Rotating wall, the error-field-induced torque and the problem of the error field shielding in tokamaks

The electromagnetic torque on the toroidal plasma is calculated analytically. The derivations basically follow the line described in [1]. The main difference is that the torque is calculated now with account of the resistive wall rotation. The model is based on the Maxwell equations for the magnetic perturbation and Ohm's law for the currents in the resistive rotating wall. The model assumes a thin wall, which is a standard approach, a linear plasma response to the applied resonant magnetic perturbation, which is a good model for naturally small error fields, a stationary rotation of the wall and, finally, adopts the cylindrical geometry. The obtained formulas are used for analysis of the error field shielding by a liquid metal wall in tokamaks predicted in a similar model with a conclusion there that a flowing liquid metal wall can prevent resonance amplification of the error field by the plasma near its no-wall stability limit. Our theory does not support this concept. Instead, it gives the expressions for the torque without singularities near the no-wall stability limit, with or without the wall rotation. Such singularities have been a reason for the 'dramatic difference' of these two cases in the mentioned theory. In contrast, our model does not allow severe peaking of the torque below the RWM stability limit, even if the most pessimistic estimate will be used for the torque. The reason of the differences is explained, the consequences are discussed and the new predictions are compared with available experimental data. Also the experiments are proposed to model the addressed effects on the existing tokamaks with conventional non-rotating walls. The competing theories can therefore be validated against the available data using the developed experimental technique. Finally, the question is discussed whether or not we need a liquid wall for mitigating the error field effects. (author)