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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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At least 577 records · Page 32
All sourcesNASA NTRSDOE OSTI
DOE OSTI2023

Laminar flame speed measurements of a gasoline surrogate and its mixtures with ethanol at elevated pressure and temperature

Laminar Flame speed measurements of a gasoline surrogate and mixtures of it with ethanol were conducted using a heated, constant-volume vessel. A spherical propagating flame was observed using a high-speed camera, and laminar flame speed was determined therefrom. Here, the gasoline surrogate, which serves as the baseline for the current study, consisted of four components, namely, iso-octane, n-heptane, toluene, and 1-hexene. Different mixtures of the gasoline surrogate and ethanol were studied, governed by the ethanol percentage in the mixture. That is, E0, E30, E50, and E85 mixtures represent 0%, 30%, 50%, and 85% ethanol in the gasoline surrogate mixture by liquid volume, respectively. Initial temperatures of 335, 359, and 408 K and initial pressures of 1 and 3 bar were investigated. The findings of this study are compared to results in the literature, which show good agreement for E0 but some deviation for the E30 blend. In general, the study showed an increase in laminar flame speed as the ethanol percentage increases in the mixture. Similarly, increasing the initial temperature with fixed ethanol percentage resulted in an increase in laminar flame speed, as expected. In contrast, increasing the initial pressure with fixed Ethanol percentage showed a decrease in laminar flame speed. Finally, the results are compared to an existing chemical kinetics model designed for ethanol and gasoline. Although agreement between the model and data is reasonable and mostly within about 10%, some improvement to the kinetics model is needed to uniformly lower the calculated flame speeds.

09 BIOMASS FUELS↗
DOE OSTI2024

Can Third-Body Stabilization of Bimolecular Collision Complexes in Cold Molecular Clouds Happen?

For more than half a century, networks of radiative association, dissociative recombination, and bimolecular reactions have been postulated to drive the low-temperature chemistry of cold molecular clouds. Third-body stabilizations of collision complexes have been assumed to be 'irrelevant' due to short lifetime of such complexes. Here, we conduct crossed molecular beam studies of ground state atomic silicon with diacetylene in combination with electronic structure calculations and microcanonical kinetics models operating under cold molecular cloud conditions. Our combined experimental, electronic structure, and microcanonical kinetics modelling investigations provide compelling evidence that three-body collisions of molecular hydrogen with long-lived reaction intermediates accessed through intersystem crossing are prevalent deep inside molecular clouds. This concept might be exportable to reactions involving polycyclic aromatic hydrocarbons thus affording a versatile machinery to complex organics via third-body stabilizations of bimolecular collision complexes deep inside cold molecular clouds.

astrochemistry↗
DOE OSTI2020

Towards a UV model of kinetic mixing and portal matter

The nature of dark matter (DM) and how it might interact with the particles of the Standard Model (SM) is an ever-growing mystery. It is possible that the existence of new “dark sector” forces, yet undiscovered, are the key to solving this fundamental problem, and one might hope that in the future such forces might even be “unified” with the ones we already know in some UV-complete framework. In this paper, following a bottom-up approach, we attempt to take the first steps in the construction of such a framework. The much-discussed possibility of the kinetic mixing (KM) of the “dark photon” with the hypercharge gauge boson of the SM via loops of portal matter (PM) fields, charged in both sectors, offers an attractive starting point for these efforts. Given the anticipated finite strength of the KM in a UV-complete theory, the absence of anomalies, and the lifetime constraints on the PM fields arising from cosmic microwave background and nucleosynthesis constraints, PM must behave as vector-like copies of the known SM fermion fields, such as those which appear naturally in, e.g., E 6 -type models. Within such a setup, the SM and their corresponding partner PM fields would be related by a new S U ( 2 ) I gauge symmetry. With this observation as a springboard, we construct a generalization of these ideas where S U ( 2 ) I is augmented by an additional U ( 1 ) I Y factor so that the light dark photon is the result of a symmetry breaking analogous to the SM, i.e., S U ( 2 ) I × U ( 1 ) I Y → U ( 1 ) D , but with U ( 1 ) D now also broken at the ≲ GeV scale. While SM fields are U ( 1 ) D singlets, as in the conventional dark photon approach, they transform nontrivially under the full S U ( 2 ) I × U ( 1 ) I Y gauge group. This approach leads to numerous interesting signatures, both at low energies and at colliders, and can be viewed as an initial step in the construction of a more UV-complete framework.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2025

A neural master equation framework for multiscale modeling of molecular processes: application to atomic-scale plasma processes

Plasma-surface interactions (PSI) play a crucial role in microelectronics fabrication; however, their multiscale nature and array of complex, often unknown interactions make computational modeling of PSIs extremely difficult. To this end, we propose a general neural master equation (NME) framework that uses master equations to describe the dynamics of a molecular process, wherein neural networks learned from atomistic simulations represent unknown transitions between different system states. By leveraging the physics-based structure of master equations and data-driven state transitions, the NME framework promotes generalizability and physics interpretability, and can bridge disparate length and time scales. The framework is demonstrated for multiscale modeling of Si atomic layer etching and reactive ion etching, where the learned NME-based surface kinetic models exhibit good predictive and extrapolative capabilities for predicting experimentally relevant observables as a function of process parameters. The NME-based surface kinetic models obey physical constraints, which are violated in models based on neural ordinary differential equations. The proposed NME framework for multiscale modeling of molecular processes can pave the way for the discovery of new chemistries and materials in atomic-scale plasma processes.

Chemical engineering↗
DOE OSTI2018

New operando method for quantifying the relative half-cycle rates of the NO SCR redox cycle over Cu-exchanged zeolites

An operando experimental method for monitoring relative variations in half-cycle rates of the Cu redox-cycle model of selective-catalytic-reduction (SCR) is demonstrated, along with a kinetic model for predicting the same. Conversion inflections (CI) can occur at SCR onset within Cu/SCR catalysts; transient CI involves initial conversion growth to an intermediate value greater than exists at steady state (SS) before degrading to the SS value. While similar CI has been reported for Fe/SCR catalysts as being due to NH 3 inhibition, Cu/SCR CI is inconsistent with a similar origin. Rather, Cu/SCR CI is due to imbalances in the redox-half-cycle rates, and will occur when reduction is faster than oxidation. The temporal CI shape varies with the redox-cycle kinetic parameters and model formulation, and can be used to study the same. Here, we demonstrate the first measurements of dynamic half-cycle rate balancing at SCR onset, use CI and onset transients to study variations in half-cycle rates under Standard, Fast and NO 2 SCR, and present the first redox-cycle model showing CI. The new operando method and model provides a basis for better understanding the SCR redox process, and determining the individual half-cycles kinetic model formulation and parameters.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2024

Toward UV models of kinetic mixing and portal matter. V. Indirect probes of the new physics scale

Kinetic mixing of the dark photon, the gauge boson of a hidden U ( 1 ) D , with the Standard Model (SM) gauge fields to induce an interaction between ordinary matter and dark matter (DM) at 1-loop requires the existence of portal matter (PM) fields having both dark and SM charges. As discussed in earlier work, these same PM fields can also lead to other loop-level mechanisms besides kinetic mixing that can generate significant interactions between SM fermions and the dark photon in a manner analogous to those that can be generated between a Dirac neutrino and a SM photon, i.e., dark moments. In either case, there are reasons to believe, e.g., due to the renormalization group equation running of the U ( 1 ) D gauge coupling, that PM fields may have ∼ TeV -scale masses that lie at or above those directly accessible to the HL-LHC. If they lie above the reach of the HL-LHC, then the only way to possibly explore the physics at this high scale in the short term is via indirect measurements made at lower energies, e.g., at lepton colliders operating in the m Z to 1 TeV range. In particular, processes such as e + e − → γ + DM or e + e − → f ¯ f , where f is a SM fermion, may be most useful in this regard. Here we explore these possibilities within the framework of a simple toy PM model, introduced in earlier work, based on a non-Abelian dark gauge group completion operating at the PM scale. In the kinetic mixing setup, we show these efforts fail due to the inherently tiny cross sections in the face of substantial SM backgrounds. However, in the case of interactions via induced dark moments, since they necessarily take the form of higher dimensional operators whose influence grows with energy, we show that access to PM-scale information may become possible for certain ranges of the toy model parameters for both of these e + e − processes at a 1 TeV collider. Published by the American Physical Society 2024

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2024

Rotating cylinder electrode in reactive CO 2 capture: Identifying active C species via transport, VLE models and kinetics

Here, this article explores technical challenges and potential methodologies for understanding electrochemical Reactive CO 2 Capture (RCC) mechanisms. RCC offers potential energy cost advantages by directly converting captured CO 2 into fuels and chemicals, unlike traditional carbon capture and utilization (CCU) processes that require sequential capture, concentration, and compression. However, direct conversion of captured CO 2 introduces complexity due to additional equilibrium buffer reactions, making it challenging to identify active species for reduction in electrochemical studies. This article discusses methods to integrate transport, thermodynamics, and kinetics concepts to identify active carbon sources in RCC. Vapor‐Liquid Equilibrium (VLE) and transport models are validated against experimental results obtained in a gastight rotating cylinder electrode reactor and are shown as useful tools for studying RCC in heterogeneous electrocatalysts across different capture agents, solvents, and temperatures. This article establishes an experimental framework for advancing research in electrochemical RCC.

Electrocatalysis↗
DOE OSTI2020

Cool flame chemistry of diesel surrogate compounds: n -Decane, 2-methylnonane, 2,7-dimethyloctane, and n -butylcyclohexane

Elucidating the formation of combustion intermediates is crucial to validate reaction pathways, develop reaction mechanisms and examine kinetic modeling predictions. While high-temperature pyrolysis and oxidation intermediates of alkanes have been thoroughly studied, comprehensive analysis of cool flame intermediates from alkane autoxidation is lacking and challenging due to the complexity of intermediate species produced. Here, jet-stirred reactor autoxidation of four C 10 alkanes: n -decane, 2-methylnonane, 2,7-dimethyloctane, and n -butylcyclohexane, as model compounds of diesel fuel, was investigated from 500 to 630 K using synchrotron vacuum ultraviolet photoionization molecular beam mass spectrometry (SVUV-PIMS). Around 100 intermediates were detected for each fuel. The classes of molecular structures present during the autoxidation of the representative paraffinic functional groups in transport fuels, i.e., n -alkanes, branched alkanes, and cycloalkanes were established and were found to be similar from the oxidation of various alkanes. A theoretical approach was applied to estimate the photoionization cross sections of the intermediates with the same carbon skeleton as the reactants, e.g., alkene, alkenyl keto, cyclic ether, dione, keto-hydroperoxide, diketo-hydroperoxide, and keto-dihydroperoxide. These species are indicators of the first, second, and third O 2 addition reactions for the four C 10 hydrocarbons, as well as bimolecular reactions involving keto-hydroperoxides. Chemical kinetic models for the oxidation of these four fuels were examined by comparison against mole fraction of the reactants and final products obtained in additional experiments using gas chromatography analysis, as well as the detailed species pool and mole fractions of aforementioned seven types of intermediates measured by SVUV-PIMS. This works reveals that the models in the literature need to be improved, not only the prediction of the fuel reactivity and final products, but also the reaction network to predict the formation of many previous undetected intermediates.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2023

Quantifying the Variation in the Number of Donors in Quantum Dots Created Using Atomic Precision Advanced Manufacturing

Atomic-precision advanced manufacturing enables unique silicon quantum electronics built on quantum dots fabricated from small numbers of phosphorus dopants. The number of dopant atoms comprising a dot plays a central role in determining the behavior of charge and spin confined to the dots and thus overall device performance. Here in this work, we use both theoretical and experimental techniques to explore the combined impact of lithographic variation and stochastic kinetics on the number of P incorporations in quantum dots made using these techniques and how this variation changes as a function of the size of the dot. Using a kinetic model of PH3 dissociation augmented with novel reaction barriers, we demonstrate that for a 2 × 3 silicon dimer window the probability that no donor incorporates goes to zero, allowing for certainty in the placement of at least one donor. However, this still comes with some uncertainty in the precise number of incorporated donors (either one or two), and this variability may still impact certain applications. We also examine the impact of the size of the initial lithographic window, finding that the incorporation fraction saturates to δ-layer-like coverage as the circumference-to-area ratio decreases. We predict that this incorporation fraction depends strongly on the dosage of the precursor and that the standard deviation of the number of incorporations scales as ~√n, as would be expected for a sequence of largely independent incorporation events. Finally, we characterize an array of 36 experimentally prepared multidonor 3 × 3 nm lithographic windows with scanning tunneling microscopy, measuring the fidelity of the lithography to the desired array and the final location of PH x fragments within these lithographic windows. We use our kinetic model to examine the expected variability due to the observed lithographic error, predicting a negligible impact on incorporation statistics. We find good agreement between our model and the inferred incorporation locations in these windows from scanning tunneling microscope measurements.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2016

Iron-Mediated Oxidation of Methoxyhydroquinone under Dark Conditions: Kinetic and Mechanistic Insights

Despite the biogeochemical significance of the interactions between natural organic matter (NOM) and iron species, considerable uncertainty still remains as to the exact processes contributing to the rates and extents of complexation and redox reactions between these important and complex environmental components. Investigations on the reactivity of low-molecular-weight quinones, which are believed to be key redox active compounds within NOM, toward iron species, could provide considerable insight into the kinetics and mechanisms of reactions involving NOM and iron. Here in this study, the oxidation of 2-methoxyhydroquinone (MH 2 Q) by ferric iron (Fe(III)) under dark conditions in the absence and presence of oxygen was investigated within a pH range of 4-6. Although Fe(III) was capable of stoichiometrically oxidizing MH 2 Q under anaerobic conditions, catalytic oxidation of MH 2 Q was observed in the presence of O 2 due to further cycling between oxygen, semiquinone radicals, and iron species. A detailed kinetic model was developed to describe the predominant mechanisms, which indicated that both the undissociated and monodissociated anions of MH 2 Q were kinetically active species toward Fe(III) reduction, with the monodissociated anion being the key species accounting for the pH dependence of the oxidation. The generated radical intermediates, namely semiquinone and superoxide, are of great importance in reaction-chain propagation. In conclusion, the kinetic model may provide critical insight into the underlying mechanisms of the thermodynamic and kinetic characteristics of metal-organic interactions and assist in understanding and predicting the factors controlling iron and organic matter transformation and bioavailability in aquatic systems.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2019

Iron-mediated oxidation of methoxyhydroquinone at Rifle, Colorado

In this study, the oxidation of 2-methoxyhydroquinone (MH2Q) by ferric iron (Fe(III)) under dark conditions in the absence and presence of oxygen was investigated within a pH range of 4 – 6. While Fe(III) was capable of stoichiometrically oxidizing MH2Q under anaerobic conditions, catalytic oxidation of MH2Q was observed in the presence of O2 due to further cycling between oxygen, semiquinone radicals, and iron species. A detailed kinetic model was developed to describe the predominant mechanisms, which indicated that both the undissociated and mono-dissociated anions of MH2Q were kinetically active species towards Fe(III) reduction, with the mono-dissociated anion being the key species accounting for the pH dependence of the oxidation. The generated radical intermediates, namely semiquinone and superoxide, are of great importance in reaction chain propagation. The kinetic model may provide critical insight into the underlying mechanisms of the thermodynamic and kinetic characteristics of metal-organic interactions and assist in understanding and predicting the factors controlling iron and organic matter transformation and bioavailability in aquatic systems.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2019

Study of the Influence of Xanthate Derivative Structures on Copper Sulfide Mineral Adsorption Under Acidic Conditions

Adsorption of commercial xanthate derivatives on copper sulfide mineral (covellite, CuS) was studied by kinetics and isotherm adsorption experiments. The adsorption of xanthate derivatives was confirmed by FTIR (Fourier transform infrared spectroscopy) and XPS (X-ray photoelectron spectroscopy) results. Experiments were performed with two different xanthate derivatives, C-4410 (O-pentyl S-2-propenyl ester) and C-4940 (isobutyl xanthogen ethyl formate), on individual doses of 0.05 g of powdered covellite. It was found that the equilibrium times at pH 2, 4, and 6 were different for both xanthate derivatives. The shortest times were achieved at pH 2 and 4. The results suggest that C-4110 can be used as collector in a wide range of pH, while C-4940 is limited to lower pH values. Pseudo first- and pseudo second-order kinetics models were thus applied to the experimental data for pH 2. The information obtained from the kinetics models combined with XPS allowed proposing the adsorption mechanism for the covellite-xanthate derivative pair. The adsorption takes place through a non-covalent interaction for C-4410 and chemisorption process for C-4940. The best-fitting isotherm models for C-4410 and C-4940 adsorption were Redlich–Peterson and Freundlich, respectively, which yield a maximum adsorption capacity of 57.07 mg g{sup −1} for C-4410 and 44.62 mg g{sup −1} for C-4940.

36 MATERIALS SCIENCE↗
DOE OSTI2021

Oxidation of an iso-paraffinic alcohol-to-jet fuel and n-heptane mixture: an experimental and modelling study

Oxidation of ATJ/n-heptane blends was studied over a wide range of test conditions, using single pulse shock tubes. Test conditions were designed to study the effect of pressure (4 and 50 bar), and fuel loading (~100-1400 ppm) on the oxidation of the blends across a wide range of temperatures (800-1300 K). These effects were observed by measuring concentrations of intermediate species formed using in-line Gas Chromatography (GC) and GCxGC TOF-MS. Results showed that increasing the initial fuel load does not have a significant impact on the results. However, increasing the pressure shifts the mixture reactivity to a lower temperature by about 150 K and causes the fuel to be oxidized instead of decomposing pyrolytically as at lower pressures. Additional experiments for pure ATJ and pure n-heptane were performed at conditions matching the ATJ/n-heptane 50 bar experiments to analyze the differences between the pure and mixed fuels. Speciation measurements were compared against predictions from a detailed kinetic model. The ability of the kinetic model to capture the effects of varying experimental test conditions on the evolution of intermediate species is discussed and kinetic analyses have been conducted to identify the important reaction pathways.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2018

Dynamic recrystallization kinetics and microstructure evolution of an AZ91D magnesium alloy during hot compression

Highlights: • DRX kinetic model is developed for the aged AZ91D magnesium alloy. • The DRX behavior in different strained regions was investigated. • Four morphologies of the second phase were proposed during the hot compression tests. • The nucleation mechanisms of the DRX grains were clarified. - Abstract: The flow behavior of as-cast AZ91D magnesium alloy was evaluated by isothermal compression tests within the temperatures of 220 °C, 260 °C, 300 °C, 340 °C, and 380 °C, and the strain rates of 0.001, 0.01, 0.1, 1 and 10s{sup −1}. Based on the stress-strain curve and hyperbolic sine function, the thermal activation energy and the strain rate sensitivity of the material were determined to be 142.2726 kJ·mol{sup −1} and 0.142, respectively. The S type evolution of the dynamic recrystallization with the increasing strain that dynamic recrystallization (DRX) model obtained from stress and strain data. There was a good consistency between the proposed DRX kinetics model and microstructure observation results. Combining isothermal compression specimens with finite element and scanning electron microscopy (SEM) analysis indicated that the sample can be divided into rarely recrystallized region, partially recrystallized region and completely recrystallized region, which falls within the dense deformation zone, free deformation zone and severe deformation zone, respectively. The different forms of the β-Mg{sub 17}Al{sub 12} phase induced by compression tests were confirmed by SEM. Nucleation mechanisms of the DRX were discussed with reference to the transmission electron microscope (TEM) analysis results.

36 MATERIALS SCIENCE↗
DOE OSTI2017

A 4 U laser heterodyne radiometer for methane (CH 4 ) and carbon dioxide (CO 2 ) measurements from an occultation-viewing CubeSat

An experimental and kinetic modeling study of the autoignition of 3-methylheptane, a compound representative of the high molecular weight lightly branched alkanes found in large quantities in conventional and synthetic aviation kerosene and diesel fuels, is reported. Shock tube and rapid compression machine ignition delay time measurements are reported over a wide range of conditions of relevance to combustion engine applications: temperatures from 678 to 1356 K; pressures of 6.5, 10, 20, and 50 atm; and equivalence ratios of 0.5, 1.0, and 2.0. The wide range of temperatures examined provides observation of autoignition in three reactivity regimes, including the negative temperature coefficient (NTC) regime characteristic of paraffinic fuels. Comparisons made between the current ignition delay measurements for 3-methylheptane and previous results for n-octane and 2-methylheptane quantifies the influence of a single methyl substitution and its location on the reactivity of alkanes. It is found that the three C8 alkane isomers have indistinguishable high-temperature ignition delay but their ignition delay times deviate in the NTC and low-temperature regimes in correlation with their research octane numbers. The experimental results are compared with the predictions of a proposed kinetic model that includes both high- and low-temperature oxidation chemistry. The model mechanistically explains the differences in reactivity for n-octane, 2-methylheptane, and 3-methylheptane in the NTC through the influence of the methyl substitution on the rates of isomerization reactions in the low-temperature chain branching pathway, that ultimately leads to ketohydroperoxide species, and the competition between low-temperature chain branching and the formation of cyclic ethers, in a chain propagating pathway.

3-Methylheptane↗
DOE OSTI2019

Mechanism of Catalytic O2 Reduction by Iron Tetraphenylporphyrin

The catalytic reduction of O2 to H2O is important for energy transduction in both synthetic and natural systems. Herein, we report a kinetic study of O2 reduction catalyzed by iron tetraphenylporphyrin in N,N-dimethylformamide using decamethylferrocene as a soluble reductant and para-toluenesulfonic acid (pTsOH) as the proton source. Reduction of the ferric porphyrin, [FeIII(TPP)]+ , forms the ferrous porphyrin, FeII(TPP), which binds O2 reversibly to form the ferric-superoxide porphyrin complex, FeIII(TPP)(O2 •?). The temperature dependence of both the electron transfer and O2 binding equilibrium constants have been determined. Kinetic studies over a range of concentrations and temperatures show that the catalyst resting state changes during the course of each catalytic run, necessitating the use of global kinetic modeling to extract rate constants and kinetic barriers. The rate-determining step in oxygen reduction is protonation of FeIII(TPP)(O2•?) by pTsOH, which proceeds with a substantial kinetic barrier. Computational studies indicate that this barrier for proton transfer arises from an unfavorable pre-association of the proton donor with the superoxide adduct and a transition state that requires significant desolvation of the proton donor. Together, these results are the first example of oxygen reduction by iron tetraphenylporphyrin where the pre-equilibria between ferric, ferrous, and ferric-superoxide intermediates have been quantified under catalytic conditions. This work gives a generalizable model for the mechanism of iron porphyrin-catalyzed ORR and provides an unusually complete mechanistic study of an ORR reaction. More broadly, this study also highlights the kinetic challenges for proton transfer to catalytic intermediates in organic media.

Pegis, Michael L.↗
DOE OSTI2020

Deep learning surrogate model for kinetic Landau-fluid closure with collision

In this work, the kinetic Landau-fluid (LF) closure with collision and periodic boundary condition is used in the development of the deep learning (DL) surrogate model. A classical neural network, namely, feedforward neural network or sometimes termed multilayer perceptron, is constructed and trained to learn the kinetic LF closure in the static limit and arbitrary mean free path in configuration space. The preliminary relation between best hyperparameters and critical parameters for data generation is found. Compared with the numerical approach (non-Fourier method) of the LF closure, the deep learning surrogate model shows an order of magnitude of improvement in terms of accuracy. Perhaps most importantly, the surrogate model closure has been integrated for the first time with fluid simulations. Our DL-enabled fluid simulations, for the first time, give the correct Landau damping rate for a wide range of wave vectors, while the Hammett–Perkins closure cannot produce the correct damping rate. We correctly connect the collisionless Hammett–Perkins closure and collisional Braginskii closure to reproduce the intrinsic nonlocal feature of the heat flux with DL techniques. We address the most concerning error accumulation problem and find that simulations with the deep learning surrogate model are as good as, if not better than, simulations with the analytic closure in terms of long-term numerical stability in the linear Landau damping test.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗