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 magnet ic perturbations such as those which may arise from the natural tokamak err or field is discussed. A threshold error field current is shown to exist: b elow which the mode frequency will not lock to the error field frequency. T he slowing down drag applied to the island by the resistive vessel of the t okamak and the unphased magnetic perturbation arising from the error field at the rational surface of the mode eventually set the island into an oscil latory motion around omega approximate to 0 Hz. An upper limit in the error field frequency exists above which the threshold current is insufficient f or locking the mode frequency to the error field frequency. This limit depe nds on the island width, the local plasma density and the non-linear wall r esponse to magnetic perturbations.