External field treshold for the unlocking of magnetic islands in the presence of resistive wall effects and toroidal mode coupling

The unlocking of static resistive tearing modes by rotating external magnetic perturbations such as those which may arise from the natural tokamak error-field is discussed. For a single mode the balance between the accelerating torque imparted by the error-field and the braking torque due to the interaction of the mode with the wall sets a threshold for the error-field current [H. P. Furth ct al. Phys. Fluids 6, 459 (1963)], below which the mode frequency will not lock to the error-field frequency. If the mode resonant with the error-field is coupled to another mode with a rational surface located elsewhere in the plasma, the unlocking process is more elaborated and substantial modifications to the current threshold are expected. The present analysis may contribute to the explanation of some mode unlocking events in tokamak discharges with a non negligible error-field.