Rotational stabilization of the resistive wall modes in tokamaks with a ferritic wall

Abstract

The dynamics of the rotating resistive wall modes (RWMs) is analyzed in the presence of a uniform ferromagnetic resistive wall withl l=l 0 4 (l is the wall magnetic permeability, and l 0 is the vacuum one). This mimics a possible arrangement in ITER with ferromagnetic steel in test blanket modules or in future experiments in JT-60SA tokamak [Y. Kamada, P. Barabaschi, S. Ishida, the JT-60SA Team, and JT-60SA Research Plan Contributors, Nucl. Fusion 53, 104010 (2013)]. The earlier studies predict that such a wall must provide a destabilizing influence on the plasma by reducing the beta limit and increasing the growth rates, compared to the reference case withl ¼ 1. This is true for the locked modes, but the presented results show that the mode rotation changes the tendency to the opposite. Atl > 1, the rotational stabilization related to the energy sink in the wall becomes even stronger than atl ¼ 1, and this "external" effect develops at lower rotation frequency, estimated as several kHz at realistic conditions. The study is based on the cylindrical dispersion relation valid for arbitrary growth rates and frequencies. This relation is solved numerically, and the solutions are compared with analytical dependences obtained for slow (s=d w ) 1) and fast (s=d w ( 1) "ferromagnetic" rotating RWMs, where s is the skin depth and d w is the wall thickness. It is found that the standard thinwall modeling becomes progressively less reliable at largerl, and the wall should be treated as magnetically thick. The analysis is performed assuming only a linear plasma response to external perturbations without constraints on the plasma current and pressure profiles. V C 2015 AIP Publishing LLC. [http://dx.

Plasma stability theory including the resistive wall effects

“…In the RWM theory, usually ferromagnetic effects are disregarded, which is justified by analytical and numerical analysis [84, 85] for slow modes. The situation is different for fast modes (at ) [86], which can be expected in future experiments in the JT-60SA tokamak [26] and, possibly in experiments with a movable ferromagnetic wall in the HBT-EP tokamak [87]. However, more often the results obtained with are good enough and can be easily extended to the area with [86].…”

“…The situation is different for fast modes (at ) [86], which can be expected in future experiments in the JT-60SA tokamak [26] and, possibly in experiments with a movable ferromagnetic wall in the HBT-EP tokamak [87]. However, more often the results obtained with are good enough and can be easily extended to the area with [86]. This is why is assumed in what follows.…”

“…In figure 8, dependence (15.3) shown by the dashed parabolas is compared with precise solutions of the cylindrical dispersion relations with the ferromagnetic effect accounted for [86]. The numbers attached to the curves indicate the magnetic permeability of the wall.…”

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Figure 8. The calculated dependences of the growth rate on the angular frequency normalized to for the mode with at fixed and varying and the walls with and magnetic permeability from 1 to 4, shown above the curves. The solid curves are calculated by the ferromagnetic equivalent of (13.2) (see (4)–(6) in [86]) and the dashed parabolas by formula (15.3) with replaced by . (Figure 6 a from [86].

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“…The solid curves are calculated by the ferromagnetic equivalent of (13.2) (see (4)–(6) in [86]) and the dashed parabolas by formula (15.3) with replaced by . (Figure 6 a from [86]. Figure courtesy by Yanovskiy.…”