Achieving magnetohydrodynamic (MHD) stability of magnetically confined plasmas is crucial in obtaining a high β plasma suitable for a fusion reactor. Here β is the ratio of the plasma pressure to magnetic pressure. For obtaining high β plasmas, stabilization of dangerous ideal kink modes is required in current carrying tokamaks. The ideal kink modes can be stabilized by a perfect conducting wall placed sufficiently close to the plasma surface. However, when the wall has a finite conductivity, the mode cannot be stabilized completely, even if the wall is close to the plasma surface. In this situation, resistive wall modes (RWMs), which grow slowly in time, become unstable and it is important to stabilize RWMs for a stationary tokamak. It is noted that the linear RWMs can be stabilized by plasma rotation. However, when the plasma rotation decreases below a critical level, the RWMs begins to grow as shown in the experiments[1]. As the RWM grows, the plasma rotation frequency decreases clearly. Finally, the high β plasma phase of discharge is destroyed.
Nonlinear behavior of RWM is studied by solving numerically the reduced MHD equations in a low beta cylindrical plasma model. The vacuum is treated with the pseudo-vacuum model. In ref.[2], the effect of poloidal rotation on nonlinear RWM was studied. We found that, when a resistive wall is close to the plasma surface, RWM grows significantly by suppressing the poloidal rotation in the nonlinear phase. Both the experimental and numerical results suggest that for stabilization of the RWM the plasma rotation is not sufficient and the feedback control is required. The effect of feedback coil on nonlinear RWM with poloidal rotation is investigated numerically in the present work.

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