X point effects on tokamak edge localized modes in the description of dual-poloidal-region safety factor

The flux coordinates with dual-region q in the poloidal direction are developed. The X-point effects on edge localized modes are then analyzed using this coordinate system. Two types of modes are studied. The first is related to the conventional peeling or peeling-ballooning modes. The mode existence aligned with the local magnetic field in the poloidally core region as observed experimentally is confirmed. The X points are shown to contribute to a stabilizing effect, as compared with the conventional treatment with the surface-averaged q and with the tokamak edge portion truncated. The other is the axisymmetric modes localized in the vicinity of X points, which can affect the cross-field-line transport near the X points. The existence of axisymmetric modes points to the possibility of applying a toroidally axisymmetric (or large m/n) resonant magnetic perturbation (RMP) in the X-point area for mitigating the edge localized modes, which can be an alternative to the current RMP design with finite m/n.