Shear Alfvén wave continuous spectrum within magnetic islands

The radial structure of the continuous spectrum of shear Alfvén waves is calculated in this paper within the separatrix of a magnetic island. Geometrical effects due to the noncircularity of the flux surface’s cross section are retained to all orders. On the other hand, only curvature effects responsible for the beta-induced gap in the low-frequency part of the continuous spectrum are kept. Modes with different helicity from that of the magnetic island are considered. The main result is that, inside a magnetic island, there is a continuous spectrum very similar to that of tokamak plasmas, where a generalized safety factor q can be defined and where a wide frequency gap is formed, analogous to the ellipticity induced Alfvén eigenmode gap in tokamaks. The presence of this gap is due to the strong eccentricity of the island cross section. The importance of the existence of such a gap is recognized in potentially hosting magnetic-island induced Alfvén eigenmodes (MiAE). Due to the frequency dependence of the shear Alfvén wave continuum on the magnetic-island size, the possibility of utilizing MiAE frequency scalings as a novel magnetic-island diagnostic is also discussed. PACS: 52.55.Tn, 52.35.Bj