2D continuous spectrum of shear Alfven waves in the presence of a magnetic island

The radial structure of the continuous spectrum of shear Alfven modes is calculated in the presence of a magnetic island in tokamak plasmas. Modes with the same helicity as the magnetic island are considered in a slab model approximation. In this framework, with an appropriate rotation of the coordinates the problem reduces to two dimensions. Geometrical effects due to the shape of the flux surface's cross-section are retained to all orders. On the other hand, we neglect toroidal couplings but fully take into account curvature effects responsible for the beta-induced gap in the low-frequency part of the continuous spectrum. New continuum accumulation points are found at the O-point of the magnetic island. The beta-induced Alfven eigenmodes (BAE) continuum accumulation point is found to be positioned at the separatrix flux surface. The most remarkable result is the modification of the BAE continuum accumulation point frequency, due to the presence of the magnetic island.