arXiv subjects

K. Pentland

Publications and source records attributed to K. Pentland.

5 recordsLinked to original sources

arXiv2026

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

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 (NNs). 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 NN models trained on a large library of simulated Grad-Shafranov equilibria. This enables magnetic controllers to accurately adapt to evolving plasma equilibria using real-time VCs (RTVCs), 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 RTVCs 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 RTVCs 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 RTVCs for closed-loop plasma shape control, representing a key step toward real-time deployment in the MAST-U PCS.

physics.plasm-ph↗

arXiv2026

The FreeGSNKE Pulse Design Tool (FPDT): a computational framework for evolutive plasma scenario and control design

We present the FreeGSNKE Pulse Design Tool (FPDT), an open-source, Python-based computational framework that enables in silico testing and predictive design of tokamak plasma scenarios and control strategies. The FPDT couples the FreeGSNKE evolutive equilibrium solver with a virtual Plasma Control System (PCS) containing modular and customisable controllers. Given a set of user-defined waveforms and control parameters, the virtual PCS uses feedback and feedforward control to modulate plasma current, position, and shape, while adhering to machine safety limits on poloidal field coil currents and voltages. The resulting framework allows simulation of the controlled dynamic evolution of plasma equilibria, along with the currents in both active poloidal field coils and passive conducting structures, under the assumption of axisymmetry. The FPDT can be used to develop plasma scenarios, test control schemes, calibrate control parameters, and perform uncertainty quantification studies, thereby reducing iterative and expensive experimental testing on a physical tokamak. The FPDT is machine-agnostic and can be customised to implement different control algorithms tailored to the specific tokamak of interest. Here, we outline the overall framework and validate its performance on plasma discharges on the MAST Upgrade tokamak in the `flat-top' phase. We demonstrate excellent quantitative agreement between the FPDT simulations, the desired control waveforms, and the experimental shot data. With this extension to the FreeGSNKE open-source suite of codes we aim to encourage more reproducible and collaborative research in plasma modelling and control.

physics.plasm-ph↗

arXiv2025

Multiple solutions to the static forward free-boundary Grad-Shafranov problem on MAST-U

The Grad-Shafranov (GS) equation is a nonlinear elliptic partial differential equation that governs the ideal magnetohydrodynamic equilibrium of a tokamak plasma. Previous studies have demonstrated the existence of multiple solutions to the GS equation when solved in idealistic geometries with simplified plasma current density profiles and boundary conditions. Until now, the question of whether multiple equilibria might exist in real-world tokamak geometries with more complex current density profiles and integral free-boundary conditions (commonly used in production-level equilibrium codes) has remained unanswered. In this work, we discover multiple solutions to the static forward free-boundary GS problem in the MAST-U tokamak geometry using the validated evolutive equilibrium solver FreeGSNKE and the deflated continuation algorithm. By varying the plasma current, current density profile coefficients, or coil currents in the GS equation, we identify and characterise distinct equilibrium solutions, including both deeply and more shallowly confined plasma states. We suggest that the existence of even more equilibria is likely prohibited by the restrictive nature of the integral free-boundary condition, which globally couples poloidal fluxes on the computational boundary with those on the interior. We conclude by discussing the implications of these findings for wider equilibrium modelling and emphasise the need to explore whether multiple solutions are present in other equilibrium codes and tokamaks, as well as their potential impact on downstream simulations that rely on GS equilibria.

physics.plasm-ph↗

arXiv2025

Validation of the static forward Grad-Shafranov equilibrium solvers in FreeGSNKE and Fiesta using EFIT++ reconstructions from MAST-U

A key aspect in the modelling of magnetohydrodynamic (MHD) equilibria in tokamak devices is having access to fast, accurate, and stable numerical simulation methods. There is an increasing demand for reliable methods that can be used to develop traditional or machine learning-based shape control feedback systems, optimise scenario designs, and integrate with other plasma edge or transport modelling codes. To handle such applications, these codes need to be flexible and, more importantly, they need to have been validated against both analytically known and real-world tokamak equilibria to ensure they are consistent and credible. In this paper, we are interested in solving the static forward Grad-Shafranov (GS) problem for free-boundary MHD equilibria. Our focus is on the validation of the static forward solver in the Python-based equilibrium code FreeGSNKE by solving equilibria from magnetics-only EFIT++ reconstructions of MAST-U shots. In addition, we also validate FreeGSNKE against equilibria simulated using the well-established MATLAB-based equilibrium code Fiesta. To do this, we develop a computational pipeline that allows one to load the same (a)symmetric MAST-U machine description into each solver, specify the required inputs (active/passive conductor currents, plasma profiles and coefficients, etc.) from EFIT++, and solve the GS equation for all available time slices across a shot. For a number of different MAST-U shots, we demonstrate that both FreeGSNKE and Fiesta can successfully reproduce various poloidal flux quantities and shape targets (e.g. midplane radii, magnetic axes, separatrices, X-points, and strikepoints) in agreement with EFIT++ calculations to a very high degree of accuracy. We also provide public access to the code/data required to load the MAST-U machine description in FreeGSNKE/Fiesta and reproduce the equilibria in the shots shown.

physics.plasm-ph↗

arXiv2024

Neural-Parareal: Dynamically Training Neural Operators as Coarse Solvers for Time-Parallelisation of Fusion MHD Simulations

The fusion research facility ITER is currently being assembled to demonstrate that fusion can be used for industrial energy production, while several other programmes across the world are also moving forward, such as EU-DEMO, CFETR, SPARC and STEP. The high engineering complexity of a tokamak makes it an extremely challenging device to optimise, and test-based optimisation would be too slow and too costly. Instead, digital design and optimisation must be favored, which requires strongly-coupled suites of High-Performance Computing calculations. In this context, having surrogate models to provide quick estimates with uncertainty quantification is essential to explore and optimise new design options. Furthermore, these surrogates can in turn be used to accelerate simulations in the first place. This is the case of Parareal, a time-parallelisation method that can speed-up large HPC simulations, where the coarse-solver can be replaced by a surrogate. A novel framework, Neural-Parareal, is developed to integrate the training of neural operators dynamically as more data becomes available. For a given input-parameter domain, as more simulations are being run with Parareal, the large amount of data generated by the algorithm is used to train new surrogate models to be used as coarse-solvers for future Parareal simulations, leading to progressively more accurate coarse-solvers, and thus higher speed-up. It is found that such neural network surrogates can be much more effective than traditional coarse-solver in providing a speed-up with Parareal. This study is a demonstration of the convergence of HPC and AI which simply has to become common practice in the world of digital engineering design.

physics.plasm-ph↗