Phase mixing of Alfvén waves in a stratified and radially diverging, open atmosphere

Phase mixing was proposed by Heyvaerts and Priest (1983) as a mechanism for heating the plasma in open magnetic field regions of coronal holes. Here the basic model is modified to include a gravitationally stratified density and a diverging background magnetic field. We present WKB solutions and use a numerical code to describe the effect of dissipation, stratification and divergence on phase mixing of Alfvén waves. It is shown that the wavelengths of an Alfvén wave is shortened as it propagates outwards which enhances the generation of gradients. Therefore, the convection of wave energy into heating the plasma occurs at lower heights than in a uniform model. The combined effect of a stratified density and a radially diverging background magnetic field on phase mixing of Alfvén waves depends strongly on the particular geometry of the configuration. Depending on the value of the pressure scale height, phase mixing can either be more or less efficient than in the uniform case.