Search NASA⌕ Search

SEARCH · Search NASA

Results for “Radiative transfer equation”

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.

Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.

107 records · Page 6
All sourcesNASA NTRSDOE OSTI
DOE OSTI2025

Nuclear fragmentation at the future electron-ion collider

We explore the potential of conducting low-energy nuclear physics studies, including nuclear structure and decay, at the future Electron-Ion Collider (EIC) at Brookhaven. By comparing the standard theory of electron-nucleus scattering with the equivalent photon method applied to Ultraperipheral Collisions (UPC) at the Large Hadron Collider (LHC) at CERN. In the limit of extremely high beam energies and small energy transfers, very transparent equations emerge. We apply these equations to analyze nuclear fragmentation in UPCs at the LHC and 𝑒𝐴 scattering at the EIC, demonstrating that the EIC could facilitate unique photonuclear physics studies. Furthermore, we have also shown that the fragmentation cross-sections at the EIC are about 1,000 times smaller than those at the LHC. At the LHC, the fragmentation of uranium nuclei displays characteristic double-hump mass distributions from fission events, while at the EIC, fragmentation is dominated by neutron emission and fewer few fission products, about 10,000 smaller number of events.

Bertulani, Carlos A. [East Texas A&M University, C↗
DOE OSTI2020

C HIMERA : A Massively Parallel Code for Core-collapse Supernova Simulations

Herein we provide a detailed description of the C HIMERA code, a code developed to model core collapse supernovae (CCSNe) in multiple spatial dimensions. The CCSN explosion mechanism remains the subject of intense research. Progress to date demonstrates that it involves a complex interplay of neutrino production, transport, and interaction in the stellar core, three-dimensional stellar core fluid dynamics and its associated instabilities, nuclear burning, and the fundamental physics of the neutrino–stellar core weak interactions and the equations of state of all stellar core constituents—particularly, the nuclear equation of state associated with core nucleons, both free and bound in nuclei. C HIMERA , by incorporating detailed neutrino transport, realistic neutrino–matter interactions, three-dimensional hydrodynamics, realistic nuclear, leptonic, and photonic equations of state, and a nuclear reaction network, along with other refinements, can be used to study the role of neutrino radiation, hydrodynamic instabilities, and a variety of input physics in the explosion mechanism itself. It can also be used to compute observables such as neutrino signatures, gravitational radiation, and the products of nucleosynthesis associated with CCSNe. The code contains modules for neutrino transport, multidimensional compressible hydrodynamics, nuclear reactions, a variety of neutrino interactions, equations of state, and modules to provide data for post-processing observables such as the products of nucleosynthesis, and gravitational radiation. C HIMERA is an evolving code, being updated periodically with improved input physics and numerical refinements. We detail here the current version of the code, from which future improvements will stem, which can in turn be described as needed in future publications.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2020

Heat Loss Correction Factor for Fireball Yield Measurements

Fireball yield calculations are performed using Taylor’s radius equation. However, at early times, the x-ray diffusion process has a significant effect on the size of the fireball, and at late times the shock wave degenerates into an acoustic wave. Thus, earlier research determined that the range of validity for Taylor’s equation was in the scaled time regime of 0.004–0.008 s. So, when performing a yield calculation, the only values that are analyzed are those that lie within that range of validity. While Taylor’s equations offer an approximation of the scaled yield, they also rely on several assumptions. For example, the equations assume that the shock wave is adiabatic, when, in fact, the first light pulse on the nuclear test films, which occurs as the shock wave is forming, suggests that the shock wave is not adiabatic. Furthermore, the amount of heat loss from the shock wave that occurs prior to the scaled time regime of 0.004–0.008 s can change significantly as a function of air density. This may cause the shock wave radius to be smaller relative to the assumed adiabatic shock wave. Therefore, the objective of this project was to determine the correction factor for heat transfer, which should be applied in order to produce a more accurate approximation of the weapon’s yield.

45 MILITARY TECHNOLOGY, WEAPONRY, AND NATIONAL DEF↗
DOE OSTI2026

Evaluating Polymer Properties with Different Additives for Carbon Capture and Other Applications

Anthropogenic climate change is one of this generation’s most pressing concerns, with the potential to completely alter the delicate balance we’ve struck with nature. Already, global temperatures have risen 1.29°C, leading to disrupted weather systems, extinctions, increased risks of wildfires, and sea level rise, to name a few effects. Carbon dioxide emission from the combustion of fossil fuels and other industrial activity is a large driver of this phenomenon, as it absorbs heat before it can be radiated away from Earth, trapping it. Carbon dioxide has reached unprecedented levels in our atmosphere, showing a 50% increase from preindustrial averages to a whopping 430 ppm. Thus, reducing the amount of carbon dioxide via carbon capture technology is an important endeavor that serves to benefit everyone. The Microencapsulated CO 2 Sorbent (MECS) team at Lawrence Livermore National Laboratory (LLNL) has turned to microencapsulation to approach this endeavor. Microcapsules provide an attractive approach to carbon capture, combining large surface areas for more efficient mass transfer, regenerative abilities, reduced solvent loss, and improved handling. Additionally, while existing carbon capture technology relies on industrial plants, capsules could present a modular approach to carbon capture, reducing the need for extensive physical infrastructure. The MECS team’s design consists of a polymer membrane that contains a liquid carbon sequestering sorbent, aqueous sodium carbonate. The carbon capturing reaction occurs in three distinct steps, the first of which is the dissolution of carbon dioxide into the sorbent solution and its conversion into carbonic acid (H 2 CO 3 ), shown in equations 1 and 2 respectively. Because this step hinges upon the ability of carbon dioxide to reach the solution inside the capsule, it is necessary that the microcapsule shell is permeable to carbon dioxide gas. The MECS team produces these microcapsules using the in-air droplet encapsulation apparatus (IDEA) shown in figure 1, which can produce uniform micron-scale droplets at speeds much faster than traditional single-dispersal microfluidic-based techniques. The IDEA Is 100 times faster than these current techniques and can reach up to 1000 times their speed when incorporating a multi-nozzle design. Additionally, because droplets are produced in-air via vibration, IDEA can decrease post-processing times and material waste by 99% and can fabricate microgels that are 10 to 100 times more viscous than can be produced via traditional microfluidics. While this design represents a breakthrough in the throughput, efficiency, and tunability of microcapsule production, it imposes a major constraint on the microcapsule curing process. Because microcapsule shells are crosslinked with UV light while falling 30 cm through the air, this gives them a reaction window of approximately 0.2 seconds. Thus, the system and shell formulations must be optimized such that the shells can be fully crosslinked within this very narrow window, prompting investigations into curing behavior.

36 MATERIALS SCIENCE↗
DOE OSTI2020

Quantifying heavy quark transport coefficients with an improved transport model

We report that the heavy-flavor transport coefficients contain important information on the strong interaction at finite temperatures. The extraction of these numbers from experimental data requires dynamical modeling of heavy-flavor transport that is coupled to realistic medium evolution. Furthermore, meaningful extractions necessitate both a faithful implementation of the physical inputs to be tested and the quantification of model uncertainty. For these purposes, we have developed a partonic transport model LIDO. It has an improved treatment of in-medium parton bremsstrahlung, which has been calibrated to theoretical calculations in a simple medium to reduce modeling uncertainty. Regarding the interaction between heavy quark and the medium, few-body perturbative scatterings are applied to large-momentum transfer (q) processes, while a diffusion equation models the dynamics of small-q processes. Such a separation restricts the explicit use of medium quasi-particles to large-q processes only. Another advantage is that deviations from the leading-order probe-medium coupling can be parametrized as an additional contribution to the diffusion constant. The heavy quark transport coefficients are then extracted with uncertainty estimation from a Bayesian analysis including both the RHIC and the LHC data. The results are found to be consistent with earlier extraction of the light-quark transport coefficients at high momentum and be comparable with lattice calculations of the heavy-flavor diffusion constant in the static limit at low momentum.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2026

An–imidophosphorane (An = U–Pu) bond covalency and proton-coupled electron transfer thermodynamics driven by orbital energy matching

A series of mid-actinide (An = U–Pu) tetrahomoleptic complexes supported by highly electron-donating imidophosphorane ligands, NPC ([NP t Bu(pyrr) 2 ] − , where t Bu = C(CH 3 ) 3 ; pyrr = pyrrolidinyl = N(C 4 H 8 )), are systematically investigated computationally and experimentally to elucidate the nature of actinide–ligand (An–L) covalency across the An 3+/4+/5+ oxidation states. Trends in An–L bonding and redox properties for these complexes, together with their protonated counterparts, are examined using orbital-, electron density-, and energy-decomposition-based methods. This integrated approach reveals progressively improved energy matching between α-spin An 5f and N im 2p orbitals with increasing atomic number and oxidation state, becoming particularly pronounced in the ligand-dominant π-bonding orbitals of An 4+ and An 5+ . In contrast to the An 3+ species, the enhanced An 5f π contributions in the higher-valent counterparts drive the increase in An–N im covalency for later An, thereby inverting the covalency trend to U < Np < Pu. Redistribution of electron density towards the An and N im atomic basins due to the growing energy-matching assisted covalency correlates with higher pKa values and increased N im –H bond dissociation free energies in protonated An 4+ complexes. Electron density at Nim in An 4+ shows a linear correlation with the p K a values calculated via the Bordwell equation. Calculations predict a cathodic shift of 0.84–1.00 V in the redox couples upon protonation, a trend validated when experimentally accessible. These findings demonstrate an increasing role of covalency driven by orbital energy matching from U to Pu in tuning the thermodynamic driving force for proton-coupled electron transfer in the An 5+ species.

38 RADIATION CHEMISTRY, RADIOCHEMISTRY, AND NUCLEA↗
DOE OSTI2021

Embedding condition describing shearing, dissipative collapse

Highlights: • Perturbative approach to the time-dependent Karmarkar condition in shearing collapse. • Analysis of the (in)stability of the collapsing fluid using the TOV equation. • Study of the temperature profiles using a causal heat transport equation. In this work we employ the time-dependent Karmarkar condition to model dissipative gravitational collapse in the presence of shear which leads to a final static configuration. We believe that this is a first attempt at using the time-dependent Karmarkar condition describing a radiating star with shear in which the collapsing core dissipates energy in the form of a radial heat flux. The final static configuration which is described by an embedding class I spacetime was obtained by Hansraj and Moodly who showed that this solution satisfies all the physical requirements for a static compact object. As the collapse proceeds and the heat flux tends to zero the dynamical core evolves into a static compact core with the exterior spacetime being described by the vacuum Schwarzschild solution.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2023

QCD running couplings and effective charges

Here we discuss our present knowledge of $\alpha_s$, the fundamental running coupling or effective charge of Quantum Chromodynamics (QCD). A precise understanding of the running of $\alpha_s(Q^2) $ at high momentum transfer, $Q$, is necessary for any perturbative QCD calculation. Equally important, the behavior of $\alpha_s$} at low $Q^2$ in the nonperturbative QCD domain is critical for understanding strong interaction phenomena, including the emergence of mass and quark confinement. The behavior of $\alpha_s(Q^2)$ at all momentum transfers also provides a connection between perturbative and nonperturbative QCD phenomena, such as hadron spectroscopy and dynamics. We first sketch the origin of the QCD coupling, the reason why its magnitude depends on the scale at which hadronic phenomena are probed, and the resulting consequences for QCD phenomenology. We then summarize latest measurements in both the perturbative and nonperturbative domains. New theory developments include the derivation of the universal nonperturbative behavior of $\alpha_s(Q^2)$ from both the Dyson-Schwinger equations and light-front holography. We also describe theory advances for the calculation of gluon and quark Schwinger functions in the nonperturbative domain and the relation of these quantities to $\alpha_s$. We conclude by highlighting how the nonperturbative knowledge of $\alpha_s$ is now providing a parameter-free determination of hadron spectroscopy and structure, a central and long-sought goal of QCD studies.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2020

A Lumped Stochastic Model of Coupled Neutronic Assemblies

The objective of the present work is to apply the Harris ansatz to coupled assemblies in a lumped setting, i.e., ignoring the neutron phase dependence, which hitherto has not been considered. A Master equation for the single-time joint distribution of neutron number in each assembly, accounting for transfer of neutrons from one assembly to another via leakage transition probabilities and intercept or view factors is derived from which equations for the mean and variance in each assembly are developed. Because of the neutronic coupling, it is necessary to additionally compute the correlation function between pairs of assemblies which gives an expanded set of moment equations to solve. The reactivity of each assembly is allowed to vary with time, although a formal mechanism that is responsible for reactivity coupling between assemblies is not considered or proposed. Following Harris, it is then hypothesized that the number distribution in each assembly is a gamma distribution with assembly-specific mean and variance computed exactly from the moment equations. Illustrative numerical results are presented for the moments of a system of four coupled assemblies under various reactivity and neutronic coupling scenarios. The gamma distribution is then used to compute the probability that the neutron population exceeds a threshold value in any assembly. The report concludes with a discussion of recommended further work on this problem.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2022

Continued Verification of MOOSE Structural Mechanics Tools for Modeling Core Bowing Phenomena in Fast Reactors

Under the U.S. Department of Energy Office of Nuclear Energy’s Advanced Modeling and Simulation (NEAMS) Program, an integrated multiphysics approach is being developed to model the core bowing phenomena important to liquid metal-cooled fast reactors. Core bowing is an important passive safety mechanism whereby increased power (which leads to temperature and flux gradients) influences the core to bow into less reactive configurations when the restraint system is properly designed. The phenomenon includes a complex interplay of radiation transport, duct temperature calculations involving fluid flow and heat transfer, and thermo-mechanical responses to the induced temperature and flux gradients. Structural material properties are also important to determining inelastic response to longer term flux gradients which cause irradiation creep and swelling. While core bowing provides a strong negative reactivity feedback when the restraint system is designed properly, it also results in additional forces between assemblies which increase the loads required to extricate them during refueling or control rod movement. Therefore, the restraint system must be designed with these tradeoffs in mind. The first stage of the work, which commenced in FY21 and continues through FY22, assesses thermo-mechanical modeling tools for producing core bowing predictions consistent with conventional tools. The Multiphysics Object Oriented Simulation Environment (MOOSE) Tensor Mechanics and Contact Modules are employed. This status report describes work on additional thermo-mechanical benchmark verification problems with increased complexity from the examples demonstrated in FY21. Several benchmark verification examples were selected from the IAEA verification and validation report. These examples involve clusters of ducts representative of a sector of a hexagonal reactor core which bow into each other and cause contact and load pad elevations, as well as single ducts subjected to irradiation fields undergoing swelling and subsequent bowing. The MOOSE-based results were compared to both IAEA benchmark participants’ results, analytic equations as available, and NUBOW-3D, a beam model code developed by Argonne National Laboratory. In every case, the MOOSE results agreed with other simulations results, providing additional verification basis of the tools for this particular physics application.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗
DOE OSTI2022

PDC Modifications for Analysis of Gas-Cooled Reactors with Direct Helium Brayton Cycle

Capabilities of the Plant Dynamics Code (PDC) have been extended to allow steady-state and transient simulation of graphite-cooled reactors with direct helium Brayton cycle. On the cycle side, the most significant code modification is the addition of helium properties, in the format required by the code’s equations. Since the code was already formulated to handle more complex real gas properties, adding helium as working fluid that behaves like ideal gas was fairly straightforward. A reactor module was added to PDC to simulate a reactor cooled by the working fluid of the Brayton cycle. Two options are supported: channel type, typical for graphite gas-cooled reactors, and pin type, typical for light-water and liquid metal-cooled reactors. The reactor module is an extension of the electrical heater model and simulates heat deposition in the fuel and transfer of this heat from the fuel to the coolant through the matrix and tube materials. The new reactor module becomes the third option in PDC for modeling heat addition to the cycle, besides previously modeled heat addition heat exchanger and electrical heater. In addition to those changes, other minor code modifications and improvements were introduced during the work of expanding PDC to modeling of gas-cooled reactors. These modifications are summarized in the last chapter of this report.

21 SPECIFIC NUCLEAR REACTORS AND ASSOCIATED PLANTS↗
DOE OSTI2022

Mechanisms of shape transfer and preheating in indirect-drive double shell collisions

Implosions of Hohlraum-driven double shell targets as an alternative inertial confinement fusion concept are underway at the National Ignition Facility. The double shell system relies on a series of energy transfer processes starting from thermal x-ray absorption by the outer shell, followed by collisional transfer of kinetic energy to a heavy metal inner shell, and finally, conversion to the internal energy of the deuterium-tritium fuel. During each of these energy transfer stages, low-mode asymmetries can act to reduce the ideal transfer efficiency degrading double shell performance. Mechanisms, such as hard x-ray preheat from the Hohlraum, not only decrease the efficiency of kinetic energy transfer but may also be a source of low-mode asymmetry. In this article, we evaluate the shape transfer processes through the time of shell collision using two-dimensional integrated Hohlraum and capsule computations. We find that the dominant mode of the shape transfer is well described using a “radial impulse” model from the shape of the foam pressure reservoir. To evaluate the importance of preheat on inner shell shape, we also report on first measurements of Au L-shell preheat asymmetry in a double shell with a tungsten pusher. These measurements showed a 65% higher preheat velocity at the pole of the capsule relative to the equator. We also found that the experiments provided rigorous constraints by which to test the Hohlraum model settings that impact the amount and symmetry of Au L-shell preheat via the plasma conditions inside the outer cone Au bubble.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2024

Muon capture on Li 6 , C 12 , and O 16 from ab initio nuclear theory

Muon capture on nuclei is one of the most promising probes of the nuclear electroweak current driving the yet-hypothetical neutrinoless double-beta (0νββ) decay. Both processes involve vector and axial-vector currents at finite momentum transfer, q ~ 100 MeV, as well as the induced pseu doscalar and weak-magnetism currents. Comparing measured muon-capture rates with reliable ab initio nuclear-theory predictions could help us validate these currents. To this end, we compute partial muon-capture rates for 6 Li, 12 C and 16 O, feeding the ground and excited states in 6 He, 12 B and 16 N, using ab initio no-core shell model with two- and three-nucleon chiral interactions. Here, we remove the spurious center-of-mass motion by introducing translationally invariant operators and approximate the effect of hadronic two-body currents by Fermi-gas model. We solve the bound-muon wave function from the Dirac wave equations in the Coulomb field created by a finite nucleus. We find that the computed rates to the low-lying states in the final nuclei are in good agreement with the measured counterparts. We highlight sensitivity of some of the transitions to the sub-leading three-nucleon interaction terms. We also compare summed rates to several tens of final states with the measured total capture rates and note that we slightly underestimate the total rate with this simple approach due to limited range of excitation energies

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2020

Quantal diffusion approach for multinucleon transfer processes in the 58,64 Ni + 208 Pb reactions: Toward the production of unknown neutron-rich nuclei

In recent years, substantial efforts have been made for the study of multinucleon transfer reactions at energies around the Coulomb barrier both experimentally and theoretically, aiming at the production of unknown neutron-rich heavy nuclei. It is crucial to provide reliable theoretical predictions based on microscopic theories with sufficient predictive power. Purpose: This article aims to clarify the applicability of the quantal diffusion approach based on the stochastic mean-field (SMF) theory for multinucleon transfer processes. Isotope production cross sections are evaluated for the reactions of 64 Ni + 208 Pb at E c.m. = 268 MeV and 58 Ni + 208 Pb at E c.m. = 270 MeV and are compared with available experimental data. Methods: Three-dimensional time-dependent Hartree-Fock (TDHF) calculations are carried out for a range of initial orbital angular momenta with Skyrme SLy4d functional. Quantal diffusion equations, derived based on the SMF theory, for variances and covariance of neutron and proton numbers of reaction products are solved, with microscopic drift and diffusion coefficients obtained from time evolution of occupied single-particle orbitals in TDHF. Secondary de-excitation processes, both particle evaporation and fission, are simulated by a statistical compound-nucleus de-excitation model, gemini++. Dynamics of a fast isospin equilibration process followed by a slow drift toward the mass symmetry are commonly observed, as expected. Various reaction outcomes are evaluated, including average mass and charge numbers of reaction products, total kinetic energy loss (TKEL), scattering angle, contact time, and production cross sections for primary and secondary products. By comparing with the experimental data, we find that SMF and TDHF quantitatively reproduce experimental data for few-nucleon-transfer channels around the average values. In contrast, for many-nucleon-transfer channels, we find that the SMF approach provides much better description of the experimentally measured isotopic distributions. The results underline the importance of beyond-mean-field effects, especially one-body (mean-field) fluctuations and correlations, in describing multinucleon transfer processes. Moreover, through a combined analysis of SMF with a statistical model, gemini++, we find a significant contribution of transfer-induced fission, which is consistent with the experimental observation. In some cases, the SMF approach overestimates the isotopic width, requiring further improvements of the theoretical description. Possible ways to improve the description are discussed. The SMF approach is designed to describe the quantum many-body problem according to an ensemble of mean-field trajectories, taking into account part of many-body correlations in the description. As it requires feasible computational costs comparable to the ordinary TDHF approach, together with further model improvements, it will be a promising tool in the search for optimal reaction conditions to produce yet-unknown neutron-rich heavy nuclei through the multinucleon transfer reaction.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2024

Examining Graphite Degradation in Molten Salt Environments: A Chemical, Physical, and Material Analysis

Molten-salt reactors (MSRs) are Generation IV nuclear reactors that use liquid salt as a coolant and/or fuel. In several MSR designs, graphite serves as a moderator and/or reflector. However, due to limited experimental data and operational experience, our understanding of graphite behavior in molten salt environments remains incomplete. This report aims to identify the degradation mechanisms of nuclear graphite in MSRs, detail the mechanisms of each factor, and provide an initial assessment of their impact on the structural integrity of graphite components. This assessment is based on an extensive literature review and insights from subject matter experts. Furthermore, given the limited data, a modeling strategy using existing Grizzly software is proposed for a more thorough analysis where appropriate. Additionally, it presents mitigation strategies where applicable. The report covers physical degradation mechanisms such as infiltration, erosion, and abrasion, as well as chemical degradation mechanisms including fluorination, intercalation, corrosion, and oxidation. Molten salt can infiltrate the porous structure of graphite, leading to several detrimental effects. Entrapment of fissile products within the graphite pores can cause radiation damage and could pose challenges in the handling and disposal of contaminated components. The differential thermal expansion between the infiltrated salt and graphite, along with internal stress from pressurized molten salt and volumetric heating, can compromise the structural integrity of graphite. To mitigate these effects, employing ultra-fine graphite grades and applying sealants and coatings are effective strategies. A computational model based on coupled solid mechanics and heat transfer phenomena could be used to predict the internal stresses using Grizzly software. In pebble-bed MSRs, graphite fuel pebbles can cause abrasion against reactor components due to friction and wear. The severity of wear is influenced by various factors such as temperature, environment, and the presence of lubricants. Tribological studies reveal that higher temperatures and molten salt environments, such as FLiBe, significantly reduce wear rates compared to dry conditions. Additionally, the chemical composition of the salt can further optimize graphite's tribological performance. Long-term wear effects can be modeled by incorporating surface defects into the geometry and predict stresses under thermal and radiation effects using Grizzly software. Chemical degradation of graphite in a molten salt environment can occur through fluorination and intercalation. Fluorination can occur via replacement of hydrogen or oxygen atoms, or at the active sites, but does not cause structural degradation. Intercalation, on the other hand, can lead to exfoliation, where layers of graphite separate and peel away, damaging the graphite. Protective coatings can enhance graphite's resistance to intercalation. Graphite generally exhibits good chemical stability in molten salt environments, though it can corrode under specific conditions, particularly in the presence of impurities or oxidants. Studies have shown that protective coatings, such as plasma-sprayed partially stabilized zirconia (PSZ), can effectively prevent such degradation. Corrosion behavior varies significantly with different graphite grades and coating applications, underscoring the need for detailed studies on uncoated and coated graphite to understand and mitigate corrosion mechanisms in MSRs. Research indicates that the presence of oxidants and impurities can accelerate graphite degradation in molten salts, making it essential to explore acceptable impurity limits. Oxidation is another critical degradation mechanism, leading to weight loss and structural damage due to the formation of CO and CO 2 from the reaction of carbon atoms with oxygen. This process creates new porosity and compromises graphite's integrity. While extensive research on graphite oxidation has been conducted for gas-cooled reactors, studies specific to MSRs are limited. Findings from the coal industry suggest that molten alkali metal salts can significantly accelerate graphite oxidation, a hypothesis worth exploring for fluoride salts in MSRs. Understanding oxidation behavior in MSRs is vital for developing protective measures. The analysis of post-irradiated graphite from the MSRE experiment demonstrated exceptional chemical compatibility with molten fluoride salt, suggesting that the extent of chemical attack on graphite largely depends on the salt's infiltration capability. Therefore, the use of ultra-fine grade graphite could help mitigate chemical degradation effects. Existing oxidation modeling capabilities in Grizzly, which use reaction-diffusion equations to model graphite-air interactions, could be adapted to simulate the chemical degradation effects of graphite in molten salt environments.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗
DOE OSTI2025

Production of neutron-rich heavy nuclei in deep-inelastic 208 Pb + 208 Pb collisions within the stochastic mean-field theory

In deep-inelastic collisions of heavy nuclei, reaction products with a wide range of mass and charge are produced. Such collisions been considered as a possible way to produce superheavy nuclei, as an alternative to fusion reactions. To provide reliable theoretical predictions, it is desired to develop microscopic approaches that correctly and accurately describe nucleon transfer processes in dissipative collisions of heavy nuclei. The purpose of the present work is (1) to investigate the mechanism of nucleon transfers in dissipative collisions of two heavy nuclei, and (2) to explore possible pathways to produce neutron-rich heavy nuclei, through detailed theoretical analyses of fluctuations and correlations in nucleon transfers in 208 Pb + 208 Pb reactions. Three-dimensional time-dependent Hartree-Fock (TDHF) calculations are performed for the collisions of 208 Pb + 208 Pb at 𝐸 c.m. = 832, 936, and 1040 MeV, using the Skyrme SLy4d energy density functional. To calculate fluctuations and correlations in nucleon transfers, we employ the stochastic mean-field (SMF) theory, and the results are compared with another theoretical framework currently available, the time-dependent random phase approximation (TDRPA). Primary and secondary production cross sections are calculated with the SMF theory combined with a statistical model, GEMINI ++ . Using information of nucleon flow across a neck of colliding nuclei in TDHF calculations, we solve quantal diffusion equations for fluctuations and correlations in nucleon transfers based on the SMF theory. From the SMF calculations, we obtain the time evolution of diffusion coefficients as well as fluctuations and correlations in nucleon transfers for a range of initial orbital angular momenta. We compare the results of the SMF calculations with those of TDRPA, showing that TDRPA tends to predict substantially larger fluctuations and correlations in strongly damped collisions of heavy nuclei, which exhibit complex initial angular momentum dependence, while the SMF results provide almost constant (stable) values. Using the obtained fluctuations and correlations, we calculate primary and secondary production cross sections for the 208 Pb + 208 Pb collisions. From the results, we find that both lighter and heavier reaction products as compared to 208 Pb are produced for a wide region in the 𝑁−𝑍 plane as primary products, thanks to the quantal diffusion mechanism in the dissipative collisions. However, we show that cross sections for production of heavy nuclei with 𝑍 ≳ 90 or 𝑁 ≳ 135 are washed out due to secondary particle evaporation and/or fission processes. On the other hand, we find that there remain sizable cross sections for production of neutron-rich nuclei along 𝑁 = 126 with 𝑍< 82, even after secondary disintegration processes. We demonstrate that the secondary production cross sections depend weakly on incident energies, but lower (higher) energy is slightly preferred for production of nuclei with smaller (larger) atomic numbers as compared to 𝑍 = 82. Here, based on the microscopic SMF calculations, it has been shown that deep-inelastic collisions of heavy nuclei, such as 208 Pb + 208 Pb examined in this study, can be a promising means to produce neutron-rich heavy nuclei along 𝑁=126. Discrepancies between the SMF and TDRPA approaches are left unsolved for future investigations.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2020

A quadratic programming flux correction method for high-order DG discretizations of S transport

In this work, we present a new flux-fixup approach for arbitrarily high-order discontinuous Galerkin (DG) discretizations of the S N transport equation, and we demonstrate the compatibility of this approach with the Variable Eddington Factor (VEF) method. The new fixup approach is sweep-compatible: during a transport sweep (block Gauss-Seidel iteration in which the scattering source is lagged), a local quadratic programming (QP) problem is solved in each spatial element to ensure that the solution satisfies certain physical constraints, including local particle balance. In this paper, we describe two choices of physical constraints, resulting in two variants of the method: QP Zero (QPZ) and QP Maximum Principle (QPMP). In QPZ, the finite element coefficients of the solution are constrained to be nonnegative. In QPMP, they are constrained to adhere to an approximate discrete maximum principle. There are two primary takeaways in this paper. First, when the positive Bernstein basis is used for DG discretization, the QPMP method eliminates negativities, preserves high-order accuracy for smooth problems, and significantly dampens unphysical oscillations in the solution. The latter feature – the dampening of unphysical oscillations – is an improvement upon standard, simpler fixup approaches such as the approach described in (denoted as the “zero and rescale” (ZR) method in this paper). This improvement comes at a moderate computational cost, but it is not prohibitive. Our results show that, even in an unrealistic worst-case scenario where 83% of the spatial elements require a fixup, the computational cost of performing a transport sweep with fixup is only ~31% greater than performing one without fixup. The second takeaway is that the VEF method can be used to accelerate the convergence of transport sweeps even when a fixup is applied. When optically thick regions are present, transport sweeps converge slowly, regardless of whether a fixup is applied, and acceleration is needed. However, attempting to apply standard diffusion synthetic acceleration (DSA) to fixed-up transport sweeps results in divergence for optically thick problems. Our results show that the same is not true for VEF. When VEF is combined with fixed-up transport sweeps, the result is a scheme that produces a nonnegative solution, converges independently of the mean free path, and, in the case of the QPMP fixup, adheres to an approximate discrete maximum principle.

97 MATHEMATICS AND COMPUTING↗