Real-time virtual circuits for plasma shape control via neural network surrogates: dynamic validation in closed-loop simulations

Abstract

Reliable confinement and stable performance of tokamak fusion plasmas require accurate real-time magnetic shape control. A promising route to reduced latency and increased flexibility in plasma control systems (PCS) is to emulate physics-based controllers using neural networks. In prior work, we have demonstrated that virtual circuits (VCs), which define the poloidal field coil current vectors able to modify each plasma shape parameter independently, can be accurately emulated with neural network models trained on a large library of simulated Grad-Shafranov equilibria. This enables magnetic controllers to accurately adapt to evolving plasma equilibria, in contrast to pre-set VC schedules whose performance degrades upon departure from their reference equilibria. Here, we investigate the performance and robustness of these emulators in closed-loop simulations using the FreeGSNKE Pulse Design Tool (FPDT): a framework that couples the FreeGSNKE evolutive equilibrium solver with a virtual PCS. The FPDT models the coupling between controllers, plasma current and shape response, and actuator constraints. Using the emulated VCs within the FPDT, we demonstrate effective in-silico control of MAST Upgrade (MAST-U) plasma scenarios and show that the emulators are robust in the presence of input measurement uncertainty and under different update frequencies. These results establish the viability of neural network emulated VCs for closed-loop plasma shape control, representing a key step toward real-time deployment in the MAST-U PCS.

Figures (4)

• Figure 1: Poloidal cross-section of a MAST-U plasma (shot $53278$$t=0.5$s) equilibrium generated using FreeGSNKE. Displayed are the contours of total poloidal flux (yellow/green), the separatrix (red), and the shape parameters (labelled black dots). Also shown are the PF coils (blue), vessel structures (grey), and first wall outline (black).
• Figure 2: FPDT-simulated evolution of shape parameters $\bm{P}$ using emulated VCs for two plasma scenarios: scenario 1 (blue) and scenario 2 (pink). Solid and dashed lines correspond to $\gamma$ intervals of $2ms$ and $20ms$, respectively. The corresponding feedback reference waveforms are also shown (dashed black for scenario 1 and dashed brown for scenario 2) with green shading indicating when feedback control in on. The respective grey lines show the effect of including measurement uncertainty within the simulations (see main text for further details).
• Figure 3: Plasma separatrices at three different times for scenario 1 (dashed blue) and scenario 2 (solid pink) during the ($\gamma = 2ms$) FPDT simulations in Fig. \ref{['fig:53152_shapes']}. Also shown are the X-points (crosses) in the core region.
• Figure 4: FPDT-simulated evolution of shape parameters $\bm{P}$ using the emulated VCs, updated every $\gamma=5ms$. The simulator uses the same $\bm{\theta}$ as in the reference shot (solid blue), as in shot $53098$ (dashed pink), and as in shot $53097$ (dotted dark blue). Also shown are the feedback (dashed black) reference waveforms used in the virtual PCS and green background shading, indicating that feedback control is switched on.