The external kink mode and the role of q₉₅ in diverted tokamaks

The disruptive instability in diverted tokamaks when q at the 95% poloidal flux surface, q₉₅, is driven below 2.0 is shown to be a resistive kink. The mode is a resistive counterpart to the current driven ideal mode that traditionally explained the disruption in limited cross sections when q_a, the safety factor at the outermost closed flux surface, lies just below a rational value. Diverted plasmas, in which q_a 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. Numerical calculations show the resistive kink mode is linearly destabilized by the rapidly increasing resistivity at the plasma edge when q₉₅ < 2, but q_a >> 2. The resistive kink also occurs for limiter plasmas but quickly transforms to the ideal mode when the rational surface exits the plasma; this also explains an observed small discrepancy in onset conditions.