Solar Physics

, Volume 263, Issue 1–2, pp 63–85 | Cite as

Magneto-Acoustic Waves in Compressible Magnetically Twisted Flux Tubes



The oscillatory modes of a magnetically twisted compressible flux tube embedded in a compressible magnetic environment are investigated in cylindrical geometry. Solutions to the governing equations to linear wave perturbations are derived in terms of Whittaker’s functions. A general dispersion equation is obtained in terms of Kummer’s functions for the approximation of weak and uniform internal twist, which is a good initial working model for flux tubes in solar applications. The sausage, kink and fluting modes are examined by means of the derived exact dispersion equation. The solutions of this general dispersion equation are found numerically under plasma conditions representative of the solar photosphere and corona. Solutions for the phase speed of the allowed eigenmodes are obtained for a range of wavenumbers and varying magnetic twist. Our results generalise previous classical and widely applied studies of MHD waves and oscillations in magnetic loops without a magnetic twist. Potential applications to solar magneto-seismology are discussed.


Twisted magnetic flux tube MHD waves Solar atmosphere Magneto-seismology 


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  1. Abramowitz, M., Stegun, I.A.: 1964, Handbook of Mathematical Functions, National Bureau of Standards, Washington. MATHGoogle Scholar
  2. Appert, K., Gruber, R., Vaclavik, J.: 1974, Phys. Fluids 17, 1471. CrossRefADSGoogle Scholar
  3. Bennett, K., Roberts, B., Narain, U.: 1999, Solar Phys. 185, 41. CrossRefADSGoogle Scholar
  4. Edwin, P.M., Roberts, B.: 1983, Solar Phys. 88, 179. CrossRefADSGoogle Scholar
  5. Erdélyi, R., Fedun, V.: 2006, Solar Phys. 238, 41. CrossRefADSGoogle Scholar
  6. Erdélyi, R., Fedun, V.: 2007, Solar Phys. 246, 101. CrossRefADSGoogle Scholar
  7. Erdélyi, R., Taroyan, Y.: 2008, Astron. Astrophys. 489, L49. CrossRefADSGoogle Scholar
  8. Goedbloed, J.P.: 1971, Physica 53, 412. CrossRefADSGoogle Scholar
  9. Goossens, M.: 1991, Advances in Solar System Magnetohydrodynamics, Cambridge University Press, Cambridge. Google Scholar
  10. Hain, K., Lüst, R.: 1958, Z. Naturforsch. 13a, 936. ADSGoogle Scholar
  11. Kadomtsev, B.B.: 1966, In: Leontovich, M.A. (ed.) Reviews of Plasma Physics, Consultants Bureau, New York, 153. Google Scholar
  12. Klimchuk, J.A., Antiochos, S.K., Norton, D.: 2000, Astrophys. J. 542, 504. CrossRefADSGoogle Scholar
  13. Nakariakov, V.M., Verwichte, E.: 2005, Living Rev. Solar Phys. 2, 3. ADSGoogle Scholar
  14. Ruderman, M.S.: 2005, Phys. Plasmas 12, 034701. CrossRefMathSciNetADSGoogle Scholar
  15. Ruderman, M.S.: 2007, Solar Phys. 246, 119. CrossRefADSGoogle Scholar
  16. Sakurai, T., Goossens, M., Hollweg, J.V.: 1991, Solar Phys. 133, 227. CrossRefADSGoogle Scholar
  17. Uberoi, C., Somasundaram, K.: 1980, Plasma Phys. 22, 747. CrossRefADSGoogle Scholar
  18. Whittaker, E.T.: 1903, Bull. Am. Math. Soc. 10, 125. CrossRefMathSciNetGoogle Scholar

Copyright information

© Springer Science+Business Media B.V. 2010

Authors and Affiliations

  1. 1.Solar Physics and Space Plasma Research Centre (SP²RC), Dept. of Applied MathematicsUniversity of SheffieldSheffieldUK

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