Solar Physics

, Volume 264, Issue 2, pp 311–327 | Cite as

Resonant Absorption of Fast Magnetoacoustic Waves due to Coupling into the Slow and Alfvén Continua in the Solar Atmosphere



Resonant absorption of fast magnetoacoustic (FMA) waves in an inhomogeneous, weakly dissipative, one-dimensional planar, strongly anisotropic and dispersive plasma is investigated. The magnetic configuration consists of an inhomogeneous magnetic slab sandwiched between two regions of semi-infinite homogeneous magnetic plasmas. Laterally driven FMA waves penetrate the inhomogeneous slab interacting with the localised slow or Alfvén waves present in the inhomogeneous layer and are partly reflected, dissipated and transmitted by this region. The presented research aims to find the coefficient of wave energy absorption under solar chromospheric and coronal conditions. Numerical results are analysed to find the coefficient of wave energy absorption at both the slow and Alfvén resonance positions. The mathematical derivations are based on the two simplifying assumptions that i) nonlinearity is weak, and ii) the thickness of the inhomogeneous layer is small in comparison to the wavelength of the wave, i.e. we employ the so-called long wavelength approximation. Slow resonance is found to be described by the nonlinear theory, while the dynamics at the Alvén resonance can be described within the linear framework. We introduce a new concept of coupled resonances, which occurs when two different resonances are in close proximity to each other, causing the incoming wave to act as though it has been influenced by the two resonances simultaneously. Our results show that the wave energy absorption is heavily dependent on the angle of the incident wave in combination with the inclination angle of the equilibrium magnetic field. In addition, it is found that FMA waves are very efficiently absorbed at the Alvén resonance under coronal conditions. Under chromospheric conditions the FMA waves are far less efficiently absorbed, despite an increase in efficiency due to the coupled resonances.


Magnetohydrodynamics (MHD) Sun: atmosphere Sun: magnetic field Sun: waves 


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  1. Aschwanden, M.J.: 1999, Solar Phys. 199, 233. CrossRefADSGoogle Scholar
  2. Aschwanden, M.J., Fletcher, L., Schrijver, C.J., Alexander, D.: 1999, Astrophys. J. 520, 880. CrossRefADSGoogle Scholar
  3. Athay, R.G., White, O.R.: 1978, Astrophys. J. 526, 1026. Google Scholar
  4. Ballai, I., Erdélyi, R.: 1998, Solar Phys. 180, 65. CrossRefADSGoogle Scholar
  5. Ballai, I., Douglas, M., Marcu, A.: 2008, Astron. Astrophys. 488, 1125. CrossRefADSGoogle Scholar
  6. Ballai, I., Erdélyi, R., Pintér, B.: 2005, Astrophys. J. Lett. 633, 145. CrossRefADSGoogle Scholar
  7. Ballai, I., Erdélyi, R., Ruderman, M.S.: 1998, Phys. Plasmas 5, 2264. CrossRefADSGoogle Scholar
  8. Ballai, I., Ruderman, M.S., Erdélyi, R.: 1998, Phys. Plasmas 5, 252. CrossRefADSGoogle Scholar
  9. Belien, A.J.C., Martens, P.C.H., Keppens, R.: 1999, Astrophys. J. 526, 478. CrossRefADSGoogle Scholar
  10. Braginskii, S.I.: 1965, Rev. Plasma Phys. 1, 205. ADSGoogle Scholar
  11. C̆adez̆, V.M., Csík, A., Erdélyi, R., Goossens, M.: 1997, Astron. Astrophys. 326, 1241. ADSGoogle Scholar
  12. Chen, L., Hasegawa, A.: 1974, Phys. Fluids 17, 1399. CrossRefADSGoogle Scholar
  13. Clack, C.T.M., Ballai, I.: 2008, Phys. Plasmas 15, 082310. CrossRefADSGoogle Scholar
  14. Clack, C.T.M., Ballai, I.: 2009a, Phys. Plasmas 16, 0402305. Google Scholar
  15. Clack, C.T.M., Ballai, I.: 2009b, Phys. Plasmas 16, 072115. CrossRefADSGoogle Scholar
  16. Clack, C.T.M., Ballai, I., Ruderman, M.S.: 2009, Astron. Astrophys. 494, 317. MATHCrossRefADSGoogle Scholar
  17. Csík, A., C̆adez̆, V.M., Goossens, M.: 1998, Astron. Astrophys. 339, 215. ADSGoogle Scholar
  18. Erdélyi, R., Ballai, I.: 2001, Astron. Astrophys. 368, 662. MATHCrossRefADSGoogle Scholar
  19. Erdélyi, R., Goossens, M.: 1995, Astron. Astrophys. 294, 575. ADSGoogle Scholar
  20. Erdélyi, R., Goossens, M.: 1996, Astron. Astrophys. 313, 664. ADSGoogle Scholar
  21. Goossens, M., Poedts, S.: 1992, Astrophys. J. 384, 348. CrossRefADSGoogle Scholar
  22. Goossens, M., Andries, J., Aschwanden, M.J.: 2002, Astron. Astrophys. Lett. 394, 39. CrossRefADSGoogle Scholar
  23. Goossens, M., Ruderman, M.S., Hollweg, J.V.: 1995, Solar Phys. 157, 75. CrossRefADSGoogle Scholar
  24. Grossmann, M., Tataronis, J.: 1973, Z. Phys. 261, 217. CrossRefADSGoogle Scholar
  25. Hasegawa, A., Chen, L.: 1976, Phys. Fluids 19, 1924. CrossRefADSGoogle Scholar
  26. Hollweg, J.V.: 1985, J. Geophys. Res. 90, 7620. CrossRefADSGoogle Scholar
  27. Hollweg, J.V.: 1988, Astrophys. J. 335, 1005. CrossRefADSGoogle Scholar
  28. Ionson, J.A.: 1978, Astrophys. J. 226, 650. CrossRefADSGoogle Scholar
  29. Lou, Y.Q.: 1990, Astrophys. J. 350, 452. CrossRefADSGoogle Scholar
  30. Mocanu, G., Marcu, A., Ballai, I., Orza, B.: 2008, Astron. Nachr. 329, 780. MATHCrossRefADSGoogle Scholar
  31. Nakariakov, V.M., Ofman, L.: 2001, Astron. Astrophys. Lett. 372, 53. CrossRefADSGoogle Scholar
  32. Nakariakov, V.M., Ofman, L., Deluca, E.E., Roberts, B., Davila, J.M.: 1999, Science 285, 862. CrossRefADSGoogle Scholar
  33. Ofman, L., Davila, J.M.: 1995, J. Geophys. Res. 100, 23427. CrossRefADSGoogle Scholar
  34. Parker, E.N.: 1988, Astrophys. J. 330, 474. CrossRefADSGoogle Scholar
  35. Poedts, S., Goossens, M., Kerner, W.: 1989, Solar Phys. 123, 83. CrossRefADSGoogle Scholar
  36. Poedts, S., Goossens, M., Kerner, W.: 1990a, Astrophys. J. 360, 279. CrossRefADSGoogle Scholar
  37. Poedts, S., Goossens, M., Kerner, W.: 1990b, Comput. Phys. Commun. 59, 95. MATHCrossRefADSGoogle Scholar
  38. Poedts, S., Kerner, W., Goossens, M.: 1990, Comput. Phys. Commun. 59, 75. MATHCrossRefADSGoogle Scholar
  39. Priest E.R.: 1984, Solar Magnetohydrodynamics. Springer, Berlin, 86. Google Scholar
  40. Roberts, B., Edwin, P.M., Benz, A.O.: 1984, Astrophys. J. 279, 857. CrossRefADSGoogle Scholar
  41. Roussev, I., Doyle, J.G., Galsgaard, K., Erdélyi, R.: 2001a, Astron. Astrophys. 380, 719. CrossRefADSGoogle Scholar
  42. Roussev, I., Galsgaard, K., Erdélyi, R., Doyle, J.G.: 2001b, Astron. Astrophys. 370, 298. CrossRefADSGoogle Scholar
  43. Roussev, I., Galsgaard, K., Erdélyi, R., Doyle, J.G.: 2001c, Astron. Astrophys. 375, 228. CrossRefADSGoogle Scholar
  44. Ruderman, M.S.: 2000, J. Plasma Phys. 63, 43. CrossRefADSGoogle Scholar
  45. Ruderman, M.S., Roberts, B.: 2002, Astrophys. J. 577, 475. CrossRefADSGoogle Scholar
  46. Ruderman, M.S., Goossens, M., Hollweg, J.V.: 1997, Phys. Plasmas 4, 91. CrossRefADSGoogle Scholar
  47. Ruderman, M.S., Hollweg, J.V., Goossens, M.: 1997, Phys. Plasmas 4, 75. CrossRefADSGoogle Scholar
  48. Ruderman, M.S., Berghmans, D., Goossens, M., Poedts, S.: 1997a, Astron. Astrophys. 320, 305. ADSGoogle Scholar
  49. Ruderman, M.S., Goossens, M., Ballester, J.L., Oliver, R.: 1997b, Astron. Astrophys. 328, 361. ADSGoogle Scholar
  50. Sakurai, T., Goossens, M., Hollweg, J.V.: 1991, Solar Phys. 133, 227. CrossRefADSGoogle Scholar
  51. Spruit, H.C., Bogdan, T.J.: 1992, Astrophys. J. Lett. 391, 109. CrossRefADSGoogle Scholar
  52. Tataronis, J., Grossmann, M.: 1973, Z. Phys. 261, 203. CrossRefADSGoogle Scholar
  53. Terradas, J., Goossens, M., Ballai, I.: 2010, Astron. Astrophys., accepted. Google Scholar
  54. Terradas, J., Arregui, I., Oliver, R., Ballester, J.L., Andries, J., Goossens, M.: 2008, Astrophys. J. 679, 1611. CrossRefADSGoogle Scholar
  55. Uchida, Y., Altschuler, M.D., Newkirk, G.: 1973, Solar Phys. 28, 495. CrossRefADSGoogle Scholar
  56. Vasquez, B.J.: 2005, J. Geophys. Res. 110, A10S10. CrossRefGoogle Scholar
  57. Woodward, T.I., McKenzie, J.F.: 1994a, Planet Space Sci. 42, 463. CrossRefADSGoogle Scholar
  58. Woodward, T.I., McKenzie, J.F.: 1994b, Planet Space Sci. 42, 481. CrossRefADSGoogle Scholar

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© Springer Science+Business Media B.V. 2010

Authors and Affiliations

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

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