Correction: Optimizing 3D magnetic perturbations for edge instability control in the KSTAR tokamak

A small non-axisymmetric (3D) magnetic field can offer invaluable ways for instability control in tokamaks when optimally used, as has been highlighted by the edge-localized mode (ELM) control using a resonant magnetic perturbation (RMP). While the inherent complexity due to its 3D nature constantly poses scientific challenges, recent research progresses have been increasing the prospects of universal predictive capabilities on RMP ELM suppression. A successful framework has been developed based on integrated perturbative models under international collaborations centered around the Korean Superconducting Tokamak Advanced Research (KSTAR), as will be reviewed in this article. This framework separates the interaction between 3D coils and resonant fields as the ideal magnetohydrodynamic (MHD) outer-layer process in fast time scales, from the dynamics of resonant field penetration as the narrow boundary layer process in non-ideal MHD time scales. The major profile alterations can occur only when the resonant field becomes strong enough to penetrate and bifurcate to new magnetic island topologies. This hypothesis enables simplified 3D field optimizations once the field penetration thresholds are identified. The prediction of the field penetration thresholds require non-linear MHD simulations but can be simplified by isolating it from outer-layer response, successfully explaining key parametric dependencies and accessibility conditions for RMP ELM suppression. Improved understanding has been leveraged to expand physics basis for underlying transport in fully geometry, as recent perturbative 3D simulations are revealing the complex interplays across classical and non-classical transport, between Kink and tearing mode structures, between closed- and open-field lines which are important to optimize power flux to plasma facing components. The pre-programmed predictive optimization of 3D tokamak scenarios can then be combined with an adaptive RMP control to find the optimal trade-off between stability and confinement. The above approaches under this framework are not based on the first principles but are indeed providing unique guidances for 3D tokamak design, optimization, and control.