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Mean Field Magnetohydrodynamic Dynamo in Partially Ionized Plasma: Nonlinear, Numerical Results

  • K. A. P. Singh
Chapter
Part of the Advances in Mechanics and Mathematics book series (AMMA, volume 41)

Abstract

A magnetohydrodynamic dynamo operating in partially ionized surface and atmospheric layers of stars can produce variety of magnetic field structures. In partially ionized plasma such as in the solar photosphere and the solar chromosphere, the magnetic induction equation is subjected to the Hall drift and the ambipolar diffusion (arising due to ion-neutral collisions) along with the Ohmic dissipation. It has been found out that in the presence of a shear flow, the Hall and the ambipolar diffusion, magnetic field components can grow rapidly to form the horizontal structures with small spatial scales. The effects of nonlinear dynamo, along with a shearing flow, Hall drift, ambipolar diffusion and the density gradient can play an important role in the evolution of magnetic field in the partially ionized surface layers of cool stars.

Keywords

Numerical Magnetohydrodynamics (MHD) Solar Magnetic Fields MHD Dynamo 

Notes

Acknowledgements

The author gratefully acknowledges Joint ICTP-IAEA College on Advance Plasma Physics, 2014 and the financial support from International Centre for Theoretical Physics (ICTP), Trieste, Italy for providing an important platform for useful discussions on MHD Dynamo with Prof. Swadesh Mahajan. The author would also like to thank S.M. Chitre, Vinod Krishan and R.T. Gangadhara for useful discussions and support.

References

  1. 1.
    Moffatt, H.K.: Magnetic field generation in electrically conducting fluids, Cambridge University Press, England (1978)Google Scholar
  2. 2.
    Parker, E.N.: Cosmical magnetic fields: Their origin and their activity, Oxford University Press, New York (1979)Google Scholar
  3. 3.
    Krishan, V., Gangadhara, R.T.: Mean – field dynamo in partially ionized plasmas - I, Mon. Not. Royal Astron. Soc., 385, 849 - 853 (2008)CrossRefGoogle Scholar
  4. 4.
    Singh, K.A.P., Krishan, V.: Alfvén-like mode in partially ionized solar atmosphere, New Astron., 15, 119 – 125 (2010)CrossRefGoogle Scholar
  5. 5.
    Singh, K.A.P., Hillier, A., Isobe, H., Shibata, K.: Nonlinear Instability and intermittent nature of magnetic reconnection in solar chromosphere, Pub. Astron. Soc. Japan, 67, 96 (1-11) (2015)CrossRefGoogle Scholar
  6. 6.
    Leake, J.E., Arber, T.D.: The emergence of magnetic flux through a partially ionized solar chromosphere, Astron. Astrophys., 450, 805-818 (2006)Google Scholar
  7. 7.
    Krishan, V., Varghese, B.A.: Cylindrical Hall-MHD waves: a nonlinear solution, Solar Phys., 247, 343-349, (2008)CrossRefGoogle Scholar
  8. 8.
    Krishan, V., Yoshida, Z.: Equilibrium structures in partially ionized rotating plasmas within Hall magnetohydrodynamics, Phys. Plasmas, 13, 092303 (5pp.) (2006)CrossRefGoogle Scholar
  9. 9.
    Brandenburg, A., Zweibel, E.G.: The formation of sharp structures by ambipolar diffusion Astrophys. J., 427, L91-L94 (1994)CrossRefGoogle Scholar
  10. 10.
    Schüssler, M.: Flux tubes, surface magnetism, and the solar dynamo: constraints and open problems, Astron. Nachr., 326, 194-204 (2005)CrossRefGoogle Scholar
  11. 11.
    Brandenburg, A.: The case for a distributed solar dynamo shaped by near-surface shear Astrophys. J., 625, 539-547 (2005)Google Scholar
  12. 12.
    Orozco Suaréz, D., Bellot Rubio, L.R., del Toro Iniesta, J.C., et al.: Quiet-Sun internetwork magnetic fields from the inversion of Hinode measurements, Astrophys. J., 670, L61-L64 (2007)CrossRefGoogle Scholar
  13. 13.
    Lites, B.W., Kubo, M., Socas-Navarro, H., et al.: The horizontal magnetic flux of the quiet-Sun internetwork as observed with the Hinode spectro-polarimeter, Astrophys. J., 672, 1237-1253 (2008)CrossRefGoogle Scholar
  14. 14.
    Vögler, A., Schüssler, M.: A solar surface dynamo, Astron. Astrophys., 465, L43-L46 (2007)CrossRefGoogle Scholar
  15. 15.
    Schüssler, M., Vögler, A.: Strong horizontal photospheric magnetic field in a surface dynamo simulation, Astron. Astrophys., 481, L5-L8 (2008)CrossRefGoogle Scholar
  16. 16.
    Tobias, S.M., Weiss, N.O.: The solar dynamo and tachocline (Eds. D.W. Hughes, R. Rosner, N.O. Weiss), Cambridge University Press, Cambridge, UK (2007)Google Scholar
  17. 17.
    Hindman, B.W., Gizon, L., Duvall, T., et al.: Comparison of solar subsurface flows assessed by ring and time-distance analyses, Astrophys. J., 613, 1253-1262 (2004)Google Scholar
  18. 18.
    Krause, F. and Rädler, K. H.: Mean-field magnetohydrodynamics and dynamo theory, Pergamon Press, Oxford, New York (1980)CrossRefGoogle Scholar
  19. 19.
    Stix, M.: Non-linear dynamo waves, Astron. Astrophys., 20, 9-12 (1972)Google Scholar
  20. 20.
    Schüssler, M.: The Sun, a laboratory for astrophysics (Eds. J.T. Schmelz, J. C. Brown), Kluwer Academic Publishers, Netharlands, 191 (1992)Google Scholar
  21. 21.
    de Wijn, A.G., Stenflo, J.O., Solanki, S.K., Tsuneta, S.: Small-scale solar magnetic fields, Space Science Rev., 144, 275-315 (2009)Google Scholar
  22. 22.
    Pietarila Graham, J., Danilovic, S., Schüssler, M.: Turbulent magnetic fields in the quiet Sun: implications of Hinode observations and small-scale dynamo simulations, Astrophys. J., 693, 1728-1735 (2009)CrossRefGoogle Scholar
  23. 23.
    Lites, B.W.: Hinode observations suggesting the presence of a local small-scale turbulent dynamo, Astrophys. J., 737, 52 (9pp.) (2011)CrossRefGoogle Scholar
  24. 24.
    Mininni, P. D., Gómez, D.O., Mahajan, S. M.: Role of the Hall current in magnetohydrodynamic dynamos, Astrophys. J., 584, 1120-1126 (2003)CrossRefGoogle Scholar
  25. 25.
    Gómez, D.O., Mininni, P.D., Dmitruk, P.: Hall-magnetohydrodynamic small-scale dynamos, Physical Rev. E, 82, 036406 (10pp.) (2010)Google Scholar
  26. 26.
    Mininni, P. D., Gómez, D.O., Mahajan, S. M.: Dynamo action in magnetohydrodynamics and Hall-magnetohydrodynamics, Astrophys. J., 587, 472-481 (2003)CrossRefGoogle Scholar
  27. 27.
    Mahajan, S.M., Shatashvili, N.L., Mikeladze, S.V.: Acceleration of plasma flows due to reverse dynamo mechanism, Astrophys. J., 634, 419-425 (2005)CrossRefGoogle Scholar
  28. 28.
    Zweibel, E.G.: Ambipolar diffusion drifts and dynamos in turbulent gases, Astrophys. J., 329, 384-391 (1988)CrossRefGoogle Scholar
  29. 29.
    Proctor, M.R.E., Zweibel, E.G.: Dynamos with ambipolar diffusion drifts, Geophys. Astrophys. Fluid Dyn., 64, 145-161 (1992)CrossRefGoogle Scholar
  30. 30.
    Brandenburg, A., Subramanian, K.: Large scale dynamos with ambipolar diffusion nonlinearity, Astron. Astrophys., 361, L33-L36 (2000)Google Scholar
  31. 31.
    Zweibel, E. G., Heitsch, F.: Fast Dynamos in weakly ionized gases, Astrophys. J., 684, 373-379 (2008)CrossRefGoogle Scholar
  32. 32.
    Mininni, P. D., Gómez, D.O., Mahajan, S. M.: Dynamo action in Hall magnetohydrodynamics, ApJ., 567, L81 - L83 (2002)CrossRefGoogle Scholar
  33. 33.
    Kunz, M.W.: On the linear stability of weakly ionized, magnetized planar shear flows, Mon. Not. Royal Astron. Soc., 385, 1494-151 (2008)CrossRefGoogle Scholar
  34. 34.
    Bejarano C., Gómez D.O., Brandenburg, A.: Shear-driven instabilities in Hall-magnetohydrodynamic plasmas, Astrophys. J., 737, 62 (11pp.) (2011)CrossRefGoogle Scholar
  35. 35.
    Danilovic, S., Schüssler, M., Solanki, S.: Probing quiet Sun magnetism using MURaM simulations and Hinode/SP results: support for a local dynamo, Astron. Astrophys., 513, A1 (8pp.) (2010)CrossRefGoogle Scholar
  36. 36.
    Rempel, M.: Numerical simulations of quiet Sun magnetism: On the Contribution from a Small-scale Dynamo, Astrophys. J., 789, 132 (22pp.) (2014)CrossRefGoogle Scholar

Copyright information

© Springer Nature Switzerland AG 2019

Authors and Affiliations

  • K. A. P. Singh
    • 1
  1. 1.Department of PhysicsInstitute of Science, Banaras Hindu UniversityVaranasiIndia

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