NONLINEAR-THEORY OF THE INTERACTION OF SOUND-WAVES WITH AN INHOMOGENEOUS MAGNETIZED PLASMA IN THE RESONANT SLOW-WAVE LAYER

The nonlinear theory of driven magnetohydrodynamic (MHD) waves in the resonant slow wave dissipative layer developed by Ruderman, Hollweg, a nd Goossens [Phys. Plasmas 4, 75 (1997)] is used to study the interact ion of sound waves with a static one-dimensional planar magnetic plasm a configuration, This configuration is a nonhomogeneous magnetic slab (region II) sandwiched by a homogeneous magnetic field free plasma (re gions I) and a homogeneous magnetic plasma (region III). The equilibri um magnetic field is unidirectional. An incoming sound wave is launche d from region I, and the equilibrium quantities and the parameters of the incoming sound wave are chosen in such a way that the wave is evan escent in region III and resonates with a slow local MHD wave in regio n II. The analysis is restricted to incoming sound waves with wave vec tors in the plane determined by the equilibrium magnetic field and the direction of inhomogeneity, so that there is no resonance with a loca l Alfven wave. Partial reflection of the incoming sound wave from regi on II generates an outgoing sound wave in region I. The nonlinearity p arameter introduced by Ruderman et al, is assumed to be small, and a r egular perturbation analysis is used to determine the wave solution. T he present analysis shows that nonlinearity in the resonant slow wave dissipative layer causes the following new effects in comparison with results obtained on the basis of linear theory: (i) higher harmonic co ntributions are generated in the wave solution in the dissipative laye r and also in the outgoing sound wave in addition to the fundamental h armonic. Outside the dissipative layer the amplitude of each harmonic contribution is of a higher order with respect to the small nonlineari ty parameter than inside the dissipative layer. This property reflects the fact that nonlinearity is only taken into account in the dissipat ive layer, so that the higher harmonic contributions to the outgoing w ave are only due to the interaction of the external plasma motions wit h the plasma motions in the dissipative layer; (ii) the coefficient of wave energy absorption and the absolute value of the jump in the norm al velocity are decreased. (C) 1997 American Institute of Physics.