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Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

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DOE OSTI2022

A classical equation that accounts for observations of non-Arrhenius and cryogenic grain boundary migration

Observations of microstructural coarsening at cryogenic temperatures, as well as numerous simulations of grain boundary motion that show faster migration at low temperature than at high temperature, have been troubling because they do not follow the expected Arrhenius behavior. This work demonstrates that classical equations, that are not simplified, account for all these oddities and demonstrate that non-Arrhenius behavior can emerge from thermally activated processes. According to this classical model, this occurs when the intrinsic barrier energies of the processes become small, allowing activation at cryogenic temperatures. Additional thermal energy then allows the low energy process to proceed in reverse, so increasing temperature only serves to frustrate the forward motion. This classical form is shown to reconcile and describe a variety of diverse grain boundary migration observations.

36 MATERIALS SCIENCE↗
DOE OSTI2025

Recommendations for Comprehensive and Independent Evaluation of Machine Learning‐Based Earth System Models

Abstract Machine learning (ML) is a revolutionary technology with demonstrable applications across multiple disciplines. Within the Earth science community, ML has been most visible for weather forecasting, producing forecasts that rival modern physics‐based models. Given the importance of deepening our understanding and improving predictions of the Earth system on all time scales, efforts are now underway to develop Earth‐system models (ESMs) capable of representing all components of the coupled Earth system (or their aggregated behavior) and their response to external changes over long timescales. Building trust in ESMs is a much more difficult problem than for weather forecast models, not least because the model must represent the alternate (e.g., future or paleoclimatic) coupled states of the system for which there are no direct observations. Given that the physical principles that enable predictions about the response of the Earth system are often not explicitly coded in these ML‐based models, demonstrating the credibility of ML‐based ESMs thus requires us to build evidence of their consistency with the physical system. To this end, this paper puts forward five recommendations to enhance comprehensive, standardized, and independent evaluation of ML‐based ESMs to strengthen their credibility and promote their wider use.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2022

Computational Tools and Workflows for Quantitative Risk Assessment and Decision Support for Geologic Carbon Storage Sites: Progress and Insights from the U.S. DOE’s National Risk Assessment Partnership

The 2005 Intergovernmental Panel on Climate Change (IPCC) Special Report on CCS raised the profile of CO2 capture and storage (CCS) as an important technology for reducing greenhouse gas (GHG) emissions. CCS is now recognized as a key component of most climate change mitigation scenarios. Since publication of that report the international research, development, and deployment (RD&D) community has advanced key technical aspects, clarified regulatory requirements, explored value chain and infrastructure solutions, and developed incentive paradigms to enable and promote large-scale deployment of CCS. These efforts have included research to better characterize geologic storage resources, to improve injection performance and storage efficiency, to assess and manage subsurface environmental risks, and to advance monitoring technologies to assure system conformance. These efforts have helped to build confidence in the viability of geologic carbon storage (GCS), but stakeholder concerns about long-term risks and liability associated with GCS remain a hurdle to broad acceptance and large-scale deployment of CCS. Since 2010, the U.S. DOE’s National Risk Assessment Partnership (NRAP) – a research collaboration between five contributing national laboratories – has worked to establish and demonstrate methods and tools to quantify and manage the subsurface environmental risks associated with GCS, amidst uncertainty. This work supports the Office of Fossil Energy and Carbon Management Carbon Transport and Storage Program’s goal of advancing safe and secure commercial-scale GCS deployment. To address the technical challenge of simulating the physical response of the GCS site to large-scale CO2 injection, NRAP has adopted an approach that relies on coupling computationally efficient reduced-order and/or data-driven proxy models of important system components (i.e., storage reservoir, sealing caprock, leakage pathways, intermediate formations, overlying groundwater aquifers, and the atmosphere) in integrated assessment framework. That integrated model of the physical system is complemented with fit-for purpose functionality to support site characterization and risk-related decisions. The recently released NRAP Phase II toolset includes the Open-Source Integrated Assessment Model (NRAP-Open-IAM) for evaluation of trends in leakage risk and potential impact, tools to support monitoring design optimization (Designs for Risk Evaluation and Management – DREAM v3.0 and Passive Seismic Monitoring Tool - PSMT), and tools for state of stress evaluation (State-of-Stress Analysis Tool - SOSAT) and forecasting induced seismicity risk. The NRAP team has also released a pair of reports describing conceptual workflows to incorporate physics-based, quantitative risk assessment into many of the design, planning, operation, and closure decisions for GCS projects. An online catalogue highlights published studies where these tools and methods are demonstrated. In this presentation, the utility of these products to assess risks and address key stakeholder questions will be highlighted through examples, and related insights about the safety and security of geologic carbon storage in qualified storage sites will be discussed. The prospect of rapid, large-scale deployment of GCS technology to aggressively reduce anthropogenic CO2 emissions requires careful consideration of interference between multiple commercial-scale storage projects within a basin. Going forward, NRAP is expanding and adapting site-scale risk quantification tools and methods to enable assessment of risks and inform management decisions for basin-scale deployment. Increasingly, this work will leverage next-generation approaches for surrogate modelling, fast prediction, and advanced visualization enabled by machine learning and artificial intelligence to promote virtual learning, scenario evaluation, and augment risk-based decision making.

quantitative risk assessment, geologic carbon stor↗
DOE OSTI2020

Learning in Modal Space: Solving Time-Dependent Stochastic PDEs Using Physics-Informed Neural Networks

One of the open problems in scientific computing is the long-time integration of nonlinear stochastic partial differential equations (SPDEs), especially with arbitrary initial data. We address this problem by taking advantage of recent advances in scientific machine learning and the spectral dynamically orthogonal (DO) and borthogonal (BO) methods for representing stochastic processes. The recently introduced DO/BO methods reduce the SPDE to solving a system of deterministic PDEs and a system of stochastic ordinary differential equations. Specifically, we propose two new physics-informed neural networks (PINNs) for solving time-dependent SPDEs, namely the neural network (NN)-DO/BO methods. The proposed methods incorporate the DO/BO constraints into the loss function (along with the modal decomposition of the SPDE) with an implicit form instead of generating explicit expressions for the temporal derivatives of the DO/BO modes. Hence, the NN-DO/BO methods can overcome some of the drawbacks of the original DO/BO methods. For example, we do not need the assumption that the covariance matrix of the random coefficients is invertible as in the original DO method, and we can remove the assumption of no eigenvalue crossing as in the original BO method. Moreover, the NN-DO/BO methods can be used to solve time-dependent stochastic inverse problems with the same formulation and same computational complexity as for forward problems. Furthermore, we demonstrate the capability of the proposed methods via several numerical examples, namely: (1) A linear stochastic advection equation with deterministic initial condition: we obtain good results with the proposed methods, while the original DO/BO methods cannot be applied directly in this case. (2) Long-time integration of the stochastic Burgers' equation: we show the good performance of NN-DO/BO methods, especially the effectiveness of the NN-BO approach for such problems with many eigenvalue crossings during the whole time evolution, while the original BO method fails. (3) Nonlinear reaction diffusion equation: we consider both the forward problem and the inverse problems, including very noisy initial point values, to investigate the flexibility of the NN-DO/BO methods in handling inverse and mixed type problems. Taken together, these simulation results demonstrate that the NN-DO/BO methods can be employed to effectively quantify uncertainty propagation in a wide range of physical problems, but future work should address the efficiency issue of PINNs for forward problems.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2021

The Attraction Indian Buffet Distribution

We propose the attraction Indian buffet distribution (AIBD), a distribution for binary feature matrices influenced by pairwise similarity information. Binary feature matrices are used in Bayesian models to uncover latent variables (i.e., features) that explain observed data. The Indian buffet process (IBP) is a popular exchangeable prior distribution for latent feature matrices. In the presence of additional information, however, the exchangeability assumption is not reasonable or desirable. The AIBD can incorporate pairwise similarity information, yet it preserves many properties of the IBP, including the distribution of the total number of features. Thus, much of the interpretation and intuition that one has for the IBP directly carries over to the AIBD. A temperature parameter controls the degree to which the similarity information affects feature-sharing between observations. Unlike other nonexchangeable distributions for feature allocations, the probability mass function of the AIBD has a tractable normalizing constant, making posterior inference on hyperparameters straight-forward using standard MCMC methods. A novel posterior sampling algorithm is proposed for the IBP and the AIBD. We demonstrate the feasibility of the AIBD as a prior distribution in feature allocation models and compare the performance of competing methods in simulations and an application.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2020

Basic Research Needs for Transformative Manufacturing (Brochure)

Manufacturing is central to the nation’s prosperity and security. Manufacturing currently represents about 12% of the gross domestic product, provides nearly 13 million jobs, and accounts for about 25% of energy use. The nation’s economy relies heavily on wide-ranging manufacturing sectors - all of which share common challenges including data issues, lack of physics and chemistry-based models across scales, and resource constraints in a global environment. Furthermore, there are many hurdles that must be overcome to move basic science innovations to market. Addressing broad-ranging challenges demands a basic-science strategy that underpins applied research activities. This strategy would accelerate innovation and transform manufacturing. A Basic Research Needs workshop for Transformative Manufacturing was held in March 2020. The focus of the workshop was to identify the basic science research priorities that could accelerate innovation to transform manufacturing in the future. This was the first workshop of its kind to examine how basic energy science can drive manufacturing forward and innovate new ways to manufacture goods. Five Priority Research Directions were identified that address these science challenges: (1) innovative synthetic approaches to enable scalable assembly of matter, (2) computational methods and theoretical models to transform how manufacturing processes are controlled, (3) new characterization tools that can handle the necessary complexity, scales, and processing speeds to meet manufacturing needs, (4) new science to address opportunities relevant to sustainable and energy-efficient manufacturing, and (5) foundational approaches to co-design of materials, process, and products.

32 ENERGY CONSERVATION, CONSUMPTION, AND UTILIZATI↗
DOE OSTI2022

Stochastic Modeling in a Multimaterial Continuum Mixture Shock Physics Code

Stochastic modelling approaches are presented to capture random effects at multiple time and length scales. Random processes that occur at the microscale produce nondeterministic effects at the macroscale. Here we present three stochastic modeling approaches that describe random processes at microscopic length scales and map these processes to the macroscopic length scale. The first stochastic modeling approach is based upon a particle based numerical technique to solve a Stochastic Differential Equation (SDE) using an arbitrary diffusion process to capture random processes at the microstructural level. The second approach prescribes a Probability Density Function (PDF) for the drift and diffusion of the random variable derived using the forward and backward Kolmogorov equations. This method requires mean and drift evolution PDF transport equations. The third approach is the coupling of multiple random variables which are dependent on each other. The relationship of the PDFs and a coupling function, known as a copula, produces a Joint Probability Density Function (JPDF). These stochastic modeling approaches are implemented into a Multiple Component (MC) shock physics computational code and used to model statistical fracture and reactive flow applications.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2020

Double differential distributions of e-emission in ionization of N 2 by 3,4 and 5 keV electron impact

In this paper, we report the measurement of the absolute double differential cross sections (DDCS) of secondary electrons emitted due to the ionization of N2 molecule in collisions with fast electrons having energies between 3 and 5 keV. The emitted electrons with energies from 1-500 eV have been measured for different forward and backward emission angles. The measured DDCS have been compared with the state-of-the-art first Born approximation with correct boundary condition (CB1) model calculations as well as with the classical trajectory Monte Carlo (CTMC) method. From the measured DDCS, the single differential cross sections (SDCS) as a function of the emission energies have been computed and eventually the total ionization cross sections (TCS) have been derived. The TCS values are also compared with a semi-empirical calculation, namely, the CSP-ic (complex scattering potential-ionization contribution) model.

74 ATOMIC AND MOLECULAR PHYSICS↗
DOE OSTI2023

Impact of high invariant-mass Drell-Yan forward-backward asymmetry measurements on SMEFT fits

We study the impact of LHC forward-backward asymmetry (AFB) measurements at high invariant mass in the Drell-Yan process on probes of semileptonic four-fermion operators in the Standard Model effective field theory (SMEFT). In particular, we study whether AFB measurements can resolve degeneracies in the Wilson coefficient parameter space that appear when considering invariant-mass and rapidity measurements alone. We perform detailed fits of the available high-energy and high-luminosity ATLAS and CMS data for both invariant-mass distributions and AFB. While each type of measurement separately exhibits degeneracies, combining them removes these blind spots in some cases. In other situations, it does not, highlighting the importance of incorporating future datasets from other experiments to fully explore this sector of the SMEFT. We investigate the impact of contributions quadratic in the Wilson coefficients on the description of Drell-Yan data and discuss when such terms are important in joint fits of the AFB and invariant-mass data.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2021

Spatiotemporal spread of perturbations in power-law models at low temperatures: Exact results for classical out-of-time-order correlators

Here, we present exact results for the classical version of the out-of-time-order commutator (OTOC) for a family of power-law models consisting of N particles in one dimension and confined by an external harmonic potential. These particles are interacting via power-law interaction of the form ∝ $Σ_{i,j=(i≠j)}^{N}$ |x i -x j | -k for every k>1 where x i is the position of the i th particle. We present numerical results for the OTOC for finite N at low temperatures and short enough times so that the system is well approximated by the linearized dynamics around the many-body ground state. In the large-N limit, we compute the ground-state dispersion relation in the absence of external harmonic potential exactly and use it to arrive at analytical results for OTOC. We find excellent agreement between our analytical results and the numerics. We further obtain analytical results in the limit where only linear and leading nonlinear (in momentum) terms in the dispersion relation are included. The resulting OTOC is in agreement with numerics in the vicinity of the edge of the “light cone.” We find remarkably distinct features in OTOC below and above k=3 in terms of going from non-Airy behavior (1 < k < 3) to an Airy universality class (k>3). We present certain additional rich features for the case k=2 that stem from the underlying integrability of the Calogero-Moser model. We present a field theory approach that also assists in understanding certain aspects of OTOC such as the sound speed. Our findings are a step forward towards a more general understanding of the spatiotemporal spread of perturbations in long-range interacting systems.

1-dimensional systems↗
DOE OSTI2025

Measurement of the production cross section of prompt $\Xi ^0_{\textrm{c}}$ baryons in p–Pb collisions at $\sqrt{s_{{\textrm{NN}}}}=5.02$ TeV

The transverse momentum (p T ) differential production cross section of the promptly produced charm-strange baryon $\Xi ^0_{\textrm{c}}$ (and its charge conjugate $\Xi ^0_{\textrm{c}}$) is measured at midrapidity via its hadronic decay into π + $\Xi$ – in p–Pb collisions at a centre-of-mass energy per nucleon–nucleon collision $\sqrt{s_{{\textrm{NN}}}}=5.02$ TeV with the ALICE detector at the LHC. The $\Xi ^0_{\textrm{c}}$ nuclear modification factor (R pPb ), calculated from the cross sections in pp and p–Pb collisions, is presented and compared with the R pPb of Λ$^{+}_{c}$ baryons. The ratios between the p T -differential production cross section of $\Xi ^0_{\textrm{c}}$ baryons and those of D 0 mesons and Λ$^{+}_{c}$ baryons are also reported and compared with results at forward and backward rapidity from the LHCb Collaboration. The measurements of the production cross section of prompt $\Xi ^0_{\textrm{c}}$ baryons are compared with a model based on perturbative QCD calculations of charm-quark production cross sections, which includes only cold nuclear matter effects in p–Pb collisions, and underestimates the measurement by a factor of about 50. This discrepancy is reduced when the data is compared with a model that includes string formation beyond leading-colour approximation or in which hadronisation is implemented via quark coalescence. The p T -integrated cross section of prompt $\Xi ^0_{\textrm{c}}$-baryon production at midrapidity extrapolated down to p T = 0 is also reported. These measurements offer insights and constraints for theoretical calculations of the hadronisation process. Additionally, they provide inputs for the calculation of the charm production cross section in p–Pb collisions at midrapidity.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2022

Theoretical tools for neutrino scattering: interplay between lattice QCD, EFTs, nuclear physics, phenomenology, and neutrino event generators

Maximizing the discovery potential of increasingly precise neutrino experiments will require an improved theoretical understanding of neutrino-nucleus cross sections over a wide range of energies. Low-energy interactions are needed to reconstruct the energies of astrophysical neutrinos from supernovae bursts and search for new physics using increasingly precise measurement of coherent elastic neutrino scattering. Higher-energy interactions involve a variety of reaction mechanisms including quasi-elastic scattering, resonance production, and deep inelastic scattering that must all be included to reliably predict cross sections for energies relevant to DUNE and other accelerator neutrino experiments. This white paper discusses the theoretical status, challenges, required resources, and path forward for achieving precise predictions of neutrino-nucleus scattering and emphasizes the need for a coordinated theoretical effort involved lattice QCD, nuclear effective theories, phenomenological models of the transition region, and event generators.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2023

Correct Compilation of Concurrent C Code

The CompCert compiler represents a landmark effort in program verification as both a piece of verified software and as a compiler for verified C programs. A key shortcoming of CompCert however is that it does not support multithreaded programs. Prior work to add threads to CompCert has either required major rewrites of parts of the proof or only works for well synchronized programs. The problem is that CompCert’s backward simulation derives from a forward simulation via the determinism of the semantics of intermediate representation languages. This makes the proofs in CompCert easier but also makes them incompatible with standard models of multithreading which are non-deterministic. Here we propose an alternate formulation of CompCert’s proof structure that parameterizes the existing single threaded semantics with nondeterministic behavior generated at the multithreading level. While this is an old trick where program equivalence is concerned, performing it in the context of CompCert is quite subtle. Our approach allows for expressive concurrent semantics and does not require major proof rewrites but still results in a global backward simulation for multithreaded programs.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2023

First Measurement of Inclusive Muon Neutrino Charged Current Triple Differential Cross Section on Argon

The field of accelerator neutrino experiments is entering an era of precision oscillation measurements where the remaining unknown neutrino measurements will be determined. The upcoming DUNE and Hyper-K experiments aim to determine the neutrino mass hierarchy and degree of Charge-Parity (CP) violation in the neutrino sector, providing potential insight on the matter-antimatter imbalance observed in the universe. However, these experiments require highly accurate measurements, and neutrino cross section modeling uncertainties may limit their capabilities. Cross section measurements at current- generation experiments can aid the development of neutrino interaction models to reduce these uncertainties. This is especially true for measurements of neutrino energy, as it drives neutrino oscillations and is of key importance to oscillation experiments. The MicroBooNE experiment uses a Liquid Argon Time Projection Chamber (LArTPC) to produce neutrino-argon cross sections as one of its physics goals. The MicroBooNE detector’s fully active volume, precision reconstruction, and calorimetry information are leveraged in the Wire-Cell analysis to produce a muon neutrino selection that is 92% pure while maintaining 68% efficiency. A reconstruction chain featuring a fully 3D charge reconstruction and a graph-based particle trajectory fit are used to produce accurate measurements of lepton kinematics as well as visible hadronic energy produced in a neutrino interaction. This thesis presents the first neutrino-argon triple-differential cross section measurement, targeting inclusive charged-current final states. Wiener SVD unfolding is used to produce a measurement over neutrino energy, muon momentum, and muon scattering angle. A series of constrained goodness of fit tests are used to demonstrate the validity of MicroBooNE’s model in describing the distribution of reconstructed kinematics seen in data to ensure the accuracy of unfolding. The validated unfolding to neutrino energy represents a step forward in the field of neutrino cross sections, and demonstrates the capabilities of the LArTPC detector.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2024

Surrogate construction via weight parameterization of residual neural networks

Surrogate model development is a critical step for uncertainty quantification or other sample-intensive tasks for complex computational models. Here, in this work, we develop a multi-output surrogate form using a class of neural networks (NNs) that employ shortcut connections, namely Residual NNs (ResNets). ResNets are known to regularize the surrogate learning problem and improve the efficiency and accuracy of the resulting surrogate. Inspired by the continuous, Neural ODE analogy, we augment ResNets with weight parameterization strategy with respect to ResNet depth. Weight-parameterized ResNets regularize the NN surrogate learning problem and allow better generalization with a drastically reduced number of learnable parameters. We demonstrate that weight-parameterized ResNets are more accurate and efficient than conventional feed-forward multi-layer perceptron networks. We also compare various options for parameterization of the weights as functions of ResNet depth. We demonstrate the results on both synthetic examples and a large scale earth system model of interest.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2021

Bayesian Poroelastic Aquifer Characterization From InSAR Surface Deformation Data. 2. Quantifying the Uncertainty

Uncertainty quantification of groundwater (GW) aquifer parameters is critical for efficient management and sustainable extraction of GW resources. These uncertainties are introduced by the data, model, and prior information on the parameters. We develop a Bayesian inversion framework that uses Interferometric Synthetic Aperture Radar (InSAR) surface deformation data to infer the laterally heterogeneous permeability of a transient linear poroelastic model of a confined GW aquifer. The Bayesian solution of this inverse problem takes the form of a posterior probability density of the permeability. Exploring this posterior using classical Markov chain Monte Carlo (MCMC) methods is computationally prohibitive due to the large dimension of the discretized permeability field and the expense of solving the poroelastic forward problem. However, in many partial differential equation (PDE)-based Bayesian inversion problems, the data are only informative in a few directions in parameter space. For the poroelasticity problem, we prove this property theoretically for a one-dimensional problem and demonstrate it numerically for a three-dimensional aquifer model. Here we design a generalized preconditioned Crank-Nicolson (gpCN) MCMC method that exploits this intrinsic low dimensionality by using a low-rank-based Laplace approximation of the posterior as a proposal, which we build scalably. The feasibility of our approach is demonstrated through a real GW aquifer test in Nevada. The inherently two-dimensional nature of InSAR surface deformation data informs a sufficient number of modes of the permeability field to allow detection of major structures within the aquifer, significantly reducing the uncertainty in the pressure and the displacement quantities of interest.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2022

Evaluation of a collisional radiative model for electron temperature determination in hydrogen plasma

A collisional-radiative (CR) model that extracts the electron temperature, T e , of hydrogen plasmas from Balmer-line-ratio measurements is examined for the plasma electron density, n e , and T e ranges of 10 10 –10 15 cm –3 and 5–500 eV, respectively. The CR code, developed and implemented in Python, has a forward component that computes the densities of excited states up to n = 15 as functions of T e , n e , and the molecular-to-atomic neutral ratio r(H 2 /H). The backward component provides ne and r(H 2 /H) as functions of the Balmer ratios to predict the T e . The model assumes Maxwellian electrons. Furthermore, the density profiles of the electrons and of the molecular and atomic hydrogen neutrals are shown to be of great importance, as is the accuracy of the line-ratio measurement method.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2022

Neural net modeling of equilibria in NSTX-U

Neural networks (NNs) offer a path towards synthesizing and interpreting data on faster timescales than traditional physics-informed computational models. In this work we develop two NNs relevant to equilibrium and shape control modeling, which are part of a suite of tools being developed for the National Spherical Torus Experiment-Upgrade for fast prediction, optimization, and visualization of plasma scenarios. The networks include Eqnet, a free-boundary equilibrium solver trained on the EFIT01 (Equilibrium FITtting 01) reconstruction algorithm, and Pertnet, which is trained on the Gspert code and predicts the non-rigid plasma response, a nonlinear term that arises in shape control modeling. The NNs are trained with different combinations of inputs and outputs in order to offer flexibility in use cases. In particular, Eqnet can use magnetic diagnostics as inputs and act as an EFIT-like reconstruction algorithm, or, by using pressure and current profile information the NN can act as a forward Grad–Shafranov equilibrium solver. This forward-mode version is envisioned to be implemented in the suite of tools for simulation of plasma scenarios. The reconstruction-mode version gives some performance improvements compared to the online reconstruction code real-time EFIT, especially when vessel eddy currents are significant. Here, we report strong performance for all NNs indicating that the models could reliably be used within closed-loop simulations or other applications. Some limitations are discussed.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗