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DOE OSTI2022

Anisotropic-strain-enhanced hole mobility in GaN by lattice matching to ZnGeN 2 and MgSiN 2

The key obstacle toward realizing integrated gallium nitride (GaN) electronics is its low hole mobility. Here, we explore the possibility of improving the hole mobility of GaN via epitaxial matching to II–IV nitride materials that have recently become available, namely, ZnGeN 2 and MgSiN 2 . We perform state-of-the-art calculations of the hole mobility of GaN using the ab initio Boltzmann transport equation. We show that effective uniaxial compressive strain of GaN along the [$1\bar{1}00$] by lattice matching to ZnGeN 2 and MgSiN 2 results in the inversion of the heavy hole band and split-off hole band, thereby lowering the effective hole mass in the compression direction. We find that lattice matching to ZnGeN 2 and MgSiN 2 induces an increase in the room-temperature hole mobility by 50% and 260% as compared to unstrained GaN, respectively. Further, examining the trends as a function of strain, we find that the variation in mobility is highly nonlinear; lattice matching to a hypothetical solid solution of Zn 0.75 Ge 0.75 Mg 0.25 Si 0.25 N 2 would already increase the hole mobility by 160%.

36 MATERIALS SCIENCE↗

DOE OSTI2022

Monte-Carlo modeling of phonon thermal transport using DFT-based anisotropic dispersion relations over the full Brillouin zone

In this work, we present a Monte Carlo (MC) approach to solve the phonon Boltzmann transport equation (BTE) in which the anisotropic phonon dispersion relations over the full Brillouin zone (BZ) are used. In this approach, the discretization of the BZ used to compute the phonon relaxation time places constraints on the direction of scattered phonons in the real-space simulation domain. The phonon dispersion and phonon relaxation times are calculated using the density functional theory (DFT) approach. The modified MC approach is validated by a close examination of its ability to simulate phonon transport in both the ballistic and diffusive regimes for multiple materials including GaAs, InAs, ThO 2 , and α-U. In doing so, the phonon thermal conductivities from 100 K to 1000 K are calculated and compared with traditional non-transport solution of the phonon BTE. It is found that the phonon thermal conductivities of α-U and ThO 2 obtained from MC simulations using isotropic dispersion are larger than the values obtained using anisotropic phonon dispersion relations over the full BZ. The effect of phonon-defect scattering on the thermal conductivity of ThO 2 is also studied as an application of the current MC approach and found to agree with previously computed values in the literature. The MC solver developed here has been parallelized as a step to demonstrate its potential to solving computationally intensive phonon thermal transport problems at the mesoscale.

36 MATERIALS SCIENCE↗

DOE OSTI2022

A combined theoretical-experimental investigation of thermal transport in low-dose irradiated thorium dioxide

During reactor operation, nuclear fuels are subject to extreme temperature and irradiation conditions which can significantly degrade the fuel's thermal transport properties. The reduction in thermal conductivity of the fuel as a result of irradiation-induced lattice defects is arguably the most important fuel performance metric in regard to reactor efficiency and safety. Because thorium dioxide (ThO2) is suitable as a model system for more complex materials such as UO2 and its mixed oxides, we present a theoretical investigation of thermal conductivity reduction seen in defect-bearing thorium dioxide and compare directly to experimental measurements. Phonon-mediated thermal transport of the fuel is modeled by a solution to the Boltzmann transport equation (BTE) for phonons. A cluster dynamics (CD) model for lattice defect evolution during irradiation predicts defect densities which are used as input to the BTE for modeling phonon-defect scatterings. Phonon scatterings by lattice defects include those from point defects and vacancy clusters and interstitial clusters of various sizes. The CD model is benchmarked against structural defect characterization of irradiated thorium dioxide using electron microscopy. Thermal conductivity predicted by the BTE model is compared to measured values for irradiated thorium dioxide specimens below room temperature to isolate effects of phonon-defect scattering from intrinsic 3-phonon processes, which dominate at higher temperatures. The computed conductivity values are in partial agreement at temperatures close to room temperature while slight deviations are observed at the lowest measured temperatures, suggesting that implemented phonon-defect scattering cross-section expressions may not be adequate for low temperatures. The presented work provides a necessary investigation of the influence of irradiation induced defects on fuel performance and represents a first step toward a full characterization of phonon mediated thermal transport in irradiated materials with complex defect microstructure.

36 MATERIALS SCIENCE↗

NASA NTRS1961

Consistent Pl Analysis of Aqueous Uranium-235 Critical Assemblies

The lethargy-dependent equations of the consistent Pl approximation to the Boltzmann transport equation for slowing down neutrons have been used as the basis of an IBM 704 computer program. Some of the effects included are (1) linearly anisotropic center of mass elastic scattering, (2) heavy element inelastic scattering based on the evaporation model of the nucleus, and (3) optional variation of the buckling with lethargy. The microscopic cross-section data developed for this program covered 473 lethargy points from lethargy u = 0 (10 Mev) to u = 19.8 (0.025 ev). The value of the fission neutron age in water calculated here is 26.5 square centimeters; this value is to be compared with the recent experimental value given as 27.86 square centimeters. The Fourier transform of the slowing-down kernel for water to indium resonance energy calculated here compared well with the Fourier transform of the kernel for water as measured by Hill, Roberts, and Fitch. This method of calculation has been applied to uranyl fluoride - water solution critical assemblies. Theoretical results established for both unreflected and fully reflected critical assemblies have been compared with available experimental data. The theoretical buckling curve derived as a function of the hydrogen to uranium-235 atom concentration for an energy-independent extrapolation distance was successful in predicting the critical heights of various unreflected cylindrical assemblies. The critical dimensions of fully water-reflected cylindrical assemblies were reasonably well predicted using the theoretical buckling curve and reflector savings for equivalent spherical assemblies.

Fieno, Daniel↗

DOE OSTI2022

A Forward Analytic Model of Neutron Time-of-Flight Signals for Inferring Ion Temperatures from MagLIF Experiments

A forward analytic model is required to rapidly simulate the neutron time-of-flight (nToF) signals that result from magnetized liner inertial fusion (MagLIF) experiments at Sandia’s Z Pulsed Power Facility. Various experimental parameters, such as the burn-weighted fuel-ion temperature and liner areal density, determine the shape of the nToF signal and are important for characterizing any given MagLIF experiment. Extracting these parameters from measured nToF signals requires an appropriate analytic model that includes the primary deuterium-deuterium neutron peak, once-scattered neutrons in the beryllium liner of the MagLIF target, and direct beamline attenuation. Here, mathematical expressions for this model were derived from the general-geometry time- and energy-dependent neutron transport equation with anisotropic scattering. Assumptions consistent with the time-of-flight technique were used to simplify this linear Boltzmann transport equation into a more tractable form. Models of the uncollided and once-collided neutron scalar fluxes were developed for one of the five nToF detector locations at the Z-Machine. Numerical results from these models were produced for a representative MagLIF problem and found to be in good agreement with similar neutron transport simulations. Twenty experimental MagLIF data sets were analyzed using the forward models, which were determined to only be significantly sensitive to the ion temperature. The results of this work were also found to agree with values obtained separately using a zero scatter analytic model and a high-fidelity Monte Carlo simulation. Finally, inherent difficulties in this and similar techniques are identified, and a new approach forward is suggested.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

DOE OSTI2023

A finite element method for angular discretization of the radiation transport equation on spherical geodesic grids

Discrete ordinate (S N ) and filtered spherical harmonics (FP N ) based schemes have been proven to be robust and accurate in solving the Boltzmann transport equation but they have their own strengths and weaknesses in different physical scenarios. We present a new method based on a finite element approach in angle that combines the strengths of both methods and mitigates their disadvantages. The angular variables are specified on a spherical geodesic grid with functions on the sphere being represented using a finite element basis. A positivity-preserving limiting strategy is employed to prevent non-physical values from appearing in the solutions. Here, the resulting method is then compared with both S N and FP N schemes using four test problems and is found to perform well when one of the other methods fail.

79 ASTRONOMY AND ASTROPHYSICS↗

NASA NTRSDate not supplied

Radiation Transport Models in Space: from Supernovae to Cells

Humans embarking on deep space exploration missions will encounter persistent exposure to galactic cosmic rays (GCR) - an energetic and highly complex radiation field that is unlike anything found on Earth. Exposure to such radiation fields is attributed to various adverse health effects, including cancer, cardiovascular disease, and cognitive impairment and is identified by NASA as one of the five main hazards of human spaceflight. It is therefore critical to be able to fully characterize the exposure received by humans behind shielding in space and project consequent health risks. A wide variety of computational models have been developed over the years to help meet this requirement. In this talk, an overview of the GCR environment in deep space is provided. Methods of propagating GCR fields through the shielding that protects humans in space are described along with simulation tools used to assess biological damage at the cellular scale. Finally, the NASA cancer risk model is briefly described, and risk projections are provided for various mission scenarios. Radiation transport models and solution methods pervade many aspects of this talk. For example, the GCR spectrum impinging on spacecraft is determined by solving the Fokker-Planck transport equation to propagate cosmic rays (believed to originate from supernovae) from the edge of the heliosphere to the vicinity of Earth. The Boltzmann transport equation is solved to transport this GCR spectrum through shielding and human tissue. Monte Carlo methods are used to simulate the transport of low energy electrons that dominate biological damage at the cellular scale. Progress and challenges in each of these areas will be highlighted.

Tony C. Slaba↗

NASA NTRS2014

Path Toward a Unifid Geometry for Radiation Transport

The Direct Accelerated Geometry for Radiation Analysis and Design (DAGRAD) element of the RadWorks Project under Advanced Exploration Systems (AES) within the Space Technology Mission Directorate (STMD) of NASA will enable new designs and concepts of operation for radiation risk assessment, mitigation and protection. This element is designed to produce a solution that will allow NASA to calculate the transport of space radiation through complex computer-aided design (CAD) models using the state-of-the-art analytic and Monte Carlo radiation transport codes. Due to the inherent hazard of astronaut and spacecraft exposure to ionizing radiation in low-Earth orbit (LEO) or in deep space, risk analyses must be performed for all crew vehicles and habitats. Incorporating these analyses into the design process can minimize the mass needed solely for radiation protection. Transport of the radiation fields as they pass through shielding and body materials can be simulated using Monte Carlo techniques or described by the Boltzmann equation, which is obtained by balancing changes in particle fluxes as they traverse a small volume of material with the gains and losses caused by atomic and nuclear collisions. Deterministic codes that solve the Boltzmann transport equation, such as HZETRN [high charge and energy transport code developed by NASA Langley Research Center (LaRC)], are generally computationally faster than Monte Carlo codes such as FLUKA, GEANT4, MCNP(X) or PHITS; however, they are currently limited to transport in one dimension, which poorly represents the secondary light ion and neutron radiation fields. NASA currently uses HZETRN space radiation transport software, both because it is computationally efficient and because proven methods have been developed for using this software to analyze complex geometries. Although Monte Carlo codes describe the relevant physics in a fully three-dimensional manner, their computational costs have thus far prevented their widespread use for analysis of complex CAD models, leading to the creation and maintenance of toolkit-specific simplistic geometry models. The work presented here builds on the Direct Accelerated Geometry Monte Carlo (DAGMC) toolkit developed for use with the Monte Carlo N-Particle (MCNP) transport code. The workflow for achieving radiation transport on CAD models using MCNP and FLUKA has been demonstrated and the results of analyses on realistic spacecraft/habitats will be presented. Future work is planned that will further automate this process and enable the use of multiple radiation transport codes on identical geometry models imported from CAD. This effort will enhance the modeling tools used by NASA to accurately evaluate the astronaut space radiation risk and accurately determine the protection provided by as-designed exploration mission vehicles and habitats

Lee, Kerry↗

DOE OSTI2021

Perspective on Tsallis statistics for nuclear and particle physics

This is a concise introduction to the topic of nonextensive Tsallis statistics meant especially for those interested in its relation to high-energy proton–proton, proton–nucleus and nucleus–nucleus collisions. The three types of Tsallis statistics are reviewed. Only one of them is consistent with the fundamental hypothesis of equilibrium statistical mechanics. The single-particle distributions associated with it, namely Boltzmann, Fermi–Dirac and Bose–Einstein, are derived. These are not equilibrium solutions to the conventional Boltzmann transport equation which must be modified in a rather nonintuitive manner for them to be so. Nevertheless, the Boltzmann limit of the Tsallis distribution is extremely efficient in representing a wide variety of single-particle distributions in high-energy proton–proton, proton–nucleus and nucleus–nucleus collisions with only three parameters, one of them being the so-called nonextensitivity parameter [Formula: see text]. This distribution interpolates between an exponential at low transverse energy, reflecting thermal equilibrium, to a power law at high transverse energy, reflecting the asymptotic freedom of Quantum Chromodynamics (QCD). It should not be viewed as a fundamental new parameter representing nonextensive behavior in these collisions.

Physics↗

NASA NTRS1993

Development of deterministic transport methods for low energy neutrons for shielding in space

Transport of low energy neutrons associated with the galactic cosmic ray cascade is analyzed in this dissertation. A benchmark quality analytical algorithm is demonstrated for use with BRYNTRN, a computer program written by the High Energy Physics Division of NASA Langley Research Center, which is used to design and analyze shielding against the radiation created by the cascade. BRYNTRN uses numerical methods to solve the integral transport equations for baryons with the straight-ahead approximation, and numerical and empirical methods to generate the interaction probabilities. The straight-ahead approximation is adequate for charged particles, but not for neutrons. As NASA Langley improves BRYNTRN to include low energy neutrons, a benchmark quality solution is needed for comparison. The neutron transport algorithm demonstrated in this dissertation uses the closed-form Green's function solution to the galactic cosmic ray cascade transport equations to generate a source of neutrons. A basis function expansion for finite heterogeneous and semi-infinite homogeneous slabs with multiple energy groups and isotropic scattering is used to generate neutron fluxes resulting from the cascade. This method, called the FN method, is used to solve the neutral particle linear Boltzmann transport equation. As a demonstration of the algorithm coded in the programs MGSLAB and MGSEMI, neutron and ion fluxes are shown for a beam of fluorine ions at 1000 MeV per nucleon incident on semi-infinite and finite aluminum slabs. Also, to demonstrate that the shielding effectiveness against the radiation from the galactic cosmic ray cascade is not directly proportional to shield thickness, a graph of transmitted total neutron scalar flux versus slab thickness is shown. A simple model based on the nuclear liquid drop assumption is used to generate cross sections for the galactic cosmic ray cascade. The ENDF/B V database is used to generate the total and scattering cross sections for neutrons in aluminum. As an external verification, the results from MGSLAB and MGSEMI were compared to ANISN/PC, a routinely used neutron transport code, showing excellent agreement. In an application to an aluminum shield, the FN method seems to generate reasonable results.

Ganapol, Barry↗

DOE OSTI2024

Dynamic mode decomposition of nonequilibrium electron-phonon dynamics: accelerating the first-principles real-time Boltzmann equation

Abstract Nonequilibrium dynamics governed by electron–phonon ( e -ph) interactions plays a key role in electronic devices and spectroscopies and is central to understanding electronic excitations in materials. The real-time Boltzmann transport equation (rt-BTE) with collision processes computed from first principles can describe the coupled dynamics of electrons and atomic vibrations (phonons). Yet, a bottleneck of these simulations is the calculation of e –ph scattering integrals on dense momentum grids at each time step. Here we show a data-driven approach based on dynamic mode decomposition (DMD) that can accelerate the time propagation of the rt-BTE and identify dominant electronic processes. We apply this approach to two case studies, high-field charge transport and ultrafast excited electron relaxation. In both cases, simulating only a short time window of ~10% of the dynamics suffices to predict the dynamics from initial excitation to steady state using DMD extrapolation. Analysis of the momentum-space modes extracted from DMD sheds light on the microscopic mechanisms governing electron relaxation to a steady state or equilibrium. The combination of accuracy and efficiency makes our DMD-based method a valuable tool for investigating ultrafast dynamics in a wide range of materials.

36 MATERIALS SCIENCE↗

NASA NTRS2003

An Improved Green's Function for Ion Beam Transport

Ion beam transport theory allows testing of material transmission properties in the laboratory environment generated by particle accelerators. This is a necessary step in materials development and evaluation for space use. The approximations used in solving the Boltzmann transport equation for the space setting are often not sufficient for laboratory work and those issues are the main emphasis of the present work. In consequence, an analytic solution of the linear Boltzmann equation is pursued in the form of a Green's function allowing flexibility in application to a broad range of boundary value problems. It has been established that simple solutions can be found for the high charge and energy (HZE) by ignoring nuclear energy downshifts and dispersion. Such solutions were found to be supported by experimental evidence with HZE ion beams when multiple scattering was added. Lacking from the prior solutions were range and energy straggling and energy downshift with dispersion associated with nuclear events. Recently, we have found global solutions including these effects providing a broader class of HZE ion solutions.

Tweed, J.↗

NASA NTRS2004

An improved Green's function for ion beam transport

Ion beam transport theory allows testing of material transmission properties in the laboratory environment generated by particle accelerators. This is a necessary step in materials development and evaluation for space use. The approximations used in solving the Boltzmann transport equation for the space setting are often not sufficient for laboratory work and those issues are the main emphasis of the present work. In consequence, an analytic solution of the linear Boltzmann equation is pursued in the form of a Green's function allowing flexibility in application to a broad range of boundary value problems. It has been established that simple solutions can be found for high charge and energy (HZE) ions by ignoring nuclear energy downshifts and dispersion. Such solutions were found to be supported by experimental evidence with HZE ion beams when multiple scattering was added. Lacking from the prior solutions were range and energy straggling and energy downshift with dispersion associated with nuclear events. Recently, we have found global solutions including these effects providing a broader class of HZE ion solutions. c2004 COSPAR. Published by Elsevier Ltd. All rights reserved.

NASA Center LaRC↗

NASA NTRS1991

Computational attributes of the integral form of the equation of transfer

Difficulties can arise in radiative and neutron transport calculations when a highly anisotropic scattering phase function is present. In the presence of anisotropy, currently used numerical solutions are based on the integro-differential form of the linearized Boltzmann transport equation. This paper, departs from classical thought and presents an alternative numerical approach based on application of the integral form of the transport equation. Use of the integral formalism facilitates the following steps: a reduction in dimensionality of the system prior to discretization, the use of symbolic manipulation to augment the computational procedure, and the direct determination of key physical quantities which are derivable through the various Legendre moments of the intensity. The approach is developed in the context of radiative heat transfer in a plane-parallel geometry, and results are presented and compared with existing benchmark solutions. Encouraging results are presented to illustrate the potential of the integral formalism for computation. The integral formalism appears to possess several computational attributes which are well-suited to radiative and neutron transport calculations.

Frankel, J. I.↗

DOE OSTI2020

SCEPTRE 2.1 Quick Start Guide

This report provides a summary of notes for building and running the Sandia Computational Engine for Particle Transport for Radiation Effects (SCEPTRE) code. SCEPTRE is a general purpose C++ code for solving the Boltzmann transport equation in serial or parallel using unstructured spatial finite elements, multigroup energy treatment, and a variety of angular treatments including discrete ordinates and spherical harmonics. Either the first-order form of the Boltzmann equation or one of the second-order forms may be solved. SCEPTRE requires a small number of open-source Third Party Libraries (TPL) to be available, and example scripts for building these TPL's are provided. The TPL's needed by SCEPTRE are Trilinos, boost, and netcdf. SCEPTRE uses an autoconf build system, and a sample configure script is provided. Running the SCEPTRE code requires that the user provide a spatial finite-elements mesh in Exodus format and a cross section library in a format that will be described. SCEPTRE uses an xml-based input, and several examples will be provided.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2021

SCEPTRE 2.2 Quick Start Guide

This report provides a summary of notes for building and running the Sandia Computational Engine for Particle Transport for Radiation Effects (SCEPTRE) code. SCEPTRE is a general- purpose C++ code for solving the li near Boltzmann transport equation in serial or parallel using unstructured spatial finite elements, multigroup energy treatment, and a variety of angular treatments including discrete ordinates and spherical harmonics. Either the first-order form of the Boltzmann equation or one of the second-order forms may be solved. SCEPTRE requires a small number of open-source Third Part y Libraries (TPL) to be available, and example scripts for building these TPLs are provided. The TPLs needed by SCEPTRE are Trilinos, boost, and netcdf. SCEPTRE uses an autotools build system , and a sample configure script is provided. Running the SCEPTRE code requires that the user provide a spatial finite-elements mesh in Exodus format and a cross section library in a format that will be described. SCEPTRE uses an xml-based input, and several examples will be provided.

38 RADIATION CHEMISTRY, RADIOCHEMISTRY, AND NUCLEA↗

DOE OSTI2021

SCEPTRE 2.3 Quick Start Guide

This report provides a summary of notes for building and running the Sandia Computational Engine for Particle Transport for Radiation Effects (SCEPTRE) code. SCEPTRE is a general- purpose C++ code for solving the linear Boltzmann transport equation in serial or parallel using unstructured spatial finite elements, multigroup energy treatment, and a variety of angular treatments including discrete ordinates (Sn) and spherical harmonics (Pn). Either the first-order form of the Boltzmann equation or one of the second-order forms may be solved. SCEPTRE requires a small number of open-source Third Party Libraries (TPL) to be available, and example scripts for building these TPL are provided. The TPL needed by SCEPTRE are Trilinos, Boost, and Netcdf. SCEPTRE uses an autotools build system, and a sample configure script is provided. Running the SCEPTRE code requires that the user provide a spatial finite-elements mesh in Exodus format and a cross section library in a format that will be described. SCEPTRE uses an xml-based input, and several examples will be provided.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

DOE OSTI2025

Quarkonium Polarization Kinetic Equation from Open Quantum Systems and Effective Field Theories

Recent measurements of polarization phenomena in relativistic heavy ion collisions have aroused a great interest in understanding dynamical spin evolution of the QCD matter. In particular, the spin alignment signature of J/ψ has been recently observed in Pb-Pb collisions at LHC, which may infer nontrivial spin transport of quarkonia in quark gluon plasmas. Motivated by this, we study the spin-dependent in-medium dynamics of quarkonia by using the potential nonrelativistic QCD (pNRQCD) and the open quantum system framework. By applying the Markovian approximation and Wigner transformation, we systematically derive the Boltzmann transport equation for vector quarkonia with polarization dependence in the quantum optical limit. As opposed to the previous study for the spin-independent case where the collision terms depend on chromoelectric correlators, the new kinetic equation incorporates gauge invariant correlators of chromomagnetic fields that determine the recombination and dissociation terms with polarization dependence at the order we are working in the multipole expansion. In the quantum Brownian motion limit, the Lindblad equation with new transport coefficients defined in terms of the chromomagnetic field correlators have also been derived. Our formalism is generic and valid for both weakly-coupled and strongly-coupled quark gluon plasmas. It may be further applied to study spin alignment of vector quarkonia in heavy ion collisions.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗