Abstract
The linear theory of MHD resonant waves in inhomogeneous plasmas is reviewed. The review starts from discussing the properties of driven resonant MHD waves. The dissipative solutions in Alfvén and slow dissipative layers are presented. The important concept of connection formulae is introduced. Next, we proceed on to non-stationary resonant MHD waves. The relation between quasi-modes of ideal MHD and eigenmodes of dissipative MHD are discussed. The solution describing the wave motion in non-stationary dissipative layers is given. It is shown that the connection formulae remain valid for non-stationary resonant MHD waves. The initial-value problem for resonant MHD waves is considered. The application of theory of resonant MHD waves to solar physics is discussed.
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H. Alfvén, Nature 150, 405 (1942)
J. Andries, M. Goossens, Astron. Astrophys. 368, 1083 (2001a)
J. Andries, M. Goossens, Astron. Astrophys. 375, 1100 (2001b)
J. Andries, W.J. Tirry, M. Goossens, Astrophys. J. 531, 561 (2000)
J. Andries, M. Goossens, J.V. Hollweg, I. Arregui, T. Van Doorsselaere, Astron. Astrophys. 430, 1109 (2005a)
J. Andries, I. Arregui, M. Goossens, Astrophys. J. 624, L57 (2005b)
J. Andries, I. Arregui, M. Goossens, Astron. Astrophys. 497, 265 (2009a)
J. Andries, T. Van Doorsselaere, B. Roberts, G. Verth, E. Verwichte, R. Erdélyi, Space Sci. Rev. 149, 3 (2009b)
K. Appert, K. Gruber, J. Vaclavik, Phys. Fluids 17, 1471 (1974)
K. Appert, B. Balet, K. Gruber, F. Troyon, J. Vaclavik, Plasma Phys. Control. Fusion 2, 43 (1981)
K. Appert, J. Vaclavik, L. Villard, Phys. Fluids 27, 432 (1984)
I. Arregui, R. Oliver, J.L. Ballester, Astron. Astrophys. 402, 1129 (2003)
I. Arregui, R. Oliver, J.L. Ballester, Astron. Astrophys. 425, 729 (2004a)
I. Arregui, R. Oliver, J.L. Ballester, Astrophys. J. 602, 1006 (2004b)
I. Arregui, T. Van Doorsselaere, J. Andries, M. Goossens, D. Kimpe, Astron. Astrophys. 441, 361 (2005)
I. Arregui, J. Andries, T. Van Doorsselaere, M. Goossens, S. Poedts, Astron. Astrophys. 463, 333 (2007a)
I. Arregui, J. Terradas, R. Oliver, J.L. Ballester, Astron. Astrophys. 466, 1145 (2007b)
I. Arregui, J. Terradas, R. Oliver, J.L. Ballester, Sol. Phys. 246, 213 (2007c)
I. Arregui, J.L. Ballester, M. Goossens, Astrophys. J. 676, L77 (2008a)
I. Arregui, R. Oliver, J.L. Ballester, Astrophys. J. 642, L141 (2008b)
M.J. Aschwanden, Philos. Trans. R. Soc. A 364, 417 (2006)
M.J. Aschwanden, L. Fletcher, C.J. Schrijver, D. Alexander, Astrophys. J. 520, 880 (1999)
M.J. Aschwanden, B. De Pontieu, C.J. Schrijver, A.M. Tilte, Sol. Phys. 206, 99 (2002)
M.J. Aschwanden, R. Nightingale, J. Andries, T. Van Doorsselaere, M. Goossens, Astrophys. J. 598, 1375 (2003)
B. Balet, K. Appert, J. Vaclavik, Plasma Phys. Control. Fusion 24, 1005 (1982)
I. Ballai, R. Erdélyi, Sol. Phys. 180, 65 (1998)
I. Ballai, M.S. Ruderman, Space Sci. Rev. (2010, this issue)
I. Ballai, R. Erdélyi, M.S. Ruderman, Phys. Plasmas 5, 2264 (1998a)
I. Ballai, M.S. Ruderman, R. Erdélyi, Phys. Plasmas 5, 252 (1998b)
D. Banerjee, R. Erdélyi, R. Oliver, E. O’Shea, Sol. Phys 246, 3 (2007)
L.R. Bellot Rubio, H. Balthasar, M. Collados, R. Schliechenmeier, Astron. Astrophys. 403, L47 (2003)
A. Bondeson, R. Iacono, A. Bhattacharjee, Phys. Fluids 30, 2167 (1987)
S.I. Braginskii, Rev. Plasma Phys. 1, 205 (1965)
P. Brekke, D.M. Hassler, K. Wilhelm, Sol. Phys. 175, 349 (1997)
J.P. Boris, Ph.D. Thesis Princeton University, UMI Dissertation Services, Ann Arbor, Michigan (1968), 172 p.
V.M. C̆adez̆, Á. Csík, R. Erdélyi, M. Goossens, Astron. Astrophys. 326, 1241 (1997)
J. Chae, K. Ahn, E.-K. Lim, G.S. Choe, T. Sakurai, Astrophys. J. 689, 73 (2008)
L. Chen, A. Hasegawa, Phys. Fluids 17, 1399 (1974a)
L. Chen, A. Hasegawa, J. Geophys. Res. 79, 1024 (1974b)
L. Chen, A. Hasegawa, J. Geophys. Res. 79, 1033 (1974c)
N.F. Cramer, The Physics of Alfvén Waves (Wiley-VCH, New York, 2001)
Á. Csík, R. Erdélyi, V.M. C̆adez̆, Sol. Phys. 172, 61 (1997)
Á. Csík, V.M. C̆adez̆, M. Goossens, Astron. Astrophys. 339, 215 (1998)
A. De Groof, M. Goossens, Astron. Astrophys. 356, 724 (2000)
A. De Groof, M. Goossens, Astron. Astrophys. 386, 691 (2002)
A. De Groof, K. Paes, M. Goossens, Astron. Astrophys. 386, 681 (2002)
I. De Moortel, Space Sci. Rev. 149, 65 (2009)
B. De Pontieu, S.W. McIntosh, M. Carlsson, V.H. Hansteen, T.D. Tarbell et al., Science 318, 1574 (2007)
G.A. Doschek, U. Feldman, J.D. Bohlin, Astrophys. J. Lett. 205, 177 (1976)
J.G. Doyle, E. O’Shea, R. Erdélyi, K.P. Dere, D.G. Socker et al., Sol. Phys. 173, 243 (1997)
J.G. Doyle, M. Madjarska, I. Roussev, L. Teriaca, J. Giannikakis, Astron. Astrophys. 396, 255 (2002)
M. Dymova, M.S. Ruderman, Sol. Phys. 229, 79 (2005)
M. Dymova, M.S. Ruderman, Astron. Astrophys. 457, 1059 (2006a)
M. Dymova, M.S. Ruderman, Astron. Astrophys. 459, 241 (2006b)
P.M. Edwin, B. Roberts, Sol. Phys. 88, 179 (1983)
G. Einaudi, Y. Mok, J. Plasma Phys. 34, 259 (1985)
R. Erdélyi, PhD Thesis, K.U. Leuven, Belgium (1996)
R. Erdélyi, Sol. Phys. 171, 49 (1997)
R. Erdélyi, Sol. Phys. 180, 213 (1998)
R. Erdélyi, in MHD Waves Astrophysical Plasmas, ed. by J.L. Ballester, B. Roberts (UIB Press, 2001), pp. 69–78
R. Erdélyi, in Solar Variability: From Core to Outer Frontiers, ed. by A. Wilson, vol. 506 (ESA, Noordwijk, 2002), p. 869
R. Erdélyi, in Beyond the Spherical Sun: A New era for Helio- and Asteroseismology, ed. by K. Fletcher, vol. 624 (ESA, Noordwijk, 2006a), p. 15.1
R. Erdélyi, Philos. Trans. R. Soc. A 364, 351 (2006b)
R. Erdélyi, I. Ballai, Sol. Phys. 186, 67 (1999)
R. Erdélyi, I. Fedun, Science 38, 1572 (2007)
R. Erdélyi, V. Fedun, Sol. Phys. 263, 63 (2010)
R. Erdélyi, M. Goossens, Astrophys. Space Sci. 213, 273 (1994)
R. Erdélyi, M. Goossens, Astron. Astrophys. 294, 575 (1995)
R. Erdélyi, M. Goossens, Astron. Astrophys. 313, 664 (1996)
R. Erdélyi, Y. Taroyan, J. Geophys. Res. 108, 1043 (2003)
R. Erdélyi, M. Goossens, M.S. Ruderman, Sol. Phys. 161, 123 (1995)
R. Erdélyi, I. Ballai, M. Goossens, Astron. Astrophys. 368, 662 (2001)
R. Erdélyi, K. Al-Ghafri, R. Morton, Sol. Phys. (2010, submitted)
J.P. Goedbloed, Lecture notes on ideal magnetohydrodynamics. Rijnhuizen Report, 83-145, 1983
J.P. Goedbloed, S. Poedts, Principles of Magnetohydrodynamics (Cambridge University Press, Cambridge, 2004)
M. Goossens, in Advances in Solar System Magnetohydrodynamics (Cambridge University Press, Cambridge, 1991), p. 135
M. Goossens, in Waves & Oscillations in the Solar Atmosphere: Heating and Magneto-Seismology, ed. by R. Erdélyi, C.A. Mendoza-Briceño. Proceedings of IAU Symposium, vol. 247 (2008), p. 228
M. Goossens, A. De Groof, Phys. Plasmas 8, 2371 (2001)
M. Goossens, J.V. Hollweg, Sol. Phys. 145, 19 (1993)
M. Goossens, S. Poedts, Astrophys. J. 384, 348 (1992)
M. Goossens, M.S. Ruderman, Phys. Scr. T60, 171 (1995)
M. Goossens, J.V. Hollweg, T. Sakurai, Sol. Phys. 138, 233 (1992)
M. Goossens, M.S. Ruderman, J.V. Hollweg, Sol. Phys. 157, 75 (1995)
M. Goossens, J. Andries, M.J. Aschwanden, Astron. Astrophys. 394, L39 (2002a)
M. Goossens, A. De Groof, J. Andries, ESA 505, 137 (2002b)
M. Goossens, A. De Groof, J. Andries, Roy Soc. Lond. Philos. Trans., Ser. A 364, 433 (2006)
M. Goossens, I. Arregui, J.L. Ballester, T.J. Wang, Astron. Astrophys. 484, 851 (2008)
M. Goossens, J. Terradas, J. Andries, I. Arregui, J.L. Ballester, Astron. Astrophys. 503, 213 (2009)
W. Grossmann, R.A. Smith, Astrophys. J. 332, 476 (1988)
W. Grossmann, J. Tataronis, Z. Phys. 261, 217 (1973)
A. Hasegawa, L. Chen, Phys. Fluids 17, 1924 (1974)
A. Hasegawa, C. Uberoi, The Alfvén wave, DOE/TIC-11197, 1982
J. He, E. Marsch, C. Tu, H. Tian, Astrophys. J. 705, L217 (2009a)
J. He, C. Tu, E. Marsch, L.J. Guo, S. Yao, H. Tian, Astron. Astrophys. 497, 525 (2009b)
J. Heyvaerts, E.R. Priest, Astron Astrophys. 117, 220 (1983)
J.V. Hollweg, Astrophys. J. 312, 880 (1987a)
J.V. Hollweg, Astrophys. J. 320, 875 (1987b)
J.V. Hollweg, Astrophys. J. 335, 1005 (1988)
J.V. Hollweg, Comput. Phys. Rep. 12, 205 (1990)
J.V. Hollweg, G. Yang, J. Geophys. Res. 93, 5423 (1988)
J.V. Hollweg, G. Yang, V.M. C̆adez̆, B. Gakovic̆, Astrophys. J. 349, 335 (1990)
B. Inhester, J. Geophys. Res. 91, 1509 (1986)
J.A. Ionson, Astrophys. J. 226, 650 (1978)
J.A. Ionson, Sol. Phys. 100, 289 (1985)
D.B. Jess, M. Mathioudakis, R. Erdélyi, P.J. Crockett, F.P. Keenan et al., Science 323, 1582 (2009)
J.M. Kappraff, M. Tataronis, J. Plasma Phys. 18, 209 (1977)
R. Keppens, T.J. Bogdan, M. Goossens, Astrophys. J. 436, 372 (1994)
M.G. Kivelson, D.J. Southwood, J. Geophys. Res. 91, 4345 (1986)
L.J. Lanzerotti, H. Fukunishi, A. Hasegawa, L. Chen, Phys. Rev. Lett. 31, 624 (1973)
M.A. Lee, B. Roberts, Astrophys. J. 301, 430 (1986)
Y.-Q. Lou, Astrophys. J. 350, 452 (1990)
M.P. McEwan, G.R. Donnelly, A.J. Diaz, B. Roberts, Astron. Astrophys. 460, 893 (2006)
M.P. McEwan, G.R.A.J. Diaz, B. Roberts, Astron. Astrophys. 481, 819 (2008)
M. Mathioudakis, R. Erdélyi, D.J. Jess, Space Sci. Rev. (2010, this issue)
Y. Mok, G. Einaudi, J. Plasma Phys. 33, 199 (1985)
R. Morton, R. Erdélyi, Astrophys. J. 707, 750 (2009)
R. Morton, R. Erdélyi, Astron. Astrophys. 519, 43 (2010)
R. Morton, A.W. Hood, R. Erdélyi, Astron. Astrophys. 512, 23 (2010)
V.M. Nakariakov, L. Ofman, E.E. DeLuca, B. Roberts, J. Davila, Science 285, 862 (1999)
L. Ofman, J.M. Davila, R.S. Steinolfson, Astrophys. J. 421, 360 (1994)
L. Ofman, J.M. Davila, R.S. Steinolfson, Astrophys. J. 444, 471 (1995)
T.J. Okamoto, S. Tsuneta, T.E. Berger, K. Ichimoto, Y. Katsukawa et al., Science 318, 1577 (2007)
B. Pintér, R. Erdélyi, Space Sci. Rev. (2010, this issue)
B. Pintér, M. Goossens, Astron. Astrophys. 347, 321 (1999)
B. Pintér, R. Erdélyi, M. Goossens, Astron. Astrophys. 466, 377 (2007)
S. Poedts, W. Kerner, Phys. Rev. Lett. 66, 2871 (1991)
S. Poedts, W. Kerner, J. Plasma Phys. 47, 139 (1992)
S. Poedts, M. Goossens, W. Kerner, Sol. Phys. 123, 83 (1989a)
S. Poedts, W. Kerner, M. Goossens, J. Plasma Phys. 42, 27 (1989b)
S. Poedts, M. Goossens, W. Kerner, Astrophys. J. 360, 279 (1990a)
S. Poedts, M. Goossens, W. Kerner, Computer Phys. Commun. 59, 75 (1990b)
S. Poedts, M. Goossens, W. Kerner, Computer Phys. Commun. 59, 95 (1990c)
I.C. Rae, B. Roberts, Moth. Not. R. Astron. Soc. 201, 1171 (1982)
B. Roberts, Sol. Phys. 69, 27 (1981)
M.S. Ruderman, Sol. Phys. 131, 11 (1991)
M.S. Ruderman, J. Plasma Phys. 63, 43 (2000)
M.S. Ruderman, Astron. Astrophys. 409, 287 (2003)
M.S. Ruderman, Phys. Plasmas 16, 042109 (2009)
M.S. Ruderman, B. Roberts, Astrophys. J. 577, 475 (2002)
M.S. Ruderman, A.N. Wright, J. Geophys. Res. 103, 26573 (1998)
M.S. Ruderman, A.N. Wright, Phys. Plasmas 7, 3515 (2000)
M.S. Ruderman, W. Tirry, M. Goossens, J. Plasma Phys. 54, 129 (1995)
M.S. Ruderman, J.V. Hollweg, M. Goossens, Phys. Plasmas 4, 75 (1997a)
M.S. Ruderman, M. Goossens, J.V. Hollweg, Phys. Plasmas 4, 91 (1997b)
M.S. Ruderman, G. Verth, R. Erdélyi, Astrophys. J. 686, 694 (2008)
T. Sakurai, M. Goossens, J.V. Hollweg, Sol. Phys. 133, 227 (1991a)
T. Sakurai, M. Goossens, J.V. Hollweg, Sol. Phys. 133, 247 (1991b)
C.J. Schrijver, D.S. Brown, Astrophys. J. 537, L69 (2000)
C.J. Schrijver, M.J. Aschwanden, A.M. Tilte, Sol. Phys. 206, 69 (2002)
Z. Sedlaček, J. Plasma Phys. 5, 239 (1971)
R.A. Smith, C.K. Goertz, W. Grossmann, Geophys. Res. Lett. 13, 1380 (1986)
R. Soler, R. Oliver, L.J. Ballester, M. Goossens, Astrophys. J. Lett. 695, L166 (2009a)
R. Soler, R. Oliver, L.J. Ballester, Astrophys. J. 707, 662 (2009b)
D.J. Southwood, Planet. Space Sci. 22, 483 (1974)
D.J. Southwood, M.G. Kivelson, J. Geophys. Res. 91, 4345 (1986)
H.C. Spruit, Sol. Phys. 75, 3 (1982)
R.S. Steinolfson, J.M. Davila, Astrophys. J. 415, 354 (1993)
H. Stenuit, S. Poedts, M. Goossens, Sol. Phys. 147, 13 (1993)
H. Stenuit, R. Erdélyi, M. Goossens, Sol. Phys. 161, 139 (1995)
H. Stenuit, R. Keppens, M. Goossens, Astron. Astrophys. 331, 392 (1998)
H. Stenuit, W.J. Tirry, R. Keppens, M. Goossens, Astron. Astrophys. 342, 863 (1999)
Y. Taroyan, R. Erdélyi, Phys. Plasmas 9, 3121 (2002)
Y. Taroyan, R. Erdélyi, Phys. Plasmas 10, 266 (2003a)
Y. Taroyan, R. Erdélyi, J. Geophys. Res. 108, 1301 (2003b)
Y. Taroyan, M.S. Ruderman, Space Sci. Rev. (2010, this issue)
J. Tataronis, W. Grosmann, Z. Phys. 261, 203 (1973)
J. Terradas, Space Sci. Rev. 149, 255 (2009)
J. Terradas, R. Oliver, J.L. Ballester, Astrophys. J. 642, 533 (2006a)
J. Terradas, R. Oliver, J.L. Ballester, Astrophys. J. 650, L91 (2006b)
J. Terradas, J. Andries, M. Goossens, Astron. Astrophys. 469, 1135 (2007)
J. Terradas, I. Arregui, R. Oliver, J.L. Ballester, J. Andries et al., Astrophys. J. 687, L115 (2008)
J. Terradas, M. Goossens, I. Ballai, Astron. Astrophys. 515, A46 (2010a)
J. Terradas, M. Goossens, G. Verth, Astron. Astrophys. (2010b, accepted). doi:10.1051/0004-6361/201014845
W.J. Tirry, M. Goossens, J. Geophys. Res. 100, 23687 (1995)
W.J. Tirry, M. Goossens, Astrophys. J. 471, 501 (1996)
W.J. Tirry, M. Goossens, B. Pinter, V.M. C̆adez̆, P. VanLommel, Astrophys. J. 503, 422 (1998a)
W.J. Tirry, V.M. C̆adez̆, R. Erdélyi, M. Goossens, Astron. Astrophys. 332, 786 (1998b)
S. Tomczyk, S.W. McIntosh, S.L. Keil, P.G. Judge, T. Schad et al., Science 317, 1192 (2007)
S. Tomczyk, S.W. McIntosh, Astrophys. J. 697, 1384 (2009)
S. Van Doorsselaere, J. Andries, S. Poedts, M. Goossens, Astrophys. J. 606, 1223 (2004)
S. Van Doorsselaere, V.M. Nakariakov, E. Verwichte, Astrophys. J. 676, L73 (2008)
P. Van Lommel, M. Goossens, Sol. Phys. 187, 357 (1999)
P. Van Lommel, A. De Bosscher, J. Andries, M. Goossens, Sol. Phys. 205, 1 (2002)
S. Vasheghani Farahani, T. Van Doorsselaere, E. Verwichte, V.M. Nakariakov, Astron. Astrophys. 498, L29 (2009)
G. Verth, R. Erdélyi, Astron. Astrophys. 486, 1015 (2008)
G. Verth, J. Terradas, M. Goossens, Astrophys. J. 718, L102 (2010)
H.P. Warren, J.T. Mariska, K. Wilhelm, P. Lemaire, Astrophys. J. Lett. 484, L91 (1997)
D.G. Wentzel, Astron. Astrophys. 76, 20 (1979a)
D.G. Wentzel, Astrophys. J. 233, 756 (1979b)
A.N. Wright, W. Allan, J. Geophys. Res. 101, 17399 (1995)
A.N. Wright, G.J. Rickard, Astrophys. J. 444, 458 (1995)
G. Yang, J.V. Hollweg, J. Geophys. Res. 96, 13807 (1991)