The External Kink Mode and the Role of q 95 in Diverted Tokamaks

An explanation is provided for the disruptive instability in diverted tokamaks when the safety factor EUR q at the 95% poloidal flux surface, q95 , 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 [V.D. Shafranov, Sov. Phys. Tech. Phys. 1970 15, 175] when qedge, the safety factor at the outermost closed flux surface, lies just below a rational value EUR m n. Experimentally, external kink modes are observed in limiter configurations as the current in a tokamak is ramped up and qedge decreases through successive rational surfaces. For qedge < 2, the instability is always encountered and is highly disruptive. However, diverted plasmas, in which qedge is formally infinite in the MHD model, have presented a longstanding difficulty since the theory would predict stability, yet, the disruptive limit occurs in practice when q95, 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 q95 < 2, but qedge >> 2. The resistive kink behaves much like the ideal kink with no sign of a tearing component. However, the growth rates scale with a fractional power of the resistivity near the q = 2 surface, similar to but more complicated than the usual resistive internal kink scalings. The resistive kink also occurs for limiter plasmas but quickly transforms to the ideal mode when the rational surface exits the plasma; this, however, also explains an observed small discrepancy in onset conditions. The results have a direct bearing on the conventional edge cutoff procedures used in most ideal MHD codes, as well as implications for ITER projections involving q95, and for future reactor options.