Phase mixing of Alfvén waves in a stratified and open atmosphere

Phase mixing was introduced by Heyvaerts and Priest (1983) as a mechanism for heating the plasma in the open magnetic field regions of coronal holes. Here the basic process is modified to include a stratified atmosphere in which the density decreases with height. We present an analytical solution in the case of zero dissipation and use a numerical code in the non-zero dissipation case to describe the effect of stratification on phase mixing. The exponential damping behaviour derived by Heyvaerts and Priest is largely confirmed in the non stratified limit. However, it is shown that the decrease in density lengthens the oscillation wavelengths and thereby reduces the generation of transverse gradients. Furthermore we found that in a stratified atmosphere the perturbed magnetic field and velocity behave quite differently depending on whether we consider resistivity or viscosity. Ohmic heating is spread out over a greater height range in a stratified medium whereas viscous heating is not strongly influenced by the stratification.