Nonlinear theory of the interaction of sound waves with an inhomogeneous magnetized plasma in the resonant slow wave layer

Abstract

The nonlinear theory of driven magnetohydrodynamic (MHD) waves in the resonant slow wave dissipative layer developed by Ruderman, Hollweg, and Goossens [Phys. Plasmas 4, 75 (1997)] is used to study the interaction of sound waves with a static one-dimensional planar magnetic plasma configuration. This configuration is a nonhomogeneous magnetic slab (region II) sandwiched by a homogeneous magnetic field free plasma (regions I) and a homogeneous magnetic plasma (region III). The equilibrium magnetic field is unidirectional. An incoming sound wave is launched 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 evanescent in region III and resonates with a slow local MHD wave in region II. The analysis is restricted to incoming sound waves with wave vectors in the plane determined by the equilibrium magnetic field and the direction of inhomogeneity, so that there is no resonance with a local Alfvén wave. Partial reflection of the incoming sound wave from region II generates an outgoing sound wave in region I. The nonlinearity parameter introduced by Ruderman et al. is assumed to be small, and a regular perturbation analysis is used to determine the wave solution. The 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 contributions are generated in the wave solution in the dissipative layer and also in the outgoing sound wave in addition to the fundamental harmonic. Outside the dissipative layer the amplitude of each harmonic contribution is of a higher order with respect to the small nonlinearity parameter than inside the dissipative layer. This property reflects the fact that nonlinearity is only taken into account in the dissipative layer, so that the higher harmonic contributions to the outgoing wave are only due to the interaction of the external plasma motions with the plasma motions in the dissipative layer; (ii) the coefficient of wave energy absorption and the absolute value of the jump in the normal velocity are decreased.