NONLINEAR-THEORY OF RESONANT SLOW WAVES IN DISSIPATIVE LAYERS

Linear dissipative magnetohydrodynamics (MHD) shows that driven MHD wa ves in magnetic plasmas with high Reynolds number exhibit a near reson ant behaviour if the frequency of the wave becomes equal to the local Alfven or slow frequency of a magnetic surface. This near resonant beh aviour is confined to a thin dissipative layer which embraces the reso nant magnetic surface. Although the driven MHD waves have small amplit udes far away from the resonant magnetic surface, this near-resonant b ehaviour in the dissipative layer may cause a breakdown of linear theo ry. In the present paper we deal with the nonlinear behaviour of drive n MHD waves in the slow wave dissipative layer. The method of matched asymptotic expansions is used to obtain the nonlinear equation for wav e variables inside the dissipative layer. The concept of connection fo rmulae introduced into the theory of linear resonant MHD waves by Saku rai, Goossens, and Hollweg [Sol. Phys. 133, 227 (1991)] is extended to include nonlinear effects in the dissipative layer for slow resonant waves. The absorption of the slow resonant wave in the dissipative lay er generates a shear flow parallel to the magnetic surfaces with a cha racteristic velocity of the order of epsilon(1/2) where epsilon is the dimensionless amplitude of perturbations far away from the dissipativ e layer. (C) 1997 American Institute of Physics.