  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.
