Spontaneous healing and growth of locked magnetic island chains in toroidal plasmas

Recent experiments have demonstrated that locked magnetic island chains in stellarator plasmas spontaneously heal under certain conditions, and spontaneously grow under others. A formalism initially developed to study magnetic island dynamics in tokamak plasmas is employed to investigate this phenomenon. It is found that island healing/growth transitions can be caused either by a breakdown in torque balance in the vicinity of the island chain, or by an imbalance between the various terms in the island width evolution equation. The scaling of the healing/growth thresholds with the standard dimensionless plasma parameters $β, ν∗$⁠, and $ρ∗$ is determined. In accordance with the experimental data, it is found that island healing generally occurs at high $β$ and low $ν∗$⁠, and island growth at low $β$ and high $ν∗$⁠. In further agreement, it is found that island healing is accompanied an ion poloidal velocity shift in the electron diamagnetic direction, and island growth by a velocity shift in the ion diamagnetic direction. Finally, it is found that there is considerable hysteresis in the healing/growth cycle, as is also seen experimentally.