The effect of the aspect ratio on the external kink-ballooning instability in high-β tokamaks.

N.Aiba, S.Tokuda1), T.Ishizawa2), M.Okamoto3)

The gratuate school for Advanced studies, Toki, Gifu 509-5292, Japan
1) Japan Atomic Energy Research Institute, Naka-gun, Ibaraki
2) Research Organization for Information Science and Technology, Ibaraki 319-11, Japan
3) National Institute for Fusion Science, Toki, Gifu 509-5292, Japan

Ideal kink-ballooning instability limits the performance of tokamak, and resistive wall modes (RWMs) should be stabilized or be controlled in order to realize a stationary high-performance tokamak. RWMs are the ideal kink-ballooning modes that are stable when the plasma is surrounded by a perfect conducting wall but become unstable due to the resistivity of the wall.
We developed a theory where the change of the potential energy δ Wp for external modes in a toroidal system is expressed in terms of the boundary values by using the property of Newcomb equation[1]. This theory computes δ Wp + δ WV, WV is the change of the vacuum magnetic energy, in the quadratic form with respect to the plasma displacement at the surface, and the matrix in the form is called the stability matrix. This implies that the stability of the ideal external mode is decided by the minimum eigenvalue of the stability matrix. When the minimum eigenvalue of this matrix is negative, the ideal external mode is unstable. This method has the great advantage point that we can decide the marginally stable point(γ = 0) numerically.
We apply the theory thus developed to analyze the stability of the external kink-ballooning mode in high-β tokamaks. Emphasis is put on the aspect ratio dependence of the kink-ballooning stability, which get attention recently in the design research on high-performance tokamaks. Troyon et al. have taken the study of the beta limit decided by the external kink-ballooning instability in high-β tokamaks and have shown that the value ε βpmax, where ε is the inverse aspect ratio and βpmax is the limit value of a poloidal beta, only depends on the safety factor at plasma surface when the equilibrium is a circular case and the aspect ratio is large[2]. In the present research, the stability of the external kink-ballooning mode is investigated from the stability matrix. We show that the mode is destabilized in high-β tokamaks when the aspect ratio is increased and ε βp is fixed.

References

[1]S.Tokuda, J.Plasma Fusion Res. 78 No.9 (2002) 913
[2]F.Troyon, R.Gruber et al, Plasma Phys. 26 (1984), 209