Resonant absorption in expanding coronal magnetic flux tubes with uniform density

Aims. We investigate the transfer of energy between a fundamental standing kink mode and azimuthal Alfvén waveswithin an expanding coronal magnetic flux tube. We consider the process of resonant absorption in a loop with anon-uniform Alfvén frequency profile but in the absence of a radial density gradient.Methods. Using the three dimensional MHD code, Lare3d, we modelled a transversely oscillating magnetic flux tubethat expands radially with height. An initially straight loop structure with a magnetic field enhancement was allowedto relax numerically towards a force-free state before a standing kink mode was introduced. The subsequent dynamics,rate of wave damping and formation of small length scales are considered.Results. We demonstrate that the transverse gradient in Alfvén frequency required for the existence of resonant fieldlines can be associated with the expansion of a high field-strength flux tube from concentrated flux patches in the lowersolar atmosphere. This allows for the conversion of energy between wave modes even in the absence of the transversedensity profile typically assumed in wave heating models. As with standing modes in straight flux tubes, small scalesare dominated by the vorticity at the loop apex and by currents close to the loop foot points. The azimuthal Alfvénwave exhibits the structure of the expanded flux tube and is therefore associated with smaller length scales close to thefoot points of the flux tube than at the loop apex.Conclusions. Resonant absorption can proceed throughout the coronal volume, even in the absence of visible, dense, loopstructures. The flux tube and MHD waves considered are difficult to observe and our model highlights how estimatinghidden wave power within the Sun’s atmosphere can be problematic. We highlight that, for standing modes, the globalproperties of field lines are important for resonant absorption and coronal conditions at a single altitude will not fullydetermine the nature of MHD resonances. In addition, we provide a new model in partial response to the criticism thatwave heating models cannot self-consistently generate or sustain the density profile upon which they typically rely.