Dissipation of Alfven waves in complex 3D coronal force-free structures

The propagation and dissipation of Alfven waves in a three-dimensional inhomogeneous force-free equilibrium structure is considered. Assuming small wavelengths the wave propagation is described within the framework of a WKB theory. The equilibrium structure is a complex magnetic field, resulting from a superposition of several harmonics, which represents a model of the coronal magnetic field above a quiet-Sun region. The properties of wave dissipation are related to the topological complexity of the background magnetic field, and the typical scale law of fast dissipation is recovered. A partial reflection of waves is included in the model by calculating reflection and transmission coefficients of both Alfven and magnetosonic waves. An energy balance is derived between the wave energy dissipated inside the coronal structure and the energy lost through the lower boundary. We find that even for large values of the Reynolds number, a non-negligible fraction of the Alfven wave energy is dissipated inside the corona.