Propagation and dissipation of long MHD waves in a strongly nonuniform plasma

The propagation and the anomalous dissipation of long magnetohydrodynamic waves (characterized by the wavelength λ) in a plasma with small-scale (of the order of a), large-amplitude spatial nonuniformities of density and magnetic field are investigated for λ >> a . The criteria for defining suitable averaging procedures in order to treat the propagation of long waves in terms of macroscopic plasma parameters, independently of the specific nature of the small scale fluctuations, are given. It is demonstrated that the presence of the small-scale random stratification of the plasma affects substantially the dispersive properties of MHD waves with respect to the uniform plasma case. In particular, new branches of the dispersion relation may appear in the form of extra modes of the slow type, the collisional dissipation of the waves may be strongly enhanced by a factor (λ / a)^2, a collisionless dissipation may take place due to the Landau damping-type coupling between the long MHD waves and the longitudinal perturbations excited inside the sheets of plasmas where the magnetic field is concentrated.