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.
Similar content being viewed by others
References
V.M. Nakariakov, Adv. Space Res. 39, 1804 (2007); V.M. Nakariakov, E. Verwichte, http://solarphysics.livingreviews.org/Articles/lrsp-2005-3/
C. Vocks, U. Motschmann, K.-H. Glassmeir, Ann. Geophysicæ 17, 712 (1999)
V.M. Nakariakov, B. Roberts, Solar Phys. 159, 213 (1995)
V.M. Nakariakov, B. Roberts, G. Mann, Astron. Astrophys. 311, 311 (1996)
J. Andries, M. Goossens, Astron. Astrophys. 368, 1083 (2001)
M. Terra-Homem, R. Erdélyi, I. Ballai, Solar Phys. 217, 199 (2003)
M.J. Lighthill, Phil. Trans. Roy. Soc. A 252, 397 (1960)
J.D. Huba, Phys. Plasmas 2, 2504 (1995)
N.F. Cramer, I.J. Donnelly, Plasma Phys. 25, 703 (1983)
N.F. Cramer, J. Plasma Phys. 46, 15 (1991)
J.A. Almaguer, Phys. Fluids B 4, 3443 (1992)
I. Zhelyazkov, A. Debosscher, M. Goossens, Phys. Plasmas 3, 4346 (1996)
I. Zhelyazkov, G. Mann, Contr. Plasma Phys. 40, 569 (2000)
I. Zhelyazkov, G. Mann, Phys. Plasmas 10, 484 (2003)
R. Miteva, I. Zhelyazkov, R. Erdélyi, Phys. Plasmas 10, 4463 (2003)
R. Miteva, I. Zhelyazkov, R. Erdélyi, New J. Phys. 6, 14 (2004)
H. Sikka, N. Kumar, I. Zhelyazkov, Phys. Plasmas 11, 4904 (2004)
M.S. Ruderman, J. Plasma Phys. 67, 271 (2002)
M.S. Ruderman, Plasma Phys. 9, 2940 (2002)
I. Ballai, J.C. Thelen, B. Roberts, Astron. Astrophys. 404, 701 (2003)
S.M. Mahajan, V. Krishan, Mon. Not. R. Astron. Soc. 359, L27 (2005)
I. Ballai, E. Forgács-Dajka, A. Marcu, Astron. Nachr. 328, 734 (2007)
C.T.M. Clack, I. Ballai, Phys. Plasmas 15, 082310 (2008)
R. Miteva, G. Mann, J. Plasma Phys. 74, 607 (2008)
Y. Nariyuki, T. Hada, Earth Planets Space 59, e13 (2007)
M.S. Ruderman, Ph. Caillol, J. Plasma Phys. 74, 119 (2008)
B.P. Pandey, M. Wardle, Mon. Not. R. Astron. Soc. 385, 2269 (2008)
V. Krishan, B.A. Varghese, Solar Phys. 247, 343 (2008)
V. Krishan, S.M. Mahajan, Solar Phys. 220, 29 (2004)
S. Galtier, J. Plasma. Phys. 72, 721 (2006)
S. Galtier, E. Buchlin, Astrophys. J. 656, 560 (2007)
S. Galtier, Nonlinear Processes in Geophysics 16, 83 (2009)
D. Shaikh, P.K. Shukla, Phys. Rev. Lett. 102, 045004 (2009)
A. Bhattacharjee, Z.W. Ma, X. Wang, Phys. Plasmas 8, 1829 (2001)
L.F. Morales, S. Dasso, D.O. Gómez, P. Mininni, J. Atmos. Sol.-Terr. Phys. 67, 1821 (2005)
T.D. Arber, M. Haynes, Phys. Plasmas 13, 112105 (2006)
P.A. Cassak, J.F. Drake, M.A. Shay, B. Eckhardt, Phys. Rev. Lett. 98, 215001 (2007)
J.D. Craig, Y.E. Litvinenko, Astron. Astrophys. 484, 847 (2008)
M. Wardle, C. Ng, Mon. Not. R. Astron. Soc. 303, 239 (1999)
T. Sano, J.M. Stone, Astrophys. J. 577, 534 (2002)
M. Wardle, Astrophys. Space Sci. 292, 317 (2004)
E.M. Rossi, P.J. Armitage, K. Menou, Mon. Not. R. Astron. Soc. 391, 922 (2008)
T.E. Cravens, Physics of Solar System Plasmas (Cambridge University Press, Cambridge, 1997), Chap. 4
S. Chandrasekhar, Hydrodynamic and Hydromagnetic Stability (Oxford University Press, Oxford, 1961)
D.G. Swanson, Plasma Waves (Academic Press, San Diego CA, 1989), p. 53
F.S. Acton, Numerical Methods That (Usually) Work (Mathematical Association of America, Washington DC, 1990), Chap. 14
P.M. Edwin, B. Roberts, Solar Phys. 76, 239 (1982)
A.G. Kurosh, Lectures in General Algebra (Pergamon Press, Oxford, 1965)
D.A. Muller, Mathematical Tables and Other Aids to Computation 10, 208 (1956)
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
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Zhelyazkov, I. MHD waves and instabilities in flowing solar flux-tube plasmas in the framework of Hall magnetohydrodynamics. Eur. Phys. J. D 55, 127–137 (2009). https://doi.org/10.1140/epjd/e2009-00217-3
Received:
Revised:
Published:
Issue Date:
DOI: https://doi.org/10.1140/epjd/e2009-00217-3