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

The nonlinear evolution of monochromatic large-amplitude circularly polariz ed Alfven waves subject to the decay instability is studied via numerical s imulations 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 tran sferred to waves propagating in the opposite direction at lower wave number s, for each saturation step. Correspondingly. the other half of the total t ransverse energy (kinetic and magnetic) goes into energy carried by the dau ghter 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 Alfvenic modes, a feature similar to the observed decrease with dis tance in the solar wind. Although the instability mainly takes place along the propagation direction, in the two and three-dimensional case a turbulen t cascade occurs also transverse to the field. The asymptotic state of dens ity fluctuations appears to be rather isotropic, whereas: a slight preferen tial 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 front o ne side. In two and three dimensions a strong transverse filamentation is f ound at long times, reminiscent of density ray-like features observed ill t he extended solar corona and pressure-balanced structures found ill solar w ind data.