Nonlinear Effects in Resonant Layers in Solar and Space Plasmas
- 123 Downloads
The present paper reviews recent advances in the theory of nonlinear driven magnetohydrodynamic (MHD) waves in slow and Alfvén resonant layers. Simple estimations show that in the vicinity of resonant positions the amplitude of variables can grow over the threshold where linear descriptions are valid. Using the method of matched asymptotic expansions, governing equations of dynamics inside the dissipative layer and jump conditions across the dissipative layers are derived. These relations are essential when studying the efficiency of resonant absorption. Nonlinearity in dissipative layers can generate new effects, such as mean flows, which can have serious implications on the stability and efficiency of the resonance.
KeywordsSun Magnetohydrodynamics Resonant waves Nonlinearity
Unable to display preview. Download preview PDF.
- C.M. Bender, S.A. Országh, Advanced Methods for Scientists and Engineers: Asymptotics (Springer, New York, 1991) Google Scholar
- S.I. Braginskii, in Reviews of Plasma Physics, vol. 1, ed. by M.A. Leontovich (Consultants Bureau, New York, 1965), p. 205 Google Scholar
- R. Erdélyi, PhD Thesis. K.U. Leuven, Belgium (1996) Google Scholar
- J.P. Goedbloed, Lecture Notes on Ideal Magnetohydrodynamics. Rijnhuizen Report, 1983 Google Scholar
- M. Goossens, in Advances in Solar System Magnetohydrodynamics, ed. by E.R. Priest, A.W. Hood (Cambridge University Press, Cambridge, 1991) Google Scholar
- M. Goossens, R. Erdélyi, M.S. Ruderman, Space Sci. Rev. (2010, this issue). doi: 10.1007/s11214-010-9702-7
- J.V. Hollweg, in Mechanisms of Chromospheric and Coronal Heating, ed. by P. Ulmschneider, E.R. Priest, R. Rosner (Springer, Berlin, 1991) Google Scholar
- M. Mathioudakis, D.J. Jess, R. Erdélyi, Space Sci Rev. (2010, this issue) Google Scholar
- E.R. Priest, Solar Magnetohydrodynamics (Reidel, Dordrecht, 2000) Google Scholar
- M.S. Ruderman, R. Erdélyi, in Waves in Dusty, Solar, and Space Plasmas, ed. by F. Verheest, M. Goossens, M.A. Hellberg, R. Bharuthram. AIP Conference Proceedings, vol. 537 (2000), p. 279 Google Scholar