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MHD waves and instabilities in flowing solar flux-tube plasmas in the framework of Hall magnetohydrodynamics

  • I. ZhelyazkovEmail author
Plasma Physics

Abstract

It is well established now that the solar atmosphere, from photosphere to the corona and the solar wind is a highly structured medium. Satellite observations have confirmed the presence of steady flows. Here, we investigate the parallel propagation of magnetohydrodynamic (MHD) surface waves travelling along an ideal incompressible flowing plasma slab surrounded by flowing plasma environment in the framework of the Hall magnetohydrodynamics. The propagation properties of the waves are studied in a reference frame moving with the mass flow outside the slab. In general, flows change the waves’ phase velocities compared to their magnitudes in a static MHD plasma slab and the Hall effect limits the range of waves’ propagation. On the other hand, when the relative Alfvénic Mach number is negative, the flow extends the waves propagation range beyond that limit (owing to the Hall effect) and can cause the triggering of the Kelvin-Helmholtz instability whose onset begins at specific critical wave numbers. It turns out that the interval of Alfvénic Mach numbers for which the surface modes are unstable critically depends on the ratio between mass densities outside and inside the flux tube.

PACS

96.50.Tf MHD waves; plasma waves, turbulence 96.50.Ci Solar wind plasma; sources of solar wind 

References

  1. V.M. Nakariakov, Adv. Space Res. 39, 1804 (2007); V.M. Nakariakov, E. Verwichte, http://solarphysics.livingreviews.org/Articles/lrsp-2005-3/ Google Scholar
  2. C. Vocks, U. Motschmann, K.-H. Glassmeir, Ann. Geophysicæ 17, 712 (1999) Google Scholar
  3. V.M. Nakariakov, B. Roberts, Solar Phys. 159, 213 (1995) Google Scholar
  4. V.M. Nakariakov, B. Roberts, G. Mann, Astron. Astrophys. 311, 311 (1996) Google Scholar
  5. J. Andries, M. Goossens, Astron. Astrophys. 368, 1083 (2001) Google Scholar
  6. M. Terra-Homem, R. Erdélyi, I. Ballai, Solar Phys. 217, 199 (2003) Google Scholar
  7. M.J. Lighthill, Phil. Trans. Roy. Soc. A 252, 397 (1960) Google Scholar
  8. J.D. Huba, Phys. Plasmas 2, 2504 (1995) Google Scholar
  9. N.F. Cramer, I.J. Donnelly, Plasma Phys. 25, 703 (1983) Google Scholar
  10. N.F. Cramer, J. Plasma Phys. 46, 15 (1991) Google Scholar
  11. J.A. Almaguer, Phys. Fluids B 4, 3443 (1992) Google Scholar
  12. I. Zhelyazkov, A. Debosscher, M. Goossens, Phys. Plasmas 3, 4346 (1996) Google Scholar
  13. I. Zhelyazkov, G. Mann, Contr. Plasma Phys. 40, 569 (2000) Google Scholar
  14. I. Zhelyazkov, G. Mann, Phys. Plasmas 10, 484 (2003) Google Scholar
  15. R. Miteva, I. Zhelyazkov, R. Erdélyi, Phys. Plasmas 10, 4463 (2003) Google Scholar
  16. R. Miteva, I. Zhelyazkov, R. Erdélyi, New J. Phys. 6, 14 (2004) Google Scholar
  17. H. Sikka, N. Kumar, I. Zhelyazkov, Phys. Plasmas 11, 4904 (2004) Google Scholar
  18. M.S. Ruderman, J. Plasma Phys. 67, 271 (2002) Google Scholar
  19. M.S. Ruderman, Plasma Phys. 9, 2940 (2002) Google Scholar
  20. I. Ballai, J.C. Thelen, B. Roberts, Astron. Astrophys. 404, 701 (2003) Google Scholar
  21. S.M. Mahajan, V. Krishan, Mon. Not. R. Astron. Soc. 359, L27 (2005) Google Scholar
  22. I. Ballai, E. Forgács-Dajka, A. Marcu, Astron. Nachr. 328, 734 (2007) Google Scholar
  23. C.T.M. Clack, I. Ballai, Phys. Plasmas 15, 082310 (2008) Google Scholar
  24. R. Miteva, G. Mann, J. Plasma Phys. 74, 607 (2008) Google Scholar
  25. Y. Nariyuki, T. Hada, Earth Planets Space 59, e13 (2007) Google Scholar
  26. M.S. Ruderman, Ph. Caillol, J. Plasma Phys. 74, 119 (2008) Google Scholar
  27. B.P. Pandey, M. Wardle, Mon. Not. R. Astron. Soc. 385, 2269 (2008) Google Scholar
  28. V. Krishan, B.A. Varghese, Solar Phys. 247, 343 (2008) Google Scholar
  29. V. Krishan, S.M. Mahajan, Solar Phys. 220, 29 (2004) Google Scholar
  30. S. Galtier, J. Plasma. Phys. 72, 721 (2006) Google Scholar
  31. S. Galtier, E. Buchlin, Astrophys. J. 656, 560 (2007) Google Scholar
  32. S. Galtier, Nonlinear Processes in Geophysics 16, 83 (2009) Google Scholar
  33. D. Shaikh, P.K. Shukla, Phys. Rev. Lett. 102, 045004 (2009) Google Scholar
  34. A. Bhattacharjee, Z.W. Ma, X. Wang, Phys. Plasmas 8, 1829 (2001) Google Scholar
  35. L.F. Morales, S. Dasso, D.O. Gómez, P. Mininni, J. Atmos. Sol.-Terr. Phys. 67, 1821 (2005) Google Scholar
  36. T.D. Arber, M. Haynes, Phys. Plasmas 13, 112105 (2006) Google Scholar
  37. P.A. Cassak, J.F. Drake, M.A. Shay, B. Eckhardt, Phys. Rev. Lett. 98, 215001 (2007) Google Scholar
  38. J.D. Craig, Y.E. Litvinenko, Astron. Astrophys. 484, 847 (2008) Google Scholar
  39. M. Wardle, C. Ng, Mon. Not. R. Astron. Soc. 303, 239 (1999) Google Scholar
  40. T. Sano, J.M. Stone, Astrophys. J. 577, 534 (2002) Google Scholar
  41. M. Wardle, Astrophys. Space Sci. 292, 317 (2004) Google Scholar
  42. E.M. Rossi, P.J. Armitage, K. Menou, Mon. Not. R. Astron. Soc. 391, 922 (2008) Google Scholar
  43. T.E. Cravens, Physics of Solar System Plasmas (Cambridge University Press, Cambridge, 1997), Chap. 4 Google Scholar
  44. S. Chandrasekhar, Hydrodynamic and Hydromagnetic Stability (Oxford University Press, Oxford, 1961) Google Scholar
  45. D.G. Swanson, Plasma Waves (Academic Press, San Diego CA, 1989), p. 53 Google Scholar
  46. F.S. Acton, Numerical Methods That (Usually) Work (Mathematical Association of America, Washington DC, 1990), Chap. 14 Google Scholar
  47. P.M. Edwin, B. Roberts, Solar Phys. 76, 239 (1982) Google Scholar
  48. A.G. Kurosh, Lectures in General Algebra (Pergamon Press, Oxford, 1965) Google Scholar
  49. D.A. Muller, Mathematical Tables and Other Aids to Computation 10, 208 (1956) Google Scholar
  50. I. Zhelyazkov, in PLASMA 2007, Proceedings of the International Conference on Research and Applications of Plasmas, Greifswald, Germany, edited by H.-J. Hartfuss, M. Dudeck, J. Musielok, M.J. Sadowski, AIP Conference Proceedings 993 (American Institute of Physics, Melville, New York, 2008), p. 281 Google Scholar

Copyright information

© EDP Sciences, SIF, Springer-Verlag Berlin Heidelberg 2009

Authors and Affiliations

  1. 1.Faculty of Physics, Sofia UniversitySofiaBulgaria

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