Real-Time Applicability of Emulated Virtual Circuits for Tokamak Plasma Shape Control

Machine learning has recently been adopted to emulate sensitivity matrices for real-time magnetic control of tokamak plasmas. However, these approaches would benefit from a quantification of possible inaccuracies. We report on two aspects of real-time applicability of emulators. First, we quantify the agreement of target displacement from VCs computed via Jacobians of the shape emulators with those from finite differences Jacobians on exact Grad-Shafranov solutions. Good agreement <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$(\approx \mathbf{5 - 1 0 \%})$</tex> can be achieved on a selection of geometric targets using combinations of neural network emulators with <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$\approx 10^{5}$</tex> parameters. A sample of <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$\approx 10^{5}-10^{6}$</tex> synthetic equilibria is essential to train emulators that are not over-regularised or overfitting. Smaller models trained on the shape targets may be further fine-tuned to better fit the Jacobians. Second, we address the effect of vessel currents that are not directly measured in real-time and are typically subsumed into effective “shaping currents” when designing virtual circuits. We demonstrate that shaping currents can be inferred via simple linear regression on a trailing window of active coil current measurements with residuals of only a few Ampères, enabling a choice for the most appropriate shaping currents at any point in a shot. While these results are based on historic shot data and simulations tailored to MAST-U, they indicate that emulators with few-millisecond latency can be developed for robust real-time plasma shape control in existing and upcoming tokamaks.