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At least 1,387 records · Page 77
All sourcesNASA NTRSDOE OSTI
NASA NTRS2016

Simulation of a Rapid Dropout Event for Highly Relativistic Electrons with the RBE Model

A flux dropout is a sudden and sizable decrease in the energetic electron population of the outer radiation belt on the time scale of a few hours. We simulated a flux dropout of highly relativistic 2.5 MeV electrons using the Radiation Belt Environment model, incorporating the pitch angle diffusion coefficients caused by electromagnetic ion cyclotron (EMIC) waves for the geomagnetic storm events of 23-26 October 2002. This simulation showed a remarkable decrease in the 2.5 MeV electron flux during main phase of the storm, compared to those without EMIC waves. This decrease was independent of magnetopause shadowing or drift loss to the magnetopause. We suggest that the flux decrease was likely to be primarily due to pitch angle scattering to the loss cone by EMIC waves. Furthermore, the 2.5 MeV electron flux calculated with EMIC waves correspond very well with that observed from Solar Anomalous and Magnetospheric Particle EXplorer spacecraft. EMIC wave scattering is therefore likely one of the key mechanisms to understand flux dropouts. We modeled EMIC wave intensities by the Kp index. However, the calculated dropout is a several hours earlier than the observed one. We propose that Kp is not the best parameter to predict EMIC waves.

Kang, S-B.↗
NASA NTRS2018

Precipitating Electron Energy Flux and Characteristic Energies in Jupiter's Main Auroral Region as Measured by Juno/JEDI

The relationship between electron energy flux and the characteristic energy of electron distributions in the main auroral loss cone bridges the gap between predictions made by theory and measurements just recently available from Juno. For decades such relationships have been inferred from remote sensing observations of the Jovian aurora, primarily from the Hubble Space Telescope, and also more recently from Hisaki. However, to infer these quantities, remote sensing techniques had to assume properties of the Jovian atmospheric structure - leading to uncertainties in their profile. Juno's arrival and subsequent auroral passes have allowed us to obtain these relationships unambiguously for the first time, when the spacecraft passes through the auroral acceleration region. Using Juno /Jupiter Energetic particle Detector Instrument (JEDI), an energetic particle instrument, we present these relationships for the 30-kiloelectronvolts to 1-megaelectronvolts electron population. Observations presented here show that the electron energy flux in the loss cone is a nonlinear function of the characteristic or mean electron energy and supports both the predictions from Knight (1973, https://doi.org/10.1016/0032-0633(73)90093-7) and magnetohydrodynamic turbulence acceleration theories (e.g., Saur et al., 2003, https://doi.org/10.1029/2002GL015761). Finally, we compare the in situ analyses of Juno with remote Hisaki observations and use them to help constrain Jupiter's atmospheric profile. We find a possible solution that provides the best agreement between these data sets is an atmospheric profile that more efficiently transports the hydrocarbons to higher altitudes. If this is correct, it supports the previously published idea (e.g., Parkinson et al., 2006, https://doi.org/10.1029/2005JE002539) that precipitating electrons increase the hydrocarbon eddy diffusion coefficients in the auroral regions.

Auroral↗
NASA NTRS2019

Planetary Boundary Layer Height from AIRS, MERRA-2, and GPS Radio Occultation Data Products at NASA GES DISC, and Insights from Their Profiles Intercomparison

The NASA Goddard Earth Sciences Data and Information Services Center (GES DISC) provides archive and distribution services for several data products in the Planetary Boundary Layer (PBL) category. As a new variable added to the Atmospheric Infrared Sounder (AIRS) Version 6 support product, the PBL height from AIRS is derived based on the gradients of the retrieved relative humidity profile, and provides the atmospheric pressure at the top of the PBL over the ocean. The GES DISC also hosts the Modern-Era Retrospective analysis for Research and Applications-2 (MERRA-2) product generated by the Goddard Earth Observing System Model Version 5 (GEOS-5) data assimilation system. The PBL height from MERRA-2 is based on the total eddy diffusion coefficient of heat. The monthly PBL height has been made available in the Giovanni system (Giovanni is a Web-based application developed by the GES DISC providing a simple and intuitive way to visualize, analyze, and access vast amounts of Earth science remote sensing data). Recently, the GES DISC began serving the global PBL height climatology product derived from the COSMIC/FORMOSAT-3 and TerraSAR-X Global Positioning System (GPS) radio occultation (RO) measurements from June 2006 to December 2015. In a previous study, we presented the monthly PBL height data from AIRS and MERRA-2 and demonstrated the GES DISC services which support data intercomparison, such as access, plotting, sub-setting, regridding, and generation of a multi-year monthly mean. We also provided intercomparison results, and found that different PBL height definitions contributed to significant differences of PBL height values between AIRS and MERRA-2. In this work, we present the 10-year seasonal climatologies from the AIRS, MERRA-2 and GPS-RO. We also used the cross section and vertical profile services in Giovanni to display and analyze the vertical atmosphere structure over regions where the PBL height derived from the AIRS and MERRA-2 are quite different. The examination of the AIRS and MERRA-2 three-dimensional data found that the relative humidity profiles had larger differences than the temperature profiles. The MERRA-2 gives more details than the AIRS for the vertical distribution of the humidity.

Ding, Feng↗
NASA NTRS2020

Ion Channels – From Structure to Electrophysiology and Back

A reliable way to establish whether our understanding of a channel is satisfactory is to reproduce its measured ionic conductance over a broad range of applied voltages in computer simulations. In molecular dynamics (MD), this can be done by way of applying an external electric field to the system and counting the number of ions that traverse the channel per unit time. Since this approach is computationally very expensive, we have developed a markedly more efficient alternative in which MD is combined with the electrodiffusion (ED) equation. In this approach, the assumptions of the ED equation can be rigorously tested, and the precision and consistency of the calculated conductance can be determined. We have demonstrated that the full current/voltage dependence and the underlying free energy profile for a simple channel can be reliably calculated from equilibrium or non-equilibrium MD simulations at a single voltage. Free energy profiles can be obtained from non-equilibrium simulations without a loss of accuracy even without the knowledge of diffusion coefficient. To carry out MD simulations, a structural model of a channel has to be assumed, which is an important constraint, considering that high-resolution structures are available for only very few simple channels. If the comparison of calculated ionic conductance with electrophysiological data is satisfactory, it greatly increases our confidence that the structure and the function are described sufficiently accurately. We examined the validity of the ED for several channels embedded in phospholipid membranes - four naturally occurring channels: trichotoxin, alamethicin, p7 from hepatitis C virus (HCV) and Vpu from the HIV-1 virus, a synthetic, hexameric channel, formed by a 21-residue peptide that contains only leucine and serine and a bacterial pentameric ligand-gated ion channel, GLIC. All these channels mediate transport of potassium and chloride ions. It was found that the ED equation is satisfactory for these systems. In some of them, experimental and calculated electrophysiological properties are in good agreement, whereas in others there are strong indications that the structural models are incorrect.

Pohorille, Andrew↗
NASA NTRS2023

Homogeneity Study of ZrC, NbC, and TaC Binary Carbide Fuels for the Application of Nuclear Thermal Propulsion

In alignment with NASA and DARPA goals, efforts towards Nuclear Thermal Propulsion (NTP) have increased in recent years. As progress is made, a main challenge still exists; the fuel in an NTP system must survive the extreme environment experienced during operating conditions. Three fuel forms have been studied including a ceramic-metallic matrix, a ceramic-ceramic matrix, and solid solution carbides. Solid solution carbides were studied previously as a fuel for NTP and was shown to be a promising technology; however, the programs were canceled before demonstration in an NTP engine test. Of the refractory metal carbides of interest, zirconium carbide (ZrC), niobium carbide (NbC) and tantalum carbide (TaC) were studied. ZrC, NbC, and TaC powders were consolidated in monocarbide (ZrC, NbC, TaC) and bi-carbide (ZrC-NbC, ZrC-TaC, NbC-TaC) forms using spark plasma sintering (SPS), with 50-50 mol% compositions of the bi-carbides of interest. The time and temperature conditions to achieve a completely homogeneous solid solution for the mixed carbides is of interest for NTP fuel applications, since this homogeneity is considered to be essential for this fuel form. Homogeneity is typically not achieved during sintering, as surface diffusion (predominant for sintering to near ideal density) tends to occur at lower temperatures than bulk volumetric diffusion (required for solute interdiffusion to achieve a homogeneous solid solution). High temperature isochronal annealing was performed to identify the conditions to achieve a chemically homogeneous sample. The solute interpenetration vs annealing temperature was quantified using energy dispersion spectroscopy (EDS) in a scanning electron microscope (SEM). X-ray diffraction (XRD) was used to accurately measure the phase stability and lattice parameter as a function of annealing conditions. The diffusion data from each sample was then used to determine self-diffusion coefficients for interdiffusion of the Nb, Zr, and Ta solutes and compared to existing literature values. The minimum annealing conditions to achieve complete chemical homogeneity for each carbide was determined.

nuclear thermal propulsion↗
DOE OSTI2020

AGC 4 Graphite Specimen Postirradiation Characterization Plan

This characterization plan describes the thermal, physical, and mechanical measurement techniques that will be used to characterize graphite samples being tested in the fourth Advanced Graphite Creep experiment (AGC-4). Instruments, fixtures, and methods are currently in place for both pre and postirradiation material property measurements of bulk density, thermal diffusivity, coefficient of thermal expansion, elastic modulus, and electrical resistivity. Postirradiation testing procedures used to characterize the samples are described and discussed in the plan. Where they exist, American Society for Testing and Materials (ASTM) International testing standards will apply to the tests. Any departure from ASTM International testing standards or the approved laboratory procedures are documented within this characterization plan. Deviations that occur during testing will be documented in data reports.

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗
DOE OSTI2020

Generation IV Benchmarking of TRISO Fuel Performance Models Under Accident Conditions Final Report

The Generation IV International Forum (GIF) is a co-operative international endeavor of fourteen members organized to carry out the research and development needed to establish the feasibility and performance capabilities of the next generation nuclear energy systems. GIF selected six reactor technologies, amongst which is the Very High Temperature Reactor (VHTR) that is primarily dedicated to the cogeneration of electricity and hydrogen. The technical basis for VHTR is the tristructural isotropic (TRISO)-coated particle fuel, the graphite as the core structure, helium coolant, as well as the dedicated core layout and lower power density to removal decay heat in a natural way. At the heart of safety features of the VHTR concept lie the TRISO fuel particles that are designed to keep their structural integrity and retain fission products at temperatures up to 1600°C. As part as the design and future operation of VHTRs, a key aspect is the accurate prediction of fuel performance under irradiation and accident conditions. Modeling and simulation allow prediction of TRISO fuel behavior when subject to neutron flux and in high temperature accident scenarios. The refinement of the fuel performance models and codes is performed by comparison to in-pile and out-of-pile experimental data that reproduce the expected irradiation conditions in high temperature gas-cooled reactors (HTGRs). Historically, the International Atomic Energy Agency (IAEA) developed a benchmark dedicated to the validation of predictive methods for fuel and fission product behavior through the Coordinated Research Program CRP-2 (IAEA, 1997). CRP-2 was later updated to cover fuel fabrication, quality assurance, irradiation performance, safety testing, and spent fuel. The scope of the resulting CRP-6 benchmarks focused on HTGR fuel performance and fission product release (IAEA, 2012). Taking advantage of additional TRISO fuel fabrication, irradiation, and safety testing campaigns, GIF launched a Generation IV Benchmarking of TRISO Fuel Performance Models under Accident Conditions in late 2015. This GIF benchmark is a three-year program steered by Idaho National Laboratory (INL, USA). The other participants include the Japan Atomic Energy Agency (JAEA, Japan) and the Korea Atomic Energy Research Institute (KAERI, Korea). The objectives of the benchmark are to: follow on the IAEA CRP benchmarks, (2) model fission product release under accident conditions, (3) compare results obtained by the fuel performance modeling codes of the benchmark participants, and (4) compare these code predictions to experimental data. Safety tests chosen for modeling include the first and second experiments of the Advanced Gas Reactor program (AGR-1 and AGR-2) and the High Flux Reactor (HFR) EU1bis experiment. This report presents the results obtained by the three research institutions using their respective fuel performance modeling codes. Comparisons of the corresponding fission product release predictions are made with experimental data from AGR-1, AGR-2, and HFR-EU1bis. The benchmark results show good agreements between all participants but also show a general trend of over-prediction of the experimental release data, which is mainly attributed to the use of over-estimated diffusion coefficients.

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗
DOE OSTI2022

MODELLING FIBER ORIENTATION DURING ADDITIVE MANUFACTURING COMPRESSION MOLDING PROCESSES

The production of high-performance thermoplastic composites reinforced with short carbon fibers can be achieved by a novel “additive manufacturing-compression molding” technique. An advantage of such combination is two-fold: controlled fiber orientation in additive manufacturing and less void content by compression molding. In this study, a computational fluid dynamics model has been developed to predict the behavior of printed layers during fiber-reinforced thermoplastic extrusion and subsequent compression molding. The fiber orientation was modelled with a simple quadratic closure model. The interaction between the fibers is included using a rotary diffusion coefficient which becomes significant in concentrated regimes. Finally, the second order orientation tensor is coupled with the momentum equation as an anisotropic part of the stress term. The effect of processing parameters on the behavior of printed layers was investigated to determine the favorable printing scenarios. The developed numerical model enables design of high-performance composites with tunable mechanical properties.

Seta, Berin↗
DOE OSTI2022

Ligand-Assisted Separation of Rare Earth Elements via Capillary Electrophoresis

Rare earth elements (REEs) are a class of critical materials vital in applications such as EVs, batteries, and defense weapons systems. These elements are found primarily in ores, and due to their similar chemical behavior, the challenge remains to find an effective means of separation. The addition of ligands of varying charge, size, denticity, etc. can help to increase separation, yet the mechanistic behavior and factors influencing separation are still poorly understood. Here, iminodiacetic acid (IDA) is used to exploit and maximize differences in electrophoretic mobilities between adjacent REEs. Mobilities and diffusion coefficients of REEs in aqueous media are measured via CE and are compared to MD and FEM simulations.

36 MATERIALS SCIENCE↗
DOE OSTI2022

Comparison of Fission Product Release Predictions using PARFUME and BISON with Results from the AGR-3/4 Irradiation Experiment

The PARFUME (PARticle Fuel ModEl) fuel performance modeling code and the BISON nuclear fuel performance application built on the Multiphysics Object-Oriented Simulation Environment (MOOSE) finite element library were used to predict the fission product release from tristructural isotropic (TRISO) coated fuel particles and compacts during the third and fourth irradiation experiment of the Advanced Gas Reactor (AGR-3/4) Fuel Development and Qualification Program. The fuel performance modeling codes PARFUME and BISON modeled the AGR-3/4 irradiation experiment using the fuel compact time-averaged volume averaged (TAVA) daily temperatures for a total irradiation duration of 369.1 effective full power days (EFPD) to predict the release fraction of the fission product silver (Ag-110m) from a representative TRISO-coated fuel particle from AGR-3/4 compacts. Post-irradiation examination (PIE) measurements provided data on the release of these fission products in the compacts outside of the silicon carbide (SIC) layer. The PARFUME and BISON results were then compared to the silver release measured from compact gamma scanning. The results showed good agreement between PARFUME and BISON but both codes under-predicted the silver release fraction for all the compacts. In addition, BISON was used to model and predict the fission product concentration radial profile outside of the compacts in capsules’ inner and outer rings. These rings were either comprised of matrix and/or structural graphite. To obtain the concentration profiles of silver, cesium, and strontium, a sorption isotherm model was developed in BISON to capture the effects of fission product transport across the gaps between the concentric rings. The general shape of the concentration radial profiles as calculated by BISON were similar in the inner ring (IR) but varied in the outer ring (OR) depending on the fission product of interest or capsule temperature. Using this methodology and model, BISON now has the capability to aid in developing new fission product diffusion coefficients for matrix or structural graphite materials.

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗
DOE OSTI2023

MATBOX, an Open-Source Microstructure Analysis Toolbox for Meshing, Generation, Segmentation, and Characterization of 3D Heterogenous Volumes

Battery performance is strongly correlated with electrode microstructural properties. To account for its impact, lithium-ion battery (LIB) models either abstract the microstructural heterogeneity of composite electrodes using effective macroscopic properties (macro- or meso- scale models) or directly solve the system of equations on the microstructure geometry or mesh (microstructure-scale models). Therefore, to be adequate, both families of models require information from the microstructure geometry, which can be provided by the numerical tool presented in this work. MATBOX is a MATLAB open-source application [1] developed by NREL for performing various microstructure-related tasks including microstructure numerical generation, image filtering and microstructure segmentation, microstructure characterization and correlation, visualization, and microstructure meshing. MATBOX was originally developed for the analysis of LIB electrode microstructures; however, the algorithms provided by the toolbox are widely applicable to other heterogeneous materials. The toolbox provides a user-friendly experience thanks to a Graphical-User Interface, requires no coding by the user, and is well documented. This presentation will illustrate various MATBOX features for the characterization of a LIB electrode, including a fully automated Representative Volume Element (RVE) analysis, the numerical generation of complex 'virtual' microstructure, including dual-layer electrodes and carbon-binder additive phase, and the meshing of a complex NMC/graphite full cell microstructure suitable for 3D finite-element modeling. Other modules (segmentation, visualization, and correlation) will be briefly presented. Thanks to its modular, open-source approach, MATBOX can easily incorporate third-party algorithms to eventually build a standard in the field that will benefit the whole scientific community. Effective diffusion coefficient [2], additive phase numerical generation [3], and meshing [4] third-party algorithms have been already integrated in the toolbox with more to come.

DIRECT ENERGY CONVERSION,MATHEMATICS AND COMPUTING↗
DOE OSTI2022

On the effect of scalar flux weighing of linearly anisotropic scattering matrices in few-group transport calculations

The majority of the codes available for homogenized group constant generation for deterministic transport calculations apply the approximation of scalar flux weighting during energy group condensation of higher-order anisotropic scattering matrices. In this paper, we discuss the effect of scalar flux weighting of the linearly anisotropic scattering matrices in the frame of S P{sub 3} and S{sub 12} calculations performed for a two-dimensional VVER-440 reactor benchmark. To compare group constants generated for two neutron energy groups, an infinite pin cell was homogenized with Serpent 2 and ERANOS ECCO. Serpent 2 applies scalar flux, while ERANOS ECCO performs current weighting of the linearly anisotropic scattering matrices during energy group condensation. For analyzing the effect of the various weighting options, three simple reactor models were built assuming different core sizes using standard rectangular assemblies with 15*15 fuel pins. Diffusion, SP{sub 3} and S{sub 12} calculations were performed for the 3 models using group constants generated with Serpent 2 and ERANOS ECCO. The effect of scalar flux weighting of linearly anisotropic scattering matrices is shown by comparing the decrease in reactivity due to the decreased reactor size, as well as the assembly power distribution to reference results obtained with Serpent 2 Monte Carlo calculations. Neglecting higher than linearly anisotropic scattering and indirect application of diffusion coefficients in higher-order transport calculations is advised if angular flux-moment spectra weighted higher-order scattering matrices cannot be generated. (authors)

22 GENERAL STUDIES OF NUCLEAR REACTORS↗
DOE OSTI2024

Post-Deployment Characterization of Glass Fiber-Reinforced Thermoset and Thermoplastic Composite Tidal Turbine Blades: Preprint

In 2021, the National Renewable Energy Laboratory (NREL) supported Verdant Power with the most successful tidal energy deployment in U.S. history. Three of their tidal turbines were deployed as part of the Roosevelt Island Tidal Energy project. Initially, the three rotors were manufactured from glass fiber-reinforced epoxy composites. Midway through the deployment, one rotor was replaced with one manufactured at NREL. Instead, it was infused with a novel, infusible thermoplastic resin system. Since the deployment, one epoxy rotor and one thermoplastic rotor were returned to NREL for continued materials and manufacturing research. The two rotors underwent full-scale structural testing before being sectioned and cut into specimens for a variety of manufacturing quality tests, thermos-mechanical characterization, and evaluation of material performance in marine environments, to understand the key differences between the fiberglass reinforced epoxy and Elium composites used for the respective rotors. Matrix burnoff tests showed that the Elium blades had a considerably higher fiber volume fraction compared to the epoxy blades (61% vs. 49%). Environmental aging of the specimens showed that the epoxy laminates absorbed more water over the conditioning period, however, it was determined that the Elium laminates had higher diffusion coefficients, so initially absorbed water faster. Finally, one full epoxy blade and one full Elium blade were conditioned at ambient temperatures for up to 11 months, while taking periodic mass measurements. The datasets were extrapolated out to assume a full 20 year operational life span and it was determined that the blades would not reach full saturation during that time span.

composite manufacturing↗
DOE OSTI2024

Post-Deployment Characterization of Glass Fiber-Reinforced Thermoset and Thermoplastic Composite Tidal Turbine Blades

In 2021, the National Renewable Energy Laboratory (NREL) supported Verdant Power with the most successful tidal energy deployment in U.S. history. Three of their Gen5d 5 m turbines were deployed as part of the Roosevelt Island Tidal Energy project. Initially, the three deployed rotors were manufactured from glass fiber-reinforced epoxy composites. Midway through the deployment, one rotor was replaced with one manufactured at NREL. The new rotor utilized a novel infusible thermoplastic resin system (Elium from Arkema). Since the deployment, one epoxy rotor and one thermoplastic rotor were returned to NREL for continued materials and manufacturing research. The two rotors underwent full-scale structural testing before being sectioned and cut into specimens for a variety of manufacturing quality tests, thermomechanical characterization, and evaluation of material performance in marine environments to understand the key differences between the fiberglass-reinforced epoxy and Elium composites used for the respective rotors. Matrix burn-off tests showed that the Elium blades had a considerably higher fiber volume fraction compared to the epoxy blades (61% vs. 49%). Environmental aging of the specimens showed that the epoxy laminates absorbed more water over the conditioning period; however, it was determined that the Elium laminates had higher diffusion coefficients, so they initially absorbed water faster. Finally, one full epoxy blade and one full Elium blade were conditioned at ambient temperatures for up to 11 months, while periodic mass measurements were taken. The datasets were extrapolated to assume a full 20-year operational life span, and it was determined that the blades would not reach full saturation during that time span.

composite manufacturing↗
DOE OSTI2024

Theory of Beam Echoes

We develop the theory of beam echoes in circular accelerators under several different conditions. We derive detailed expressions for the echo amplitude and pulse width with nonlinear quadrupole and dipole kicks, first without and then with momentum spread. We use the theory with the linearized dipole and quadrupole kicks to solve the diffusion equation for different dependencies of the diffusion coefficient on the action. We then consider the use of multiple quadrupole kicks to increase the maximum echo amplitude. We have extended these calculations partially to the 2D case and we also have partial results for longitudinal echoes.

43 PARTICLE ACCELERATORS↗
DOE OSTI2023

ADCP Upsample

This R script takes reads the csv file of stream-wise velocity data and generates a new time series of with comparable but distinct noise using the Langevin method and library. It simulates a time series measured at 1/10 the sampling rate by calculating a moving average of 10, though other sampling rates can be calculated by adjusting the moving average window. A stationary signal is calculated by taking the difference of the original signal and the moving average, then normalizing by the standard deviation of the moving average. The stationary signal is used to calculate drift and diffusion coefficients. Those coefficients are used to generate a new stationary signal. The new stationary signal is un-normalized and added to the moving average (or new equivalent signal) to create a new up-sampled velocity time-series.

Green, Nathan↗
DOE OSTI2022

Atomic Mixing of Initially Separated Mixtures

We consider the atomic mixing of two materials, initially separated in space, at fixed temperature– pressure conditions [T, p], and zero mass-mean velocity. Each material is composed of a specified set of atomic species whose density corresponds to the specieswise real Equation of State (EOS) $\tilde{&#961}$ i [T, p]. Because there are no spatial gradients in the mean [T, p] state, the only mechanism for mixing is a specieswise nonequilibrium thermal velocity distribution. The recipe for nonequilibrium species mass fluxes is taken directly from Hirschfelder, Curtiss, and Bird, who express the diffusion velocities in terms of gradients in the molar concentrations and pairwise coefficients of diffusion. EOS data from the SESAME library is used for all species. Data for the specieswise self diffusion coefficients is adopted from the Orbital Free Molecular Dynamics (OFMD) simulations of Ticknor et al.; the so-called Darken approximation is used to express the mutual diffusion coefficients of a mixture in the manner used by White et al. A one-dimensional spatial domain is used; with the left half occupied by one multispecies material and the right half occupied by the other, and with zero–gradient boundary conditions at the ends of the domain. Hence the total mass in the domain is a constant. At time t = 0 the materials are separated. Accordingly, spatial gradients at the separation point are infinite and the species fluxes are also infinite. As t → $\textbf{∞}$ the spatial gradients approach zero and a uniform set of species concentrations is obtained; at this point the system is said to be at “thermodynamic equilibrium.” Analytic solution of the problem is not possible in general due to the nonlinear concentration dependence of the species fluxes. Hence we utilize the numerical solution apparatus in Mathematica for obtaining accurate time-dependent solutions for the mixing of various initial species masses for conditions of interest in laser-driven Inertial Confinement Fusion. Concentration profiles and the speed of propagation of the mixing fronts are discussed in light of the nonlinearity of the problem.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗