Comprehensive linear stability studies of resistive modes are presented for Wendelstein 7-X-type stellarator equilibria with electron cyclotron current drive (ECCD). The external co-current drive leads to an increase of the rotational transform and the formation of one or two ι = 1 rational flux surfaces. Using the 3D linear stability CASTOR3D code, low n*-type resistive modes (n* = 1,2...,8 with n* being the dominant toroidal Fourier harmonic contributing to the mode) are investigated. We studied the dependence of their growth rates on plasma resistivity, parallel viscosity, and shape of the rotational transform profile (especially various distances between two ι = 1 flux surfaces). Similarly to tokamak configurations, single and double tearing modes, and internal resistive kink modes are found. In addition, modes oscillating between two n*-types of the same mode family are observed. The frequencies of those modes are in the range of ≈ 10–260 Hz. Equilibria with either a large distance between the ι = 1 flux surfaces, or a single ι = 1 surface are most unstable with respect to n* = 1 resistive kink modes. The latter finding fits to the experimental observation of sawtooth-like oscillations followed by a thermal quench in W7-X discharges with ECCD.
Pressure-driven relaxation instability in a current-free high-shear helical system