Simultaneous stabilization and control of the n = 1 and n = 2 resistive wall mode

DIII-D experiments demonstrate simultaneous stability measurements and control of resistive wall modes (RWMs) with toroidal mode numbers n = 1 and n = 2. RWMs with n > 1 are sometimes observed on DIII-D following the successful feedback stabilization of the n = 1 mode, motivating the development of multi- n control. A new model-based multi-mode feedback algorithm based on the VALEN physics code has been implemented on the DIII-D tokamak using a real-time GPU installed directly into the DIII-D plasma control system. In addition to stabilizing RWMs, the feedback seeks to control the stable plasma error field response, enabling compensation of the typically unaddressed DIII-D n = 2 error field component. Experiments recently demonstrated this algorithm’s ability to simultaneously control n = 1 and n = 2 perturbed fields for the first time in a tokamak, using reactor relevant external coils. Control was maintained for hundreds of wall-times above the n = 1 no-wall pressure limit and approaching the n = 1 and n = 2 ideal-wall limits. Furthermore, a rotating non-zero target was set for the feedback, allowing stability to be assessed by monitoring the rotating plasma response (PR) while maintaining control. This novel technique can be viewed as a closed-loop extension of active MHD spectroscopy, which has been used to validate stability models through comparisons of the PR to applied, open-loop perturbations. The closed-loop response measurements are consistent with open-loop MHD spectroscopy data over a wide range of β _N approaching the n = 1 ideal-wall limit. These PR measurements were then fit to produce both VALEN and single-mode stability models. These models allowed for important plasma stability information to be determined and have been shown to agree with experimentally observed RWM growth rates.