Three-scale expansion of the solution of the magnetohydrodynamic equations and the Reynolds equation for a tokamak

An asymptotic solution of the magnetohydrodynamic equations is constructed. The three scales asymptotic solution describes the non-linear evolution of small, rapidly varying perturberation of equilibrium. It is shown, that an anisotropic coherent structure appears in the linear nonstability situation, and the structures evolution directs to energy interaction between high-frequency and low-frequency waves. The closed system of MHD Reynolds equations for anisotropic atructure is derived.