  The radial structure of the continuous spectrum of shear Alfven 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, we keep only curvature
effects responsible for the beta-induced gap in the low-frequency part of the
continuous spectrum. 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 Alfven 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 Alfven eigenmodes (MiAE). Due to
the frequency dependence of the shear Alfven wave continuum on the
magnetic-island size, the possibility of utilizing MiAE frequency scalings as a
novel magnetic-island diagnostic is also discussed.
