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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 397 records · Page 22
All sourcesNASA NTRSDOE OSTI
DOE OSTI2020

Updates to Relevance Vector Machine: Multiclass Classification, Variable Selection, and Proof-of-Concept Application to Safeguards Fresh Fuel Verification using List-Mode Neutron Collar Data

To expand the capabilities of safeguards authorities to verify the integrity of fresh fuel assemblies, Oak Ridge National Laboratory has retrofit the existing electronics of the JCC-71 uranium neutron coincidence collar, which contains 18 3 He neutron detectors and an external 241 AmLi(α, n) neutron interrogation source arranged to surround a fresh nuclear fuel assembly. The new electronics system allows analysts to record list-mode neutron multiplicity data in addition to the singles and doubles rates that are currently measured. Based on previous proof-of-concept research, analysis of these new data will identify off-normal fuel configurations in an assembly and characterize or localize the specific partial fuel defects. The purpose of this report it to document the analysis algorithm development and then to demonstrate its capability for the safeguards verification of fresh fuel assemblies using list mode neutron collar data. To analyze the complex list-mode data collected with the upgraded uranium neutron collar, multivariate classification algorithms are being developed using a novel classification method, the relevance vector machine. This approach may be applied to multiclass problems to estimate the probability that test data belongs to one of many possible classes of data. In addition, our method identifies the most useful variables/channels for making predictions, which illuminates the basis for the model’s predictions, and this interpretability is largely unique among data analytics methods. Variable selection occurs during model training and parameter tuning and does not need any external hyperparameter tuning routines. Finally, we apply the modified relevance vector machine to a simulated dataset of list-mode neutron collar data generated with the radiation transport code MCNP. The method can correctly identify off-normal fuel configurations, categorize the data according to four fuel defect scenarios, and rank the channels in the data according to prediction utility. For nuclear safeguards applications, it is concluded that this method has the potential to increase the sensitivity and reliability to detect missing fuel rods from a standard 17 x 17 Pressurized Water Reactor (PWR) fresh fuel assembly. Within this analysis, “off-normal” (i.e., missing fuel rods) were correctly classified in 17 simulated test scenarios with one quarter (25%) of the fresh fuel rods missing using a training data set of 58 simulated measurements.

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗
DOE OSTI2020

Assessing the blockage effect of wind turbines and wind farms using an analytical vortex model

Wind farm blockage effects are currently neglected in the prediction of wind farm energy yield, typically leading to an overestimation of the production. This work presents a novel method to assess wind farm production, while accounting for blockage effects. We apply a vortex model, based on a cylindrical wake, to assess induction effects. We present variations of the model to account for finite wake length, finite tip-speed ratios, and the proximity to the ground. The results are applied to single rotors in aligned and yawed conditions and to different wind farm layouts. We provide far-field approximations for faster estimates of the velocity field. Further, this article includes a new methodology to couple the induction model to engineering wake models, such as the ones present in the FLOw Redirection and Induction in Steady State (FLORIS). We compare the results to actuator disk simulations for various operating conditions of a single turbine and different wind farm layouts. We found that the mean relative error of the model in the induction zone is typically around 0.2% compared with actuator disk simulations. The computational time of the velocity field using the analytical vortex model is three orders of magnitude less than the one obtained with the actuator disk simulation.

17 WIND ENERGY↗
DOE OSTI2021

A Deep Learning Modeling Framework to Capture Mixing Patterns in Reactive-Transport Systems

Prediction and control of chemical mixing are vital for many scientific areas such as subsurface reactive transport, climate modeling, combustion, epidemiology, and pharmacology. Due to the complex nature of mixing in heterogeneous and anisotropic media, the mathematical models related to this phenomenon are not analytically tractable. Numerical simulations often provide a viable route to predict chemical mixing accurately. However, contemporary modeling approaches for mixing cannot utilize available spatial-temporal data to improve the accuracy of the future prediction and can be compute-intensive, especially when the spatial domain is large and for long-term temporal predictions. To address this knowledge gap, in this work we will present in this paper a deep learning (DL) modeling framework applied to predict the progress of chemical mixing under fast bimolecular reactions. This framework uses convolutional neural networks (CNN) for capturing spatial patterns and long short-term memory (LSTM) networks for forecasting temporal variations in mixing. By careful design of the framework—placement of non-negative constraint on the weights of the CNN and the selection of activation function, the framework ensures non-negativity of the chemical species at all spatial points and for all times. Our DL-based framework is fast, accurate, and requires minimal data for training. The time needed to obtain a forecast using the model is a fraction (≈ O(-6)) of the time needed to obtain the result using a high-fidelity simulation. To achieve an error of 10% (measured using the infinity norm) for capturing local-scale mixing features such as interfacial mixing, only 24% to 32% of the sequence data for model training is required. To achieve the same level of accuracy for capturing global-scale mixing features, the sequence data required for model training is 64% to 70% of the total spatial-temporal data. Hence, the proposed approach—a fast and accurate way to forecast long-time spatial-temporal mixing patterns in heterogeneous and anisotropic media—will be a valuable tool for modeling reactive-transport in a wide range of applications.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2023

Temperature Dependence of Band Gap Renormalization in High-T Sensor Materials via First-Principles and Experimental Corroboration

Understanding the temperature dependence of functional properties of high-T gas sensing materials is vital for their applications in combustion environments. The electron-phonon coupling that derives the electronic structure change with temperatures is a key property of interest as it affects other sensing responses. Herein, we assess the temperature dependence of band gap renormalization in metal oxides and perovskites by employing Allen-Heine-Cardona theory with first-principles simulations and corroborate with experimental observation. The calculated temperature-dependent band gap changes of these materials studied are in good agreement with in-house experimental data, proving that the theory can adequately predict renormalization on the band gap in the system of interest. The predicted and measured band gap variations are characterized using an analytical model, which can provide useful insights on the simulated zero-temperature band gaps. Based on the available data, a set of 53 metal oxides and perovskites were identified as potential high-T gas sensors. A machine learning model has been developed to predict the band-gap change by capturing the overall trend of the empirical parameters with respect to a reduced feature obtained by transforming the set of available physical features.

Park, Jongwoo↗
DOE OSTI2023

Lithium-Ion Battery Diagnostics Using Electrochemical Impedance via Machine-Learning

Diagnosing battery states such as health, state-of-charge, or temperature is crucial for ensuring the safety and reliability of electrochemical energy storage systems. While some states, such as temperature, may be measured using cheap sensors, accurate diagnosis of battery health metrics usually requires time-consuming performance measurements, making them infeasible for use in real-world operation. These health metrics can be measured during lab-testing and then estimated on-line using predictive life models or via state observer algorithms such as Kalman filters, but these predictive methods should be supplemented by actual measurement of battery health whenever possible to ensure reliability. Rapid measurement of battery health may be done by various types of fast diagnostic techniques such as electrochemical impedance spectroscopy (EIS), which can be performed in only a few minutes and require only a fraction of the energy and power needed for a full charge and discharge measurement. But there is a substantial challenge for estimating battery health using EIS data, as EIS is sensitive to cell temperature, state-of-charge, current, and resting time in addition to health. Thus, utilizing EIS data to predict battery capacity requires correcting for all these additional variables, a task that is extremely difficult to handle analytically. This talk utilizes machine-learning methods to estimate the effectiveness of battery capacity prediction from EIS data, leveraging a data set of hundreds of EIS measurements recorded at varying temperature and state-of-charge throughout a 500-day aging study of 32 commercial, large-format NMC-Graphite lithium-ion batteries. Using EIS as input to machine-learning models is complicated by the nonlinear response of impedance to battery health, temperature, and state-of-charge, as well as the collinearity between the impedance response at neighboring frequencies, which can easily lead to overfit models. To train robust models, features from EIS data need to be extracted from the data or some subset of critical frequencies selected. Many approaches for extracting and selecting features from EIS data from electrochemical analysis and machine-learning fields were identified for analysis: using the entire raw spectra; selection of one, two, or many frequencies from the entire spectra; selecting interesting points from the EIS measurement using domain knowledge; fitting EIS with an equivalent-circuit model; calculating statistics on the raw impedance values; and reducing the dimensionality of the data using unsupervised linear (principal component analysis) and non-linear (uniform manifold approximation and projection) methods. These approaches were rigorously compared using a machine-learning pipeline approach, training linear, Gaussian process, and random forest regression models and quantifying performance using cross-validation as well as a held-out test set. An artificial neural network model trained on the raw spectra was also tested. Promising pipelines were fine-tuned via Bayesian hyperparameter optimization using cross-validation loss and training with class-specific weights to counter data set imbalance. The most reliable method for utilizing impedance in this work was the selection of two optimal frequencies through an exhaustive search, resulting in about 2% mean absolute error on test data for both Gaussian process and random forest model architectures. Interrogation of a variety of models reveals critical frequencies of 100 Hz and 103 Hz for this data set, though the optimal set of frequencies is not necessarily intuitive, i.e., the best performing models are not simply those that use impedance at frequencies that have the highest correlation to the relative discharge capacity. The best performing model is an ensemble model, which is able to predict battery capacity with 1.9% mean absolute error for unseen cells using impedance recorded at a variety of temperatures and states-of-charge.

battery↗
DOE OSTI2020

Towards Trust-Augmented Visual Analytics for Data-Driven Energy Modeling

The promise of data-driven predictive modeling is being increasingly realized in various science and engineering disciplines, where experts are used to the more conventional, simulation-driven modeling practices. However, trust remains a bottleneck for greater adoption of machine learning-based models for domain experts, who might not be necessarily trained in data science. In this paper, we focus on the building energy domain, where physics-based simulations are being complemented or replaced by machine learning-based methods for forecasting energy supply and demand at various spatio-temporal scales. We study the trust problem in close collaboration with energy scientists and engineers and describe how visual analytics can be leveraged for alleviating this trust bottleneck for stakeholders with varying degrees of expertise and analytics goals in this domain.

Kandakatla, Akshith R.↗
DOE OSTI2022

New large-strain FFT-based formulation and its application to model strain localization in nano-metallic laminates and other strongly anisotropic crystalline materials

This paper presents a new robust large-strain (LS) elasto-viscoplastic (EVP) formulation based on Fast Fourier Transforms (FFTs) for the prediction of the micro-mechanical response and microstructure evolution of polycrystalline and multiphase materials, with emphasis on the effect of strong crystallographic and/or morphologic anisotropy on localization of plastic deformation. In this work, the novel LS-EVPFFT formulation allows treatment of complex initial geometries and large deformations considering three grids of material points: a regular grid in the reference configuration, where FFTs can be performed; an irregular grid in the initial configuration, created by applying a stress-free displacement field to the reference regular grid; and an irregular grid in the current configuration, undergoing large strains and rotations as the material is loaded. Further numerical stability of the new formulation also required the use of a novel expression for the discrete modified Green’s operator, which reduces spurious field oscillations. After presenting and validating the new formulation by comparison with preexisting implementations and analytical solutions, LS-EVPFFT is applied to the prediction of slip and kink bands formation in polycrystalline columnar ice, and kink bands in single crystal zinc wires, showing good agreement with classic experiments. Finally, the model is used to study kink band formation during compression of Cu–Nb nano-metallic laminates (NMLs), in which accurate treatment of the complex geometry associated with the tortuosity of interfaces and large deformations become critical, showing consistency with corresponding micropillar experiments.

36 MATERIALS SCIENCE↗
DOE OSTI2024

Non-relativistic quantum chromodynamics in parton showers

Measurements of quarkonia isolation in jets at the Large Hadron Collider (LHC) have been shown to disagree with fixed-order non-relativistic quantum chromodynamics (NRQCD) calculations, even at higher orders. Calculations using the fragmenting jet function formalism are able to better describe data but cannot provide full event-level predictions. In this work we provide an alternative model via NRQCD production of quarkonia in a timelike parton shower. We include this model in the PYTHIA 8 event generator and validate our parton-shower implementation against analytic forms of the relevant fragmentation functions. Finally, we make inclusive predictions of quarkonia production for the decay of the standard-model Higgs boson.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2021

Thermodynamics of Light Management in Near-Field Thermophotovoltaics

We evaluate near-field thermophotovoltaic (TPV) energy-conversion systems focusing in particular on their open-circuit voltage (V OC ). Unlike previous analyses based largely on numerical simulations with fluctuational electrodynamics, here, we develop an analytic model that captures the physics of near-field TPV systems and can predict their performance metrics. Using our model, we identify two opportunities of TPV systems operating in the near field. First, we show analytically that enhancement of radiative recombination is a natural consequence of operating in the near field. Second, we note that, owing to photon recycling and minimal radiation leakage in near-field operation, the PV cell used in near-field TPV systems can be much thinner compared to those used in solar PV systems. Since nonradiative recombination is a volumetric effect, use of a thinner cell reduces nonradiative losses per unit area. The combination of these two opportunities leads to increasingly large values of V OC as the TPV vacuum gap decreases. Hence, although operation in the near-field was previously perceived to be beneficial for electrical power-density enhancement, here, we emphasize that thin-film near-field TPVs are also significantly advantageous in terms of V OC and consequently conversion efficiency as well as power density. We provide numerical results for an InAs-based thin-film TPV that exhibits efficiency >50% at an emitter temperature as low as 1100 K.

42 ENGINEERING↗
DOE OSTI2022

Correcting for filter-based aerosol light absorption biases at the Atmospheric Radiation Measurement program's Southern Great Plains site using photoacoustic measurements and machine learning

Abstract. Measurement of light absorption of solar radiation by aerosols is vital for assessing direct aerosol radiative forcing, which affects local and global climate. Low-cost and easy-to-operate filter-based instruments, such as the Particle Soot Absorption Photometer (PSAP), that collect aerosols on a filter and measure light attenuation through the filter are widely used to infer aerosol light absorption. However, filter-based absorption measurements are subject to artifacts that are difficult to quantify. These artifacts are associated with the presence of the filter medium and the complex interactions between the filter fibers and accumulated aerosols. Various correction algorithms have been introduced to correct for the filter-based absorption coefficient measurements toward predicting the particle-phase absorption coefficient (Babs). However, the inability of these algorithms to incorporate into their formulations the complex matrix of influencing parameters such as particle asymmetry parameter, particle size, and particle penetration depth results in prediction of particle-phase absorption coefficients with relatively low accuracy. The analytical forms of corrections also suffer from a lack of universal applicability: different corrections are required for rural and urban sites across the world. In this study, we analyzed and compared 3 months of high-time-resolution ambient aerosol absorption data collected synchronously using a three-wavelength photoacoustic absorption spectrometer (PASS) and PSAP. Both instruments were operated on the same sampling inlet at the Department of Energy's Atmospheric Radiation Measurement program's Southern Great Plains (SGP) user facility in Oklahoma. We implemented the two most commonly used analytical correction algorithms, namely, Virkkula (2010) and the average of Virkkula (2010) and Ogren (2010)–Bond et al. (1999) as well as a random forest regression (RFR) machine learning algorithm to predict Babs values from the PSAP's filter-based measurements. The predicted Babs was compared against the reference Babs measured by the PASS. The RFR algorithm performed the best by yielding the lowest root mean square error of prediction. The algorithm was trained using input datasets from the PSAP (transmission and uncorrected absorption coefficient), a co-located nephelometer (scattering coefficients), and the Aerosol Chemical Speciation Monitor (mass concentration of non-refractory aerosol particles). A revised form of the Virkkula (2010) algorithm suitable for the SGP site has been proposed; however, its performance yields approximately 2-fold errors when compared to the RFR algorithm. To generalize the accuracy and applicability of our proposed RFR algorithm, we trained and tested it on a dataset of laboratory measurements of combustion aerosols. Input variables to the algorithm included the aerosol number size distribution from the Scanning Mobility Particle Sizer, absorption coefficients from the filter-based Tricolor Absorption Photometer, and scattering coefficients from a multiwavelength nephelometer. The RFR algorithm predicted Babs values within 5 % of the reference Babs measured by the multiwavelength PASS during the laboratory experiments. Thus, we show that machine learning approaches offer a promising path to correct for biases in long-term filter-based absorption datasets and accurately quantify their variability and trends needed for robust radiative forcing determination.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2020

Analytic marginalization of N(z) uncertainties in tomographic galaxy surveys

In this paper, we present a new method to marginalize over uncertainties in redshift distributions, N(z), within tomographic cosmological analyses applicable to current and upcoming photometric galaxy surveys. We allow for arbitrary deviations from the best-guess N(z) governed by a general covariance matrix describing the uncertainty in our knowledge of redshift distributions. In principle, this is marginalization over hundreds or thousands of new parameters describing potential deviations as a function of redshift and tomographic bin. However, by linearly expanding the theory predictions around a fiducial model, this marginalization can be performed analytically, resulting in a modified data covariance matrix that effectively downweights the modes of the data vector that are more sensitive to redshift distribution variations. We showcase this method by applying it to the galaxy clustering measurements from the Hyper Suprime-Cam first data release. We illustrate how to marginalize over sample variance of the calibration sample and a large general systematic uncertainty in photometric estimation methods, and explore the impact of priors imposing smoothness in the redshift distributions.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2022

Near-Infrared Spectroscopy can Predict Anatomical Abundance in Corn Stover

Feedstock heterogeneity is a key challenge impacting the deconstruction and conversion of herbaceous lignocellulosic biomass to biobased fuels, chemicals, and materials. Upstream processing to homogenize biomass feedstock streams into their anatomical components via air classification allows for a more tailored approach to subsequent mechanical and chemical processing. Here, we show that differing corn stover anatomical tissues respond differently to pretreatment and enzymatic hydrolysis and therefore, a one-size-fits-all approach to chemical processing biomass is inappropriate. To inform on-line downstream processing, a robust and high-throughput analytical technique is needed to quantitatively characterize the separated biomass. Predictive correlation of near-infrared spectra to biomass chemical composition is such a technique. Here, we demonstrate the capability of models developed using an “off-the-shelf,” industrially relevant spectrometer with limited spectral range to make strong predictions of both cell wall chemical composition and the relative abundance of anatomical components of the corn stover, the latter for the first time ever. Gaussian process regression (GPR) yields stronger correlations (average R 2 v = 88% for chemical composition and 95% for anatomical relative abundance) than the more commonly used partial least squares (PLS) regression (average R 2 v = 84% for chemical composition and 92% for anatomical relative abundance). In nearly all cases, both GPR and PLS outperform models generated using neural networks. These results highlight the potential for coupling NIRS with predictive models based on GPR due to the potential to yield more robust correlations.

09 BIOMASS FUELS↗
DOE OSTI2023

Data-driven methods for diffusivity prediction in nuclear fuels

The growth rate of structural defects in nuclear fuels under irradiation is intrinsically related to the diffusion rates of the defects in the fuel lattice. The generation and growth of atomistic structural defects can significantly alter the performance characteristics of the fuel. This alteration of functionality must be accurately captured to qualify a nuclear fuel for use in reactors. Predicting the diffusion coefficients of defects and how they impact macroscale properties such as swelling, gas release, and creep is therefore of significant importance in both the design of new nuclear fuels and the assessment of current fuel types. In this article, we apply data-driven methods focusing on machine learning (ML) to determine various diffusion properties of two nuclear fuels—uranium oxide and uranium nitride. We show that using ML can increase, often significantly, the accuracy of predicting diffusivity in nuclear fuels in comparison to current analytical models. We also illustrate how ML can be used to quickly develop fuel models with parameter dependencies that are more complex and robust than what is currently available in the literature. In conclusion, these results suggest there is potential for ML to accelerate the design, qualification, and implementation of nuclear fuels.

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗
DOE OSTI2023

Automated fault detection and diagnosis of airflow and refrigerant charge faults in residential HVAC systems using IoT-enabled measurements

While automated fault detection and diagnosis (AFDD) in residential heating, ventilation, and air-conditioning (HVAC) using smart thermostat data is gaining increasing attention in recent times, it still requires in-depth investigation for market adoption, especially with real-life data. Furthermore, this paper proposes an Internet of Things (IoT) - based approach that adds a smart sensor to the smart thermostat data to carry out AFDD. The approach uses a model which predicts enthalpy change across the evaporator and compares the prediction to the measured enthalpy change. Deviations which exceed analytically determined thresholds then signal faults in the HVAC system. The faults detected are either installation related or degradation related. Experimental tests were carried out in four homes located in Norman, Oklahoma. From the tests, installation issues like indoor/outdoor mismatch were detected in two homes, while a 30% low charge and low indoor airflow rate were detected in one home. The results show that the proposed AFDD algorithm was able to successfully detect two prevalent faults, namely low indoor airflow and low refrigerant charge. Unlike most of the smart thermostat-based approaches, the proposed IoT-based approach can detect and diagnose both faults but only require one additional sensor which is provided by smart thermostat manufacturers.

32 ENERGY CONSERVATION, CONSUMPTION, AND UTILIZATI↗
DOE OSTI2025

The scoping, design, and plasma physics optimization of the Eos neutron source stellarator

On the path to a fusion pilot plant, Thea Energy plans to build Eos, a sub-breakeven, deuterium-deuterium, beam-target fusion, stellarator neutron source facility for producing tritium and other valuable radioisotopes. In this paper, a set of 1D plasma physics models are coupled and used to design the operating point of the facility and predict performance. At this foundational stage of the design, analytic and approximate models are sufficient to capture the leading-order effects, and fast enough to run in the inner loop of an optimizer. Higher-fidelity analyses will follow. Models of 1D profile-dependent neutral beam stopping, ion beam slowing down, beam-target fusion, electron-ion classical heat transfer, energy confinement (ISS04), beam pressure, beam heating of ions and electrons, beam-beam fusion fraction, and neutral beam injection and gyrotron heating electrical efficiencies are included. A numerical optimizer is used to determine the minimum required facility electric power to generate tritium at a given rate. A potentially advantageous regime is described in which modern precisely-quasisymmetric stellarators, new high-temperature superconductors, ITER-derived neutral beam injection, and new high-frequency gyrotrons enable a suitible target plasma with hot electrons, cold ions, peaked density and temperature profiles, and high beam-injected ion density. It appears possible at this time for a facility with a medium-scale and medium-strength stellarator whose required facility electric power is less than 40 MW to produce $2.5\times 10^{17}$ neutrons s -1 for the production of radioisotopes. With the addition of a tritium breeding blanket, such a facility could produce 0.2 grams d -1 or 70 grams yr -1 of tritium.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2020

Size- and temperature-dependent magnetization of iron nanoclusters

In this paper, the magnetic behavior of bcc iron nanoclusters, with diameters between 2 and 8 nm, is investigated by means of spin dynamics simulations coupled to molecular dynamics, using a distance-dependent exchange interaction. Finite-size effects in the total magnetization as well as the influence of the free surface and the surface/core proportion of the nanoclusters are analyzed in detail for a wide temperature range, going beyond the cluster and bulk Curie temperatures. Comparison is made with experimental data and with theoretical models based on the mean-field Ising model adapted to small clusters, and taking into account the influence of low coordinated spins at free surfaces. Our results for the temperature dependence of the average magnetization per atom M (T), including the thermalization of the transnational lattice degrees of freedom, are in very good agreement with available experimental measurements on small Fe nanoclusters. In contrast, significant discrepancies with experiment are observed if the translational degrees of freedom are artificially frozen. The finite-size effects on M (T) are found to be particularly important near the cluster Curie temperature. Simulated magnetization above the Curie temperature scales with cluster size as predicted by models assuming short-range magnetic ordering. Analytical approximations to the magnetization as a function of temperature and size are proposed.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2024

Pairing and Pair Breaking by Gauge Fluctuations in Bilayer Composite Fermion Metals

We study interlayer pairing of composite fermions in the total $\nu=1/2+1/2$ quantum Hall bilayer as a possible framework for understanding the experimentally observed transition from a compressible state at large layer spacing to a bilayer quantum Hall state at small layer spacing. We consider a model in which the effective interlayer composite fermion pairing interaction mediated by the Chern-Simons gauge fields in the two layers is singular with both attractive (out-of-phase) and repulsive (in-phase) components diverging at low frequency. If only the more singular attractive interaction is included the pairing gap obtained by solving the gap equation is proportional to the inverse of the layer spacing squared. In the so-called local approximation, we find that when the less singular repulsive interactions are also included the pairing gap still falls off as inverse layer spacing squared, consistent with recent analyses, but is strongly suppressed to a degree that may account for the fact that this predicted inverse square dependence is not observed experimentally. The analytically obtained local approximation solutions are then used as a starting point to numerically iterate the full gap equation to assess the validity of the approximation in this limit.

Deng, Haoyun↗
DOE OSTI2020

Simulating pitch angle scattering using an explicitly solvable energy-conserving algorithm

Particle distribution functions evolving under the Lorentz operator can be simulated with the Langevin equation for pitch angle scattering. This approach is frequently used in particle based Monte-Carlo simulations of plasma collisions, among others. However, most numerical treatments do not guarantee energy conservation, which may lead to unphysical artifacts such as numerical heating and spectra distortions. In this paper, we present a novel structure-preserving numerical algorithm for the Langevin equation for pitch angle scattering. Similar to the well-known Boris algorithm, the proposed numerical scheme takes advantage of the structure-preserving properties of the Cayley transform when calculating the velocity-space rotations. The resulting algorithm is explicitly solvable, while preserving the norm of velocities down to machine precision. We demonstrate that the method has the same order of numerical convergence as the traditional stochastic Euler-Maruyama method. The numerical scheme is benchmarked by simulating the pitch angle scattering of a particle beam, and comparing with the analytical solution. Benchmark results show excellent agreement with theoretical predictions, showcasing the remarkable long time accuracy of the proposed algorithm.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗