Thick-wall effects on the rotational stabilization of resistive wall modes in tokamaks

This paper is devoted to studying the combined effect of mode rotation and energy dissipation in the resistive wall on plasma stability. The problem is analysed on the basis of the energy approach complementing the standard methods of the traditional MHD theory of plasma stability. The key element that makes our model different from this theory and commonly used thin-wall approaches to the stability analysis of resistive wall modes (RWMs) is the incorporation of the skin effect. In the ideal MHD theory of plasma stability, the skin depth is, formally, zero. In contrast, the conventional thin-wall theory of RWM stability assumes a skin depth much larger than the wall thickness. The presented model considers the intermediate case with a finite skin depth compared with the wall thickness. This covers the modes in between the typical RWMs and the ideal MHD modes when wall resistivity still affects the mode dynamics. It is shown that, in this region, the growth rate of the locked modes must be substantially larger than that calculated in the thin-wall models. On the other hand, the fast RWMs can be completely stabilized by mode rotation above some critical level. Qualitatively, this corresponds to the rotational stabilization observed in the DIII-D tokamak and allowing the plasma operation above the no-wall stability limit (Strait et al 2003 Nucl. Fusion 43 430). This is the main result of this study, which is completely analytical with all dependences explicitly shown. In particular, the dispersion relations for the fast RWMs and the critical frequency of mode rotation necessary for rotational stabilization are expressed through quantities that depend on the plasma parameters or can be experimentally found by magnetic measurements outside the plasma.