Solar Physics

, Volume 246, Issue 1, pp 119–131 | Cite as

Nonaxisymmetric Oscillations of Thin Twisted Magnetic Tubes

Article

Abstract

In this paper we study nonaxisymmetric oscillations of thin twisted magnetic tubes taking the density variation along the tube into account. We use the approximation of the zero-beta plasma. The magnetic field outside the tube is straight and homogeneous; however, it is twisted inside the tube. We assume that the azimuthal component of the magnetic field is proportional to the distance from the tube axis and that the tube is only weakly twisted (i.e., the ratio of the azimuthal and axial components of the magnetic field is small). Using the asymptotic analysis we show that the eigenmodes and eigenfrequencies of the kink and fluting oscillations are described by a classical Sturm – Liouville problem for a second-order ordinary differential equation. The main result is that the twist does not affect the kink mode.

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References

  1. Abramowitz, M., Stegun, A.: 1964, Handbook of Mathematical Functions, Wiley, New York. MATHGoogle Scholar
  2. Andries, J., Goossens, M., Hollweg, J.V., Arregui, I., Van Doorsselaere, T.: 2005, Astron. Astrophys. 430, 1109. CrossRefADSGoogle Scholar
  3. Appert, K., Gruber, R., Vacklavik, J.: 1974, Phys. Fluids 17, 1471. CrossRefADSGoogle Scholar
  4. Arregui, I., Van Doorsselaere, T., Andries, J., Goossens, M., Kimpe, D.: 2005, Astron. Astrophys. 441, 361. CrossRefADSGoogle Scholar
  5. Aschwanden, M.J., Fletcher, L., Schrijver, C.J., Title, A.M.: 1999, Astrophys. J. 520, 880. CrossRefADSGoogle Scholar
  6. Ballai, I., Erdélyi, R.: 2002, J. Plasma Phys. 67, 79. CrossRefADSGoogle Scholar
  7. Bennett, K., Roberts, B., Narain, U.: 1999, Solar Phys. 185, 41. CrossRefADSGoogle Scholar
  8. Bogdan, T.J.: 1984, Astrophys. J. 282, 769. CrossRefADSGoogle Scholar
  9. Browning, P.K., Priest, E.R.: 1983, Astrophys. J. 266, 848. CrossRefADSMathSciNetGoogle Scholar
  10. Carter, B.K., Erdélyi, R.: 2007, Astron. Astrophys., in press. Google Scholar
  11. Dungey, J.W., Loughhead, R.E.: 1954, Austr. J. Phys. 7, 5. MATHADSMathSciNetGoogle Scholar
  12. Dymova, M., Ruderman, M.S.: 2005, Solar Phys. 229, 79. CrossRefADSGoogle Scholar
  13. Dymova, M., Ruderman, M.S.: 2006a, Astron. Astrophys. 457, 1059. MATHCrossRefADSGoogle Scholar
  14. Dymova, M., Ruderman, M.S.: 2006b, Astron. Astrophys. 459, 241. CrossRefADSGoogle Scholar
  15. Dymova, M., Ruderman, M.S.: 2007, Astron. Astrophys. 463, 759. CrossRefADSGoogle Scholar
  16. Edwin, P.M., Roberts, B.: 1983, Solar Phys. 88, 179. CrossRefADSGoogle Scholar
  17. Erdélyi, R.: 1997, Solar Phys. 171, 49. CrossRefADSGoogle Scholar
  18. Erdélyi, R., Carter, B.K.: 2006, Astron. Astrophys. 455, 361. CrossRefADSGoogle Scholar
  19. Erdélyi, R., Fedun, V.: 2006, Solar Phys. 238, 41. CrossRefADSGoogle Scholar
  20. Erdélyi, R., Fedun, V.: 2007, Solar Phys., in press. Google Scholar
  21. Erdélyi, R., Goossens, M.: 1995, Astron. Astrophys. 294, 575. ADSGoogle Scholar
  22. Erdélyi, R., Goossens, M.: 1996, Astron. Astrophys. 313, 664. ADSGoogle Scholar
  23. Erdélyi, R., Goossens, M., Ruderman, M.S.: 1995, Solar Phys. 161, 123. CrossRefADSGoogle Scholar
  24. Erdélyi, R., Verth, G.: 2007, Astron. Astrophys. 462, 743. CrossRefADSGoogle Scholar
  25. Goedbloed, J.P.: 1971, Physica 53, 412. CrossRefADSGoogle Scholar
  26. Goossens, M., Andries, J., Aschwanden, M.J.: 2002, Astron. Astrophys. 394, L39. CrossRefADSGoogle Scholar
  27. Goossens, M., Hollweg, J.V., Sakurai, T.: 1992, Solar Phys. 138, 233. CrossRefADSGoogle Scholar
  28. Goossens, M., Ruderman, M.S., Hollweg, J.V.: 1995, Solar Phys. 157, 75. CrossRefADSGoogle Scholar
  29. Hain, K., Lüst, R.: 1958, Z. Naturforsch. 13a, 936. ADSGoogle Scholar
  30. Hollweg, J.V., Yang, G.: 1988, J. Geophys. Res. 93, 5423. ADSCrossRefGoogle Scholar
  31. Kruskal, M., Tuck, J.L.: 1958, Proc. R. Soc. Lond. A 245, 222. MATHADSMathSciNetCrossRefGoogle Scholar
  32. Ionson, J.A.: 1978, Astrophys. J. 226, 650. CrossRefADSGoogle Scholar
  33. Nakariakov, V., Ofman, L., DeLuca, E.E., Roberts, B., Davila, J.M.: 1999, Science 285, 862. CrossRefADSGoogle Scholar
  34. Parker, E.N.: 1974, Astrophys. J. 191, 245. CrossRefADSGoogle Scholar
  35. Roberts, B.: 1981, Solar Phys. 69, 27. CrossRefADSGoogle Scholar
  36. Roberts, P.H.: 1956, Astrophys. J. 124, 430. CrossRefADSGoogle Scholar
  37. Ruderman, M.S.: 2003, Astron. Astrophys. 409, 287. CrossRefADSGoogle Scholar
  38. Ruderman, M.S., Roberts, B.: 2002, Astrophys. J. 577, 475. CrossRefADSGoogle Scholar
  39. Ruderman, M.S., Roberts, B.: 2006, J. Plasma Phys. 72, 285. CrossRefADSGoogle Scholar
  40. Ryutov, D.D., Ryutova, M.P.: 1976, Sov. Phys. – JETP 43, 491. ADSGoogle Scholar
  41. Sakurai, T., Goossens, M., Hollweg, J.V.: 1991, Solar Phys. 133, 227. CrossRefADSGoogle Scholar
  42. Shafranov, V.D.: 1957, J. Nucl. Energy II 5, 86. MathSciNetGoogle Scholar
  43. Spruit, H.C.: 1981, Astron. Astrophys. 98, 155. MATHADSGoogle Scholar
  44. Spruit, H.C.: 1982, Solar Phys. 75, 3. CrossRefADSGoogle Scholar
  45. Terradas, J., Andries, J., Goossens, M.: 2007a, Solar Phys., submitted. Google Scholar
  46. Terradas, J., Andries, J., Goossens, M.: 2007b, Astron. Astrophys. 469, 1135. CrossRefADSGoogle Scholar
  47. Terradas, J., Oliver, R., Ballester, J.L.: 2006a, Astrophys. J. 642, 533. CrossRefADSGoogle Scholar
  48. Terradas, J., Oliver, R., Ballester, J.L.: 2006b, Astrophys. J. 650, L91. CrossRefADSGoogle Scholar
  49. Van Doorsselaere, T., Andries, J., Poedts, S., Goossens, M.: 2004a, Astrophys. J. 606, 1223. CrossRefADSGoogle Scholar
  50. Van Doorsselaere, T., Debosscher, A., Andries, J., Poedts, S.: 2004b, Astron. Astrophys. 424, 1065. CrossRefADSGoogle Scholar

Copyright information

© Springer Science+Business Media B.V. 2007

Authors and Affiliations

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

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