Parametric decay of circularly polarized Alfvén waves: Multidimensional simulations in periodic and open domains

The nonlinear evolution of monochromatic large-amplitude circularly polarized Alfvén waves subject to the decay instability is studied via numerical simulations in one, two, and three spatial dimensions. The asymptotic value of the cross helicity depends strongly on the plasma beta: in the low beta case multiple decays are observed, with about half of the energy being transferred to waves propagating in the opposite direction at lower wave numbers, for each saturation step. Correspondingly, the other half of the total transverse energy (kinetic and magnetic) goes into energy carried by the daughter compressive waves and to the associated shock heating. In higher beta conditions we find instead that the cross helicity decreases monotonically with time towards zero, implying an asymptotic balance between inward and outward Alfvénic modes, a feature similar to the observed decrease with distance in the solar wind. Although the instability mainly takes place along the propagation direction, in the two and three-dimensional case a turbulent cascade occurs also transverse to the field. The asymptotic state of density fluctuations appears to be rather isotropic, whereas a slight preferential cascade in the transverse direction is seen in magnetic field spectra. Finally, parametric decay is shown to occur also in a non-periodic domain with open boundaries, when the mother wave is continuously injected from one side. In two and three dimensions a strong transverse filamentation is found at long times, reminiscent of density ray-like features observed in the extended solar corona and pressure-balanced structures found in solar wind data.