Geomagnetism and Aeronomy

, Volume 58, Issue 7, pp 942–946 | Cite as

On the Description of Transverse Wave Propagation Along Thin Magnetic Flux Tubes

  • Yu. T. TsapEmail author
  • A. V. StepanovEmail author
  • Yu. G. KopylovaEmail author


Two approaches are used for description of linear transverse (kink) modes excited in a vertical thin magnetic flux tube. First one is based on the elastic thread model (Spruit, 1981). The second one follows from the the Taylor and Laurent series expansions of wave variables with respect to the tube radius inside and outside of the magnetic flux tube (Lopin and Nagorny, 2013). It has been shown that the main reason of the discrepancy of these approaches is related to the phenomenological equation of plasma motion used in the former case. This suggests that results obtained on the basis of this equation should be revised.


  1. 1.
    Cheng, J., Equations for the motion of an isolated thin magnetic flux tube, Astron. Astrophys., 1992, vol. 264, no. 1, pp. 243–248.Google Scholar
  2. 2.
    Choudhuri, A.R., A correction to Spruit’s equation for the dynamics of thin flux tubes, Astron. Astrophys., 1990, vol. 239, nos. 1–2, pp. 335–339.Google Scholar
  3. 3.
    De Pontieu, B., Martens, P.C.H., and Hudson, H.S., Chromospheric damping of Alfvén waves, Astrophys. J., 2001, vol. 558, no. 2, pp. 859–871.CrossRefGoogle Scholar
  4. 4.
    Fan, Y., Magnetic fields in the solar convection zone, Living Rev. Sol. Phys., 2009, vol. 6, no. 1, id 4.Google Scholar
  5. 5.
    Fan, Y., Fisher, G.H., and McClymont, A.N., Dynamics of emerging active region flux loops, Astrophys. J., 1994, vol. 436, no. 2, pp. 907–928.CrossRefGoogle Scholar
  6. 6.
    Ferriz-Mas, A. and Schüssler, M.A.V., Dynamics of magnetic flux concentrations: The second-order thin flux tube approximation, Astron. Astrophys., 1989, vol. 210, nos. 1–2, pp. 425–432.Google Scholar
  7. 7.
    Fujimura, D. and Tsuneta, S., Properties of magnetohydrodynamic waves in the solar photosphere obtained with HINODE, Astrophys. J., 2009, vol. 702, no. 2, pp. 1443–1457.CrossRefGoogle Scholar
  8. 8.
    Gelfreikh, G.B., Tsap, Yu.T., Kopylova, Yu.G., et al., Variations of microwave emission from solar active regions, Astron. Lett., 2004, vol. 30, pp. 489–495.CrossRefGoogle Scholar
  9. 9.
    Hollweg, J.V., Alfvén waves in the solar atmosphere. II. Open and closed magnetic flux tubes, Sol. Phys., 1981, vol. 70, pp. 25–66.CrossRefGoogle Scholar
  10. 10.
    Hollweg, J.V., Resonances of coronal loops, Astrophys. J., 1984, vol. 277, pp. 392–403.CrossRefGoogle Scholar
  11. 11.
    Howard, R. and Stenflo, J.O., On the filamentary nature of solar magnetic fields, Sol. Phys., 1972, vol. 22, no. 2, pp. 402–417.CrossRefGoogle Scholar
  12. 12.
    Jess, D.B., Van Doorsselaere, T., Verth, G., et al., An inside look at sunspot oscillations with higher azimuthal wavenumbers, Astrophys. J., 2017, vol. 842, no. 1, id 59.Google Scholar
  13. 13.
    Ji, H., Cao, W., and Goode, P.R., Observation of ultrafine channels of solar corona heating, Astrophys. J. Lett., 2012, vol. 750, no. 1, id 25.Google Scholar
  14. 14.
    Leake, J.E., Arber, T.D., and Khodachenko, M.L., Collisional dissipation of Alfvén waves in a partially ionised solar chromosphere, Astron. Astrophys., 2005, vol. 442, no. 3, pp. 1091–1098.CrossRefGoogle Scholar
  15. 15.
    Longcope, D.W. and Klapper, I., Dynamics of a thin twisted flux tube, Astrophys. J., 1997, vol. 488, no. 1, pp. 443–453.CrossRefGoogle Scholar
  16. 16.
    Lopin, I. and Nagorny, I., Conditions for transverse waves propagation along thin magnetic flux tubes on the Sun, Astrophys. J., 2013, vol. 774, no. 2, id 121.Google Scholar
  17. 17.
    Lopin, I.P., Nagorny, I.G., and Nippolainen, E., Kink wave propagation in thin isothermal magnetic flux tubes, Sol. Phys., 2014, vol. 289, no. 8, pp. 3033–3041.CrossRefGoogle Scholar
  18. 18.
    Lopin, I. and Nagorny, I., Kink waves in thin stratified magnetically twisted flux tubes, Astrophys. J., 2017, vol. 840, no. 1, id 26.Google Scholar
  19. 19.
    Moreno-Insertis, F., Ferriz-Mas, A., and Schlüssler, M., Enhanced inertia of thin magnetic flux tubes, Astron. Astrophys., 1996, vol. 312, pp. 317–326.Google Scholar
  20. 20.
    Morton, R.J., Tomczyk, S., and Pinto, R., Investigating Alfvénic wave propagation in coronal open-field regions, Nat. Commun., 2015, vol. 6, id 7813.Google Scholar
  21. 21.
    Musielak, Z.E. and Ulmschneider, P., Excitation of transverse magnetic tube waves in stellar convection zones. I. Analytical approach, Astron. Astrophys., 2001, vol. 370, pp. 541–554.CrossRefGoogle Scholar
  22. 22.
    Nisticó, G., Nakariakov, V.M., and Verwichte, E., Decaying and decayless transverse oscillations of a coronal loop, Astron. Astrophys., 2013, vol. 552, id A57.Google Scholar
  23. 23.
    Osin, A., Volin, S., and Ulmschneider, P., Propagation of nonlinear longitudinal-transverse waves along magnetic flux tubes in the solar atmosphere. III. Modified equation of motion, Astron. Astrophys., 1999, vol. 351, pp. 359–367.Google Scholar
  24. 24.
    Roberts, B. and Webb, A.R., Vertical motions in an intense magnetic flux tube, Sol. Phys., 1978, vol. 56, pp. 5–35.CrossRefGoogle Scholar
  25. 25.
    Routh, S., Musielak, Z.E., and Hammer, R., Conditions for propagation of torsional waves in solar magnetic flux tubes, Sol. Phys., 2007, vol. 246, no. 1, pp. 133–143.CrossRefGoogle Scholar
  26. 26.
    Rüedi, I., Solanki, S.K., Livingston, W., and Stenflo, J.O., Infrared lines as probes of solar magnetic features. III. Strong and weak magnetic fields in plages, Astron. Astrophys., 1992, vol. 263, nos. 1–2, pp. 323–338.Google Scholar
  27. 27.
    Ryutov, D.D. and Ryutova, M.P., Sound oscillations in a plasma with “magnetic filaments”, Sov. Phys. JETP, 1976, vol. 43, no. 3, pp. 491–497.Google Scholar
  28. 28.
    Sharykin, I.N. and Kosovichev, A.G., Fine structure of flare ribbons and evolution of electric currents, Astrophys. J. Lett., 2014, vol. 788, no. 1, id L18.Google Scholar
  29. 29.
    Soler, R., Terradas, J., Oliver, R., and Ballester, J.L., Propagation of torsional Alfvén waves from the photosphere to the corona: Reflection, transmission, and heating in expanding flux tubes, Astrophys. J., 2017, vol. 840, id 20.Google Scholar
  30. 30.
    Spruit, H.C., Motion of magnetic flux tubes in the solar convection zone and chromosphere, Astron. Astrophys., 1981, vol. 98, pp. 155–160.Google Scholar
  31. 31.
    Stenflo, J.O., Collapsed, uncollapsed, and hidden magnetic flux on the quiet Sun, Astron. Astrophys., 2011, vol. 529, A42.CrossRefGoogle Scholar
  32. 32.
    Tsap, Y.T., On the penetration of Alfvén waves from the chromosphere into the corona, Proc. IAU Symp. no. 233, Solar Activity and its Magnetic Origin, Bothmer, V. and Hady, A.A., Eds., Cambridge: Cambridge Univ. Press, 2006, pp. 253–254.Google Scholar
  33. 33.
    Tsap, Yu.T. and Kopylova, Yu.G., Acoustic damping of fast kink oscillations of coronal loops, Astron. Lett., 2001, vol. 27, no. 11, pp. 737–744.CrossRefGoogle Scholar
  34. 34.
    Weber, M.A. and Browning, M.K., Modeling the rise of fibril magnetic fields in fully convective stars, Astrophys. J., 2016, vol. 827, id 95.Google Scholar

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© Pleiades Publishing, Ltd. 2018

Authors and Affiliations

  1. 1.Crimean Astrophysical Observatory of the Russian Academy of SciencesCrimeaRussia
  2. 2.Pulkovo Observatory of the Russian Academy of SciencesSt. PetersburgRussia

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