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The present paper reviews recent advances in the theory of nonlinear driven magnetohydrodynamic (MHD) waves in slow and Alfven 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.
Solar photosphere and chromosphere are composed of weakly ionized plasma for which collisional coupling decreases with height. This implies a breakdown of some hypotheses underlying magnetohydrodynamics at low altitudes and gives rise to non-ideal MH
The solar corona is a typical example of a plasma with strongly anisotropic transport processes. The main dissipative mechanisms in the solar corona acting on slow magnetoacoustic waves are the anisotropic thermal conductivity and viscosity. Ballai e
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In the approximation of linear dissipative magnetohydrodynamics (MHD) it can be shown that driven MHD waves in magnetic plasmas with high Reynolds number exhibit a near resonant behaviour if the frequency of the wave becomes equal to the local Alfven
We explore the suggestions by Uzdensky (2007) and Cassak et al. (2008) that coronal loops heated by magnetic reconnection should self-organize to a state of marginal collisionality. We discuss their model of coronal loop dynamics with a one-dimension