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At least 235 records · Page 13
All sourcesNASA NTRSDOE OSTI
NASA NTRS2015

Physics-Based Modeling of Meteor Entry and Breakup

A new research effort at NASA Ames Research Center has been initiated in Planetary Defense, which integrates the disciplines of planetary science, atmospheric entry physics, and physics-based risk assessment. This paper describes work within the new program and is focused on meteor entry and breakup. Over the last six decades significant effort was expended in the US and in Europe to understand meteor entry including ablation, fragmentation and airburst (if any) for various types of meteors ranging from stony to iron spectral types. These efforts have produced primarily empirical mathematical models based on observations. Weaknesses of these models, apart from their empiricism, are reliance on idealized shapes (spheres, cylinders, etc.) and simplified models for thermal response of meteoritic materials to aerodynamic and radiative heating. Furthermore, the fragmentation and energy release of meteors (airburst) is poorly understood. On the other hand, flight of human-made atmospheric entry capsules is well understood. The capsules and their requisite heat shields are designed and margined to survive entry. However, the highest speed Earth entry for capsules is 13 kms (Stardust). Furthermore, Earth entry capsules have never exceeded diameters of 5 m, nor have their peak aerothermal environments exceeded 0.3 atm and 1 kWcm2. The aims of the current work are: (i) to define the aerothermal environments for objects with entry velocities from 13 to 20 kms; (ii) to explore various hypotheses of fragmentation and airburst of stony meteors in the near term; (iii) to explore the possibility of performing relevant ground-based tests to verify candidate hypotheses; and (iv) to quantify the energy released in airbursts. The results of the new simulations will be used to anchor said risk assessment analyses.With these aims in mind, state-of-the-art entry capsule design tools are being extended for meteor entries. We describe: (i) applications of current simulation tools to spherical geometries of diameters ranging from 1 to 100 m for an entry velocity of 20 kms and stagnation pressures ranging from 1 to 100 atm; (ii) the influence of shape and departure of heating environment predictions from those for a simple spherical geometry; (iii) assessment of thermal response models for silica subject to intense radiation; and (iv) results for porosity-driven gross fragmentation of meteors, idealized as a collection of smaller objects. Lessons learned from these simulations will be used to help understand the Chelyabinsk meteor entry up to its first point of fragmentation.

Atmospheric Entry↗
NASA NTRS2015

Physics-Based Modeling of Meteor Entry and Breakup

A new research effort at NASA Ames Research Center has been initiated in Planetary Defense, which integrates the disciplines of planetary science, atmospheric entry physics, and physics-based risk assessment. This paper describes work within the new program and is focused on meteor entry and breakup.Over the last six decades significant effort was expended in the US and in Europe to understand meteor entry including ablation, fragmentation and airburst (if any) for various types of meteors ranging from stony to iron spectral types. These efforts have produced primarily empirical mathematical models based on observations. Weaknesses of these models, apart from their empiricism, are reliance on idealized shapes (spheres, cylinders, etc.) and simplified models for thermal response of meteoritic materials to aerodynamic and radiative heating. Furthermore, the fragmentation and energy release of meteors (airburst) is poorly understood.On the other hand, flight of human-made atmospheric entry capsules is well understood. The capsules and their requisite heatshields are designed and margined to survive entry. However, the highest speed Earth entry for capsules is 13 kms (Stardust). Furthermore, Earth entry capsules have never exceeded diameters of 5 m, nor have their peak aerothermal environments exceeded 0.3 atm and 1 kW/sq cm. The aims of the current work are: (i) to define the aerothermal environments for objects with entry velocities from 13 to 20 kms; (ii) to explore various hypotheses of fragmentation and airburst of stony meteors in the near term; (iii) to explore the possibility of performing relevant ground-based tests to verify candidate hypotheses; and (iv) to quantify the energy released in airbursts. The results of the new simulations will be used to anchor said risk assessment analyses. With these aims in mind, state-of-the-art entry capsule design tools are being extended for meteor entries. We describe: (i) applications of current simulation tools to spherical geometries of diameters ranging from 1 to 100 m for an entry velocity of 20 kms and stagnation pressures ranging from 1 to 100 atm; (ii) the influence of shape and departure of heating environment predictions from those for a simple spherical geometry; (iii) assessment of thermal response models for silica subject to intense radiation; and (iv) results for porosity-driven gross fragmentation of meteors, idealized as a collection of smaller objects. Lessons learned from these simulations will be used to help understand the Chelyabinsk meteor entry up to its first point of fragmentation.

Near-Earth Asteroids↗
NASA NTRS2015

Physics-Based Modeling of Meteor Entry and Breakup

A new research effort at NASA Ames Research Center has been initiated in Planetary Defense, which integrates the disciplines of planetary science, atmospheric entry physics, and physics-based risk assessment. This paper describes work within the new program and is focused on meteor entry and breakup. Over the last six decades significant effort was expended in the US and in Europe to understand meteor entry including ablation, fragmentation and airburst (if any) for various types of meteors ranging from stony to iron spectral types. These efforts have produced primarily empirical mathematical models based on observations. Weaknesses of these models, apart from their empiricism, are reliance on idealized shapes (spheres, cylinders, etc.) and simplified models for thermal response of meteoritic materials to aerodynamic and radiative heating. Furthermore, the fragmentation and energy release of meteors (airburst) is poorly understood. On the other hand, flight of human-made atmospheric entry capsules is well understood. The capsules and their requisite heatshields are designed and margined to survive entry. However, the highest speed Earth entry for capsules is less than 13 km/s (Stardust). Furthermore, Earth entry capsules have never exceeded diameters of 5 m, nor have their peak aerothermal environments exceeded 0.3 atm and 1 kW/cm2. The aims of the current work are: (i) to define the aerothermal environments for objects with entry velocities from 13 to greater than 20 km/s; (ii) to explore various hypotheses of fragmentation and airburst of stony meteors in the near term; (iii) to explore the possibility of performing relevant ground-based tests to verify candidate hypotheses; and (iv) to quantify the energy released in airbursts. The results of the new simulations will be used to anchor said risk assessment analyses. With these aims in mind, state-of-the-art entry capsule design tools are being extended for meteor entries. We describe: (i) applications of current simulation tools to spherical geometries of diameters ranging from 1 to 100 m for an entry velocity of 20 km/s and stagnation pressures ranging from 1 to 100 atm; (ii) the influence of shape and departure of heating environment predictions from those for a simple spherical geometry; (iii) assessment of thermal response models for silica subject to intense radiation; and (iv) results for porosity-driven gross fragmentation of meteors, idealized as a collection of smaller objects. Lessons learned from these simulations will be used to help understand the Chelyabinsk meteor entry up to its first point of fragmentation.

Aerothermodynamics↗
DOE OSTI2025

Numerical simulation of compressible fluid-dynamics in the chamber of inertial fusion energy systems

Here, this paper aims to establish new and innovative modeling capabilities for analyzing chambers in Inertial Fusion Energy (IFE) systems. IFE is emerging as a promising method to achieve fusion power production, but several challenges must be overcome to develop an IFE pilot plant or deploy commercial IFE systems. These challenges are both theoretical and technical, encompassing a deeper understanding of the underlying physical phenomena and the development of new technologies and materials. One of the needs is to develop mathematical models to describe IFE systems and numerical tools to simulate them. This paper contributes to this endeavor by presenting a new OpenFOAM solver for IFE systems, focusing on gas dynamics in their chambers. The analysis and development of chamber designs will play a significant role in the transition from single-shot experiments to high-repetition rates, as there is a need to protect the chamber walls from the intense radiation fields produced by fusion reactions. A promising design option, normally referred to as thick wall chamber design, consists in using lithium or molten salt jet arrays within the chamber. A critical phenomenon is the venting of high-pressure gases from the center to the external part of the chamber, passing through the blanket array. This process involves the propagation and attenuation of strong pressure waves, requiring suitable modeling approaches for compressible fluid-dynamics. The solver proposed in this work implements a multi-material hydrodynamics model tailored to accurately describe the non-linear propagation of pressure waves while avoiding numerical oscillation issues typical of high-velocity compressible simulation. This solver is verified against numerical test cases, validated against experimental data, and applied to the analysis of the High-Yield Lithium-Injection Fusion-Energy (HYLIFE-I) concept. The relevance of this paper is threefold. Firstly, it contributes to developing and testing modeling approaches for compressible fluid-dynamics phenomena, with specific focus on the new and unexplored topic of IFE thick-liquid-wall blanket modeling. Secondly, it marks one of the first applications of the OpenFOAM library in the research field of IFE systems. Finally, the investigated problem is of practical interest for IFE developers, as it provides useful indications about relevant phenomena in pressure wave propagation in the chamber of these systems.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2025

The total neutron cross section of liquid and solid ammonia

Ammonia is a material of interest for future neutron moderators at high-power sources due to its high hydrogen density, low melting point, and resistance to polymerization in an intense radiation field. Its performance in such applications cannot currently be calculated due to the absence of suitable computer models for the interaction of neutrons with ammonia under relevant conditions. In an effort to develop suitable scattering kernels for computer simulations of moderator performance, we have conducted a series of Density Functional Theory and Molecular Dynamics calculations of the molecular-level thermal properties of ammonia at various temperatures within both the solid and liquid phases. In this paper, we compare computer calculations for the energy-dependent total neutron cross section of ammonia, based on these models, to experimental measurements of those cross sections at temperatures of 221 K, 180 K, and 35 K. The experimental data were collected over an energy range from 0.1 meV to 10 eV using time-of-flight techniques at the Low Energy Neutron Source (LENS) facility at Indiana University. This comparison provides a first validation in the development of thermal scattering libraries for Monte Carlo source design simulations based on liquid and solid ammonia. In conclusion, we also provide some insights into where additional development of tools for creating such models may be needed.

Ammonia↗
DOE OSTI2024

Phonon-mediated temperature dependence of Er 3+ optical transitions in Er 2 O 3

Characterization of the atomic level processes that determine optical transitions in emerging materials is critical to the development of new platforms for classical and quantum networking. Such understanding often emerges from studies of the temperature dependence of the transitions. We report measurements of the temperature dependent Er 3+ photoluminescence in single crystal Er 2 O 3 thin films epitaxially grown on Si(111) focused on transitions that involve the closely spaced Stark-split levels. Radiative intensities are compared to a model that includes relevant Stark-split states, single phonon-assisted excitations, and the well-established level population redistribution due to thermalization. This approach, applied to the individual Stark-split states and employing Er 2 O 3 specific single-phonon-assisted excitations, gives good agreement with experiment. This model allows us to demonstrate the difference in the electron-phonon coupling of the 4 S 3/2 and 2 H 11/2 states of Er 3+ in E 2 O 3 and suggests that the temperature dependence of Er 3+ emission intensity may vary significantly with small shifts in the wavelength (~0.1 nm) of the excitation source.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2021

The Phase-2 Upgrade of the CMS Data Acquisition

The High Luminosity LHC (HL-LHC) will start operating in 2027 after the third Long Shutdown (LS3), and is designed to provide an ultimate instantaneous luminosity of 7:5 × 10$^{34}$ cm$^{-2}$ s$^{-1}$, at the price of extreme pileup of up to 200 interactions per crossing. The number of overlapping interactions in HL-LHC collisions, their density, and the resulting intense radiation environment, warrant an almost complete upgrade of the CMS detector. The upgraded CMS detector will be read out by approximately fifty thousand highspeed front-end optical links at an unprecedented data rate of up to 80 Tb/s, for an average expected total event size of approximately 8 - 10 MB. Following the present established design, the CMS trigger and data acquisition system will continue to feature two trigger levels, with only one synchronous hardware-based Level-1 Trigger (L1), consisting of custom electronic boards and operating on dedicated data streams, and a second level, the High Level Trigger (HLT), using software algorithms running asynchronously on standard processors and making use of the full detector data to select events for offline storage and analysis. The upgraded CMS data acquisition system will collect data fragments for Level-1 accepted events from the detector back-end modules at a rate up to 750 kHz, aggregate fragments corresponding to individual Level- 1 accepts into events, and distribute them to the HLT processors where they will be filtered further. Events accepted by the HLT will be stored permanently at a rate of up to 7.5 kHz. This paper describes the baseline design of the DAQ and HLT systems for the Phase-2 of CMS.

Badaro, Gilbert↗
DOE OSTI2020

Design and performance of high-temperature furnace and cell holder for in situ spectroscopic, electrochemical, and radiolytic investigations of molten salts

To facilitate the development of molten salt reactor technologies, a fundamental understanding of the physical and chemical properties of molten salts under the combined conditions of high temperature and intense radiation fields is necessary. Optical spectroscopic (UV–Vis–near IR) and electrochemical techniques are powerful analytical tools to probe molecular structure, speciation, thermodynamics, and kinetics of solution dynamics. In this paper, we report the design and fabrication of three custom-made apparatus: (i) a multi-port spectroelectrochemical furnace equipped with optical spectroscopic and electrochemical instrumentation, (ii) a high-temperature cell holder for time-resolved optical detection of radiolytic transients in molten salts, and (iii) a miniaturized spectroscopy furnace for the investigation of steady-state electron beam effects on molten salt speciation and composition by optical spectroscopy. Initial results obtained with the spectroelectrochemical furnace (i) and high-temperature cell holder (ii) are reported.

38 RADIATION CHEMISTRY, RADIOCHEMISTRY, AND NUCLEA↗
DOE OSTI2022

Validation of ablation model for polyethylene using pulsed x-ray and proton exposures

The surface erosion of polyethylene is interrogated using pulsed x rays at the Z Machine (Sandia National Laboratories) and with proton beams at the Gamble II generator (Naval Research Laboratory) to validate a coupled model for volumetric thermal ablation, photoionization, finite-rate decomposition, and molecular recombination of radicals. The intense radiation pulses (up to ∼1014W/m2 over tens of nanoseconds) are used to generate one-dimensional vapor flows with low ionization fractions and a simplified geometry compared to typical laser ablation, allowing for evaluation of the model under local thermal equilibrium conditions. Areal momentum carried by the ensuing uniaxial hydrodynamic shock is used to indicate the extent of ablation. The threshold fluence for ablation is found to be in close correspondence with the bulk melt transition, and reasonable agreement with the model is obtained for peak temperatures in polyethylene up to 5500 K and heating rates up to 1011K/s where thermal decomposition reactions are also active.

Moore, N. W. (ORCID:0000000272259674)↗
DOE OSTI2020

Generalised hyper-Ramsey spectroscopy of two-level atoms in an optically dense medium

The peculiarities of Ramsey resonance and its sensitivity to the light shift from an optically dense medium of cold atoms are investigated. Different composite pulse protocols for clock spectroscopy, including hyper-Ramsey, modified and generalised hyper-Ramsey schemes, are compared. Error signals change significantly due to the processes of absorption and dispersion in the atomic medium. The dependence of the position of the central fringe resonance with a residual uncompensated light shift of the atomic transition is studied with the attenuation of the radiation intensity in the medium taken into account. It is shown that using a combination of generalised hyper-Ramsey error signals allows one to suppress the sensitivity to the light shift for any length of the medium. (laser cooling of atoms)

74 ATOMIC AND MOLECULAR PHYSICS↗
DOE OSTI2023

Observation of impurity accumulation and its compatibility with high plasma performance in W7-X

At the W7-X stellarator, the bolometer system has measured an intensive radiation zone in the inner plasma region (at a normalized radius $ρ$ ~ 0.3–0.4) in the hydrogen plasma generated by electron cyclotron resonance heating; it differs from the normal plasma radiation distribution with an edge-localized emission zone. Spectroscopic diagnostics have recorded high-Z elements such as iron. This phenomenon happens in the plasma phases after gas supply turn-off, which results in all impurity relevant diagnostic signals increasing for several seconds. Despite the enhancement of the core radiation, the plasma energy confinement is improved. A transport analysis shows that this impurity radiation behavior is associated with a low diffusion coefficient ($D$~ 0.02 m 2 s -1 ) and a reversal of the convection around the radial position of the emission peak, which, under normal conditions, separates the zones of outward convection in the central (|$V$| ~ 0.1 m s -1 ) and inward convection in the outer region (|$V$| ~ 0.3 m s -1 ). An impurity accumulation around this radial position has been identified. The transport coefficients obtained are comparable with the theoretical predictions of collisional impurity transport. In the plasma phases studied, both impurity and energy confinement are enhanced. The mechanism responsible for the improvement is believed to be a reduction of micro-instabilities associated with the observed steepening of the density profile, initiated by a low edge plasma density (<1.0 × 10 19 m -3 ) after switching off the gas fueling. The normalized temperature and density gradients fulfil the condition for the suppression of ITG turbulence.

suppression of ITG turbulence↗
DOE OSTI2020

Charge collection and electrical characterization of neutron irradiated silicon pad detectors for the CMS High Granularity Calorimeter

The replacement of the existing endcap calorimeter in the Compact Muon Solenoid (CMS) detector for the high-luminosity LHC (HL-LHC), scheduled for 2027, will be a high granularity calorimeter. It will provide detailed position, energy, and timing information on electromagnetic and hadronic showers in the immense pileup of the HL-LHC. The High Granularity Calorimeter (HGCAL) will use 120-, 200-, and 300-$\mu\textrm{m}$ thick silicon (Si) pad sensors as the main active material and will sustain 1-MeV neutron equivalent fluences up to about $10^{16}~\textrm{n}_\textrm{eq}\textrm{cm}^{-2}$. In order to address the performance degradation of the Si detectors caused by the intense radiation environment, irradiation campaigns of test diode samples from 8-inch and 6-inch wafers were performed in two reactors. Characterization of the electrical and charge collection properties after irradiation involved both bulk polarities for the three sensor thicknesses. Since the Si sensors will be operated at -30 $^\circ$C to reduce increasing bulk leakage current with fluence, the charge collection investigation of 30 irradiated samples was carried out with the infrared-TCT setup at -30 $^\circ$C. TCAD simulation results at the lower fluences are in close agreement with the experimental results and provide predictions of sensor performance for the lower fluence regions not covered by the experimental study. All investigated sensors display 60$\%$ or higher charge collection efficiency at their respective highest lifetime fluences when operated at 800 V, and display above 90$\%$ at the lowest fluence, at 600 V. The collected charge close to the fluence of $10^{16}~\textrm{n}_\textrm{eq}\textrm{cm}^{-2}$ exceeds 1 fC at voltages beyond 800 V.

46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND ↗
DOE OSTI2022

Na 22 activation level measurements of fused silica rods in the LHC target absorber for neutrals compared to simulations

The Target Absorbers for Neutrals (TANs) are located in a high intensity radiation environment inside the tunnel of the Large Hadron Collider (LHC). TANs are positioned about 140 m downstream from the beam interaction points. Seven 40-cm long fused silica rods with different dopant specifications were irradiated in the TAN by the Beam RAte of Neutrals (BRAN) detector group during p + p data taking from 2016 to 2018 at the LHC. The peak dose delivered to the fused silica rods was 18 MGy. We report measurements of the 22 Na activation of the fused silica rods carried out at the University of Illinois at Urbana-Champaign and Argonne National Laboratory. At the end of the irradiation campaign, the maximum 22 Na activity observed was A = 21 kBq/cm 3 corresponding to a density, ρ = 2.5 x 10 12 /cm 3 , of 22 Na nuclei. FLUKA Monte Carlo simulations have been performed by the CERN FLUKA team to estimate 22 Na activities for the irradiated BRAN rod samples. The simulations reproduce the 22 Na activity profile measured along the rods, with a 35% underestimation of the experimental measurement results.

43 PARTICLE ACCELERATORS↗
DOE OSTI2020

Nonlinear self-focusing in strongly magnetized pair plasma

An intense radiation field can modify plasma properties and the corresponding refractive index and lead to nonlinear propagation effects such as self-focusing. In this work, we estimate the corresponding effects in pair plasmas for circularly polarized waves, in both unmagnetized and strongly magnetically dominated cases. First, in the unmagnetized pair plasma the ponderomotive force does not lead to charge separation but to density depletion. Second, for astrophysically relevant plasmas of pulsar magnetospheres [and possible loci of fast radio bursts (FRBs)], where the cyclotron frequency $ω_B$ dominates over the plasma frequency $ω_p$ and the frequency of the electromagnetic wave $ω_B \gg ω_p, ω$, we show that (i) there is virtually no nonlinearity due to changing effective mass in the field of the wave; (ii) the ponderomotive force is $F^{(B)}_p = –m_ec^2/4B^2_0∇E^2$, which is reduced by a factor $(ω/ω_B)^2$ if compared to the unmagnetized case ($B_0$ is the external magnetic field and $\textit{E}$ is the electric field of the wave); and (iii) for a radiation beam propagating along a constant magnetic field in the pair plasma with density $n_±$, the ponderomotive force leads to the appearance of circular currents that lead to a decrease of the field within the beam by a factor $ΔB/B_0 = 2πn_±m_ec^2E^2 /B^4_0$. Applications to the physics of FRBs are discussed; we conclude that for the parameters of FRBs, the dominant magnetic field completely suppresses nonlinear self-focusing or filamentation.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2024

The Effects of Threshold Voltage and Number of Fins per Transistor on the TID Response of GF 12LP Technology

This abstract presents a comprehensive analysis of total ionizing dose (TID) response in GlobalFoundries’ 12LP 12nm bulk FinFET technology using 10keV X-rays. Devices with higher threshold voltages (VTs) demonstrated lower increases in off-state leakage current (IDS,OFF) post-irradiation, highlighting the mitigating role of high VT in TID response. Our data shows that transistors with fewer fins exhibit superior TID resistance, implying lower susceptibility to radiation effects. Our study also probed two bias conditions, "Gate-On" and "Pass-Gate," with the former displaying more severe TID degradation. Interestingly, p-type devices displayed negligible degradation, underscoring their inherent resilience to TID effects. Additionally, medium thick n-type devices echoed the fin-count-dependent TID response observed in other transistor types, further strengthening our findings. These results underscore the importance of strategic transistor selection and design for enhancing the TID resilience of future CMOS FinFET architectures, particularly critical in radiation-intense environments.

42 ENGINEERING↗
DOE OSTI2021

Cherenkov and Transition Radiation as Low-Energy Background Sources in SuperCDMS Detectors

The Weakly Interacting Massive Particle (WIMP) has historically been a prime candidate for dark matter due to its elegant compatibility with the Minimally Supersymmetric Standard Model (MSSM). Recent dark matter experiments have ruled out much of the GeV-TeV mass range predicted by the MSSM, however, and the newest generation of direct detection experiments, such as SuperCDMS SNOLAB, have begunto explore sub-GeV dark matter. As experiments push towards lower masses, sensitivity to eV-scale electron recoil events has become increasingly important. A variety of unexplained excesses at energy deposits of 1-100 eV have been found inmany such low-mass experiments, across different detection techniques and at different excess rates. These low-energy events are not thought to be dark matter, and they must be understood and effectively removed to further improve detector energy resolution. This thesis will outline the simulation of one possible source of low-energy excess at SuperCDMS: optical photons produced from charges in uniform motion, specifically from Cherenkov radiation (CR), transition radiation (TR), and the intermediate hybrid transition-Cherenkov radiation (HR). In the latter case, the standard formulae for HR contain divergences at certain angles in transparent media, which are an artifact of their derivation and become problematic to simulate. To rsolve this, we present a novel approach to normalize the divergent HR peaks, which allows HR to transition smoothly between TR and CR in a numerical simulation. We also add TR and CR as a physics process to the SuperCDMS Monte Carlo simulation package SuperSim, based on the Geant4 simulation toolkit. To verify the physics of our addition, we show some test simulations in comparison to theoretical predictions of optical radiation intensity. We also use the simulation to make some preliminary predictions on the contribution of TR and CR to the low energy background, with the expectation that more thorough analyses will be conducted in the future.

46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND ↗
DOE OSTI2021

Transport in Stochastic Media with Random Chord Length Distributions

Thermal radiation transport computations in binary Markovian random mixtures rely almost exclusively on the Levermore-Pomraning (LP) model which is obtained by applying a heuristic closure to the ensemble averaged random medium transport equation. The validity of this model has been extensively tested by comparing numerical results over a broad parameter range (material types and mixing parameters) against benchmark solutions in planar geometry. The conditions under which the LP-model provides useful results and when it breaks down are now well established, but work to date has been largely restricted to homogeneous mixing statistics, i.e., the mean chord lengths of both materials are taken to be spatially constant. In recent work, this limitation was relaxed by allowing the mean chord lengths and, in a consistent fashion, the volume fractions in the LP-model to vary spatially and in a follow-up investigation benchmark solutions were obtained by ensemble averaging results over material realizations sampled from a nonhomogeneous Poisson process (NHPP). Numerical experiments in rod geometry with specifically linear and quadratic spatial dependence of chord lengths showed that the material averaged radiation intensities vary nonmonotonically with depth into the medium, in stark contrast to solutions obtained assuming uniform chord lengths. Moreover, depending on the local optical thickness and strength of scattering, the LP-model results showed locally more nuanced deviations from the benchmark solutions than was the case with constant chord lengths. These limited numerical investigations highlight the nontrivial qualitative and quantitative consequences of nonhomogeneous mixing statistics, in particular that closure approximations may not be uniformly valid or invalid over the problem domain.

42 ENGINEERING↗