formulation of the problem and the search for methods of its solution was supported by the Russian Foundation for Basic Research (project no. 18-02-00085). The numerical experiment carried out by E.V.Yu. and the interpretation of results by all authors were supported by the BAZIS Foundation (project no. 18-1-1-77-3).

Author information

Correspondence to E. V. Yushkov.

Additional information

Translated by V. Astakhov

Rights and permissions

Reprints and Permissions

About this article

Verify currency and authenticity via CrossMark

Cite this article

Yushkov, E.V., Lukin, A.S. & Sokoloff, D.D. Suppression of Small-Scale Magnetic Field Generation by Transformation of the Kinetic Energy Spectrum. J. Exp. Theor. Phys. 129, 1086–1093 (2019). https://doi.org/10.1134/S1063776119110189

Download citation