Nonlinear evolution of parametric instability of a large-amplitude nonmonochromatic Alfven wave

The nonlinear evolution of the parametric instability of a finite amplitude Alfven wave is studied in a one-dimensional geometry. The linear stage of this instability had been examined in a previous paper [Malara and Velli, P hys. Plasmas 3, 4427 (1996)], in which it has been shown that even a nonmon ochromatic broad-band wave is unstable. In the present paper, the time evol ution is followed up to saturation, by numerically integrating the full set of magnetohydrodynamic (MHD) equations. Several configurations of the Alfv enic pump wave, as well as different values of the plasma beta are examined . The saturation level of the instability does not depend on the spectral w idth of the pump wave, but it depends on the value of beta. For beta less t han or similar to 0.5 the final state is characterized by a cross-helicity similar to 0 and a moderate level of density fluctuations: The Alfvenic cor relation of the initial wave is completely destroyed, even for a broad-band initial spectrum. For beta=1 the final cross-helicity is closer to that of the initial wave, indicating a lower saturation level. The parametric proc ess appears to be nonlocal in the wave-vector space also in the nonmonochro matic case, this feature becoming more relevant with increasing beta. (C) 2 000 American Institute of Physics. [S1070-664X(00)03507-2].