Magnetic Control with an Inverse Grad-Shafranov Neural Network

SPARC will require extremely robust and precise magnetic control. Furthermore, the heat flux challenge may motivate real-time adaptation of the shape in response to heat flux. Such a control strategy is already under development for ITER [1]. These challenges motivate further advancements in robust and real-time adaptable magnetic control. We make the observation that a real-time capable inverse Grad-Shafranov solver would, in principle, enable extremely low control errors relative to reconstruction and enable real-time adaptation. Since implementing a sufficiently fast and numerically stable solver is a challenge, we train a neural network surrogate of FBT [2], the inverse Grad-Shafranov solver used for Tokamak à Configuration Variable (TCV) and SPARC. The resulting neural network integrates naturally with existing classical control solutions by adjusting the coil current references in response to real-time plasma conditions and control targets. Concerns with using a real-time neural network can be addressed by replacing or augmenting it with a real-time inverse Grad-Shafranov solver. Experiments at TCV demonstrate its ability to help improve disturbance rejection, maintaining millimeter precision in radial position control, even with the introduction of auxiliary heating. Further experiments demonstrating real-time adaptation are planned at the time of writing. Finally, we report on developments of its application to SPARC simulations.

[1] Frattolillo, Domenico, et al. "Magnetic control strategies to reduce first wall heat loads in ITER." Fusion Engineering and Design 219 (2025): 115203.

[2] Hofmann, Ferdinand. "FBT-a free-boundary tokamak equilibrium code for highly elongated and shaped plasmas." Computer Physics Communications 48.2 (1988): 207-221.