Extended spectral scaling laws for shear-Alfven wave turbulence

In this paper, resonant interactions among three shear-Alfven waves is investigated in weak incompressible magnetohydrodynamics (MHD) turbulence, neglecting interactions involving the pseudo-Alfven waves. It is found that these interactions lead to a wave kinetic equation that has the same compact form as the full nonlinear MHD system in the highly anisotropic limit (k(perpendicular to)> k(parallel to)). These results have important implications for interpreting the effects of resonant three-wave interactions among shear-Alfven waves throughout k space. In particular, it shows that resonant three-wave interactions involving only shear-Alfven waves attempt to set up a k(perpendicular to)(s)(n)f(k(parallel to)) 3D shear-Alfven-wave spectrum (with -4 < n(s)<-2, and f an arbitrary function depending on the initial conditions). The results also provide a framework for estimating the time scale on which the three shear-Alfven-wave interactions transfer energy to larger k(perpendicular to) everywhere in the k(perpendicular to)-k(parallel to) plane. The compatibility of the results with previous predictions and the possible astrophysical implications of these extended spectral solutions for anisotropic plasmas is discussed. (c) 2006 American Institute of Physics.