Space Science Reviews

, Volume 158, Issue 2–4, pp 205–236 | Cite as

Review Article: MHD Wave Propagation Near Coronal Null Points of Magnetic Fields

Article

Abstract

We present a comprehensive review of MHD wave behaviour in the neighbourhood of coronal null points: locations where the magnetic field, and hence the local Alfvén speed, is zero. The behaviour of all three MHD wave modes, i.e. the Alfvén wave and the fast and slow magnetoacoustic waves, has been investigated in the neighbourhood of 2D, 2.5D and (to a certain extent) 3D magnetic null points, for a variety of assumptions, configurations and geometries. In general, it is found that the fast magnetoacoustic wave behaviour is dictated by the Alfvén-speed profile. In a β=0 plasma, the fast wave is focused towards the null point by a refraction effect and all the wave energy, and thus current density, accumulates close to the null point. Thus, null points will be locations for preferential heating by fast waves. Independently, the Alfvén wave is found to propagate along magnetic fieldlines and is confined to the fieldlines it is generated on. As the wave approaches the null point, it spreads out due to the diverging fieldlines. Eventually, the Alfvén wave accumulates along the separatrices (in 2D) or along the spine or fan-plane (in 3D). Hence, Alfvén wave energy will be preferentially dissipated at these locations. It is clear that the magnetic field plays a fundamental role in the propagation and properties of MHD waves in the neighbourhood of coronal null points. This topic is a fundamental plasma process and results so far have also lead to critical insights into reconnection, mode-coupling, quasi-periodic pulsations and phase-mixing.

Keywords

Magnetic fields: coronal Magnetic fields: models Waves: magnetohydrodynamic Waves: propagation Magnetohydrodynamics 

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References

  1. S.K. Antiochos, Astrophys. J. 502, L181 (1998) ADSCrossRefGoogle Scholar
  2. S.K. Antiochos, C.R. DeVore, J.A. Klimchuk, Astrophys. J. 510, 485 (1999) ADSCrossRefGoogle Scholar
  3. T.D. Arber, A.W. Longbottom, C.L. Gerrard, A.M. Milne, J. Comput. Phys. 171, 151 (2001) MathSciNetADSMATHCrossRefGoogle Scholar
  4. M.J. Aschwanden, L. Fletcher, C.J. Schrijver, D. Alexander, Astrophys. J. 520, 880 (1999) ADSCrossRefGoogle Scholar
  5. M.J. Aschwanden, B. De Pontieu, C.J. Schrijver, A.M. Title, Sol. Phys. 206, 99 (2002) ADSCrossRefGoogle Scholar
  6. G. Aulanier, E.E. DeLuca, S.K. Antiochos, R.A. Mullen, L. Golub, Astrophys. J. 540, 1126 (2000) ADSCrossRefGoogle Scholar
  7. D. Banerjee, L. Teriaca, J.G. Doyle, K. Wilhelm, Astron. Astrophys. 339, 208–214 (1998) ADSGoogle Scholar
  8. N. Ben Ayed, K.G. McClements, A. Thyagaraja, J. Plasma Phys. 75, 203–215 (2009) ADSCrossRefGoogle Scholar
  9. C.M. Bender, S.A. Orszag, Advanced Mathematical Methods for Scientists and Engineers (McGraw-Hill, New York, 1978) MATHGoogle Scholar
  10. D. Berghmans, F. Clette, Sol. Phys. 186, 207 (1999) ADSCrossRefGoogle Scholar
  11. C. Beveridge, E.R. Priest, D.S. Brown, Sol. Phys. 209, 333 (2002) ADSCrossRefGoogle Scholar
  12. T.J. Bogdan, M.C.V. Hansteen, A. McMurry, C.S. Rosenthal, M. Johnson, S. Petty-Powell, E.J. Zita, R.F. Stein, S.W. McIntosh, Nordlund, Astrophys. J. 599, 626–660 (2003) ADSCrossRefGoogle Scholar
  13. S.I. Braginskii, Rev. Plasma Phys. 1, 205 (1965) ADSGoogle Scholar
  14. D.S. Brown, E.R. Priest, Publ. Astron. Soc. Pac. Conf. Ser. 155, 90–94 (1998) ADSGoogle Scholar
  15. D.S. Brown, E.R. Priest, Astron. Astrophys. 367, 339 (2001) ADSCrossRefGoogle Scholar
  16. S.V. Bulanov, S.G. Shasharina, F. Pegoraro, Plasma Phys. Control. Fusion 34, 33–48 (1992) ADSCrossRefGoogle Scholar
  17. S.V. Bulanov, S.I. Syrovatskii, Fiz. Plazmy 6, 1205 (1980) Google Scholar
  18. R.A. Cairns, C.N. Lashmore-Davies, Phys. Fluids 26, 1268–1274 (1983) ADSMATHCrossRefGoogle Scholar
  19. P.S. Cally, Sol. Phys. 103, 27 (1986) CrossRefGoogle Scholar
  20. G.S. Choe, C.Z. Cheng, J. Lee, B.J. Lynch, S.K. Antiochos, C.R. Devore, T.H. Zurbuchen, AGU Spring Meeting Abstracts (2005), p. 2 Google Scholar
  21. R.M. Close, C.E. Parnell, E.R. Priest, Sol. Phys. 225, 21–46 (2004) ADSCrossRefGoogle Scholar
  22. G.R. Cook, D.H. Mackay, D. Nandy, Astrophys. J. 704, 1021–1035 (2009) ADSCrossRefGoogle Scholar
  23. T.G. Cowling, Magnetohydrodynamics (Adam Hilger, Bristol, 1976) MATHGoogle Scholar
  24. I.J. Craig, Astron. Astrophys. 487, 1155–1161 (2008) ADSMATHCrossRefGoogle Scholar
  25. I.J. Craig, Y.E. Litvinenko, Astrophys. J. 667, 1235–1242 (2007) ADSCrossRefGoogle Scholar
  26. I.J.D. Craig, A.N. McClymont, Astrophys. J. 371, L41 (1991) ADSCrossRefGoogle Scholar
  27. I.J. Craig, A.N. McClymont, Astrophys. J. 405, 207–215 (1993) ADSCrossRefGoogle Scholar
  28. I.J. Craig, P.G. Watson, Astrophys. J. 393, 385–395 (1992) ADSCrossRefGoogle Scholar
  29. I.J. Craig, Y.E. Litvinenko, T. Senanayake, Astron. Astrophys. 433, 1139–1143 (2005) ADSCrossRefGoogle Scholar
  30. I. De Moortel, Philos. Trans. R. Soc. A 363, 2743 (2005) ADSCrossRefGoogle Scholar
  31. I. De Moortel, S.J. Bradshaw, Sol. Phys. 252, 101–119 (2008) ADSCrossRefGoogle Scholar
  32. I. De Moortel, A.W. Hood, J. Ireland, T.D. Arber, Astron. Astrophys. 346, 641 (1999) ADSGoogle Scholar
  33. I. De Moortel, J. Ireland, R.W. Walsh, Astron. Astrophys. 355, L23 (2000) ADSGoogle Scholar
  34. B. De Pontieu, S.W. McIntosh, M. Carlsson et al., Science 318, 1574 (2007) ADSCrossRefGoogle Scholar
  35. C.E. DeForest, J.B. Gurman, Astron. Astrophys. 501, L217 (1998) ADSGoogle Scholar
  36. J.W. Dungey, Philos. Mag. 44, 725 (1953) Google Scholar
  37. J.W. Dungey, Electromagnetic Phenomena in Cosmical Physics, IAU Symposium 6 (1958), p. 135 Google Scholar
  38. P.M. Edwin, B. Roberts, Sol. Phys. 88, 179–191 (1983) ADSCrossRefGoogle Scholar
  39. R. Erdélyi, V. Fedun, Science 318, 1572 (2007) ADSCrossRefGoogle Scholar
  40. R. Erdélyi, M. Goossens, Astron. Astrophys. 213, 273 (1994) MATHGoogle Scholar
  41. R. Erdélyi, M. Goossens, Astron. Astrophys. 294, 575 (1995) ADSGoogle Scholar
  42. R. Erdélyi, J.G. Doyle, M.E. Perez, K. Wilhelm, Astron. Astrophys. 337, 287 (1998) ADSGoogle Scholar
  43. T. Forbes, Sol. Phys. 117, 97 (1988) ADSCrossRefGoogle Scholar
  44. G. Fruit, I.J.D. Craig, Astron. Astrophys. 448, 753–761 (2006) ADSCrossRefGoogle Scholar
  45. K. Galsgaard, Å. Nordlund, J. Geophys. Res. 102, 231–248 (1997) ADSCrossRefGoogle Scholar
  46. K. Galsgaard, G.J. Rickard, R.V. Reddy, Å. Nordlund, Publ. Astron. Soc. Pac. Conf. Ser. 111, 82 (1996) ADSGoogle Scholar
  47. K. Galsgaard, G.J. Rickard, R.V. Reddy, Å. Nordlund, Adv. Space Res. 19, 1785–1788 (1997a) ADSCrossRefGoogle Scholar
  48. K. Galsgaard, R.V. Reddy, G.J. Rickard, Sol. Phys. 176, 299–325 (1997b) ADSCrossRefGoogle Scholar
  49. K. Galsgaard, E.R. Priest, V.S. Titov, J. Geophys. Res. 108, 1–12 (2003) CrossRefGoogle Scholar
  50. G.A. Gary, Sol. Phys. 203, 71 (2001) ADSCrossRefGoogle Scholar
  51. R.A. Harrison, A.W. Hood, C.D. Pike, Astron. Astrophys. 392, 319 (2002) ADSCrossRefGoogle Scholar
  52. A.B. Hassam, Astrophys. J. 399, 159–163 (1992) ADSCrossRefGoogle Scholar
  53. A.B. Hassam, R.P. Lambert, Astrophys. J. 472, 832 (1996) ADSCrossRefGoogle Scholar
  54. J. Heyvaerts, E.R. Priest, Astron. Astrophys. 117, 220 (1983) ADSMATHGoogle Scholar
  55. J.V. Hollweg, Astrophys. J. 306, 730–739 (1986) ADSCrossRefGoogle Scholar
  56. A.W. Hood, S.J. Brooks, A.N. Wright, Proc. R. Soc. A 458, 2307 (2002) MathSciNetADSMATHCrossRefGoogle Scholar
  57. A.R. Inglis, V.M. Nakariakov, Astron. Astrophys. 493, 259–266 (2009) ADSCrossRefGoogle Scholar
  58. A.R. Inglis, V.M. Nakariakov, V.F. Melnikov, Astron. Astrophys. 487, 1147–1153 (2008) ADSCrossRefGoogle Scholar
  59. D.B. Jess, M. Mathioudakis, R. Erdélyi, P.J. Crockett, F.P. Keenan, D.J. Christian, Science 323, 1582 (2009) ADSCrossRefGoogle Scholar
  60. J.A. Kilmchuck, P.J. Cargill, Astrophys. J. 553, 440 (2001) ADSCrossRefGoogle Scholar
  61. B. Kliem, M. Karlický, A.O. Benz, Astron. Astrophys. 360, 715 (2000) ADSGoogle Scholar
  62. B. Kliem, I.E. Dammasch, W. Curdt, K. Wilhelm, Astrophys. J. 568, L61 (2002) ADSCrossRefGoogle Scholar
  63. S. Landi, M. Velli, G. Einaudi, Astrophys. J. 624, 392–401 (2005) ADSCrossRefGoogle Scholar
  64. D.W. Longcope, Living Rev. Sol. Phys. 2 (2005). http://www.livingreviews.org/lrsp-2005-7
  65. D.W. Longcope, C.E. Parnell, Sol. Phys. 254, 51 (2009) ADSCrossRefGoogle Scholar
  66. B.J. Lynch, S.K. Antiochos, C.R. Devore, T.H. Zurbuchen, AGU Fall Meeting Abstracts (2004), p. 400 Google Scholar
  67. P. MacNeice, S.K. Antiochos, A. Phillips, D.S. Spicer, C.R. DeVore, K. Olson, Astrophys. J. 614, 1028 (2004) ADSCrossRefGoogle Scholar
  68. M. Mathioudakis, J.H. Seiradakis, D.R. Williams, S. Avgoloupis, D.S. Bloomfield, R.T.J. McAteer, Astron. Astrophys. 403, 1101–1104 (2003) ADSCrossRefGoogle Scholar
  69. M. Mathioudakis, D.S. Bloomfield, D.B. Jess, V.S. Dhillon, T.R. Marsh, Astron. Astrophys. 456, 323–327 (2006) ADSCrossRefGoogle Scholar
  70. K.G. McClements, A. Thyagaraja, N. Ben Ayed, L. Fletcher, Astrophys. J. 609, 423 (2004) ADSCrossRefGoogle Scholar
  71. K.G. McClements, N. Shah, A. Thyagaraja, J. Plasma Phys. 72, 571–585 (2006) ADSCrossRefGoogle Scholar
  72. A.M.D. McDougall, A.W. Hood, Sol. Phys. 246, 259 (2007) ADSCrossRefGoogle Scholar
  73. J.A. McLaughlin, A.W. Hood, Astron. Astrophys. 420, 1129–1140 (2004) ADSCrossRefGoogle Scholar
  74. J.A. McLaughlin, A.W. Hood, Astron. Astrophys. 435, 313–325 (2005) ADSCrossRefGoogle Scholar
  75. J.A. McLaughlin, A.W. Hood, Astron. Astrophys. 452, 603–613 (2006a) ADSMATHCrossRefGoogle Scholar
  76. J.A. McLaughlin, A.W. Hood, Astron. Astrophys. 459, 641–649 (2006b) ADSCrossRefGoogle Scholar
  77. J.A. McLaughlin, J.S.L. Ferguson, A.W. Hood, Sol. Phys. 251, 563–587 (2008) ADSCrossRefGoogle Scholar
  78. J.A. McLaughlin, I. De Moortel, A.W. Hood, C.S. Brady, Astron. Astrophys. 493, 227–240 (2009) ADSCrossRefGoogle Scholar
  79. U. Mitra-Kraev, L.K. Harra, D.R. Williams, E. Kraev, Astron. Astrophys. 436, 1041 (2005) ADSCrossRefGoogle Scholar
  80. D.A. Murray, Differential Equations (Longmans, Green, New York, 1927) Google Scholar
  81. V.M. Nakariakov, Adv. Space Res. 39, 1804 (2006) ADSCrossRefGoogle Scholar
  82. V.M. Nakariakov, V.F. Melnikov, Space Sci. Rev. 149, 119 (2009) ADSCrossRefGoogle Scholar
  83. V.M. Nakariakov, B. Roberts, Sol. Phys. 159, 399 (1995) ADSCrossRefGoogle Scholar
  84. V.M. Nakariakov, E. Verwichte, Living Rev. Sol. Phys. 2 (2005). http://www.livingreviews.org/lrsp-2005-3
  85. V.M. Nakariakov, B. Roberts, K. Murawski, Sol. Phys. 175, 93–105 (1997) ADSCrossRefGoogle Scholar
  86. V.M. Nakariakov, L. Ofman, E.E. Deluca, B. Roberts, J.M. Davila, Science 285, 862 (1999) ADSCrossRefGoogle Scholar
  87. V.M. Nakariakov, C. Foullon, E. Verwichte, N.P. Young, Astron. Astrophys. 452, 343–346 (2006) ADSCrossRefGoogle Scholar
  88. F. Oberhettinger, Tables of Fourier Transforms and Fourier Transforms of Distributions (Springer, Berlin, 1990) MATHGoogle Scholar
  89. L. Ofman, PhD thesis, University of Texas (1992) Google Scholar
  90. L. Ofman, L. Sui, Astrophys. J. 644, L149 (2006) ADSCrossRefGoogle Scholar
  91. L. Ofman, T.J. Wang, Astron. Astrophys. 482, L9 (2008) ADSCrossRefGoogle Scholar
  92. L. Ofman, P.J. Morrison, R.S. Steinolfson, Astrophys. J. 417, 748 (1993) ADSCrossRefGoogle Scholar
  93. L. Ofman, J.M. Davila, R.S. Steinolfson, Astrophys. J. 421, 360 (1994) ADSCrossRefGoogle Scholar
  94. L. Ofman, M. Romoli, G. Poletto, G. Noci, J.L. Kohl, Astrophys. J. 491, L111 (1997) ADSCrossRefGoogle Scholar
  95. T.J. Okamoto, S. Tsuneta, T.E. Berger et al., Science 318, 1577 (2007) ADSCrossRefGoogle Scholar
  96. E. O’Shea, D. Banerjee, S. Poedts, Astron. Astrophys. 400, 1065 (2003) ADSCrossRefGoogle Scholar
  97. C.E. Parnell, K. Galsgaard, Astron. Astrophys. 428, 595 (2004) ADSCrossRefGoogle Scholar
  98. C.E. Parnell, J.M. Smith, T. Neukirch, E.R. Priest, Phys. Plasmas 3, 759–770 (1996) ADSCrossRefGoogle Scholar
  99. C.E. Parnell, A.L. Haynes, K. Galsgaard, Astrophys. J. 675, 1656 (2008) ADSCrossRefGoogle Scholar
  100. D.I. Pontin, K. Galsgaard, J. Geophys. Res. 112, 3103–3116 (2007) CrossRefGoogle Scholar
  101. D.I. Pontin, A. Bhattacharjee, K. Galsgaard, Phys. Plasmas 14, 2106–2119 (2007) ADSGoogle Scholar
  102. E.R. Priest, S.W.H. Cowley, J. Plasma Phys. 14, 271 (1975) ADSCrossRefGoogle Scholar
  103. E.R. Priest, T. Forbes, Magnetic Reconnection (Cambridge University Press, Cambridge, 2000) MATHCrossRefGoogle Scholar
  104. E.R. Priest, V.S. Titov, Philos. Trans. R. Soc. 354, 2951–2992 (1996) MathSciNetADSMATHCrossRefGoogle Scholar
  105. S. Régnier, C.E. Parnell, A.L. Haynes, Astron. Astrophys. 484, L47 (2008) ADSCrossRefGoogle Scholar
  106. G.J. Rickard, V.S. Titov, Astrophys. J. 472, 840–852 (1996) ADSCrossRefGoogle Scholar
  107. B. Roberts, Sol. Phys. 69, 27 (1981) ADSCrossRefGoogle Scholar
  108. B. Roberts, SOHO 13: waves, oscillations and small-scale transient events in the solar atmosphere: a joint view from SOHO and TRACE, ESA SP-547 (2004), p. 1 Google Scholar
  109. B. Roberts, V.M. Nakariakov, Turbulence, Waves and Instabilities in the Solar Plasma. NATO Science Series (Kluwer, Dordrecht, 2003) Google Scholar
  110. I.N. Sneddon, Elements of Partial Differential Equations (McGraw-Hill, New York, 1957) MATHGoogle Scholar
  111. R.S. Steinolfson, L. Ofman, P.J. Morrison, Space plasmas: coupling between small and medium scale processes, AGU 1995, p. 189 Google Scholar
  112. Y. Taroyan, in Waves & Oscillations in the Solar Atmosphere: Heating and Magneto-Seismology. Proceedings of the International Astronomical Union, IAU Symposium, vol. 247 (Cambridge University Press, Cambridge, 2008), pp. 184–194 Google Scholar
  113. Y. Taroyan, R. Erdélyi, Space Sci. Rev. 149(1–4), 229–254 (2009). doi:10.1007/s11214-009-9506-9 ADSCrossRefGoogle Scholar
  114. Y. Taroyan, R. Erdélyi, T.J. Wang, S.J. Bradshaw, Astrophys. J. 659(2), L173–L176 (2007). doi:10.1086/517521 ADSCrossRefGoogle Scholar
  115. V.S. Titov, G. Hornig, Phys. Plasmas 7, 3350–3542 (2000) MathSciNetCrossRefGoogle Scholar
  116. S. Tomczyk, S.W. McIntosh, S.L. Keil, P.G. Judge, T. Schad, D.H. Seeley, J. Edmondson, Science 317, 1192 (2007) ADSCrossRefGoogle Scholar
  117. D. Tsiklauri, T.D. Arber, V.M. Nakariakov, Astron. Astrophys. 379, 1098 (2001) ADSMATHCrossRefGoogle Scholar
  118. D. Tsiklauri, V.M. Nakariakov, T.D. Arber, Astron. Astrophys. 395, 285 (2002) ADSCrossRefGoogle Scholar
  119. I. Ugarte-Urra, H.P. Warren, A.R. Winebarger, Astrophys. J. 662, 1293 (2007) ADSCrossRefGoogle Scholar
  120. R. Van der Linden, M. Goossens, A.W. Hood, Sol. Phys. 115, 235 (1998) CrossRefGoogle Scholar
  121. T. Van Doorsselaere, V.M. Nakariakov, E. Verwichte, Astrophys. J. 676, L73 (2008) ADSCrossRefGoogle Scholar
  122. T.J. Wang, S.K. Solanki, Astron. Astrophys. 421, L33 (2004) ADSCrossRefGoogle Scholar
  123. T.J. Wang, S.K. Solanki, W. Curdt, D.E. Innes, I.E. Dammasch, Astrophys. J. 574, L101 (2002) ADSCrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media B.V. 2010

Authors and Affiliations

  • J. A. McLaughlin
    • 1
  • A. W. Hood
    • 1
  • I. De Moortel
    • 1
  1. 1.School of Mathematics and StatisticsUniversity of St AndrewsSt AndrewsUK
  2. 2.School of Computing and EngineeringNorthumbria UniversityNewcastle Upon TyneUK

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