Toroidal plasma rotation of the order of a few per cent of the Alfvén velocity can stabilize the resistive wall mode (RWM) and extend the operating regime of tokamaks from the conventional, ideal magnetohydrodynamic (MHD) no-wall limit up to the ideal MHD ideal-wall limit. The stabilizing effect has been measured in DIII-D passively by measuring the critical plasma rotation required for stability and actively by probing the plasma with externally applied resonant magnetic fields. The comparison of these measurements to predictions of rotational stabilization of the sound wave damping and of the kinetic damping model using the MARS-F code results in qualitative agreement, but also indicates the need for further refinement of the measurements and models.

Toroidal computations are performed using the MARS-F code [Liu Y Q et al 2000 Phys.Plasmas 7 3681], in order to understand correlations between the plasma response and the observed mitigation of the edge localized modes (ELM) using resonant magnetic perturbation fields in ASDEX Upgrade. In particular, systematic numerical scans of the edge safety factor reveal that the amplitude of the resonant poloidal harmonic of the response radial magnetic field near the plasma edge, as well as the plasma radial displacement near the X-point, can serve as good indicators for predicting the optimal toroidal phasing between the upper and lower rows of coils in ASDEX Upgrade. The optimal coil phasing scales roughly linearly with the edge safety factor 95 q , for various choices of the toroidal mode number n=1-4 of the coil configuration. The optimal coil phasing is also predicted to vary with the upper triangularity of the plasma shape in ASDEX Upgrade. Furthermore, multiple resonance effects of the plasma response, with continuously varying 95 q , are computationally observed and investigated.

This paper focuses on the coupling procedure between a 3-D integral formulation of the eddy currents problem and a linearized MHD model solved with a differential approach. The final aim is to develop a computational tool able to analyze the resistive wall modes of fusion plasmas, including the 3-D effects of nonaxisymmetric conducting structures surrounding the plasma