Shear Alfvén Waves within Magnetic Islands

Abstract We calculate Alfv\'en eigenmodes within a magnetic island (MiAE) which have been conjectured over a decade ago. Starting from a cylindrical plasma equilibrium, we calculate the complete metric of the island interior assuming an iota profile with a constant shear for Wendelstein 7-X (W7-X) parameters. Then, we solve the resulting magneto-hydrodynamic (MHD) equations inside the island optionally considering finite Larmor radius (FLR) corrections. We find various eigenmodes in the lowest gaps for $n=0$. The eigenmode with the lowest frequency shows a weakly non-linear dependence on the island width. This non-linear behaviour and the appearance of odd and even modes deviates qualitatively from an earlier frequency estimate.