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At least 19 records
All sourcesNASA NTRSDOE OSTI
DOE OSTI2021

Kinetic equilibrium reconstruction and the impact on stability analysis of KSTAR plasmas

High fidelity kinetic plasma equilibrium reconstructions are an essential requirement for accurate stability and disruption prediction analyses to support continuous operation of high beta tokamak plasmas. The present kinetic equilibrium reconstructions of plasmas in the KSTAR device include plasma density and temperature profiles from Thomson scattering and ion temperature from charge exchange spectroscopy diagnostics, and allowance for fast particle pressure. In addition, up to 25 channels of motional Stark effect diagnostic data are used to constrain the magnetic field pitch angle profile in the plasma to produce a reliable computation of the safety factor, q, profile. In this work, H-mode plasmas exhibit clear pedestal characteristics in the reconstructed pressure profile compared to internal transport barrier or L-mode plasmas. The plasma configuration and vertical position of inner strike points are validated by CCD and infrared camera images. Ideal and resistive magnetohydrodynamic (MHD) stability analyses using the DCON and resistive DCON codes utilize these kinetic equilibrium reconstructions to compare to experimental plasma stability. Equilibria with sufficiently low convergence error can provide reliable computation of ideal and resistive MHD stability analysis.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2024

Accuracy of kinetic equilibrium reconstruction of NSTX and NSTX-U plasmas and its impact on the transport and stability analysis

An accurate magnetohydrodynamic (MHD) equilibrium reconstruction is an essential starting point for stability and transport plasma analysis. Herein this work describes an approach for obtaining kinetic equilibrium reconstructions using the OMFIT framework, which has been applied for the first time to spherical tokamak data from NSTX and NSTX-U. The EFIT equilibrium solver is integrated with experimental data analysis procedures and subsequent TRANSP transport simulations to enhance the accuracy of the reconstruction, in particular, at the edge region, by adding constraints on the total pressure and current density profiles, based on the transport code solution. The accuracy of the equilibrium reconstruction depends on the uncertainty and number of constraints, as well as the choice of basis functions to represent the pressure and current density profiles. Improved fidelity of the equilibrium reconstruction is demonstrated by reducing the variability of the magnetic axis and boundary locations from several centimeters, for reconstructions based on magnetic and experimental pressure constraints, to only several millimeters, for kinetic reconstructions based on transport code constraints, when different representations of basis functions were tested. The variability of the safety factor on axis was reduced ten times in the same sensitivity study. The accuracy of the equilibrium reconstruction and subsequent mapping of the experimental kinetic profile data have a significant impact on the trapped gyro Landau fluid and linear CGYRO turbulence simulations, which predict different spectra of unstable modes and turbulent fluxes for cases with different numbers of constraints in the equilibrium reconstruction. Conversely, the stability analysis performed using the GATO code shows plasmas that are stable to n = 1 MHD modes in both equilibria using magnetic and experimental pressure constraints as well as the transport code constrained equilibrium. However, a scan of parameters away from these conditions shows considerable deviation in the threshold of unstable modes between these reconstructions. Therefore, for reliable plasma analysis and use in turbulence and stability calculations, a high-fidelity equilibrium reconstruction with accurate kinetic constraints based on transport code solutions is necessary.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2024

EFIT‐AI: Machine Learning and Artificial Intelligence Assisted Equilibrium Reconstruction for Tokamak Experiments and Burning Plasmas (Final Report)

The EFIT-AI project is creating a modern advanced equilibrium reconstruction code suitable for tokamak experiments of burning plasmas. EFIT [1,2] was the first and is the most extensively used equilibrium reconstruction code in the world. This project builds on the production-level experience and adds key elements as follows. 1. A Model Order Reduction (MOR) version of the two-dimensional (2D) Grad-Shafranov equation solver (EFIT-MORNN) using physics-informed neural networks. 2. Improved optimization and data analysis capabilities using a Bayesian framework enhanced with machine learning. 3. A MOR version of the three-dimensional (3D) perturbed equilibrium reconstruction tool.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2022

Application of machine learning and artificial intelligence to extend EFIT equilibrium reconstruction

Recent progress in the application of machine learning (ML)/artificial intelligence (AI) algorithms to improve the Equilibrium Fitting (EFIT) code equilibrium reconstruction for fusion data analysis applications is presented. A device-independent portable core equilibrium solver capable of computing or reconstructing equilibrium for different tokamaks has been created to facilitate adaptation of ML/AI algorithms. A large EFIT database comprising of DIII-D magnetic, motional Stark effect, and kinetic reconstruction data has been generated for developments of EFIT model-order-reduction (MOR) surrogate models to reconstruct approximate equilibrium solutions. Furthermore, a neural-network MOR surrogate model has been successfully trained and tested using the magnetically reconstructed datasets with encouraging results. Other progress includes developments of a Gaussian process Bayesian framework that can adapt its many hyperparameters to improve processing of experimental input data and a 3D perturbed equilibrium database from toroidal full magnetohydrodynamic linear response modeling using the Magnetohydrodynamic Resistive Spectrum - Feedback (MARS-F) code for developments of 3D-MOR surrogate models.

Gaussian process↗
DOE OSTI2023

Performance-Portable GPU Acceleration of the EFIT Tokamak Plasma Equilibrium Reconstruction Code

This paper presents the steps followed to GPU-offload parts of the core solver of EFIT-AI, an equilibrium reconstruction code suitable for tokamak experiments and burning plasmas. For this work, we will focus on the fitting procedure that consists of a Grad–Shafranov (GS) equation inverse solver that calculates equilibrium reconstructions on a grid. We will show profiling results of the original code (CPU-baseline), as well as the directives used to GPU-offload the most time-consuming function, initially to compare OpenACC and OpenMP on NVIDIA and AMD GPUs and later on to assess OpenMP performance portability on NVIDIA, AMD and Intel GPUs. We will make a performance comparison for different spatial grid sizes and show the speedup achieved on NVIDIA A100 (Perlmutter-NERSC), AMD MI250X (Frontier-OLCF) and Intel PVC GPUs (Sunspot-ALCF). Finally, we will draw some conclusions and recommendations to achieve high-performance portability for an equilibrium reconstruction code on the new HPC architectures

GPU↗
DOE OSTI2025

Systematic analysis of magnetic equilibrium reconstruction with eddy currents on LTX- β

Magnetic equilibrium reconstruction in the Lithium Tokamak Experiment-Beta (LTX-β) is complicated by strong eddy currents and toroidal asymmetries arising from its segmented, close-fitting conducting shell. In the earlier experiment LTX, these three-dimensional (3D) conductor effects significantly distorted diagnostic signals and challenged conventional axisymmetric reconstruction methods. In this work, we demonstrate that accurate plasma equilibria can be recovered on LTX-β by incorporating a small number of dominant eddy current modes derived from realistic conductor models. Using the open-source $\tt{TokaMaker}$ Grad–Shafranov solver, we reconstruct equilibria across a systematically selected set of LTX-β discharges and validate them against the legacy $\tt{PSI-Tri}$ hybrid 2D-3D code. Our results show that fully 2D $\tt{TokaMaker}$ reconstructions achieve significantly improved agreement with flux loop and Mirnov probe measurements, reducing total chi-squared fitting errors, especially during startup. Finally, we develop new hybrid 2D-3D $\tt{TokaMaker}$ reconstructions by integrating the $\tt{ThinCurr}$ 3D eddy current model, which we optimize for significant further reduction of chi-squared in most scenarios. These findings underscore the importance of realistic wall-current modeling in short-pulse tokamaks, and establish a physics-based reconstruction framework that is extensible to devices with complex passive structures and 3D wall interactions.

Grad–Shafranov solver↗
DOE OSTI2025

Large-scale tearing-mode hazard function analysis with standard matched equilibrium reconstructions

The association between features from standard tokamak equilibrium reconstructions and the onset of n = 1 tearing modes (TMs) is analyzed at scale. The TM onset rate is directly modeled with a ‘hazard’ function which gives the expected number of onsets (per unit time spent) in a given equilibrium parameter region. In particular the different statistical modeling performance achieved for magnetics-only reconstructions and motional Stark effect (MSE) enhanced reconstructions is studied. It is observed that a better hazard model for the TM onset rate can be built with the MSE-enhanced equilibria compared to the matched magnetics-only situation. This advantage disappears if internal profile details are withheld from the matched analysis. Plausibility of the hazard function is further demonstrated with visualizations of global trends in the operational space, and time-traces from specific tokamak discharges. As a result, TMs typically degrade tokamak plasma performance and may lead to plasma termination, motivating this statistical study.

equilibrium↗
DOE OSTI2024

Public Data Set: Effects of Injected Current Streams on MHD Equilibrium Reconstruction of Local Helicity Injection Plasmas in a Spherical Tokamak

This public data set contains openly-documented, machine readable digital research data corresponding to figures published in J.D. Weberski et al., 'Effects of Injected Current Streams on MHD Equilibrium Reconstruction of Local Helicity Injection Plasmas in a Spherical Tokamak,' Journal of Fusion Energy 43, 72 (2024).

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2022

3D Equilibrium Reconstruction and MHD Studies in Stellarators (Final Report)

This is the final technical report for the grant Three Dimensional Equilibrium Reconstruction and MHD Studies in Stellarators. The major goals of this project were to: further develop V3FIT code capabilities, continue to support experiments using the V3FIT code, continue theoretical support for the CTH experiment at Auburn, particularly in the area of NIMROD simulations of CTH discharges. Dr. Lopez Ortiz has made significant progress on his analysis of NIMROD simulations of CTH MHD phenomena. In particular, his study has focused on the fixed point dynamics and energy flow amongst toroidal Fourier modes in sawtooth oscillations simulations.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2024

Effects of Injected Current Streams on MHD Equilibrium Reconstruction of Local Helicity Injection Plasmas in a Spherical Tokamak

Open field line currents are intrinsic to DC helicity injection plasma startup and pose a challenge for inferring the plasma equilibrium with standard reconstruction analysis. Local helicity injection (LHI) is a type of DC helicity injection which uses small, modular current sources to drive force-free current along helical field lines to produce tokamak plasmas. MHD modeling and magnetic measurements during LHI indicate the injected current streams remain coherent as helical structures on the outboard edge of a core toroidal plasma that is tokamak-like in a toroidally averaged sense. To extract core plasma equilibrium properties, external magnetic diagnostics corrected for contributions from the injected current streams are fitted by a standard Grad-Shafranov equilibrium code. An iterative approach for estimating and subtracting the stream contributions from the diagnostic signals is described and applied to a model equilibrium database to reduce systematic errors introduced by the streams. Convergence is usually attained with 2 to 4 iterations, with derived equilibrium parameters matching the prescribed axisymmetric core values to within estimated experimental uncertainties. Accurate recovery of core parameters occurs when the ratio of the net toroidal windup current from the streams to the core plasma current is less than 0.2, which is typically satisfied in most experiments.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2024

Real-time plasma equilibrium reconstruction and shape control for the MAST Upgrade tokamak

Real-time magnetic control has been developed to deliver precise control of multiple plasma shape parameters for advanced divertor configurations, including double-null, Super-X, X-point target and X-divertor for the first time on the MAST Upgrade (MAST-U) spherical tokamak. Successful real-time magnetic equilibrium control of different plasma shape variables has been accomplished in the 2022–2023 MAST-U experimental campaign for the advanced MAST-U divertor configurations. Application of the MAST-U boundary reconstruction algorithm, LEMUR, is described and compared with off-line equilibrium reconstruction and diagnostic measurements. The process of design and verification of the axisymmetric magnetic control schemes using a suite of control analysis tools (known collectively as TokSys) is also described.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2024

EFIT-Prime: Probabilistic and physics-constrained reduced-order neural network model for equilibrium reconstruction in DIII-D

We introduce EFIT-Prime, a novel machine learning surrogate model for EFIT (Equilibrium FIT) that integrates probabilistic and physics-informed methodologies to overcome typical limitations associated with deterministic and ad hoc neural network architectures. EFIT-Prime utilizes a neural architecture search-based deep ensemble for robust uncertainty quantification, providing scalable and efficient neural architectures that comprehensively quantify both data and model uncertainties. Physically informed by the Grad–Shafranov equation, EFIT-Prime applies a constraint on the current density J tor and a smoothness constraint on the first derivative of the poloidal flux, ensuring physically plausible solutions. Furthermore, the spatial location of the diagnostics is explicitly incorporated in the inputs to account for their spatial correlation. Extensive evaluations demonstrate EFIT-Prime's accuracy and robustness across diverse scenarios, most notably showing good generalization on negative-triangularity discharges that were excluded from training. Timing studies indicate an ensemble inference time of 15 ms for predicting a new equilibrium, offering the possibility of plasma control in real-time, if the model is optimized for speed.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2022

Equilibrium reconstruction of DIII-D plasmas using predictive modeling of the pressure profile

New workflows have been developed for predictive modeling of magnetohydrodynamic (MHD) equilibrium in tokamak plasmas. The goal of this work is to predict the MHD equilibrium in tokamak discharges without having measurements of the kinetic profiles. The workflows include a cold start tool, which constructs all the profiles and power flows needed by transport codes; a Grad–Shafranov equilibrium solver; and various codes for the sources and sinks. For validation purposes, a database of DIII-D tokamak discharges has been constructed that is comprised of scans in the plasma current, toroidal magnetic field, and triangularity. Initial efforts focused on developing a workflow utilizing an empirically derived pressure model tuned to DIII-D discharges with monotonic safety factor profiles. This workflow shows good agreement with experimental kinetic equilibrium calculations, but is limited in that it is a single fluid (equal ion and electron temperatures) model and lacks H-mode pedestal predictions. The best agreement with the H-mode database is obtained using a theory-based workflow utilizing pressure profile predictions from a coupled TGLF turbulent transport and EPED pedestal models together with external magnetics and Motional Stark Effect (MSE) data to construct the equilibrium. Here, we obtain an average root mean square error of 5.1% in the safety factor profile when comparing the predicted and experimental kinetic equilibrium. We also find good agreement with the plasma stored energy, internal inductance, and pressure profiles. Including MSE data in the theory-based workflow results in noticeably improved agreement with the q-profiles in high triangularity discharges in comparison with the results obtained with magnetic data only. The predictive equilibrium workflow is expected to have wide applications in experimental planning, between-shot analysis, and reactor studies.

Kinsey, J. E. (ORCID:0000000193347473)↗
DOE OSTI2024

Augmenting machine learning of Grad–Shafranov equilibrium reconstruction with Green's functions

This work presents a method for predicting plasma equilibria in tokamak fusion experiments and reactors. The approach involves representing the plasma current as a linear combination of basis functions using principal component analysis of plasma toroidal current densities (J t ) from the EFIT-AI equilibrium database. Then utilizing EFIT's Green's function tables, basis functions are created for the poloidal flux (ψ) and diagnostics generated from the toroidal current (J t ). Similar to the idea of a physics-informed neural network (NN), this physically enforces consistency between ψ, J t , and the synthetic diagnostics. First, the predictive capability of a least squares technique to minimize the error on the synthetic diagnostics is employed. The results show that the method achieves high accuracy in predicting ψ and moderate accuracy in predicting J t with median R 2 = 0.9993 and R 2 = 0.978, respectively. A comprehensive NN using a network architecture search is also employed to predict the coefficients of the basis functions. The NN demonstrates significantly better performance compared to the least squares method with median R 2 = 0.9997 and 0.9916 for J t and ψ, respectively. The robustness of the method is evaluated by handling missing or incorrect data through the least squares filling of missing data, which shows that the NN prediction remains strong even with a reduced number of diagnostics. Additionally, the method is tested on plasmas outside of the training range showing reasonable results.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2024

Impact of various DIII-D diagnostics on the accuracy of neural network surrogates for kinetic EFIT reconstructions

Abstract Kinetic equilibrium reconstructions make use of profile information such as particle density and temperature measurements in addition to magnetics data to compute a self-consistent equilibrium. They are used in a multitude of physics-based modeling. This work develops a multi-layer perceptron (MLP) neural network (NN) model as a surrogate for kinetic Equilibrium Fitting (EFITs) and trains on the 2019 DIII-D discharge campaign database of kinetic equilibrium reconstructions. We investigate the impact of including various diagnostic data and machine actuator controls as input into the NN. When giving various categories of data as input into NN models that have been trained using those same categories of data, the predictions on multiple equilibrium reconstruction solutions (poloidal magnetic flux, global scalars, pressure profile, current profile) are highly accurate. When comparing different models with different diagnostics as input, the magnetics-only model outputs accurate kinetic profiles and the inclusion of additional data does not significantly impact the accuracy. When the NN is tasked with inferring only a single target such as the EFIT pressure profile or EFIT current profile, we see a large increase in the accuracy of the prediction of the kinetic profiles as more data is included. These results indicate that certain MLP NN configurations can be reasonably robust to different burning-plasma-relevant diagnostics depending on the accuracy requirements for equilibrium reconstruction tasks.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2023

Machine learning-based real-time kinetic profile reconstruction in DIII-D

Abstract Kinetic equilibrium reconstruction plays a vital role in the physical analysis of plasma stability and control in fusion tokamaks. However, the traditional approach is subjective and prone to human biases. To address this, the consistent automatic kinetic equilibrium reconstruction (CAKE) method was introduced, providing objective results. Nonetheless, its offline nature limits its application in real-time plasma control systems (PCSs). To address this limitation, we present RTCAKENN, a machine learning model that approximates 7 CAKE-level output profiles, namely pressure, inverse q , toroidal current density, electron temperature and density, carbon ion impurity temperature and rotation profiles, using real-time available inputs. The deep neural network consists of an encoder layer, where the scalars and interdependent inputs such as plasma boundary coordinates and motional Stark effect data are encoded using multi-layer perceptrons (MLPs), while profile inputs are encoded by 1D convolutional layers. The encoded data is passed through a MLP for latent feature extraction, before being decoded in the decoding layers, which consist of upsampling and convolutional layers. RTCAKENN has been implemented in the DIII-D PCS and our model achieves accuracy comparable to CAKE and surpasses existing real-time alternatives. Through clever dropout training, RTCAKENN exhibits robustness and can operate even in the absence of Thomson scattering data or charge exchange recombination data. It executes in under 8 ms in the real-time environment, enabling future application in real-time control and analysis.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2025

Reconstruction of current profiles from external magnetic and MSE measurements on DIII-D

This work introduces a new current model into the EFIT code for plasma current profile reconstruction. Using this model, edge-localized current density profiles are reconstructed solely from external magnetic measurements. Quantitative comparisons show that edge current profiles obtained with the new current model align closely with those from kinetic equilibrium reconstruction. The new model enables current density reconstruction with fewer diagnostics than kinetic equilibrium reconstruction (Lao et al 1990 Nucl. Fusion 30 1035–49), demonstrating that edge-localized current density information can be obtained from external magnetic measurements only, without the help of kinetic profiles and internal diagnostics, and without using the bootstrap current model. Furthermore, with the constraints of external magnetic and MSE measurements, current profiles in full radius obtained from the new model are in good agreement with the results of kinetic equilibrium reconstruction, which not only improves the efficiency of current reconstruction but also helps avoid possible errors caused by different kinds of diagnoses. Possible applications are also discussed, and a brief analysis of the evolution of the full-radius current density is performed. Noticeable decreases in both the magnitude and gradient of the edge current around the time of ELM bursts are observed. Moreover, analysis of the full radius current density profiles ( ρ N = 0 − 1.0, ρN denotes to square root of the normalized toroidal flux) reveals that as the edge current changes, the inner current also changes following a sinusoidal-like pattern at almost all time slices during four type-I ELMs in discharge 161493. The current evolution in the inner region ( ρ N = 0.2 − 0.6) is synchronized with the boundary region ( ρ N = 0.89 − 1.0), while the intermediate region ( ρ N = 0.6 − 0.89) shows opposite behavior. This sinusoidal-like variations in full-radius current density profile indicates strong core-pedestal coupling, suggesting ELMs significantly affect core plasmas, though current changes manifest differently across radial regions.

EFIT↗