Development of State-Space Model-Based Kalman Filter for n$\ge $1 Resistive Wall Mode (RWM)

While significant progress has been made for $n=$1 RWM identification and control, it is now predicted that $n$~\textbf{$>$} 1 RWMs could appear even after the $n=$1 RWM is suppressed. Algorithm development, as well as diagnostic capability enhancement, is being done in order to identify the $n=$ 2 or 3 RWMs in the presence of a stabilized $n=$1 RWM for DIII-D. Specifically, taking advantage of the successful development of the Kalman filter to discriminate ELM noise from an $n=$1 RWM [1], a more advanced Kalman filter is being developed to detect both $n$=1 and $n$ \textbf{$>$} 1 RWMs. Noise characterization and modeling is deemed critical to determine the optimized Kalman gain. This multi-mode state-space model will also serve as a basis to design a model-based RWM feedback controller. [1]~Y. In \textit{et al.}, Phys. Plasmas \textbf{13}, 062512 (2006).