Phase mixing of propagating Alfvén waves

Abstract

The propagation and damping of shear Alfvén waves in an inhomogeneous medium, recently suggested as a candidate for heating the solar corona, is considered in detail. The fundamental wave solution found by Heyvaerts and Priest (1983) is checked against their assumptions and a range of self-consistency is provided. We analyze the wave behaviour outside this range, thus discovering new properties of the wave propagation. In the limit of weak damping (large magnetic and viscous Reynolds numbers, characteristic of the coronal situation) a uniformly valid solution is obtained by the method of multiple scales. For long wavelengths ("non geometrical optics"), the diffusion of energy in the direction transverse to the wave propagation is found to be important and leads to weaker damping laws than those found by Heyvaerts and Priest (1983). In the limit of weak phase mixing, the solution is obtained in terms of hypergeometric functions; at large heights it decays like z-o.3RTot1/2 eXp - (z/Λ)2, RTot being the total Reynolds number and Λ a damping length.