Resistive drift wave instability is investigated numerically in tokamak edge plasma confined by sheared slab magnetic field geometry with an embedded magnetic island. The focus is on the structural characteristics of eigenmode inside the island, where the density profile tends to be flattened. A transition of the dominant eigenmode occurs around a critical island width wc. For thin islands with a width below wc, two global long wavelength eigenmodes with approximately the same growth rate but different eigenfrequency are excited, which are stabilized by the magnetic island through two-dimensional mode coupling in both x and y (corresponding to radial and poloidal in tokamak) directions. On the other hand, a short wavelength eigenmode, which is destabilized by thick islands with a width above wc, dominates the edge fluctuation, showing a prominent structural localization in the region between the X-point and the O-point of the magnetic island. The main destabilization mechanism is identified as the mode coupling in the y direction, which is similar to the so-called toroidal coupling in tokamak plasmas. These three eigenmodes may coexist in the drift wave fluctuation for the island with a width around wc. It is demonstrated that the structural localization results mainly from the quasilinear flattening of density profile inside the magnetic island.

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