Real-time virtual circuits for plasma shape control via neural network emulators: experimental demonstration on MAST Upgrade

Nicola C. Amorisco; Kamran Pentland; Adriano Agnello; George K. Holt; Alasdair Ross; Matthew J. Marshall; Edward Jones; Graham J. McArdle

physics.plasm-phAug 28, 2026

Real-time virtual circuits for plasma shape control via neural network emulators: experimental demonstration on MAST Upgrade

Authors: Nicola C. Amorisco, Kamran Pentland, Adriano Agnello, George K. Holt, Alasdair Ross, Matthew J. Marshall, Edward Jones, Graham J. McArdle,

Organizations: United Kingdom Atomic Energy Authority, Culham Campus, Abingdon, Oxfordshire, OX14 3DB, United Kingdom · STFC Hartree Centre, Sci-Tech Daresbury, Keckwick Lane, Daresbury, Warrington, WA4 4AD, United Kingdom

Abstract

Conventional plasma shape control in tokamaks relies on virtual circuits (VCs) that are computed offline from linearisations around a small, tailored number of reference equilibria, and deployed as expertly prepared schedules during the discharge. Here, we report on the first experimental deployment of real-time VCs. We replace pre-set look up tables with VCs updated in real time using surrogates of the plasma response. Both the existing control architecture and the interpretability of VC-based control are retained. Previous work showed that neural network emulators can produce accurate VCs, and validated their performance in closed-loop shape control simulations. Here, we report their first experimental validation on MAST Upgrade (MAST-U). Dedicated experiments spanning different scenarios, including prescribed shape perturbations, feedback-driven divertor-leg motion, and strongly evolving plasma configurations, show that real-time VCs can realise plasma shape control tasks within the MAST-U plasma control system. These results establish the experimental feasibility of real-time linearisations as a practical extension of conventional plasma shape control in tokamaks. The present implementation demonstrates a central step towards a simpler control workflow, in which manually constructed, phased VC schedules are replaced by VCs generated automatically online from a trained surrogate model, without scenario-specific retraining.

Figures & tables

Figure 1.1 : Schematic comparison between conventional virtual-circuit operation and RTVC operation. Conventional operation uses precomputed linearisations scheduled by discharge phase, whereas RTVCs generate the local linearisation from the instantaneous plasma state. The shape reconstruction, shape/VC controllers, and machine safety limits within the PCS interface are unchanged.

Shot	Objective	RTVC controlled shape pars.	Included in inverse matrix
53996	Constant shape control	( $R_{\text{out}}$ , $R_{\text{in}}$ , $Z_{\text{X}}$ )	( $R_{\text{out}}$ , $R_{\text{in}}$ , $Z_{\text{X}}$ , $S_{\text{gap}}$ , $R_{\text{nose}}$ )
54000	Minor core shape perturbations and sweep divertor-leg	( $R_{\text{out}}$ , $R_{\text{in}}$ , $Z_{\text{X}}$ , $R_{\text{s}}$ )	( $R_{\text{out}}$ , $R_{\text{in}}$ , $Z_{\text{X}}$ , $S_{\text{gap}}$ , $R_{\text{nose}}$ , $R_{\text{s}}$ )
54002	Increase elongation and sweep divertor-leg	( $R_{\text{out}}$ , $R_{\text{in}}$ , $Z_{\text{X}}$ , $R_{\text{X}}$ , $S_{\text{gap}}$ , $R_{\text{s}}$ )	( $R_{\text{out}}$ , $R_{\text{in}}$ , $Z_{\text{X}}$ , $R_{\text{X}}$ , $S_{\text{gap}}$ , $R_{\text{s}}$ )
54168	Simultaneous control of all seven shape parameters and shape perturbations	( $R_{\text{out}}$ , $R_{\text{in}}$ , $Z_{\text{X}}$ , $R_{\text{X}}$ , $S_{\text{gap}}$ , $R_{\text{nose}}$ , $R_{\text{s}}$ )	( $R_{\text{out}}$ , $R_{\text{in}}$ , $Z_{\text{X}}$ , $R_{\text{X}}$ , $S_{\text{gap}}$ , $R_{\text{nose}}$ , $R_{\text{s}}$ )

Table 3.1: Overview of the experimental validation objectives, RTVC controlled shape parameters, and shape parameters used in the matrix inversion.

Figure 3.1 : Evolution of the shape parameters in each RTVC-controlled MAST-U shot. Shown are the experimentally observed values recorded in real-time by the LEMUR algorithm (orange), the FPDT simulations made prior to the discharge (dashed-dot purple), and the pre-programmed feedback reference waveforms (dashed black). The shading indicates periods where feedback control was switched on (green with RTVC, lilac with Conventional VCs). Vertical dashed red lines indicate when the plasma went into ramp-down.

Figure 3.2 : Poloidal magnetic flux evolution in shot $54002$ during the RTVC-controlled phase, generated using EFIT ++ . Snapshots are shown at RTVC activation, $140\text{\,}\mathrm{ms}$ after activation, and $220\text{\,}\mathrm{ms}$ after activation, illustrating the evolution from a conventional configuration towards the higher elongation with near-super-X configuration.

Figure 4.1 : The VC norm $\|\mathcal{V}_{\text{act}}\|_{2}$ of the RTVC-controlled shape parameters in shots $53996$ (solid black) and $54168$ (solid red). Recall the shape matrix in shot $53996$ included $R_{\text{out}}$ , $R_{\text{in}}$ , $Z_{\text{X}}$ , $S_{\text{gap}}$ and $R_{\text{nose}}$ , while RTVC feedback was applied to the first three ( $R_{\text{nose}}$ being controlled with a static VC) The pseudoinversion with all seven shape parameters in shot $54168$ is compared with offline diagnostic inversions omitting either $R_{\text{nose}}$ (dashed blue) or $R_{\text{s}}$ (dashed green), and with the $R_{\text{nose}}$ – $R_{\text{s}}$ pair alone (dotted purple). The diagnostic inversions are shown for comparison and were not used to control the discharge. A vertical dotted line is denoted to mark the local amplification event at approximately $0.5\text{\,}\mathrm{s}$ .

Continuous Control

Continuous control studies how agents choose real-valued actions to steer dynamic systems toward goals while meeting performance and safety constraints.

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Real-time virtual circuits for plasma shape control via neural network emulators

Alasdair Ross, George K. Holt, Kamran Pentland, Adriano Agnello+6

STFC Hartree Centre, Sci-Tech Daresbury, Keckwick Lane, Daresbury, Warrington, WA4 4AD, United Kingdom · United Kingdom Atomic Energy Authority, Culham Campus, Abingdon, Oxfordshire, OX14 3DB, United Kingdom

Neural Surrogate Modeling Feedback Control Continuous Control

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Reliable position and shape control in tokamak plasmas requires accurate real-time regulation of several strongly coupled shape parameters. The control vectors that disentangle these couplings, referred to as virtual circuits (VCs), enable independent shape parameter control for a specific Grad--Shafranov (GS) equilibrium. Numerical calculation of VCs is not currently feasible in real time, therefore VCs are usually computed prior to each experiment, using a small number of reference GS equilibria sampled along the desired scenario trajectory, with each VC used to control the plasma within a preset time interval. While effective near the reference equilibrium, this approach can lead to degraded performance as the plasma departs from the reference equilibrium and/or from the desired trajectory, and it complicates the design of robust control strategies for rapidly evolving plasma configurations. In this paper, we construct neural-network-based emulators of plasma shape parameters from which VCs can be derived, to provide the MAST Upgrade (MAST-U) plasma control system with state-aware VCs in real-time. To do this, we develop an extensive library of over a million simulated GS equilibria, covering a substantial portion of the MAST-U operational space. These emulators provide differentiable functions whose gradients can be rapidly computed, enabling the derivation of accurate VCs for real-time shape control. We perform extensive verification of the emulated VCs by testing whether they disentangle the control problem. The neural-network-based approach delivers high accuracy and orthogonality across a diverse range of equilibria. This work establishes the physical validity of emulated VCs as a scalable and general alternative to schedules of precomputed VCs.

Abstract

Continuous Control

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