Numerical modelling of sawteeth and sawtooth-free regime

To better understand the sawteeth physics and the sawtooth-free regime associated with the hybrid scenario in tokamak experiments, numerical calculations up to quasi-steady state have been carried out for realistic middle-size tokamak plasma parameters, including the bootstrap current perturbation and basing on both the single- and two-fluid equations with the large aspect ratio approximation. Two types of the sawtooth crash are found in multiple sawteeth simulations: (1) For a low equilibrium bootstrap current fraction, the crash is caused by the internal kink mode, as expected; (2) When the bootstrap current density fraction is larger than 10% in the core region, however, the crash is caused by the non-ideal double kink mode, in contrary to the conventional understanding. In this case, a non-monotonic radial profile of the safety factor q with two q=1 surfaces emerges before the crash, caused by the bootstrap current density and plasma resistivity perturbations, although the original equilibrium has only single q = 1 surface. In both types of sawtooth crashes, the crash time in two-fluid simulations is tens of microseconds, as observed in experiments. Furthermore, for a relatively low ion density and finite bootstrap current density fraction, a transition from the sawtooth to the sawtooth-free regime is found, in which flat q profiles with the q value being about unity in the central region, similar to that observed in hybrid scenario experiments, are maintained by the dynamo effect. To enter into the sawtooth-free regime in two-fluid simulations, a much larger Alfvén velocity than that in single-fluid simulations is required due to the diamagnetic drift.