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Numerical investigation of active control of tearing mode by magnetic coils and the role of Δ′

Magnetic feedback stabilization of the tearing mode (TM) is numerically investigated, utilizing the MARS-F code (Liu et al 2000 Phys. Plasmas 7 3681) for toroidal tokamak equilibria. With control coil configurations assumed in this study, magnetic feedback partially or fully stabilizes the TM, with either vanishing or finite equilibrium pressure. The best control is achieved by the combination of internal active coils and internal poloidal sensors. The internal and external tearing indices are evaluated for the close-loop system, based on the MARS-F computed mode eigenvalue and eigenfunction, respectively. In the absence of the favorable curvature effect, these two indices are real-valued and quantitatively agree well with each other. For the equilibrium with finite pressure gradient at the mode rational surface, the favorable average curvature effect becomes important and the close-loop tearing index also becomes complex-valued, partly due to interaction of the feedback system with the dissipative wall eddy current response. Isolating the inner layer and outer region response to magnetic feedback, with either proportional or proportional-derivative actions, allows to establish that feedback stabilization of the TM occurs mainly due to modification of the behavior of the external ideal solution, further confirming the analytic result reported in He et al 2021 Phys. Plasmas 28 012504.