Stability and Control of Multiple Resistive Wall Modes

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 optimal 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 in the DIII-D plasma control system (PCS). In addition to stabilizing RWMs, the feedback can 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 = 1and 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 limit. Multi-mode feedback also improved the control of the ELM-driven 𝓃 = 1and 𝓃 = 2 fields which further validates the feedback performance. Furthermore, a rotating non-zero target was set for the feedback, allowing stability to be assessed by monitoring the rotating plasma response 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 plasma response to applied, open-loop perturbations. The closed-loop response measurements are consistent with open-loop MHD spectroscopy data over a range of 𝜷𝑛 approaching the 𝓃 = 1 ideal-wall limit, demonstrating the potential of this technique as a useful tool for measuring stability while maintaining control even as the marginal stability point is approached. These plasma response measurements were then fit to produce both VALEN and single-mode stability models. These models allow for important plasma stability information to be determined and have been shown to agree with experimentally observed RWM growth rates. This improved understanding and control of the 𝓃 = 1 and 𝓃 = 2 RWM will allow for more robust operation above the 𝓃 = 2 no-wall limit.