Dissipation of Alfven waves in force-free magnetic fields: Competition between phase mixing and three-dimensional effects

The propagation and the dissipation of small-amplitude Alfvenic wave packet s in a three-dimensional magnetic field is studied in the WKB approximation . In a chaotic magnetic field nearby lines exponentially diverge; thus, in propagating packets small scales are formed exponentially in time. Related to this phenomenon, a dissipation time t(d) proportional to log S is obtain ed, S being the Reynolds and/or the Lundquist number. This scaling correspo nds to a dissipation much faster than that of phase mixing (t(d) proportion al to S-1/3). I, the present work we consider force-free magnetic fields in which both phase mixing and exponential divergence are present, and we stu dy both the competition between the two scalings and the transition between phase mixing and the three-dimensional fast dissipation regimes. In a simp ler equilibrium structure (the Arnold-Beltrami-Childress field) we found th at both phenomenologies take place, in spatially separated regions. So, a f raction of the initial wave energy, proportional to the relative amplitude of the chaotic regions, is dissipated by the faster mechanism. For more com plex fields (two-dimensional flux tubes perturbed by three-dimensional smal l-amplitude components) two different regimes exist: the dissipation time f ollows either the three-dimensional or the phase-mixing scaling, when S is above or below a threshold. The threshold value decreases with increasing t he amplitude of the three-dimensional force-free component. These results a re discussed with reference to the problem of coronal heating.