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DOE OSTI2018

Modeling of Raman-Scattering Signals in Biological Tissues by Direct and Two-Step Approaches

A search for an effective method of modelling of the Raman-spectroscopy problem in turbid (scattering) media has been performed taking into account the corresponding parameters of the detector and sample volume. A solution of the radiative-transfer equation by Monte-Carlo method underlies the proposed model. Two fundamental approaches to numerical modeling of Raman scattering are considered: the direct transport problem of Rayleigh and Raman photons at each point of the medium and the two-step model, in which a photon flux in the medium is calculated in the first stage, followed by generation of the corresponding number of Raman photons at each point.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

DOE OSTI2016

MO-FG-CAMPUS-IeP2-01: Characterization of Beam Shaping Filters and Photon Spectra From HVL Profiles in CT

Purpose: Advanced dosimetry in CT (e.g. the Monte Carlo method) requires an accurate characterization of the shaped filter and radiation quality used during a scan. The purpose of this work was to develop a method where half value layer (HVL) profiles along shaped filters could be made. From the HVL profiles the beam shaping properties and effective photon spectrum for a particular scan can be inferred. Methods: A measurement rig was developed to allow determinations of the HVL under a scatter-free narrow-beam geometry and constant focal spot to ionization chamber distance for different fan angles. For each fan angle the HVL is obtained by fitting the transmission of radiation through different thicknesses of an Al absorber (type 1100) using an appropriate model. The effective Al thickness of shaped filters and effective photon spectra are estimated using a model of photon emission from a Tungsten anode. This method is used to obtain the effective photon spectra and effective Al thickness of shaped filters for a CT scanner recently introduced to the market. Results: This study resulted in a set of effective photon spectra (central ray) for each kVp along with effective Al thicknesses of the different shaped filters. The effective photon spectra and effective Al thicknesses of shaped filters were used to obtain numerically approximated HVL profiles and compared to measured HVL profiles (mean absolute percentage error = 0.02). The central axis HVL found in the vendor’s technical documentation were compared to approximated HVL values (mean absolute percentage error = 0.03). Conclusion: This work has resulted in a unique method of measuring HVL profiles along shaped filters in CT. Further the effective photon spectra and the effective Al thicknesses of shaped filters that were obtained can be incorporated into Monte Carlo simulations.

61 RADIATION PROTECTION AND DOSIMETRY↗

DOE OSTI2016

Permutation invariant potential energy surfaces for polyatomic reactions using atomistic neural networks

The applicability and accuracy of the Behler-Parrinello atomistic neural network method for fitting reactive potential energy surfaces is critically examined in three systems, H + H{sub 2} → H{sub 2} + H, H + H{sub 2}O → H{sub 2} + OH, and H + CH{sub 4} → H{sub 2} + CH{sub 3}. A pragmatic Monte Carlo method is proposed to make efficient choice of the atom-centered mapping functions. The accuracy of the potential energy surfaces is not only tested by fitting errors but also validated by direct comparison in dynamically important regions and by quantum scattering calculations. Our results suggest this method is both accurate and efficient in representing multidimensional potential energy surfaces even when dissociation continua are involved.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

DOE OSTI2013

Monte Carlo implementation of a guiding-center Fokker-Planck kinetic equation

A Monte Carlo method for the collisional guiding-center Fokker-Planck kinetic equation is derived in the five-dimensional guiding-center phase space, where the effects of magnetic drifts due to the background magnetic field nonuniformity are included. It is shown that, in the limit of a homogeneous magnetic field, our guiding-center Monte Carlo collision operator reduces to the guiding-center Monte Carlo Coulomb operator previously derived by Xu and Rosenbluth [Phys. Fluids B 3, 627 (1991)]. Applications of the present work will focus on the collisional transport of energetic ions in complex nonuniform magnetized plasmas in the large mean-free-path (collisionless) limit, where magnetic drifts must be retained.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

DOE OSTI2013

Feasibility of a Monte Carlo-deterministic hybrid method for fast reactor analysis

A Monte Carlo and deterministic hybrid method is investigated for the analysis of fast reactors in this paper. Effective multi-group cross sections data are generated using a collision estimator in the MCNP5. A high order Legendre scattering cross section data generation module was added into the MCNP5 code. Both cross section data generated from MCNP5 and TRANSX/TWODANT using the homogeneous core model were compared, and were applied to DIF3D code for fast reactor core analysis of a 300 MWe SFR TRU burner core. For this analysis, 9 groups macroscopic-wise data was used. In this paper, a hybrid calculation MCNP5/DIF3D was used to analyze the core model. The cross section data was generated using MCNP5. The k{sub eff} and core power distribution were calculated using the 54 triangle FDM code DIF3D. A whole core calculation of the heterogeneous core model using the MCNP5 was selected as a reference. In terms of the k{sub eff}, 9-group MCNP5/DIF3D has a discrepancy of -154 pcm from the reference solution, 9-group TRANSX/TWODANT/DIF3D analysis gives -1070 pcm discrepancy. (authors)

21 SPECIFIC NUCLEAR REACTORS AND ASSOCIATED PLANTS↗

DOE OSTI2016

Criticality calculation of non-ordinary systems

The specific features of calculation of the effective multiplication factor using the Monte Carlo method for weakly coupled and non-asymptotic multiplying systems are discussed. Particular examples are considered and practical recommendations on detection and Monte Carlo calculation of systems typical in numerical substantiation of nuclear safety for VVER fuel management problems are given. In particular, the problems of the choice of parameters for the batch mode and the method for normalization of the neutron batch, as well as finding and interpretation of the eigenvalue spectrum for the integral fission matrix, are discussed.

21 SPECIFIC NUCLEAR REACTORS AND ASSOCIATED PLANTS↗

DOE OSTI2013

HOT ELECTROMAGNETIC OUTFLOWS. II. JET BREAKOUT

We consider the interaction between radiation, matter, and a magnetic field in a compact, relativistic jet. The entrained matter accelerates outward as the jet breaks out of a star or other confining medium. In some circumstances, such as gamma-ray bursts (GRBs), the magnetization of the jet is greatly reduced by an advected radiation field while the jet is optically thick to scattering. Where magnetic flux surfaces diverge rapidly, a strong outward Lorentz force develops and radiation and matter begin to decouple. The increase in magnetization is coupled to a rapid growth in Lorentz factor. We take two approaches to this problem. The first examines the flow outside the fast magnetosonic critical surface, and calculates the flow speed and the angular distribution of the radiation field over a range of scattering depths. The second considers the flow structure on both sides of the critical surface in the optically thin regime, using a relaxation method. In both approaches, we find how the terminal Lorentz factor and radial profile of the outflow depend on the radiation intensity and optical depth at breakout. The effect of bulk Compton scattering on the radiation spectrum is calculated by a Monte Carlo method, while neglecting the effects of internal dissipation. The peak of the scattered spectrum sits near the seed peak if radiation pressure dominates the acceleration, but is pushed to a higher frequency if the Lorentz force dominates. The unscattered seed radiation can form a distinct, low-frequency component of the spectrum, especially if the magnetic Poynting flux dominates.

79 ASTRONOMY AND ASTROPHYSICS↗

DOE OSTI2013

Probability of initiation and extinction in the Mercury Monte Carlo code

A Monte Carlo method for computing the probability of initiation has previously been implemented in Mercury. Recently, a new method based on the probability of extinction has been implemented as well. The methods have similarities from counting progeny to cycling in time, but they also have differences such as population control and statistical uncertainty reporting. The two methods agree very well for several test problems. Since each method has advantages and disadvantages, we currently recommend that both methods are used to compute the probability of criticality. (authors)

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2018

Monte Carlo estimates of sensitivities to geometric perturbations for shielding problems using kernel density estimators - 25605

A Monte Carlo method to estimate the sensitivity of reaction rates like dose and flux spectra to geometric perturbations using kernel density estimators is demonstrated for shielding problems. The method is used to estimate the sensitivity of the spectrum emitted from a Cf-252 source at the center of an iron sphere as well as the sensitivity of the dose due to Cf-252 neutrons shielded using various materials. Results are compared against reference solutions obtained using Monte Carlo direct perturbations with central differences, with agreement within 5% and 3σ for the majority of results. The results indicate that a bandwidth that is 10-20% of the shielding thickness produces accurate results with statistically insignificant bias for the chosen test problems. (authors)

61 RADIATION PROTECTION AND DOSIMETRY↗

DOE OSTI2016

Using Green's Functions to Compute 3 Dimensional Neutron Flux Maps - 16016

The knowledge of the radionuclide content of radioactive waste is of utmost importance for safety and waste management reasons. Numerical simulations are used by EDF-DP2D to anticipate dismantling and radioactive waste management. The main numerical activation schemes include the computing of a 3 dimensional neutron flux map, obtained on the basis of a neutron propagation calculation. The codes used solve the transport equation called the Boltzmann equation without simplification. The Monte Carlo method is used to solve the Boltzmann equation. Random series of numbers are used to simulate the lives of millions of neutrons. The codes follow each neutron individually, from its birth to its disappearance by leakage, absorption, or fission, and then the neutron flux map is calculated at the nominal power rating conditions. The main drawback of the Monte Carlo codes is the large computing time needed to converge within acceptable statistical criteria. This extended time period is incompatible with the multiple fuel managements used by EDF to operate its NPPs because it is necessary to make a Monte Carlo calculation for each fuel loading pattern. The solution developed by EDF-DP2D is to use the importance factors of Green's Functions to simplify the computing of the 3 dimensional neutron flux maps. Physicists talk about Green's Functions where mathematicians talk about elementary solutions of linear equations with constant coefficients. With an activation scheme based on the Green's Functions approach the 3D neutron flux is obtained on the basis of the convolution of the normalized source contributions (i.e. normalized response matrices) with the neutrons emitted by the fuel assemblies. The response matrices to unitary sources are computed with the Monte Carlo code MCNP for different tallies of interest and the neutron sources emitted by the fuel are computed with a core code for different fuel loading patterns. The principal interest of this approach is the calculation of the response matrices to unitary sources that can be used for all power distributions, thus limiting the Monte Carlo computing time. (authors)

12 MANAGEMENT OF RADIOACTIVE AND NON-RADIOACTIVE W↗

DOE OSTI2022

Variance reduction techniques for Monte Carlo neutron noise simulations

The small fluctuations of the neutron flux caused by small perturbations of the macroscopic cross-sections take the name of neutron noise. Advanced Monte Carlo methods have been recently proposed in order to solve the neutron noise equations in the frequency domain, which allows establishing reference solutions to validate faster but approximate deterministic solvers. Due to the presence of particles carrying two statistical weights (for the real and imaginary components of the noise field), both of which may be positive or negative, Monte-Carlo simulations of neutron noise pose distinct challenges in terms of variance reduction. In this work we investigate two variance-reduction techniques, namely branchless collisions and weight cancellation, and probe their effectiveness for a benchmark con- figuration concerning the noise field induced by a pin with oscillating cross sections in a fuel assembly.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗

DOE OSTI2025

Neutron matter from local chiral effective field theory interactions at large cutoffs

Neutron matter is an important many-body system that provides valuable constraints for the equation of state (EOS) of neutron stars. Neutron-matter calculations employing chiral effective field theory (EFT) interactions have been extensively used for this purpose. Among the various many-body methods, quantum Monte Carlo (QMC) methods stand out due to their nonperturbative nature and the achievable precision. However, QMC methods require local interactions as input, which leads to the appearance of stronger regulator artifacts compared to nonlocal interactions. To circumvent this, we employ large-cutoff interactions derived within chiral EFT (400 MeV ≤ Λ 𝑐 ≤ 700MeV) for studies of pure neutron matter. These interactions have been adjusted to nucleon-nucleon scattering phase shifts, the triton binding energy, as well as the triton 𝛽-decay half-life. We find that regulator artifacts significantly decrease with increasing cutoff, leading to a significant reduction of uncertainties in the neutron-matter EOS. We discuss implications for the symmetry energy and demonstrate how our new calculations lead to a reduction in the theoretical uncertainty of predicted neutron-star radii by up to 30% for low-mass stars.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

DOE OSTI2021

A multifidelity method for a nonlocal diffusion model

Nonlocal models feature a finite length scale, referred to as the horizon, such that points separated by a distance smaller than the horizon interact with each other. Such models have proven to be useful in a variety of settings. However, due to the reduced sparsity of discretizations, they are also generally computationally more expensive compared to their local differential equation counterparts. In this work, we introduce a multifidelity Monte Carlo method that combines the high-fidelity nonlocal model of interest with surrogate models that use coarser grids and/or smaller horizons and thus have lower fidelities and lower costs. Using the multifidelity method, the overall computational cost of uncertainty quantification is reduced without compromising accuracy. It is shown for a one-dimensional nonlocal diffusion example that speedups of up to two orders of magnitude can be achieved using the multifidelity method to estimate the expectation of an output of interest.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2015

MO-FG-303-02: BEST IN PHYSICS (THERAPY): Cherenkov Emission Dosimetry: Feasibility for Electron Radiotherapy

Purpose: To investigate from first principles, corroborated by Monte Carlo simulations and experimental measurements, the feasibility of developing a relative Cherenkov emission (CE) dosimetry protocol for electron beam radiotherapy. Methods: Monte Carlo (MC) simulations of mono-energetic electrons incident on water were carried out in Geant4. Percent depth Cherenkov emission (PDCE) and dose (PDD) distributions were scored for incidence energies of 4, 6, 9, 12, 15, and 18 MeV. PDCE-to-PDD analytical conversion models were developed from least-squares data fits generated for PDD as a function of PDCE at the same depth and at different depths. Experimental techniques for validation of these models are examined. Results: Same-depth PDD versus PDCE data fits indicate that although the relationship is linear to first order (correlation r > 0.9 for all energies), it is much more accurately approximated by separate linear and quadratic models for the build-up and drop-off regions, respectively (r > 0.999), which is theoretically underpinned. To understand the source of this relationship and its basis for developing robust conversion models, an approximate quadratic first-principles model was derived and found in agreement with MC/measured data (20% deviation at worst). Conversely, data fits of PDD versus different-depth PDCE unveiled a depth-invariant effective point of measurement of 1.5–2.1 mm downstream with 4–18 MeV incidence, respectively (r > 0.999 in the drop-off region). We present an analytical first-principles justification for this shift. This method led to errors of <1% in drop-off region PDD (<2% for PDD<20% with 4 MeV incidence) and <0.2 mm in practical range prediction. Conclusion: We present robust quantitative prediction models, derived from first-principles and supported by simulation and measurement, for relative dose from Cherenkov emission by high-energy electrons. This constitutes a major step towards development of protocols for routine clinical quality assurance as well as real-time in vivo Cherenkov dosimetry in radiotherapy. The authors acknowledge partial support by Fonds de recherche du Quebec - Nature et technologies (FRQNT), CREATE Medical Physics Research Training Network grant of the Natural Sciences and Engineering Research Council of Canada (NSERC), CREATE Integrated Sensor Systems grant of NSERC, the Canadian Institutes of Health Research (CIHR), and NSERC.

60 APPLIED LIFE SCIENCES↗

DOE OSTI2016

SU-G-TeP3-14: Three-Dimensional Cluster Model in Inhomogeneous Dose Distribution

Purpose: We aim to investigate 3D cluster formation in inhomogeneous dose distribution to search for new models predicting radiation tissue damage and further leading to new optimization paradigm for radiotherapy planning. Methods: The aggregation of higher dose in the organ at risk (OAR) than a preset threshold was chosen as the cluster whose connectivity dictates the cluster structure. Upon the selection of the dose threshold, the fractional density defined as the fraction of voxels in the organ eligible to be part of the cluster was determined according to the dose volume histogram (DVH). A Monte Carlo method was implemented to establish a case pertinent to the corresponding DVH. Ones and zeros were randomly assigned to each OAR voxel with the sampling probability equal to the fractional density. Ten thousand samples were randomly generated to ensure a sufficient number of cluster sets. A recursive cluster searching algorithm was developed to analyze the cluster with various connectivity choices like 1-, 2-, and 3-connectivity. The mean size of the largest cluster (MSLC) from the Monte Carlo samples was taken to be a function of the fractional density. Various OARs from clinical plans were included in the study. Results: Intensive Monte Carlo study demonstrates the inverse relationship between the MSLC and the cluster connectivity as anticipated and the cluster size does not change with fractional density linearly regardless of the connectivity types. An initially-slow-increase to exponential growth transition of the MSLC from low to high density was observed. The cluster sizes were found to vary within a large range and are relatively independent of the OARs. Conclusion: The Monte Carlo study revealed that the cluster size could serve as a suitable index of the tissue damage (percolation cluster) and the clinical outcome of the same DVH might be potentially different.

07 ISOTOPE AND RADIATION SOURCES↗

DOE OSTI2013

DESIGN AND MEASUREMENT OF THE STOKES POLARIMETER FOR THE COSMO K-CORONAGRAPH

We present the Stokes polarimeter for the new Coronal Solar Magnetism Observatory K-coronagraph. The polarimeter can be used in two modes. In observation mode, it is sensitive to linear polarization only and operates as a ''Stokes definition'' polarimeter. In the ideal case, such a modulator isolates a particular Stokes parameter in each modulation state. For calibrations, the polarimeter can diagnose the full Stokes vector. We present here the design process of the polarimeter, analyze its tolerances with a Monte Carlo method, develop a way to align the individual elements, and measure and evaluate its performance in both modes.

46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND ↗

DOE OSTI2018

Dynamic Optimization of Switched-Reluctance Motors

A design algorithm is proposed for switched-reluctance motors used in manufacturing systems. The algorithm includes an optimization procedure and is based on the Monte Carlo method. In optimization of the magnetic system, it is advisable to take account of the motor’s operating conditions. The results of optimization are compared. Recommendations are made regarding the selection of the tooth-zone dimensions.

42 ENGINEERING↗

DOE OSTI2019

Resonant Radiation Transfer in Plasma. Boundary Effects

The problem of resonant transfer of atomic excitations in low-temperature plasma is solved by the Monte Carlo method. The boundary effect on the spatial distribution of excitations is investigated in cylindrical and spherical geometries. The concept of the boundary effect is discussed within the framework of the nonlocal Biberman–Holstein theory.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗