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DOE OSTI2024

Harmonizing direct and indirect anthropogenic land carbon fluxes indicates a substantial missing sink in the global carbon budget since the early 20th century

Inconsistencies in the calculation of the two anthropogenic land flux terms of the global carbon cycle are investigated. The two terms—the direct anthropogenic flux (caused by direct human disturbance in anthromes, currently a carbon source to the atmosphere) and the indirect anthropogenic flux (caused indirectly by human activities that lead to global change and affecting all biomes, currently an atmospheric carbon sink)—are typically calculated independently, resulting in inconsistent underlying assumptions. We harmonize the estimation of the two anthropogenic land flux terms by incorporating previous estimates of these inconsistencies. We recalculate the global carbon budget (GCB) and apply change-point analysis to the cumulative budget imbalance. Cumulative over 1850–2018 (1959–2018), harmonization results in a 13% lesser (4% greater) land use source from anthromes and a 20% (23%) lesser land sink. This recalculation yields a greater non-closure of the GCB, indicating a missing carbon sink averaging 0.65 Pg C year -1 since the early 20th century. The imbalance likely results from a combination of method discontinuity and structural errors in the assessment of the direct anthropogenic land use flux, greater ocean carbon uptake, structural errors in land models, and in how these land terms are quantified for the budget. We caution against overconfidence in considering the GCB a solved problem and recommend further study of methodological discontinuities in budget terms. We strongly recommend studies that quantify the direct and indirect anthropogenic land fluxes simultaneously to ensure consistency, with a deeper understanding of human disturbance and legacy effects in anthromes.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2026

User’s Manual for RESRAD-RDD&IND Code Version 2: Vol. 2—User’s Guide for RESRAD-RDD&IND Code

Version 2.0 of the RESRAD-RDD&IND computer code is designed to support the implementation of protective action guides (PAGs) after a nuclear emergency incident including a radiological dispersal device (RDD) and/or an improvised nuclear device (IND) incident (EPA 2017). Eight different group types, addressing various decisions, are available for selection. The RESRAD-RDD&IND code calculates radiological doses, stay times, etc., for the selected group that the user wishes to focus on. (That is, the results for all the groups are not calculated simultaneously, and the input for those other groups do not matter, although some parameter values are shared between groups.) Version 2.0 has a user-friendly interface so that the RESRAD-RDD&IND code can be used with minimal training. For example, the user can select the major characteristics of the problem-event type, source term, and decision type from the left side of the interface and then calculate the results with the default assumptions for the exposure scenarios. More in-depth analysis would include specifying site-specific exposure scenario characteristics in the right side of the interface. The procedures for data entry and results viewing are self-explanatory. This is because common window maneuvering features and text instructions were incorporated in the interface design. General and context-specific help are available to aid users entering parameter values, as well. The RESRAD-RDD&IND computer code gives the user the option to select either an RDD or IND incident for analysis. For an RDD event analysis, 11 radionuclides (Am-241, Cf-252, Cm-244, Co-60, Cs-137, Ir-192, Po-210, Pu-238, Pu-239, Ra-226, and Sr-90) are included. These 11 radionuclides are the radionuclides most likely used for an RDD. More than 90 radionuclides can be selected for an IND event analysis. Initial default concentrations are provided for 44 radionuclides for a uranium-fueled IND event. These 44 radionuclides are those that would contribute significantly to the radiation dose associated with a uranium-fueled bomb detonation. The radionuclides generated from ingrowth of these 44 initial radionuclides are also automatically included in the analysis. Pu-239, Cs-134m, Ru-105, and Rb-89 and their progeny can be selected for analysis if they are detected and their concentrations are determined. This user’s guide, which is Volume 2 of the User’s Manual for RESRAD-RDD&IND Code Version 2, provides instructions to users on how to install the RESRAD-RDD&IND code, navigate the interface, and use the various features, including those discussed above, to set up an analysis and view/print the results in text outputs. Volume 1 of the User’s Manual for RESRAD-RDD&IND Code Version 2 (Yu et al. 2026), which contains descriptions of the methodology and theoretical basis for dose modeling and the mathematical equations implemented in the code, can be accessed and viewed through the Help menu in the code or can be downloaded from the RESRAD website (https://resrad.evs.anl.gov).

22 GENERAL STUDIES OF NUCLEAR REACTORS↗
DOE OSTI2020

Energy Intensity Baselining and Tracking Guidance

Each company joining the U.S. Department of Energy’s (DOE’s) Better Buildings, Better Plants Program (Better Plants) commits to establishing an energy consumption and energy intensity (EI) baseline and to tracking its energy performance over a 10-year period against that baseline. The baseline must reflect a company’s energy consumption over a 12-month period, covering all its U.S.-based operations. Energy consumption is calculated by fuel type in terms of primary energy (also known as source energy). EI is broadly defined as the amount of energy consumed per unit of output produced. For this guidance document and for the program, the term energy performance represents an evaluation of a facility’s capacity to use energy efficiently. Metrics used to assess a facility’s energy performance can include EI, energy consumption, improvements in EI, etc. Establishing an energy baseline and tracking system is a critical first step in effectively managing energy use. Developing a baseline can help a company understand energy use within the corporation and give it a point of comparison to evaluate future efforts to improve energy performance. It can also support efforts to validate a company’s energy management activities, improve comparative analyses when using benchmarks, and help in predicting future energy needs. In addition, a company that normalizes its performance data can determine highly defensible measures of energy savings generated through implemented energy efficiency projects. Establishing a baseline and tracking energy performance is also a requirement for ISO 50001 certification. Although basic energy data can be collected through utility bills, most manufacturers will have to perform additional analyses to develop accurate and robust energy baselines and tracking systems. Energy is consumed in many ways within the manufacturing sector and can come from multiple sources. Energy is sometimes generated and sold to other parties or captured and reused on-site. External events can exert a significant impact on a facility or company’s energy use independent of any purposeful efforts to improve energy efficiency. Operational changes, such as production shifts—which may be inevitable for some companies over the 10-year period covered by the program—can also make a big difference in energy use. Since Better Plants asks companies to account for all their U.S.-based operations, mergers, acquisitions, and divestitures can also have significant implications for a company’s energy metrics. This document aims to demystify the sometimes complex baselining process. It devotes special attention to the task of normalizing and adjusting energy consumption to account for external factors, such as weather and production changes. A key recommendation is that companies use regression analysis to normalize their energy consumption data whenever possible. Regression analysis is a statistical technique that estimates the dependence of a variable (i.e., energy use in the context of Better Plants) on one or more independent variables such as ambient temperature, while controlling for the influence of other variables at the same time. A properly developed regression analysis can provide a reliable estimate of energy savings resulting from energy improvement strategies and projects by accounting for the effects of variables such as annual production levels and weather. DOE has developed a companion Energy Performance Indicator software tool (EnPI) to simplify the baselining process. This tool can run regression models, calculate changes in EI at the facility level, and automatically compile facility-level data into a corporate-wide metric. Note that although the relevant equations used to calculate EI are provided in this document, the EnPI tool will automatically perform most calculations for the user. Additionally, Better Plants Partners (Partners) can call on their Technical Account Manager (TAM) to help them establish a baseline and assist with the necessary calculations to track progress.

32 ENERGY CONSERVATION, CONSUMPTION, AND UTILIZATI↗
DOE OSTI2024

Accelerating Thermochemical Equilibrium Calculations for Nuclear Reactor Applications

Thermochemical properties play a key role in modeling and simulation of several key phenomena in nuclear reactors. There has been an increasing interest in incorporating CALPHAD-based formulations in multiphysics simulations including for Molten Salt Reactors where knowledge of phase evolution of the salt and the chemical potentials of various elements are of utmost importance in source term analyses and redox control. However, the size of such simulations is often limited by the high computational cost of full thermodynamic equilibrium calculations. This work discusses the current efforts aimed at accelerating thermochemical equilibrium calculations for multiphysics simulations performed using the open-source finite element / finite volume code Multiphysics Object Oriented Simulation Environment (MOOSE) [1]. While several methods have been proposed for accelerating phase equilibrium calculations [2], most focus on relatively small systems and often rely on a- priori knowledge of the state-space of the system. Nuclear materials, however, are often multi-component systems owing to the evolution of composition under irradiation and an approach based on a-priori mapping of phase diagram is often not enough. This work is aimed at demonstrating an on-the-fly surrogate modeling framework that uses active learning to reduce the number of full equilibrium calculations that must be performed. By combining with efficient coupling approaches, the surrogate framework helps in reducing the computational cost of thermodynamic equilibrium informed multiphysics simulations of nuclear materials. The performance is benchmarked against full coupling with the thermochemistry library Thermochimica [3]. This work uses a machine learning based approach for constructing surrogate models to predict the stable phases in a multicomponent system. The surrogates were constructed using neural networks and Gaussian process classification. In this work, we compare the relative performance of the two methods. We also demonstrate the use of caching previous calculations by interpolating the values from nearest neighbors. References [1] Lindsay, A.D., et al. "2.0 – MOOSE: Enabling massively parallel multiphysics simulation", SoftwareX, 20 (2022): 101202. [2] Roos, W.A. and Zietsman J.H. "Accelerating complex chemical equilibrium calculations – A Review", Calphad, 77 (2022): 102380. [3] Piro, M.H.A., et al. "The thermochemistry library Thermochimica", Computational Materials Science, 67 (2013): 266-272.

36 MATERIALS SCIENCE↗
DOE OSTI2021

BISON As-run AGR-3/4 Irradiation Test Predictions

BISON, a nuclear fuel performance application built using the Multiphysics Object-Oriented Simulation Environment (MOOSE) finite element library, was used to model the Advanced Gas Reactor (AGR)-3/4 irradiation test using as-run physics and thermal hydraulics data. The AGR-3/4 test consists of the combined third and fourth planned irradiations of the AGR Fuel Development and Qualification Program. The AGR-3/4 test train consists of twelve separate and independently controlled and monitored capsules. Each capsule contains four compacts filled with both uranium oxycarbide (UCO) unaltered “driver” fuel particles and UCO designed-to-fail (DTF) fuel particles. The DTF fraction was specified to be 1×10-2. This report documents the calculations performed to predict the failure probability of tristructural isotropic (TRISO) coated driver fuel particles during the AGR-3/4 experiment on a single compact. This report will demonstrate the capabilities of BISON to model the complex AGR-3/4 irradiation test and identify further development needed to capture the fuel particle failure probability and source term on every compact for further comparison from post-irradiation examination (PIE) data. The calculations include the modeling of the AGR-3/4 irradiation that occurred from December 2011 to April 2014 in the Advanced Test Reactor (ATR) over a total of 10 ATR cycles including seven normal cycles, one low power cycle, one unplanned outage cycle, and one Power Axial Locator Mechanism (PALM) cycle.

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗
DOE OSTI2020

As-Run Physics Analysis for the EPRI-1 Experiment

The purpose of this ECAR is to document the as-run physics analysis for the Electric Power Research Institute (EPRI)-1 experiment located in the Center Flux Trap (CFT). EPRI-1 was irradiated during cycle 157C. The experiment irradiation ended on February 15, 2015. The as-run heat rates, DPA, and flux/fluence results were calculated using the Monte Carlo N-Particle (MCNP) Advanced Test Reactor (ATR) full core model. The heat rates, DPA, and flux are calculated based on an average center lobe power of 21.1 MW. The fluence and DPA is based on the operating time of 5.4 days. ORIGEN2 Version 2.2 was used to calculate the isotopic concentration in grams for the EPRI-1 experiment. The source term analysis was performed as requested by the project staff. The results of this analysis may be used to support Post-Irradiation Examination (PIE)

22 GENERAL STUDIES OF NUCLEAR REACTORS↗
DOE OSTI2021

(U) Using the MCNP6 Perturbation Capability for Source Nuclide Density Sensitivities

The Taylor series (differential operator) perturbation method, as implemented in the PERT capability in MCNP6 (Ref. 1), can be used for first- and second-order sensitivity analyses in fixed-source problems. Unfortunately, the PERT capability does not yet work with point-detector (F5) or pulse-height (F8) tallies. Also, the second-order Taylor series term lacks the cross terms that would allow the calculation of mixed sensitivities. Finally, the PERT capability does not compute any sensitivities involving the source in a fixed-source problem. When neutrons or gamma rays are emitted due to radioactive decay, the source rate density depends intrinsically on the nuclide densities in the source material. When the PERT capability in MCNP6 is used to compute sensitivities of a response to nuclide and material densities, those sensitivities do not include the effect of the source.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2022

Coordinated Integration of Renewable Generation and Small Modular Reactors in Puerto Rico – an Initial Study

With a growing interest and awareness to support clean and sustainable sources of energy, several countries have ambitious plans to significantly increase the penetration of renewable energy in the grid. However, the sources of renewable energy, such as solar and wind, are highly intermittent and therefore can pose additional challenges to maintain reliable system operations; one such challenge being flexibility requirement. This paper addresses the concerns of increasing flexibility needs with high renewable penetration, and also study the coordinated integration of nuclear small modular reactor and inverter-based renewable generation sources in a system to achieve high levels of carbon-free and sustainable energy. In this paper, balancing reserve and short-term flexibility requirements were considered for the analysis purpose. Also, methodology was developed to calculate metrics for calculating short-term flexibility requirements in the time-scale of hours. Small modular reactors are considered as potential sources of generation flexibility to complement renewables.

Agrawal, Urmila↗
DOE OSTI2026

Modeling glass degradation and release of radionuclides from vitrified waste for performance assessment simulations

The release of radionuclides initially encapsulated in a slowly degrading solid waste form and contained in an eventually corroding canister defines the source term for numerical simulations for the assessment of a geologic repository for high-level radioactive waste. While the details of waste degradation, canister corrosion, and dissolution and mobilization of the radionuclides in pore water include complex chemical reaction and transport processes that are coupled to the thermal, hydrological, microbiological, and mechanical conditions in the repository, the source-term model suitable for use in a numerical performance assessment model should be a defensible abstraction of these mechanisms. We developed a radiological source-term model and implemented it into a non-isothermal flow and transport simulator. While the proposed source-term model is applicable to various waste forms, canister systems, and disposal concepts, we specifically considered radionuclide releases from vitrified high-level waste placed in a cylindrical canister disposed in a deep vertical borehole repository. In this model, waste degradation is a function of temperature, and it can be adjusted to evaluate the influence of and propagate uncertainties in pH, passivation reactions, and chemical conditions as well as geometrical factors. The time-dependent, congruent release of safety-relevant radionuclides present in the decaying inventory is then calculated. Finally, the radionuclides are mobilized by diffusive and advective transport according to the thermo-hydraulic conditions prevailing in the near field of the repository, from where they migrate through the geosphere to the accessible environment. We examine the influence of the source-term model’s parameters on performance assessment calculations through sensitivity and uncertainty propagation analyses, identifying influential factors and confirming the upper bound of their impact. These considerations align with the overarching goal of repository design, which is to demonstrate that engineered and natural barriers can collectively delay radionuclide migration for timescales far exceeding human planning, thereby providing multiple, redundant barriers against environmental contamination.

iTOUGH2↗
DOE OSTI2020

Performing a multi-unit level-3 PSA with MACCS

MACCS (MELCOR Accident Consequence Code System), WinMACCS, and MelMACCS now facilitate a multi-unit consequence analysis. MACCS evaluates the consequences of an atmospheric release of radioactive gases and aerosols into the atmosphere and is most commonly used to perform probabilistic safety assessments (PSAs) and related consequence analyses for nuclear power plants (NPPs). WinMACCS is a user-friendly preprocessor for MACCS. MelMACCS extracts source-term information from a MELCOR plot file. The current development can combine an arbitrary number of source terms, representing simultaneous releases from a multi-unit facility, into a single consequence analysis. The development supports different release signatures, fission product inventories, and accident initiation times for each unit. The treatment is completely general except that the model is currently limited to collocated units. A major practical consideration for performing a multi-unit PSA is that a comprehensive treatment for more than two units may involve an intractable number of combinations of source terms. This paper proposes and evaluates an approach for reducing the number of calculations to be tractable, even for sites with eight or ten units. The approximation error introduced by the approach is acceptable and is considerably less than other errors and uncertainties inherent in a Level 3 PSA.

42 ENGINEERING↗
DOE OSTI2020

HPAC Validation against NRC Documentation

This report describes validation of the radiological source terms in the Nuclear Facility Accident (NFAC) module of the Defense Threat Reduction Agency (DTRA)’s Hazard Prediction and Assessment Capability (HPAC) software. The validation will be conducted by comparing the source terms defined in HPAC to published data from references approved by the U. S. Nuclear Regulatory Commission (NRC). Comparisons will be done for both pressurized water reactors (PWRs) and boiling water reactors (BWRs). This comparison includes the magnitude, isotopic composition, and timing of the release fractions over the course of a severe or moderate accident. Calculations for both facility-specific nuclear power plants and for more generic reactor categories are involved. It is shown that the NFAC radiological source terms in HPAC agree well with NRC standards for moderate and severe accidents at PWRs and BWRs.

98 NUCLEAR DISARMAMENT, SAFEGUARDS, AND PHYSICAL P↗
DOE OSTI2022

3D simulations of inertial confinement fusion implosions part 1: inline modeling of polarized cross beam energy transfer and subsequent drive anomalies on OMEGA and NIF

Inertial confinement fusion experiments are sensitive to cross-beam energy transfer (CBET), a laser-plasma instability that redistributes laser energy in the coronal plasma through self-generated ion acoustic wave (IAW) gratings. The detailed CBET coupling depends on the polarization state of the crossing wavefields. CBET itself can also scramble the beam polarizations by inducing ellipticity through the IAW grating, and rotating the seed polarization toward that of the pump. We develop a ray-based model that describes the polarized CBET coupling and that is compatible with the framework of 3D inline radiative hydrodynamics simulations. The model is implemented in the ASTER/IFRIIT code and verified against an academic test case and an offline polarized CBET post-processor. It is then applied to the detailed configuration of the distributed polarization rotator system on OMEGA, where results highlight how polarized CBET induces significant low modes in the collisional absorption source term. Finally, the modeling is applied to a simple indirect-drive configuration, comparing CBET calculations with 96 unpolarized or polarized beams with 24 unpolarized quads. It is shown that these cases produce similar power amplification per cone of beams grouped with similar polar angles. However, the 96 beam geometry itself is found to reduce azimuthal variations in quad power after the interaction and favors beams with larger polar angles within the cones, an effect that is amplified by the polarized CBET. Application of the model to inline calculations of OMEGA implosions are presented in a companion paper.

3D inline modeling↗
DOE OSTI2020

Turbo FRMAC Implemetation of IAEA Radiological Assessment Methodologies for Nuclear and Radiological Emergencies.

This report documents the findings of an assessment of the Turbo FRMAC software's ability to implement International Atomic Energy Agency (IAEA) guidance for calculating Operational Intervention Levels (OIL) 1 & 2 for nuclear and radiological emergencies. The IAEA OIL and U.S. Federal Radiological Monitoring and Assessment Center (FRMAC) Derived Response Level methodology and implementation in respective tools were compared, as demonstrated through benchmarking activities for a nuclear power plant source term and potential radionuclides of concern for radiological dispersal devices. This comparison revealed some shortcomings in Turbo FRMACs ability to perform IAEA OIL calculations and resulted in recommended software modifications to be considered for future development.

61 RADIATION PROTECTION AND DOSIMETRY↗
DOE OSTI2024

SCALE 6.3 Modeling Strategies for Reactivity, Nuclide Inventory, and Decay Heat of Non-LWRs

To assess modeling and simulation capabilities for thermal hydraulics, accident progression, source term, and consequence analysis for non–light-water reactor (LWR) technologies, the US Nuclear Regulatory Commission (NRC) initiated a collaborative project between Oak Ridge National Laboratory (ORNL) and Sandia National Laboratories (SNL) in FY20, which is detailed in “Volume 3: Computer Code Development Plans for Severe Accident Progression, Source Term, and Consequence Analysis.” This project demonstrated the capabilities of the MELCOR and SCALE codes to calculate accident scenarios during operation of relevant non-LWRs. The following five non-LWR concepts were selected for capability demonstration based on recently renewed industry interest in the United States to develop and deploy such reactor technologies: pebble-bed high temperature gas-cooled reactors (HTGRs), pebble-bed fluoride salt-cooled reactors (FHRs), molten salt–fueled reactors (MSRs), heat pipe reactors (HPRs), and sodium-cooled fast reactors (SFRs).

22 GENERAL STUDIES OF NUCLEAR REACTORS↗
DOE OSTI2020

As-run physics analysis for the EPRI-2 experiment for cycle 153B

The purpose of this ECAR is to document the as-run physics analysis and source term in Curies and decay heat rate (Watts) for the shipment of the EPRI-2 experiment located in the Center Flux Trap (CFT). EPRI-2 was irradiated during cycle 153B. The experiment irradiation ended on April 13, 2013. The as-run heat rates and flux/fluence results were calculated using the MCNP ATR full core model. The heat rates and flux are calculated based on an average center lobe power of 30.8 MW. The fluence is based on the operating time of 13.45 days. ORIGEN2 Version 2.2 is used to determine the decay heat rate, gamma spectrum, and source term for the EPRI-2 experiment. The source term analysis was performed as requested by the project staff to demonstrate compliance with shipping requirements in the GE-2000 cask following irradiation as well as provide an estimated source term to support Post-Irradiation Examination as needed.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗
DOE OSTI2021

Skyshine Calculations for a Large Spent Nuclear Fuel Storage Facility with SCALE 6.2.3

The SCALE code system developed at Oak Ridge National Laboratory includes state-of-the-art capabilities for radiation source term and radiation transport simulations that can be used in numerous applications, including dose rate analyses of complex consolidated interim storage facilities (CISFs). A licensed CISF could be used to store tens of thousands of tonnes of spent nuclear fuel discharged from commercial power reactors using various cask and storage pad designs. A CISF design must comply with the regulatory requirements provided in 10 CFR Part 72, including requirements related to annual dose limits applicable to real individuals located beyond the area controlled by the licensee. Therefore, calculating a dose to the public is a necessary part of the licensing process for the construction of a CISF. These calculations are very challenging because of the complexity of the CISF design and the low magnitude of dose rate at large distances from the facility. This paper describes detailed far-field dose rate calculations performed for a proposed CISF using MAVRIC, the Monte Carlo radiation shielding sequence in SCALE 6.2.3, with automated variance reduction based on discrete ordinates calculations. The method presented in this paper uses a detailed Monte Carlo radiation transport simulation in one step from source to dose rate. A series of independent simulations was made using the complete site geometry (all casks present), but with only one cask containing radiation sources to obtain the dose rate maps produced by each storage cask. The CISF dose rate map was obtained by adding the dose rate maps produced by the independent individual cask simulations. Ample volumes of air and soil extending beyond the location of interest for dose rate calculation were included in the calculation model to properly simulate important radiation attenuation and scattering events that affect far-field dose rates. Furthermore, a comprehensive sensitivity study is included in this paper to illustrate the importance of selecting appropriate air volume, mass density, and composition for CISF skyshine dose rate calculations. Dry soil and soil containing water were analyzed to determine their effects on groundshine radiation.

12 MANAGEMENT OF RADIOACTIVE AND NON-RADIOACTIVE W↗
DOE OSTI2022

The Astronomy Commons Platform: A Deployable Cloud-based Analysis Platform for Astronomy

Abstract We present a scalable, cloud-based science platform solution designed to enable next-to-the-data analyses of terabyte-scale astronomical tabular data sets. The presented platform is built on Amazon Web Services (over Kubernetes and S3 abstraction layers), utilizes Apache Spark and the Astronomy eXtensions for Spark for parallel data analysis and manipulation, and provides the familiar JupyterHub web-accessible front end for user access. We outline the architecture of the analysis platform, provide implementation details and rationale for (and against) technology choices, verify scalability through strong and weak scaling tests, and demonstrate usability through an example science analysis of data from the Zwicky Transient Facility’s 1Bn+ light-curve catalog. Furthermore, we show how this system enables an end user to iteratively build analyses (in Python) that transparently scale processing with no need for end-user interaction. The system is designed to be deployable by astronomers with moderate cloud engineering knowledge, or (ideally) IT groups. Over the past 3 yr, it has been utilized to build science platforms for the DiRAC Institute, the ZTF partnership, the LSST Solar System Science Collaboration, and the LSST Interdisciplinary Network for Collaboration and Computing, as well as for numerous short-term events (with over 100 simultaneous users). In a live demo instance, the deployment scripts, source code, and cost calculators are accessible. 4 4 http://hub.astronomycommons.org/

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2026

A Proof of the Asymptotic Variance of Path Length Estimators for Single-Collision Monte Carlo Source Iteration in the Thick Diffusion Limit

Here, we prove a theorem relating the variance of path length estimators for single-collision Monte Carlo source iteration to a parameter that becomes infinitesimally small in an important physical regime arising in radiative transfer. In our usage, “single-collision Monte Carlo source iteration” refers to Monte Carlo Boltzmann transport methods in which each Monte Carlo particle history includes no more than a single collision, and the physics of multiple scattering is modeled by lagging the scattering source term and iterating until this term converges. Our theorem can be used to construct variance reduction techniques which improve the order of the estimator variance. This enables calculations that would otherwise require impractically large sample sizes to achieve practical estimator uncertainties. We believe this is the first postulation of a theorem relating estimator variance to a limiting case parameter for single-collision Monte Carlo source iteration, and the first proof of such a theorem. We illustrate the theorem’s value with an example in which the authors of a transport method used the theorem to design a variance reduction technique that improved the uncertainty of their solution by a factor of about 500 for a proxy problem from radiative transfer that contains both optically-thick and optically-thin material.

Mathematics and Computing↗