The locking and unlocking thresholds for tearing modes in a cylindrical tokamak

The locking and unlocking thresholds for tearing modes are in general different. In this work, the physics origin for this difference is illustrated from theory analysis, and a numerical procedure is developed to find both locking and unlocking thresholds. In particular, a new scaling law for the unlocking threshold that is valid in both weak and strong rotation regimes has been derived from the lowest amplitude of the RMP (resonant magnetic perturbation) allowed for the locked-mode solution. Above the unlocking threshold, the criterion for the phase-flip instability is extended to identify the entire locked-mode states. Two different regimes of the RMP amplitude in terms of the accessibility of the locked-mode states have been found. In the first regime, the locked-mode state may or may not be accessible depending on the initial conditions of an evolving island. In the second regime, the locked-mode state can always be reached regardless of the initial conditions of the tearing mode. The lowest RMP amplitude for the second regime is determined to be the mode-locking threshold. The different characteristics of the two regimes above the unlocking threshold reveal the underlying physics for the gap between the locking and unlocking thresholds and provide an explanation for the closely related and widely observed hysteresis phenomena in island evolution during the sweeping process of the RMP amplitude up and down across that threshold gap. (C) 2016 AIP Publishing LLC.