Evolution of safety factor profiles in sawteeth

Two different definitions of the safety factor are applied to investigate the evolution of the safety factor profile during normal sawteeth, the stationary state, and the incomplete reconnection. It is found that the safety factor profiles from the old definition are sometimes inconsistent with the Poincare plots of the magnetic field during sawteeth. The old safety factor always indicates that the safety factor around the magnetic axis is flattened and equal to 1.0 with the development of the kink instability. However, the Poincare plots of the magnetic field lines indicate that the topology of the magnetic field around the magnetic axis has not been changed. To solve the inconsistency, we propose a new definition of the safety factor, in which the poloidal angle relative to the new twisted magnetic axis is used instead of the poloidal angle to the original axis. With the new definition, the safety factor profiles are consistent with Poincare plots of the magnetic field. We also find that the safety factor profiles are significantly different from the two different q definitions. With the new q definition, the safety factor at the magnetic axis q0 remains unchanged in almost the entire period of a sawtooth and jumps up to 1.0 near the end during normal sawteeth; in the non-axisymmetric equilibrium, q0 is still far below 1.0; q0 remains its initial value throughout the incomplete reconnection.