Magnetohydrodynamic parametric instabilities driven by a standing Alfven wave in a low-beta plasma

The stability of a finite-amplitude standing Alfven ware of circular polarization in a low-beta plasma is studied using a set of nonlinearly coupled MHD wave equations. In the presence of a standing Alfven pump, two distinct gratings associated with the density fluctuations are excited: those due to the ponderomotive beating of the pump magnetic field, and those due the induced magnetic fluctuations. The roles played by the two gratings in the mode coupling are analysed. Both convective and purely growing regimes of the MHD parametric instabilities can be produced by a standing Alfven wave. In both regimes, the maximum growth rate increases as the pump amplitude increases, and decreases as beta increases. In the presence of the second grating, a new unstable convective regime appears that widens the overall instability bandwidth.