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

Abstract

The nonlinear theory of driven magnetohydrodynamic (MHD) waves in resonant slow-wave layers developed by Ruderman et al. [Phys. Plasmas4, 75 (1997)] is used to study the interaction of sound waves with a one-dimensional planar magnetic plasma configuration. The physical problem studied here is the same as that considered by Ruderman et al. [Phys. Plasmas4, 91 (1997)]. The difference is in the description of the wave motion in the resonant layer. Ruderman et al. assumed that dissipation dominates non-linearity in the resonant layer and considered the nonlinear term in the governing equation for 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 motion in the resonant layer is obtained in the approximation of strong nonlinearity, and it is shown that the amplitude of the wave motion saturates when the Reynolds number tends to infinity. This solution is then used to derive the nonlinear connection formula that determines the jump across the resonant layer in the velocity component in the direction of inhomogeneity. The nonlinear connection formula is, in turn, used to obtain a nonlinear one- dimensional integral equation describing the outgoing sound wave, which appears owing to partial reflection of the incoming sound wave from the inhomogeneous plasma. The solution to this integral equation is obtained in the form of a sinusoidal wave under the assumption that an incoming sound wave contains the fundamental harmonic only. The coefficient of wave-energy absorption is calculated analytically in the long-wavelength approximation and numerically for arbitrary wavelengths.