Effects of 3D topology in the dissipation of Alfven waves propagating in force-free magnetic equilibria

We study the propagation and the dissipation of small amplitude Alfven waves in 3D magnetic fields, using the WKB approximation. In a previous work (Petkaki et al. 1998) we showed that in a cahotic 3D magnetic field small scales are formed exponentially in time, corresponding to a dissipation time t(d) proportional to log S, S being the Reynolds and/or the Lundquist number. In a 2D structure dissipation is dominated by phase-mixing and, for large S, it is much slower (t(d) proportional to S-1/3). In the present work we consider force-free magnetic fields in which both 2D phase-mixing and exponential wavevector growth are present. We study both the competition between the two scalings and the transition between the 2D and the 3D regimes. In simple configurations (ABC field) the two scaling laws are both verified, but in spatially distinct regions. In more complex configurations, two regimes in the parameter space are observed, in which either 2D or the 3D scaling law holds. The fast 3D dissipation regime is found at large Reynolds/Lundquist numbers S similar to 10(10)-10(12), even for weakly 3D configurations. In coronal conditions, Alfven waves subject to such mechanisms are efficiently dissipated within a fraction of a solar radius. The distribution of peak dissipated power resulting from our model displays power law profiles in different ranges, indicating the intermittent character of this dissipation mechanism.