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Invisible dynamo in mean-field models

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Abstract

The inverse problem in a spherical shell to find the two-dimensional spatial distributions of the α-effect and differential rotation in a mean-field dynamo model has been solved. The derived distributions lead to the generation of a magnetic field concentrated inside the convection zone. The magnetic field is shown to have no time to rise from the region of maximum generation located in the lower layers to the surface in the polarity reversal time due to magnetic diffusion. The ratio of the maximum magnetic energy in the convection zone to its value at the outer boundary reaches two orders of magnitude or more. This result is important in interpreting the observed stellar and planetary magnetic fields. The proposed method of solving the inverse nonlinear dynamo problem is easily adapted for a wide class of mathematical-physics problems.

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References

  1. R. Kaiser and A. Tilgner, Phys. Rev. E 63, 37301 (2001).

    Article  ADS  Google Scholar 

  2. R. Kaiser, B. J. Schmitt, and F. H. Busse, Geophys. Astrophys. Fluid Dyn. 77, 93 (1994).

    Article  ADS  Google Scholar 

  3. A. G. Kosovichev, J. Schou, P. H. Scherrer, R. S. Bogart, R. I. Bush, J. T. Hoeksema, J. Aloise, L. Bacon, et al., Solar Phys. 170, 43 (1997).

    Article  ADS  Google Scholar 

  4. F. Krause and K.-H. Rädler, Mean-Field Magnetohydrodynamics and Dynamo Theory (Akademie, Berlin, 1980), p. 271.

    MATH  Google Scholar 

  5. W. N. Press, S. A. Teukolsky, W. T. Vetterling, and B. P. Flannery, Numerical Recipes. The Art of Scientific Computing (C++Code), 3rd ed. (Cambridge Univ. Press, Cambridge, 2007), p. 1262.

    MATH  Google Scholar 

  6. M. Yu. Reshetnyak, Geomagn. Aeron. 50, 263 (2010).

    Article  ADS  Google Scholar 

  7. M. Yu. Reshetnyak, Geomagn. Aeron. 52, 398 (2012).

    Article  ADS  Google Scholar 

  8. M. Yu. Reshetnyak, Russ. J. Earth Sci. 15, ES4001 (2015).

    Article  Google Scholar 

  9. M. Yu. Reshetnyak, Astron. Rep. 60, 294 (2016).

    Article  ADS  Google Scholar 

  10. G. Rüdiger, L. Kitchatinov, and R. Hollerbach, Magnetic Processes in Astrophysics: Theory, Simulations, Experiments (Willey-VCH, Berlin, 2013), p. 346.

    Book  Google Scholar 

  11. A. A. Ruzmaikin, D. D. Sokolov, and A.M. Shukurov, Magnetic Fields of Galaxies (Nauka, Moscow, 1988; Kluwer, Dordrecht, 1988), p. 280.

    Book  Google Scholar 

  12. R. Simitev, PhD Thesis (Univ. Bayreuth, 2004), p. 182.

    Google Scholar 

  13. J. Simkanin and A. Tilgner, Geophys. Astrophys. Fluid Dyn. 102, 205 (2008).

    Article  ADS  MathSciNet  Google Scholar 

  14. M. Stix, The Sun: An introduction (Springer, Berlin, 1989), p. 483.

    Book  Google Scholar 

Download references

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Authors and Affiliations

  1. Schmidt Institute of Physics of the Earth, Russian Academy of Sciences, ul. Bol’shaya Gruzinskaya 10, Moscow, 123242, Russia

    M. Yu. Reshetnyak

  2. Pushkov Institute of Terrestrial Magnetism, Ionosphere, and Radio Wave Propagation, Russian Academy of Sciences, Troitsk, Moscow oblast, 142190, Russia

    M. Yu. Reshetnyak

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  1. M. Yu. Reshetnyak
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Correspondence to M. Yu. Reshetnyak.

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Original Russian Text © M.Yu. Reshetnyak, 2016, published in Pis’ma v Astronomicheskii Zhurnal, 2016, Vol. 42, No. 7, pp. 533–539.

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Reshetnyak, M.Y. Invisible dynamo in mean-field models. Astron. Lett. 42, 482–487 (2016). https://doi.org/10.1134/S1063773716070069

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  • DOI: https://doi.org/10.1134/S1063773716070069

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