On Kink Modes and Low-n Kink β Limits in HL-2A Sawtooth Discharges

Kink mode is one of the most important macroinstabilities in sawtooth discharge. In this article, the nature of kink modes was investigated through a combination of HL-2A experiments and simulations. Multiple n (toroidal mode number) kink branches were found in HL-2A sawtooth discharges. The distinct roles of different n-kink modes in plasma instability were identified. The n = 1 mode is identified as the dominant kink mode. The mode structure shrinks toward the center with an increase in n value. The mode linear growth rate is not necessarily related to whether the mode dominates plasma. The weakening effect of the shorter wavelength and its higher internal localization partially offset the advantage of the higher n mode in the global plasma instability. In practice, multiple n-kink branches tend to be stable if n = 1 mode is stable. Among the low-n modes, the stability limits for n $\gt$ 1 modes would not be lower than n = 1 mode at $\mathbf {q}_{\mathbf {0}}=\mathbf {1.05}$ and its adjacent areas, and the stability limits of n = 1 and 2 kink modes decrease with $\mathbf {q}_{\mathbf {0}}$ and exhibit some linear relationships if a normally parabolic current density profile is considered, which hints for the determination of the operational $\boldsymbol {\beta }$ for HL-2A sawtooth discharges.