Dissipation of Alfven Waves in Force‐free Magnetic Fields: Competition between Phase Mixing and Three‐dimensional Effects

Abstract

The propagation and the dissipation of small-amplitude Alfvenic wave packets 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 td proportional to log S is obtained, S being the Reynolds and/or the Lundquist number. This scaling corresponds to a dissipation much faster than that of phase mixing (td ∝ S1/3). In the present work we consider force-free magnetic fields in which both phase mixing and exponential divergence are present, and we study both the competition between the two scalings and the transition between phase mixing and the three-dimensional fast dissipation regimes. In a simpler equilibrium structure (the Arnold-Beltrami-Childress field) we found that both phenomenologies take place, in spatially separated regions. So, a fraction of the initial wave energy, proportional to the relative amplitude of the chaotic regions, is dissipated by the faster mechanism. For more complex fields (two-dimensional flux tubes perturbed by three-dimensional small-amplitude components) two different regimes exist: the dissipation time follows either the three-dimensional or the phase-mixing scaling, when S is above or below a threshold. The threshold value decreases with increasing the amplitude of the three-dimensional force-free component. These results are discussed with reference to the problem of coronal heating.