Solar Physics

, Volume 217, Issue 2, pp 199–223 | Cite as

Linear and non-linear MHD wave propagation in steady-state magnetic cylinders

  • M. Terra-Homem
  • R. Erdélyi
  • I. Ballai


The propagation of linear and non-linear magnetohydrodynamic (MHD) waves in a straight homogeneous cylindrical magnetic flux tube embedded in a homogeneous magnetic environment is investigated. Both the tube and its environment are in steady state. Steady flows break the symmetry of forward (field-aligned) and backward (anti-parallel to magnetic field) propagating MHD wave modes because of the induced Doppler shifts. It is shown that strong enough flows change the sense of propagation of MHD waves. The flow also induces shifts in cut-off values and phase-speeds of the waves. Under photospheric conditions, if the flow is strong enough, the slow surface modes may disappear and the fast body modes may become present. The crossing of modes is also observed due to the presence of flows. The effect of steady-state background has to be considered particularly carefully when evaluating observation signatures of MHD waves for diagnostics in the solar atmosphere.


Magnetic Flux Steady Flow Flux Tube Solar Atmosphere Magnetic Flux Tube 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. Abramowitz, M. and Stegun, I. A.: 1967, Handbook of Mathematical Functions, Dover, New York.Google Scholar
  2. Ballai, I. and Zhugzhda, Y. D.: 2002, Phys. Plasmas 9, 4280.Google Scholar
  3. Ballai, I., Thelen, J. C., and Roberts, B.: 2003, Astron. Astrophys. 404, 701.Google Scholar
  4. Ballai, I., Erdélyi, R., Voitenko, Y., and Goossens, M.: 2002, Phys. Plasmas 9, 2593.Google Scholar
  5. Buchlin, E. and Hassler, D. M.: 2000, in AAS/Solar Physics Division Meeting, Vol. 32, p. 201.Google Scholar
  6. Cally, P. S.: 1986, Solar Phys. 103, 277.Google Scholar
  7. De Moortel, I., Ireland, J., Walsh, R. W., and Hood, A. W.: 2002, Solar Phys. 209, 61.Google Scholar
  8. Edwin, P. M. and Roberts, B.: 1982, Solar Phys. 76, 239.Google Scholar
  9. Edwin, P. M. and Roberts, B.: 1983, Solar Phys. 88, 179.Google Scholar
  10. Edwin, P. M. and Roberts, B.: 1986, Wave Motion 8, 151.Google Scholar
  11. Gabriel, A. H., Bely-Dubau, F., and Lemaire, P.: 2003, Astrophys. J. 589, 623.Google Scholar
  12. Gloeckler, G. and Geiss, J.: 1998, Space Sci. Rev. 86, 127.Google Scholar
  13. Innes, D. E. and Tóth, G.: 1999, Solar Phys. 185, 127.Google Scholar
  14. Joarder, P. S.: 2002, Astron. Astrophys. 384, 1086.Google Scholar
  15. Joarder, P. S. and Satya Narayanan, A.: 2000, Astron. Astrophys. 359, 1211.Google Scholar
  16. Judge, P. G., Hansteen, V., Wikstol, O., Wilhelm, K., Schuehle, U., and Moran, T.: 1998, Astrophys. J. 502, 981.Google Scholar
  17. Kondrashov, D., Feynman, J., Liewer, P. C., and Ruzmaikin, A.: 1999, Astrophys. J. 519, 884.Google Scholar
  18. Leibovich, S. J.: 1970, Fluid Mech. 42, 803.Google Scholar
  19. Marsch, M. S., Walsh, R. W., De Moortel, I., and Ireland, J.: 2003, Astron. Astrophys. 404, L37.Google Scholar
  20. Molotovshchikov, A. L. and Ruderman, M. S.: 1987, Solar Phys. 109, 247.Google Scholar
  21. Montesinos, B. and Thomas, J. H.: 1993, Astrophys. J. 402, 314.Google Scholar
  22. Nakariakov, V. M. and Roberts, B.: 1995, Solar Phys. 159, 213.Google Scholar
  23. Ofman, L. and Davila, J.: 1997, Astrophys. J. 476, 357.Google Scholar
  24. Pojoga, S. and Molowny-Horas, R.: 1999, Solar Phys. 185, 113.Google Scholar
  25. Roberts, B.: 1981a, Solar Phys. 69, 39.Google Scholar
  26. Roberts, B.: 1981b, Solar Phys. 69, 27.Google Scholar
  27. Roberts, B.: 1985, Phys. Fluids 28, 3280.Google Scholar
  28. Roberts, B.: 1987, Astrophys. J. 318, 590.Google Scholar
  29. Roberts, B. and Mangeney, A.: 1982, Monthly Notices Royal Astron. Soc. 198, 7P.Google Scholar
  30. Ruderman, M.: 2003, 'Nonlinear Waves in the Magnetically Structured Solar Atmosphere',PADEU, in press.Google Scholar
  31. Satya Narayanan, A.: 1991, Plasma Phys. Controlled Fusion 33, 333.Google Scholar
  32. Schmieder, B., Heinzel, P., Kucera, T., and Vial, J.: 1998, Solar Phys. 181, 309.Google Scholar
  33. Somasundaram, K., Venkatraman, S., and Sengottuvel, M. P.: 1999, Plasma Phys. Controlled Fusion 41, 1421.Google Scholar
  34. Watanabe, T.: 1975, Publ. Astron. Soc. Japan 27, 385.Google Scholar
  35. Weisshaar, E.: 1989, Phys. Fluids 1, 1406.Google Scholar
  36. Whitham, G. B.: 1974, Linear and Nonlinear Waves, Wiley and Sons, New York.Google Scholar
  37. Wilhelm, K., Marsch, E., Dwivedi, B. N., Hassler, D. M., Lemaire, P., Gabriel, A. H., and Huber, M. C. E.: 1998, Astrophys. J. 500, 1023.Google Scholar
  38. Winebarger, A. R., Warren, H., van Ballegooijen, A., DeLuca, E. E., and Golub, L.: 2002, Astrophys. J. 567, L89.Google Scholar
  39. Zhugzhda, Y. D.: 2000, Phys. Scripta T84, 159.Google Scholar
  40. Zhugzhda, Y. D. and Goossens, M.: 2001, Astron. Astrophys. 377, 330.Google Scholar

Copyright information

© Kluwer Academic Publishers 2003

Authors and Affiliations

  • M. Terra-Homem
    • 1
  • R. Erdélyi
    • 1
  • I. Ballai
    • 1
  1. 1.Space and Atmosphere Research Centre, Department of Applied MathematicsUniversity of SheffieldSheffieldU.K.

Personalised recommendations