Rotation and Locking of Magnetic Islands

Stationary magnetic perturbations are frequently observed to be followed by major disruptions [1–3]. They occur as a result of the locking of the plasma rotation, either by a resonant error field or through the interaction between a magnetic island and the resistive vessel wall [4,5]. This Letter examines the possibility of unlocking islands by injection of momentum. We find that inertial forces are destabilizing and lead to a threshold island width above which unlocking through momentum injection is impossible. Our results are in agreement with experimental observations [3]. The key property governing island rotation is that the plasma cannot flow across flux surfaces once the displacement amplitude exceeds the visco-resistive layer width [5]. It follows that the electrostatic potential, which acts as a stream function for the flow, must be constant on flux surfaces in the rest frame of the perturbation. The plasma velocity is thus proportional to the transverse magnetic field on each flux surface. The velocity inside the island, in particular, has odd parity about the Opoint. Since the velocity is continuous in the presence of viscosity, the even part of the velocity distribution must vanish immediately outside the separatrix. This boundary condition was violated in previous studies of island rotation [6–9]. The distortion of the flow caused by a magnetic perturbation gives rise to an inertial force proportional to the cross product of the velocity with the vorticity [8]. This force is balanced by a current directed along the axis of the island, Jz ­ 2ryyy0 yyBy , where yy and By are the transverse velocity and magnetic field, respectively, and r is the mass density. The current perturbation reaches its maximum negative amplitude outside the separatrix on either side of the O-point, where the stream lines are compressed. It thus constitutes a drive for magnetic reconnection. The origin of this drive is clearly the same as for the Kelvin-Helmholtz instability, namely, the reduction in kinetic energy resulting from the interchange of fast and slow moving fluid elements. The inertial destabilization must compete with the stabilizing effect of the viscous force [5]. This force opposes the change in plasma rotation caused by the island. It is proportional to the discontinuity in the