Interaction of sound waves with an inhomogeneous magnetized plasma in a strongly nonlinear resonant slow-wave layer

The nonlinear theory of driven magnetohydrodynamic (MHD) waves in resonant slow-wave layers developed by Ruderman et al. [Phys. Plasmas 4, 75 (1997)] is used to study the interaction of sound waves with a one-dimensional plan ar magnetic plasma configuration. The physical problem studied here is the same as that considered by Ruderman et al. [Phys. Plasmas 4, 91 (1997)]. Th e difference is in the description of the wave motion in the resonant layer . Ruderman et al. assumed that dissipation dominates nonlinearity in the re sonant layer and considered the nonlinear term in the governing equation fo r the wave motion in the resonant layer as a perturbation. In contrast, it is assumed in the present paper that nonlinearity dominates dissipation in the resonant layer. The solution to the governing equation for the wave mot ion in the resonant layer is obtained in the approximation of strong nonlin earity, and it is shown that the amplitude of the wave motion saturates whe n the Reynolds number tends to infinity. This solution is then used to deri ve the nonlinear connection formula that determines the jump across the res onant layer in the velocity component in the direction of inhomogeneity. Th e nonlinear connection formula is, in turn, used to obtain a nonlinear one- dimensional integral equation describing the outgoing sound wave, which app ears owing to partial reflection of the incoming sound wave from the inhomo geneous plasma. The solution to this integral equation is obtained in the f orm of a sinusoidal wave under the assumption that an incoming sound wave c ontains the fundamental harmonic only. The coefficient of wave-energy absor ption is calculated analytically in the long-wavelength approximation and n umerically for arbitrary wavelengths.