Coronal heating by phase-mixed shear Alfven waves.

The authors consider the physical processes which occur when a shear Alfvén wave propagates in a structure with a large gradient of the Alfvén velocity. Although these waves do not possess local resonances (unlike magneto acoustic modes) they nevertheless suffer intense phase mixing during which the oscillations of neighbouring field lines become rapidly out of phase. The authors study this effect and show that the resulting large growth of gradients dramatically enhances the viscous and ohmic dissipation. The cases of propagating and standing waves are considered, and a detailed calculation is given of the rate of dissipation achieved in a finite length structure like a loop, in the presence of a random excitation at its ends. The authors prove that, after a long enough time, phase mixing can actually ensure the dissipation of all the wave mechanical energy that a loop can pick up from the excitation, in agreement with a previous claim by Ionson. The general conclusion of the study is that phase mixing is the process most able to ensure the dissipation of shear Alfvén waves in loops and in open regions of strong reflectivity, and that loops, in particular, must be in a permanent state of Kelvin-Helmholtz and tearing turbulence.