Abstract
This review is concerned with a recent development in the analytic theory of resonant Alfvén waves in nonuniform magnetic flux tubes in the solar atmosphere. It discusses how an analytic study of simplified versions of the dissipative MHD equations for plasmas with high Reynolds numbers leads to the fundamental conservation law and simple analytic solutions for resonant Alfvén waves. Asymptotic analysis of the analytic solutions gives jump conditions that connect the solutions across the dissipative layer. The analytic results enable us to understand the basic dynamics and energetics of resonant Alfvén waves and help us with the interpretation of results of of numerical simulations in dissipative MHD. in addition, they make an accurate computation of resonant Alfvén waves possible without having to solve numerically the dissipative MHD equations.
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References
Appert, K., Gruber, R. and Vaclavik, J. (1974) Phys. Fluids 17, 1471.
Boris, J.P. (1968) Resistively modified normal modes of an inhomogeneous incompressible plasma. Ph.D. Thesis, Princeton University, UMI Dissertation Services, Ann Arbor Michigan, p. 172.
Cally, P.S. and Bogdan, T.J. (1993) Astrophys. J. 402, 721.
Chen, L. and Hasegawa, A. (1974) Phys. Fluids 17, 1399.
Davila, J.M. (1987) Astrophys. J. 317, 514.
Erdélyi, R. and Goossens, M. (1995) Astron. Astrophys. 294, 575.
Erdélyi, R., Goossens, M. and Ruderman, M.S. (1995) Solar Phys., 161, 123.
Edwin, P. and Roberts, B. (1987) MHD Waves in the Solar Atmosphere, in: Small-scale Plasma Processes, Proceedings of the 21st ESLAB Symposium ESA SP-275, p. 169.
Goedbloed, J.P. (1975) Phys. Fluids 15, 1090.
Goedbloed, J.P. (1983) Lecture Notes on Ideal Magnetohydrodynamics. Rijnhuizen Report 83–145, 113.
Goossens, M. (1991) MHD waves and wave heating in non-uniform plasmas, in: eds. Priest, E.R. and Hood A.W., Advances in Solar System Magnetohydrodynamics, Cambridge University Press, Cambridge, p. 135.
Goossens, M., Hollweg, J.V. and Sakurai, T. (1992) Solar Phys. 138, 233.
Goossens, M. and Hollweg, J.V. (1993) Solar Phys. 145, 19.
Goossens, M., Poedts, S. and Hermans, D. (1985) Solar Phys. 102, 51.
Goossens, M. and Poedts, S. (1992) Astrophys. J. 384, 348.
Goossens, M. and Ruderman, M.S. (1995)Physica Scripta 51, 1.
Goossens, M., Ruderman, M.S. and Hollweg, J.V. (1995) Solar Phys. 157, 75.
Grossman, W. and Smith, R.A. (1988) Astrophys. J. 332, 476.
Grossman, W. and Tataronis, J. (1973) Z. Phys. 261, 217.
Halberstadt, G. (1994) Magnetic heating of the solar corona. Photospheric excitation and coronal dissipation of Alfvén waves. Ph.D. thesis, Vrije Universiteit Amsterdam, Amsterdam.
Halberstadt, G. and Goedbloed, J. (1993) Astron. Astrophys., 280, 647.
Halberstadt, G. and Goedbloed, J. (1995a) Astron. Astrophys., 301, 559.
Halberstadt, G. and Goedbloed, J. (1995b) Astron. Astrophys., 301, 577.
Hasegawa, A. and Chen, L. (1974) Phys. Fluids 17, 1924.
Hollweg, J.V. (1987a) Astrophys. J. 312, 880.
Hollweg, J.V. (1987b) Astrophys. J. 320, 875.
Hollweg, J.V. (1988) Astrophys. J., 335, 1005.
Hollweg, J.V. (1990) Computer Phys. Rep. 12, 205.
Hollweg, J.V. (1991) Alfvén waves, in: eds. Ulmschneider, P., Priest, E.R. and Rosner, R., Mechanisms of Chromospheric and Coronal Heating, Springer-Verlag, Berlin, p. 423.
Hollweg, J.V. and Yang, G. (1988) J. Geophys. Res. 93, 5423.
Ionson, J.A. (1978) Astrophys. J. 226, 650.
Ionson, J.A. (1985) Solar Phys. 100, 289.
Kappraff, J.M. and Tataronis, J. (1977) J. Plasma Physics 18, 209.
Keppens, R., Bogdan, T.J. and Goossens, M. (1994) Astrophys. J. 436, 372.
Keppens, R. (1995a) On the interaction of acoustic oscillations with magnetic flux tubes in the solar photosphere, Ph.D. Thesis, K.U. Leuven.
Keppens, R. (1995b) Solar Phys., 161, 251.
Keppens, R. (1995c) Astrophys. J., submitted.
Kuperus, M., Ionson, J.A., and Spicer, D. (1981) Ann. Rev. Astron. Astrophys. 19, 7.
Lou, Y.-Q. (1990) Astrophys. J. bf 350, 452.
Mok, Y. and Einaudi, G. (1985) J. Plasma Phys. 33, 199.
Narain, U. and Ulmschneider, P. (1995) Space Sci. Rev., accepted for publication.
Nayfeh, A.H. (1981) Introduction to Perturbation Techniques, Wiley-interscience, New York.
Ofman, L., Davila, J.M. and Steinolfson, R.S. (1994a) Astrophys. J. 421, 360.
Ofman, L., Davila, J.M. and Steinolfson, R.S. (1994b) Geophys. Res. Let. 21, 2259.
Ofman, L., Davila, J.M. and Steinolfson, R.S. (1994c) Nonlinear studies of coronal heating by the resonant absorption of Alfvén waves, in: eds. Rusin, V., Heinzel, P. and Vial, J.-C., IAU Colloquium 144, Solar Coronal Structures, VEDA, Bratislava, p. 473.
Ofman, L. and Davila, J.M. (1995) J. Geophys. Res., submitted.
Pao, Y.P. (1975), Nuclear Fusion 18, 1629.
Poedts, S., Hermans, D. and Goossens, M. (1985) Astron. Astrophys. 151, 16.
Poedts, S. and Goossens, M. (1987) Solar Phys. 109, 265.
Poedts, S. and Goossens, M. (1988) Astron. Astrophys. 198, 331.
Poedts, S., Goossens, M. and Kerner, W. (1989a) Solar Phys, 123, 83.
Poedts, S., Kerner, W. and Goossens, M. (1989b) J. Plasma Physics 42, 27.
Poedts, S., Goossens, M. and Kerner, W. (1990a) Astrophys. J. 360, 279.
Poedts, S., Goossens, M. and Kerner, W. (1990b) Computer Phys, Comm. 59, 75.
Poedts, S. and Kerner, W. (1992) J. Plasma Phys. 47, 139.
Poedts, S. and Boynton, G.C. (1995) Astron. Astrophys., accepted.
Roberts, B. (1988) Solar Magnetohydrodynamics, in: ed. B. Buti Cometary and Solar Plasma Physics, World Scientific, Singapore.
Roberts, B. (1991) MHD waves in the Sun, in: eds. Priest, E.R. and Hood A.W., Advances in Solar System Magnetohydrodynamics, Cambridge University Press, Cambridge, p. 105.
Ruderman, M.S., Hollweg, J.V. and Goossens, M. (1995), in preparation.
Sakurai, T., Goossens, M. and Hollweg, J.V. (1991a) Solar Phys. 133, 227.
Sakurai, T., Goossens, M. and Hollweg, J.V. (1991b) Solar Phys, 133, 247
Spruit, H.C. and Bogdan, T.J. (1992) Astrophys. J. 391, L109.
Stenuit, H., Poedts, S. and Goossens, M. (1993) Solar Phys. 147, 13.
Stenuit, H., Erdélyi, R. and Goossens, M. (1995) Solar Phys., 161, 139.
Tataronis, J. and Grossmann, W. (1973) Z. Phys. 261, 203.
Thompson, M.J. and Wright, A.N. (1993) J. Geophys. Res. 98, 15541.
Tirry, W. and Goossens, M. (1995) J. Geophys. Res., accepted.
Wright, A.N. and Thompson, M.J. (1994) Phys. Plasmas 1, 691
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Goossens, M., Ruderman, M. (1996). MHD Waves in Magnetic Flux Tubes. In: Tsinganos, K.C. (eds) Solar and Astrophysical Magnetohydrodynamic Flows. NATO ASI Series, vol 481. Springer, Dordrecht. https://doi.org/10.1007/978-94-009-0265-7_4
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DOI: https://doi.org/10.1007/978-94-009-0265-7_4
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