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Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

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All sourcesNASA NTRSDOE OSTI
DOE OSTI2022

Nuclear data uncertainty propagation applied to the versatile test reactor conceptual design

We report the Versatile Test Reactor (VTR) currently under development is a 300 MWth sodium-cooled fast reactor (SFR) fueled with ternary metal alloy fuel, which aims to accelerate the testing of advanced nuclear fuels, materials, instrumentation, and sensors in high flux environments that are necessary to license the next generation of advanced reactor concepts. To support the VTR design process, uncertainties associated with the nuclear data has been propagated through the reactor core neutronics calculation to global parameters of interest, such as the core multiplication factor, kinetic parameters, and various reactivity feedback coefficients, following the sensitivity based uncertainty propagation approach. By folding the sensitivity coefficients, separately computed by the generalized perturbation theory code PERSENT and Monte Carlo code Serpent 2, with the variance-covariance matrices from COMMARA-2.0, we obtain the reaction-wise, isotope-wise, and overall uncertainties for each response of interest due to nuclear data uncertainty. With Serpent 2, the statistical error of the uncertainty is obtained by propagating the statistical error of the sensitivity coefficients through the same process using a newly developed uncertainty propagation method. From both codes, the overall top uncertainty contributors are found to be the cross section of Fe-56 elastic scattering, Na-23 elastic scattering, and U 238 inelastic scattering. The large contributions of the Fe-56 elastic scattering cross sections to global parameters are due to its relatively large relative uncertainty of 5–10% in nuclear data and the large volume of Fe-containing reflector assemblies in the fairly compact VTR core design. Both codes agreed well for the overall uncertainty estimates of all responses of interest, except the delayed neutron fraction, prompt neutron generation time, and the coolant density feedback coefficient, where Serpent 2 yielded a much larger value than PERSENT due to the large statistical error of sensitivity coefficients. The calculated uncertainties are also compared to those associated with other SFR cores. Another outcome of this study is a variance-covariance matrix of reactivity coefficients, which can be used in the subsequent uncertainty propagation to the system level to investigate the impact of identified uncertainties on system responses in the safety analysis.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗
DOE OSTI2025

VARI3D & PERSENT: Perturbation and Sensitivity Analysis

The nodal diffusion method is one of the most widely used approaches in modern reactor analysis. In the nodal diffusion method, a coarse multi-group set of “homogenized” parameters is constructed such that the complex geometry of a reactor core along with the energy dependence of neutron and gamma ray cross sections in a nuclear reactor are conserved in the simpler geometry. The homogenization is typically done on a fuel assembly level as is the case in the DIF3D code developed at Argonne National Laboratory. The nodal methodology is used primarily to predict fuel cycle behavior of nuclear systems of which there is a substantial amount of validation in the literature. Another use of the nodal method is to obtain reactivity coefficients and kinetics parameters for use in a safety analysis of a given nuclear reactor. While there are many ways to obtain reactivity worth and kinetics parameters, the work presented in this manuscript is unique as it provides the user with the ability to compute reactivity worths, kinetics parameters, and cross section sensitivities with a Cartesian and hexagonal geometry based transport code. This manuscript serves as a single manual for two separate codes: VARI3D and PERSENT. The VARI3D code (VARIational 3D) is based upon the classic finite difference diffusion theory solver available in DIF3D. The PERSENT code (PERturbation and SENitivity for Transport) is based upon the variational nodal method employed in DIF3D termed VARIANT. The VARIANT solver was added to DIF3D in 1995 and has seen continued development and use for the last 18 years. Because VARI3D primarily uses deprecated coding practices, rather than incorporating the perturbation and sensitivity treatments for transport within VARI3D, a new coding development was built using modern Fortran coding. The primary purpose of this manual is to describe the theory behind PERSENT (and by convenience, that of VARI3D) and discuss the input and output of PERSENT along with giving potential users an idea of how to use it. While this manuscript does describe the input and output of VARI3D, the PERSENT code is intended to be the replacement capability of VARI3D as PERSENT can generate nearly identical (if not superior) diffusion theory results. In this manuscript, the relevant aspects of generalized perturbation theory and exact perturbation theory that apply to both VARI3D and PERSENT are covered. The input and output of VARI3D is displayed by excerpting several of the example problems. Similarly, the input and output of PERSENT is displayed along with tips on how best to use the code. Note that the input and output of the inhomogeneous solver wrapped around DIF3D (DIF3D_IFS) is also discussed as it is needed to carry out some of the sensitivities in PERSENT such as reaction rate ratios. This manuscript describes several perturbation and sensitivity problems, and the results computed using PERSENT. From these sections, potential users should find that PERSENT provides not only the typical tables of numbers desired in perturbation and sensitivity analysis work, but also can visually plot the result for a more thorough understanding of the space and energy distribution (Section 5). Overall, PERSENT is observed to produce accurate reactivity worths and sensitivities for the displayed set of test problems and clearly demonstrates the need to have a transport-based sensitivity capability as evident from the thousands of percent errors observed in the 21-group hexagonal fast reactor problem (covered in Section 7). The uncertainty calculation capability is described in Section 3 and demonstrated in Section 7.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗
DOE OSTI2022

Statistical uncertainty of fission matrix eigenvalues using perturbation theory

Eigenvalue search of high dominance ratio systems may be slow to converge. The fission matrix element is defined by its element (FM){sub ij}, which are the probability for a neutron born in cell i to create a fission in cell j for a spatial mesh of n{sub i}*n{sub j} elements. Fission matrices are used in Monte Carlo criticality simulations to enhance computing speed, but also to find higher order eigenvalues. However, few studies have been made on the link between statistical uncertainties of fission matrix elements and eigenvalues uncertainties. Thus, dominance ratio statistical uncertainties remain unknown. This paper uses a new generalized perturbation theory (GPT) method to estimate sensitivities of eigenvalues to fission matrix elements and then to calculate dominance ratio uncertainties.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗
DOE OSTI2022

Implementation and testing of the GPT sensitivities in TRIPOLI-4

Computing the sensitivity of given reactor parameters with respect to nuclear data is mandatory in key applications such as the assessment of reactor safety or core design. In recent years, the development of Monte Carlo methods capable of estimating sensitivity coefficients based on the Standard or Generalized Perturbation Theory (SPT and GPT, respectively) has attracted intensive research efforts, especially in view of having reference golden standard simulations to be compared to faster but approximate deterministic calculations. Following our previous implementation and validation of the SPT functionalities in the Monte Carlo TRIPOLI-4, devoted to the sensitivity of the k eigenvalue, in this work we detail the development of GPT methods for ratios of reaction rates, and validate them against a few relevant benchmark results. (authors)

22 GENERAL STUDIES OF NUCLEAR REACTORS↗
DOE OSTI2025

Implementation of Perturbation Theory and Sensitivity Capabilities in Griffin

Griffin is a Multiphysics Object-Oriented Simulation Environment (MOOSE) based reactor Multiphysics analysis application, jointly developed by Argonne and Idaho National Laboratories under the DOE-NE NEAMS program. This fiscal year, capabilities for reactivity and sensitivity evaluation using perturbation methods were implemented and verified. The First Order Perturbation Method (FOPT) was employed to compute reactivity worth resulting from small perturbations in input parameters, while the Generalized Perturbation Theory (GPT) was used to evaluate sensitivities of a range of response types, including reaction rate ratio, k-eigenvalue, neutron generation time, and effective delayed neutron fraction. These perturbation methods enable users to quantify how response quantities change due to a perturbation in a input parameter without explicitly performing an additional transport simulation for each perturbed state. In particular, the GPT formulation accounts for indirect effects arising from flux changes by solving generalized inhomogeneous equations, for which a Neumann series-based iterative solution method was developed and implemented in Griffin. The implemented reactivity and sensitivity evaluation capabilities were verified using two test problems: an infinite homogeneous system and a two-dimensional hexagonal core. The results showed excellent agreement with reference solutions obtained by a direct method based on finite difference approximation as well as GPT-based results from the PERSENT code, confirming the accuracy of both reactivity and sensitivity evaluations. Additionally, preliminary uncertainty quantification (UQ) results were obtained by combining the sensitivity values computed using GPT and external covariance data, demonstrating that the implemented sensitivity results can be reliably used for uncertainty calculations. To further demonstrate the generality and practical strength of the implementation, the sensitivity evaluation capability was successfully applied to the Empire microreactor with a geometrically complex design that poses significant modeling challenges. The results confirm that Griffin enables sensitivity evaluations even for irregular and highly heterogeneous reactor configurations, thereby establishing a foundation for UQ applications in advanced reactor designs and analyses.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗
DOE OSTI2024

The three-pion K -matrix at NLO in ChPT

The three-particle K-matrix, Κ df,3 , is a scheme-dependent quantity that parametrizes short-range three-particle interactions in the relativistic-field-theory three-particle finite-volume formalism. In this work, we compute its value for systems of three pions in all isospin channels through next-to-leading order in Chiral Perturbation Theory, generalizing previous work done at maximum isospin. We obtain analytic expressions through quadratic order (or cubic order, in the case of zero isospin) in the expansion about the three-pion threshold.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2025

Development and application of two-step uncertainty propagation and sensitivity analysis methodology for fast reactor safety analysis

Uncertainty quantification (UQ) in nuclear reactors for transients is directly linked with safety assessment through the cross-sections uncertainties, provided as a covariance matrix, which are propagated through the reactor system to output of interest pertaining to reactor safety, such as peak temperatures in fuel/clad/coolant. Using a two-step approach, uncertainties are first quantified and propagated from basic input variables (such as reaction cross-sections) to intermediate quantities (such as reactivity feedback coefficients) through lattice level calculations. Uncertainties of intermediate quantities (from the first step) are then propagated through the system transient calculations, in the second step, to obtain uncertainties on reactor safety output parameters of interest. The scope of this work consists of Uncertainty Quantification & Propagation of nuclear data uncertainties that are highly correlated through unprotected transient overpower and unprotected loss of flow to assess their impact on core safety parameters. This two-step approach in the presence of covariance renders the sensitivity analysis very challenging. In fact, usually the sensitivity analysis is restricted to each step, which limits its application since the sensitivities between the system output quantities and the basic input variables are difficult to obtain. Here, in this work, we address this issue by proposing a simple, general methodology to combine the sensitivity indices obtained in each step by assuming the model behavior being linear. For the first step Generalized Perturbation theory based indices are used while in the second step the recently studied Johnson indices. The uncertainty quantification and sensitivity methodologies discussed here are demonstrated on a generic LFR design which is based on the 500 MWth demonstration Lead-cooled fast reactor (DLFR) using oxide fuel, developed by Westinghouse Electric Company (WEC).

42 - ENGINEERING↗
DOE OSTI2022

Impact of nuclear data covariance libraries on uncertainty quantification of sodium cooled fast reactor simulation

Uncertainty quantification in core modelling to assess reactor performance is a regular practice to identify design safety limits. Best-estimate plus uncertainty (BEPU) methods are commonly used to propagate uncertainties to core responses from input parameters, characterized by variance-covariance libraries. This study evaluates the impact of different covariance libraries on the uncertainty associated with core safety parameters and their propagation through reactor transient modelling for a metallic core (ABR-1000). The COMAC-1.0, COMMARA-2.0, and COMMARA-2.1 covariance libraries are used to propagate nuclear data uncertainties to neutron feedback coefficients using the Generalized Perturbation Theory, then through transient safety analyses to establish the confidence interval for safety performance of the reactor using stochastic sampling. The considered transients include Unprotected Transient Over Power and Unprotected Loss Of Flow. Most influential nuclide and reaction pairs in different variance-covariance libraries are identified and their impact on the uncertainty of safety parameters are evaluated. Significant differences were observed between uncertainties from COMAC compared to COMMARA libraries. Uncertainties from COMMARA libraries were consistently larger than COMAC for all cases. For structure, coolant density feedback coefficients and control rod worth, total nuclear data uncertainties were approximately 50% larger for COMMARA than COMAC. Differences were also observed in identification of top contributors of uncertainty in terms of reaction-cross sections. For instance, largest contribution to total uncertainty of radial expansion coefficient from COMMARA-2.0 and 2.1 originates from Na{sup 23} P1 Elastic cross section (0.81%) but from Pu{sup 239} Fission (0.53%) with COM C-1.0. Such differences are evaluated in this research for all quantities of interest. (authors)

21 SPECIFIC NUCLEAR REACTORS AND ASSOCIATED PLANTS↗
DOE OSTI2022

(U) SENSMG: First-Order Sensitivities of Neutron Reaction Rates, Reaction-Rate Ratios, Leakage, k eff , α , and Subcritical Multiplication Using PARTISN

SENSMG is a tool for computing first-order sensitivities of neutron reaction rates, reaction-rate ratios, leakage, k eff , α, and subcritical multiplication using the PARTISN multigroup discrete-ordinates code. SENSMG computes sensitivities to all of the transport cross sections and data (total, fission, a nu, chi, and all scattering moments), two edit cross sections (absorption and capture), and the density for every nuclide and energy group. It also computes sensitivities to the mass density for every material and derivatives with respect to all interface locations and outer boundaries. It computes sensitivities to user specified reactions whose cross sections are available in a user-supplied NJOY output file. The tool can be used for one-dimensional spherical and slab (r) and two-dimensional cylindrical (r-z) geometries. The tool can be used for fixed-source and eigenvalue problems. For most responses, the tool implements Generalized Perturbation Theory (GPT) as discussed by Williams and Stacey. The tool is thus limited to computing sensitivities only for GPT-allowable responses. For subcritical multiplication, the tool implements sensitivities derived by O’Brien and Clark. SENSMG has a similar role as the old SWANLAKE (Ref. 8), FORSS (Ref. 9), and SENSIT (Ref. 10) codes. It has capabilities similar to those of SUSD3D (Refs. 11 and 12), which also uses PARTISN. Section II of this report describes the theory behind adjoint-based sensitivities, gives the equations that SENSMG solves, and defines the sensitivities that are output. Section III describes the user interface, including the input file and command line options. Section IV describes the output. Section V gives some notes about the coding that may be of interest. Section VI presents some sample problems and discusses verification, which is ongoing. Section VII lists needs and ideas for future work. Appendix A lists most of the input files whose results are presented in Sec. VI. Appendix B provides some useful details on one of the cross-section libraries that SENSMG supports.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2024

Perturbations of Gibbons-Maeda black holes in Einstein-Maxwell-dilaton theories

The study of perturbations around black hole backgrounds in general relativity and Einstein-Maxwell theory has a long history, going back to the work of Regge and Wheeler in the 1950s. As part of a broader investigation of perturbations around black holes in supergravity, we describe here our results for the perturbations around the Gibbons-Maeda static charged black holes in a class of Einstein-Maxwell-Dilaton theories. Our analysis follows the general strategy developed by Chandrasekhar and Xanthopoulos for the perturbations of the Reissner-Nordström black hole. Here, the analysis is considerably more involved, because of the presence of the dilaton field, which couples to the other polar modes. We nonetheless find that the problem is completely solvable, in the sense that one can separate variables and eventually describe all the perturbations in terms of diagonalised second-order radial equations. We are able to prove the mode stability of all the Gibbons-Maeda black hole solutions. Published by the American Physical Society 2024

Pope, C. N. (ORCID:0000000284012564)↗
DOE OSTI2021

Algebraic Structures in the Coupling of Gravity to Gauge Theories

Highlights: • Geometric foundation for Quantum General Relativity coupled to Quantum Electrodynamics. • Rigorous introduction to Hopf algebraic renormalization. • Appropriate modifications in case renormalization Hopf algebra is ill-defined. • Generalization of Furry’s Theorem to include gravitons and ghosts. • Discussion of obstructions to multiplicative renormalization. This article is an extension of the author’s second master thesis, Prinz (2017). It aims to introduce to the theory of perturbatively quantized General Relativity coupled to Spinor Electrodynamics, provide the results thereof and set the notation to serve as a starting point for further research in this direction. It includes the differential geometric and Hopf algebraic background, as well as the corresponding Lagrange density and some renormalization theory. Then, a particular problem in the renormalization of Quantum General Relativity coupled to Quantum Electrodynamics is addressed and solved by a generalization of Furry’s Theorem. Next, the restricted combinatorial Green’s functions for all two-loop propagators and all one-loop divergent subgraphs thereof are presented. Finally, relations between these one-loop restricted combinatorial Green’s functions necessary for multiplicative renormalization are discussed.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2021

Finite-temperature many-body perturbation theory for electrons: Algebraic recursive definitions, second-quantized derivation, linked-diagram theorem, general-order algorithms, and grand canonical and canonical ensembles

A comprehensive and detailed account is presented for the finite-temperature many-body perturbation theory for electrons that expands in power series all thermodynamic functions on an equal footing. Algebraic recursions in the style of the Rayleigh–Schrödinger perturbation theory are derived for the grand potential, chemical potential, internal energy, and entropy in the grand canonical ensemble and for the Helmholtz energy, internal energy, and entropy in the canonical ensemble, leading to their sum-over-states analytical formulas at any arbitrary order. For the grand canonical ensemble, these sum-over-states formulas are systematically transformed to sum-over-orbitals reduced analytical formulas by the quantum-field-theoretical techniques of normal-ordered second quantization and Feynman diagrams extended to finite temperature. It is found that the perturbation corrections to energies entering the recursions have to be treated as a nondiagonal matrix, whose off-diagonal elements are generally nonzero within a subspace spanned by degenerate Slater determinants. They give rise to a unique set of linked diagrams—renormalization diagrams—whose resolvent lines are displaced upward, which are distinct from the well-known anomalous diagrams of which one or more resolvent lines are erased. A linked-diagram theorem is introduced that proves the size-consistency of the finite-temperature many-body perturbation theory at any order. General-order algorithms implementing the recursions establish the convergence of the perturbation series toward the finite-temperature full-configuration-interaction limit unless the series diverges. As a result, the normal-ordered Hamiltonian at finite temperature sheds light on the relationship between the finite-temperature Hartree–Fock and first-order many-body perturbation theories.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2021

Equation-of-Motion Coupled-Cluster Cumulant Green’s Function for Excited States and X-ray Spectra

Green’s function methods within many-body perturbation theory provide a general framework for treating electronic correlations in excited states and spectra. Conventional methods using the Dyson equation or the cumulant expansion are typically based on the GW self-energy approximation. In order to extend this approximation in molecular systems, a non-perturbative real-time coupled-cluster cumulant Green’s function approach has been introduced, where the cumulant is obtained as the solution to a set of coupled first order, non-linear differential equations. This approach naturally includes non-linear corrections to conventional cumulant Green’s function techniques where the cumulant is linear in the GW self-energy. The method yields the spectral function associated with the core Green’s function, which is directly related to the x-ray photoemission spectra (XPS) of molecular systems. The approach also yields very good results for binding energies and satellite excitations. The x-ray absorption spectrum (XAS) is then obtained as a convolution of the core spectral function and an effective one-body absorption spectrum. Here this approach is extended to include the full coupled-cluster-singles (CCS) core Green’s function by including the complete form of the non-linear contributions to the cumulant as well as all single, double, and triple cluster excitations in the CC amplitude equations. This approach naturally builds in orthogonality and shake-up effects analogous to those in the Mahan-Noizeres-de Dominicis edge singularity corrections that enhance the XAS near the edge. Themethod is illustrated for the XPS and XAS of NH 3 .

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2020

Real-time coupled-cluster approach for the cumulant Green's function

Green’s function methods within many-body perturbation theory provide a general framework for treating electronic correlations in excited states. Here we investigate the cumulant form of the one-electron Green’s function based on the coupled-cluster equation of motion approach in an extension of our previous study. The approach yields a non-perturbative expression for the cumulant in terms of the solution to a set of coupled first order, non-linear differential equations. The method thereby adds non-linear corrections to traditional cumulant methods linear in the self energy. The approach is applied to the core-hole Green’s function and illustrated for a number of small molecular systems. For these systems we find that the non-linear contributions lead to significant improvements both for quasiparticle properties such as core-level binding energies, as well as the satellites corresponding to inelastic losses observed in photoemission spectra.

Vila, Fernando D.↗
DOE OSTI2020

Hamiltonian formulations for perturbed dissipationless plasma equations

The Hamiltonian formulations for the perturbed Vlasov–Maxwell equations and the perturbed ideal magnetohydrodynamics (MHD) equations are expressed in terms of the perturbation derivative ∂ F / ∂ ϵ ≡ [ F , S ] of an arbitrary functional F [ ψ ] of the Vlasov–Maxwell fields ψ = ( f , E , B ) or the ideal MHD fields ψ = ( ρ , u , s , B ) , which are assumed to depend continuously on the (dimensionless) perturbation parameter ϵ . In this study, [ , ] denotes the functional Poisson bracket for each set of plasma equations and the perturbation action functional S is said to generate dynamically accessible perturbations of the plasma fields. The new Hamiltonian perturbation formulation introduces a framework for functional perturbation methods in plasma physics and highlights the crucial roles played by polarization and magnetization in Vlasov–Maxwell and ideal MHD perturbation theories. One application considered in this paper is a formulation of plasma stability that guarantees dynamical accessibility and leads to a natural generalization to higher-order perturbation theory.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2025

Quantum many-body linear algebra, Hamiltonian moments, and a coupled-cluster inspired framework

Here, we propose a general strategy to develop quantum many-body approximations of primitives in linear algebra algorithms. As a practical example, we introduce a coupled-cluster inspired framework to produce approximate Hamiltonian moments and demonstrate its application in various linear algebra algorithms for ground state estimation. Through numerical examples, we illustrate the difference between the ground-state energies arising from quantum many-body linear algebra and those from the analogous many-body perturbation theory. Our results support the general idea of designing quantum many-body approximations outside of perturbation theory, providing a route to new algorithms and approximations.

Algorithms and data structure↗
DOE OSTI2022

Proton spin structure and generalized polarizabilities in the strong quantum chromodynamics regime

The strong interaction is not well understood at low energies or for interactions with low momentum transfer. Chiral perturbation theory gives testable predictions for the nucleonic generalized polarizabilities, which are fundamental quantities describing the nucleon’s response to an external field. We report a measurement of the proton’s generalized spin polarizabilities extracted with a polarized electron beam and a polarized solid ammonia target in the region where chiral perturbation theory is expected to be valid. The investigated structure function g2 characterizes the internal spin structure of the proton. From its moments, we extract the longitudinal–transverse spin polarizability δLT and twist-3 matrix element and polarizability d2¯. Our results provide discriminating power between existing chiral perturbation theory calculations and will help provide a better understanding of this strong quantum chromodynamics regime.

Ruth, D↗