Solar Physics

, Volume 238, Issue 1, pp 41–59 | Cite as

Sausage MHD Waves in Incompressible Flux Tubes with Twisted Magnetic Fields



Twisted magnetic flux tubes are of considerable interest because of their natural occurrence from the Sun’s interior, throughout the solar atmosphere and interplanetary space up to a wide range of applicabilities to astrophysical plasmas. The aim of the present work is to obtain analytically a dispersion equation of linear wave propagation in twisted incompressible cylindrical magnetic waveguides and find appropriate solutions for surface, body and pseudobody sausage modes (i.e. m = 0) of a twisted magnetic flux tube embedded in an incompressible but also magnetically twisted plasma. Asymptotic solutions are derived in long- and short-wavelength approximations. General solutions of the dispersion equation for intermediate wavelengths are obtained numerically. We found, that in case of a constant, but non-zero azimuthal component of the equilibrium magnetic field outside the flux tube the index ν of Bessel functions in the dispersion relation is not integer any more in general. This gives rise to a rich mode-structure of degenerated magneto-acoustic waves in solar flux tubes. In a particular case of a uniform magnetic twist the total pressure is found to be constant across the boundary of the flux tube. Finally, the effect of magnetic twist on oscillation periods is estimated under solar atmospheric conditions. It was found that a magnetic twist will increase, in general, the periods of waves approximately by a few percent when compared to their untwisted counterparts.


Dispersion Relation Solar Phys Flux Tube Phase Speed Solar Atmosphere 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. Andries, J., Goossens, M., Hollweg, J.V., Arregui, I., and Van Doorsselaere, T.: 2005, Astron. Astrophys. 430, 1109.CrossRefADSGoogle Scholar
  2. Andries, J., Arregui, I., and Goossens, M.: 2005, Astrophys. J. 624, L57.CrossRefADSGoogle Scholar
  3. Appert, K., Gruber, R., and Vaclavik, J.: 1974, Phys. Fluids 17, 1471.CrossRefGoogle Scholar
  4. Arregui, I., Van Doorsselaere, T., Andries, J., Goossens, M., and Kimpe, D.: 2005, Astron. Astrophys. 441, 361.CrossRefADSGoogle Scholar
  5. Aschwanden, M.: 2004, Physics of the Solar Corona. An Introduction, Praxis, Chichester, UK.Google Scholar
  6. Bennett, K., Roberts, B., and Narain, U.: 1999, Solar Phys. 185, 41.CrossRefADSGoogle Scholar
  7. De Pontieu, B., Martens, P.C.H., and Hudson, H.S.: 2001, Astrophys. J. 558, 859.CrossRefADSGoogle Scholar
  8. Diaz, A.J., Oliver, R., and Ballester, J.L.: 2002, Astrophys. J. 580, 550.CrossRefADSGoogle Scholar
  9. Edwin, P.M. and Roberts, B.: 1983, Solar Phys. 88, 179.Google Scholar
  10. Goedbloed, J.P.: 1971, Physica 53, 412.CrossRefADSGoogle Scholar
  11. Goedbloed, J.P. and Hagebeuk, H.J.L.: 1972, Phys. Fluids 15, 1090.Google Scholar
  12. Goossens, M.: 1991, Advances in Solar System Magnetohydrodynamics, Cambridge University Press, Cambridge, UK.Google Scholar
  13. Goossens, M., Hollweg, J.V., and Sakurai, T.: 1992, Solar Phys. 138, 233.CrossRefADSGoogle Scholar
  14. Hain, K. and Lüst, R.: 1958, Z. Naturforsch. 13a, 936.Google Scholar
  15. Kadomtsev, B.B.: 1966, in M.A. Leontovich (ed.), Reviews of Plasma Physics, Vol. II, Consultants Bureau, New York, p. 153.Google Scholar
  16. Ruderman, M.S.: 2005, Phys. Plasmas 12, 034701.MathSciNetCrossRefGoogle Scholar
  17. Sakurai, T., Goossens, M., and Hollweg, J.V.: 1991, Solar Phys. 133, 227.CrossRefADSGoogle Scholar
  18. Van Doorsselaere, T., Andries, J., Poedts, S., and Goossens, M.: 2004a, Astrophys. J. 606, 1223.CrossRefADSGoogle Scholar
  19. Van Doorsselaere, T., Debosscher, A., Andries, J., and Poedts, S.: 2004b, Astron. Astrophys. 424, 1065.CrossRefADSGoogle Scholar

Copyright information

© Springer Science + Business Media, Inc. 2006

Authors and Affiliations

  1. 1.Solar Physics and Upper-Atmosphere Research Group, Department of Applied MathematicsUniversity of SheffieldSheffieldU.K.

Personalised recommendations