The physics of locked tearing mode stabilization by rotating 3D fields in the presence of static error fields

Effective screening-out of static error fields (EFs) using rotating resonant magnetic perturbation (RMP), i.e., “self-stabilized” regimes, are found by nonlinear resistive MHD simulation [Inoue$+$, NF16{\&}PPCF17] and validated using DIII-D experimental observations of tearing mode (TM) locking to uncorrected EFs. Simulations with a single rational surface have predicted the dominant single TM behaviors measured in DIII-D when applying rotating external fields. These behaviors include a standing wave type response when the internal TM is locked to the intrinsic EF and a propagating wave response when it is locked to the external rotating fields. Despite the qualitative consistency between AEOLUS-IT simulation and DIII-D experiment, details of stabilized regime measurements, where double and triple helicity responses due to toroidicity and poloidal shaping were also discovered [Okabayashi$+$, IAEA18], do not agree. Recent multi-helicity simulations suggest a self-stabilizing mechanism via anti-phasing between double-helicity structures. These improve consistency with observations and improve detailed understanding of locked TM control. This detailed cross-validation suggests that the physical process of the TM/RMP interaction proceeds quasi-/non-linearly and with multiple helicity structures, which goes beyond the linear stability model prediction. *Supported by the US DOE under DE-FC02-04ER54698 {\&} DE-AC02-09CH11466.