External current threshold for the unlocking of an island in the presence of a resistive wall

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. A threshold error field current is shown to exist, below which the mode frequency will not lock to the error field frequency. The slowing down drag applied to the island by the resistive vessel of the tokamak and the unphased magnetic perturbation arising from the error field at the rational surface of the mode eventually set the island into an oscillatory motion around w » 0 Hz. An upper limit in the error field frequency exists above which the threshold current is insufficient for locking the mode frequency to the error field frequency. This limit depends on the island width, the local plasma density and the non-linear wall response to magnetic perturbations.