Effects of field line expansion on Alfvén waves and vortices

Abstract

Simulations and observations of the solar atmosphere often reveal the presence of torsional Alfv\'en waves and vortices with sufficient power to heat the solar corona and accelerate the solar wind. We challenge the long-held view that low-frequency Alfv\'en waves are suppressed due to inhomogeneities and steep spatial gradients in the atmosphere. Alfv\'en waves and vortices in a stratified solar atmosphere are modelled with the aim of calculating and comparing their energy flux for different field line geometries. We show that the general problem of linear Alfv\'en wave propagation along field lines of arbitrary geometry can be reduced to a set of Klein-Gordon equations for the perturbations of the magnetic field and velocity. Solutions and corresponding energy fluxes are constructed for three cases with different expansion rates of the field lines in the lower atmosphere. Expansion rates that are associated with cut-off free propagation in the lower atmosphere suppress the perturbation amplitudes and the corresponding energy flux. These include the uniform field model and the thin flux tube model. A counterexample with an intermediate field line expansion rate and non-vanishing cut-offs exhibits consistently large perturbation amplitudes and unrestricted energy flux across the entire frequency spectrum. Field lines with different expansion rates and geometries in the lower atmosphere can significantly alter the amplitudes of the Alfv\'en waves and vortices and the extent of the energy flux entering the corona.