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 with two 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 profiles with the 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.