Study of the magnetic reconnection during the sawtooth instability

It is widely accepted that the sawtooth oscillations of the plasma parameters (temperature or density) in the central region of a tokamak are closely related to the configuration of the magnetic field. On the basis of some theoretical analysis on the onset of the (1,1) internal MHD mode into the nonlinear regime, we justify the use of the magnetic stochasticity hypothesis in order to explain the sawtooth crash and discuss the complete or incomplete nature of the reconnection. Two magnetic configurations, with monotonous safety factor, respectively with reversed magnetic shear, are studied using the Hamiltonian description of the magnetic field lines and of the mapping technique. A perturbation that contains not only the (1,1) mode, but also higher harmonics is considered and the role of these additional perturbations during the sawtooth crash is observed. The influence of the minimum value of the safety factor, the flatness coefficient and the amplitude of the perturbations on the reconnection process is systematically studied. It is shown that the mathematical models are able to generate poloidal cross sections of the magnetic field lines similar with the experimental ones and a scenario for the reconstruction of the magnetic field during the sawtooth instability is proposed.