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 (or slow) frequency of a magnetic surface. This near resonant behaviour is confined to a thin region, known as the dissipative layer, which embraces the resonant magnetic surface. Although driven MHD waves have small dimensionless amplitude far away from the resonant surface, this near-resonant behaviour in the dissipative layer may cause a breakdown of linear theory. Our aim is to study the nonlinear effects in the Alfven dissipative layer. In the present paper, the method of simplified matched asymptotic expansions developed for nonlinear slow resonant waves is used to describe nonlinear effects inside the Alfven dissipative layer. The nonlinear corrections to resonant waves in the Alfven dissipative layer are derived and it is proved that at the Alfven resonance (with isotropic/anisotropic dissipation) wave dynamics can be described by the linear theory with great accuracy.
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