PARAMETRIC-INSTABILITIES OF A LARGE-AMPLITUDE CIRCULARLY-POLARIZED ALFVEN-WAVE - LINEAR GROWTH IN 2-DIMENSIONAL GEOMETRIES

The growth of parametric instabilities, which may lead to the development of a turbulent cascade, is studied using a magnetohydrodynamic (MHD) code that permits nonlinear couplings in the parallel direction to the ambient magnetic field and one perpendicular direction. Compressibility is included in the form of a polytropic equation of state. Parametric instabilities associated with a parallel-propagating decay instability are found to dominate the low-beta case. An obliquely propagating filamentationlike instability dominates the high-beta case. The nonlinear growth of the nth harmonic of a daughter wave growing as a factor of n times the fundamental's growth rate is found in both cases. Nonlinear saturation is caused by the parallel decay instability in the low-beta case and by the oblique filamentationlike instability in the high-beta case.