Numerical modeling of the electron temperature crashes observed in Wendelstein 7-X stellarator experiments

Numerical calculations based on nonlinear two-fluid equations have been carried out to
understand the sawtooth-like crashes of electron temperature observed in Wendelstein 7-X stellarator experiments with electron cyclotron current drive (ECCD). The application of ECCD leads to non-monotonic radial profiles of the safety factor q with two q = 1 surfaces in the plasma core region. Using input parameters similar to the experiment, numerical calculations show two types of crashes of the central electron temperature depending on the growth of the internal kink mode coupled to double tearing modes. When the distance between two equilibrium q = 1 surfaces is sufficiently large, the internal kink mode leads to a fast radial displacement of the hot core from the center to the region of the q = 1 surfaces. In agreement with experimental observation, this causes a full crash of central electron temperature in about 20–30 microseconds. When the distance between the two q = 1 surfaces is not large enough, partial crashes of the central electron temperature are found. During these crashes the hot core only temporally moves outwards. Then it moves back, because the double tearing mode perturbation leads to an increase of the minimum q value about one.