Rotational stabilization of the resistive wall mode by coupling to a dissipative rational surface

Fusion power from a tokamak increases as β2 (β is the ratio of the plasma and magnetic field pressures) and so the mitigation of instabilities such as the resistive wall mode (RWM), that can prevent high β operation, is important. Stabilization of the RWM with a plasma rotation frequency of below 1% ΩA, where ΩA is the Alfvénic rotation frequency, has been observed in a number of tokamaks. An analytical model for this stabilization, in a cylindrical plasma with a resonant layer, is discussed here. The layer theory of Porcelli (1987 Phys. Fluids30 1734) is used to provide a model of the physics within the resonant layer. A dispersion relation connecting the plasma equilibrium to the layer physics in a rotating plasma is developed. Two mechanisms for RWM stabilization are investigated. The first includes viscosity in the resonant layer. The second assumes that stabilization occurs in the transition from one layer response to another. These models indicate a priori that there is a large parameter space where stabilization of the RWM by rotation is possible. However, if experimentally realistic timescales and rotation, namely O(1)% ΩA, are considered then only a small window for stabilization exists. It is therefore unlikely that these mechanisms explain the observed experimental RWM stabilization. It seems that other physical effects, such as toroidal mode coupling in the outer equilibrium or pressure gradients in a toroidal geometry, will be responsible for stabilization.