An explanation is provided for the disruptive instability in diverted tokamaks when the safety factor$q$at the 95 % poloidal flux surface,$q_{95}$, is driven below 2.0. The instability is a resistive kink counterpart to the current-driven ideal mode that traditionally explained the corresponding disruption in limited cross-sections (Shafranov,Sov. Phys. Tech. Phys., vol. 15, 1970, p. 175) when$q_{edge}$, the safety factor at the outermost closed flux surface, lies just below a rational value$m/n$. Experimentally, external kink modes are observed in limiter configurations as the current in a tokamak is ramped up and$q_{edge}$decreases through successive rational surfaces. For$q_{edge}<2$, the instability is always encountered and is highly disruptive. However, diverted plasmas, in which$q_{edge}$is formally infinite in the magnetohydrodynamic (MHD) model, have presented a longstanding difficulty since the theory would predict stability, yet, the disruptive limit occurs in practice when$q_{95}$, reaches 2. It is shown from numerical calculations that a resistive kink mode is linearly destabilized by the rapidly increasing resistivity at the plasma edge when$q_{95}<2$, but$q_{edge}\gg 2$. The resistive kink behaves much like the ideal kink with predominantly kink or interchange parity and no real sign of a tearing component. However, the growth rates scale with a fractional power of the resistivity near the$q=2$surface. The results have a direct bearing on the conventional edge cutoff procedures used in most ideal MHD codes, as well as implications for ITER and for future reactor options.
The external kink mode in diverted tokamaks
