Path to Stable Tokamak Operation: Plasma stability analysis using physics-based and data-based approaches for real-time control*

Fusion reactors will need stability calculations during operations to steer the plasma from disruptions. Both plasma-physics-based and experimental-data-driven real-time stability analysis techniques are presented that were applied to control DIII-D. A δW stability analysis method with a Hamilton-Jacobi theory was formulated that converts the stability calculation to a Riccati differential equation. This brings numerical methods that are well suited to robust, fast solution of ideal mode stability in ~200 ms, as implemented on DIII-D. Resistive stability was studied using the STRIDE code that expands upon the ideal case. Resistive MHD ∆′matrices for DIII-D discharges were calculated in ~300 ms.  The stability error bar is obtained using an Unscented Transform method, which is thousands of times faster than a Monte-Carlo approach. Tearing instability analysis enabled by this method shows that the stability error bar increases by an order of magnitude before a mode onset in most cases. This shows the plasma equilibrium becomes “touchy” before tearing, i.e. minor variations in profiles can lead to instability.

Data-based Machine Learning Algorithms (MLA) are necessary because not all instabilities can be quantified with first-principle approaches. The best MLA predicted DIII-D disruptions correctly >90% of the time with <1% false positives.  To show the feasibility of predicting 15 MA ITER disruptions with data only from low current disruptions (required by safety), MLA trained with low I_p DIII-D data were applied to high I_p with appropriate scaling laws. Encouraging results predict disruptions correctly >90% of the time with <5% false positives. Based on this method, a plasma control algorithm was implemented on DIII-D that regulates neutral beams to keep the plasma stable; if this fails and the predicted disruptivity becomes too high, the system ramps down the plasma.