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(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↗

Verification study of xRAGE’s multi-ion viscosity model

This report on the adequacy of the plasma viscosity model implemented in LANL’s ASC program code, xRAGE is organized as follows. Section I provides a brief introduction on the kinetic theory which underpins plasma viscosity, and Section II describes how plasma kinetic theory can be used to calculate plasma viscosity coefficients accurate within the hydrodynamic limit. Section III describes the existing model for calculating the plasma viscosity coefficient in xRAGE. Next, Section IV shows tests of the xRAGE viscosity model against established hydrodynamic theory in the case of binary and trinary plasma mixtures.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

ESR Dipole Power Supply Current Ripple and Noise Specifications

This note presents key findings for the ESR main magnet dipole power supplies (PS), where we find the current ripple specification to be close to or beyond the state-of-the-art. These specifications originate from beam-beam considerations, with the requirement to limit the ripple-induced hadron emittance growth to below 10%/hour. Beam dynamics that drive this PS ripple specification arise from the beam motions at the Interaction Point (IP). The frequency of the motions can be separated into "low", compared to the betatron frequency, and "high", i.e. around the betatron frequency and harmonics. In terms of the driving frequency, "low" implies ƒ<<ƒ 0 v x,y and "fast" means ƒ≈{ƒ 0 v x,y , ƒ 0 (1- v x,y , etc.}, where ƒ 0 =1/ T 0 =78.2 kHz is the revolution frequency, and v x,y are the fractional parts of the betatron tunes. Frequencies higher than ƒ 0 /2 will be folded back due to the particles sampling the field once per turn. To provide flexibility for future lattice adjustments and working point variations, we do not consider the tunes as fixed. Instead, we assume a certain margin and allow them to potentially fall within the range of 0.1< v x,y <0.5. In other words, the high-frequency region spans approximately from 8kHz to 40 kHz. Consequently,, we definte the dipole PS ripple in two distinct frequency ranges: the low-frequency range of [1-8000] Hz and the high-frequency range of [8-40] kHz. For the physics effects we analyzed in this note, there is no distinction between the ripple (which can be approximately reproduced in the frequency domain) and the random noise if both have some power within the frequency bandwidth of interest. Therefore, while we will use the term "ripple" for short, it should always be understood that we are referring to "ripple plus noise." Except for the lower end of the low-frequency range, the impact of the rippling PS current on the beam will be considerably reduced due to the eddy currents induced in the walls of the vacuum chamber. We will account for this effect in the PS ripple specifications to follow. The remaining sections of this note are structure as follows: Section II outlines the beam-beam physics requirements for the positional stability of the beam at the IP. Section III describes the anticipated shielding effect of the eddy currents induced in the vacuum chamber. Section IV derives the ripple requirement for the low-frequency range by propagating the closed orbit ripple resulting from the rippling dipoles to the IP (relevant lattice simulation results are summarized in the Appendix). In Section V, we present the analytical criterion for the ripple in the high-frequency range by considering resonant oscillations of the electron beam around a stable closed orbit near the betatron frequency. Finally, Section VI provides a summary of our findings and discusses related work.

43 PARTICLE ACCELERATORS↗

(U) Average Scattering Angle Cosine Sensitivities

The Evaluated Nuclear Data File (ENDF) provides covariances of the average scattering angle cosine $\overline{μ}$ for 117 nuclides, and the NJOY nuclear data processing code can process these covariances. To propagate them to the uncertainty of a response due to uncertainties in $\overline{μ}$ requires sensitivities of the response with respect to $\overline{μ}$. This report uses NJOY’s definition of $\overline{μ}$ and derives a relationship between the sensitivity of a response to $\overline{μ}$ and the sensitivity of the response to the anisotropic P 1 elastic scattering cross section. This relationship has been implemented in the multigroup neutron sensitivity code SENSMG, which relies on the discrete ordinates code PARTISN for the neutron transport calculations. Kodeli has also calculated sensitivities with respect to $\overline{μ}$ and associated uncertainties. However, the formal derivation of this paper shows that the definition of the sensitivity with respect to $\overline{μ}$ is ambiguous because there are multiple ways to change $\overline{μ}$ by changing scattering cross sections. Here we derive two such ways. Both are implemented in SENSMG. This report is organized as follows. Section II discusses $\overline{μ}$ and its significance. Section III presents the equations used for the sensitivity of a response with respect to $\overline{μ}$, and Section IV discusses how to compute these sensitivities with SENSMG and MCNP6.3. Section V is a fast-spectrum test problem, and Sec. VI is a thermal-spectrum problem. Section VII is a summary. The example problem inputs are listed in the appendix.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

Analysis of the ASME Code Rules for Subsection III-5-HHB (Composite Materials) for Current HTR Design Requirements

This document includes the critical analysis review of the American Society of Mechanical Engineers (ASME) Section III Division 5 Subsection HH Subpart B (HHB), including Mandatory Appendices, that was published in 2023. In the context of this document, reference to “the code” is specific to this subsection unless otherwise specified. A specific composites task group within the ASME Nonmetallic Design and Materials Working Group, with the support of external experts, was established to perform a gap analysis review. The significant findings are summarized here. The committee response with suggested action items are detailed in the body of the report.

36 MATERIALS SCIENCE↗

FY25 status report on the addition of candidate materials in Class B Code Case

This report provides the time-dependent allowable stress calculation strategy leveraging the limited creep rupture tests data generated to support the allowable stress for 100,000 hours in American Society of Mechanical Engineers (ASME) Boiler and Pressure Vessel Code (BPVC), Section II, Part D. A variable confidence index procedure to extrapolate material properties to support 500,000 hours design life is discussed. Time-dependent allowable stresses for Class B component design and analysis are presented for Grade 1 and Grade 2 of Alloy 625. The presented data extrapolation and allowable stress calculation method will support new material addition using limited creep rupture data in the new ASME Boiler and BPVC, Section III, Division 5, Class B rules.

Part D↗

The National Diagnostic Plan (NDP) for HED Science September 2022

This documents the National Diagnostic Plan as of September 2022. The major changes in this version compared to the NDP document issued in 2021 are the new schedules and the text for the national transformative diagnostics - section III. The many local diagnostics for our three Inertial Confinement Fusion (ICF) facilities; NIF, Z and OMEGA are updated and captured in section V.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

The National Diagnostic Plan (NDP) for HED Science September 2023

This documents the National Diagnostic Plan as of September 2023. The major changes in this version compared to the NDP document issued in 2021 are the new schedules and the text for the national transformative diagnostics - section III. The many local diagnostics for our three Inertial Confinement Fusion (ICF) facilities; NIF, Z and OMEGA are updated and captured in section V.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

The National Diagnostic Plan (NDP) for HED Science September 2025

This documents the National Diagnostic Plan as of September 2025. The major changes in this version compared to the NDP document issued in 2024 are the new schedules and the text for the national transformative diagnostics - section III. The many local diagnostics for our three Inertial Confinement Fusion (ICF) facilities; NIF, Z and OMEGA are also updated and captured in section V.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

R-matrix calculations for opacities: I. Methodology and computations

Abstract An extended version of the R -matrix methodology is presented for calculation of radiative parameters for improved plasma opacities. Contrast and comparisons with existing methods primarily relying on the distorted wave approximation are discussed to verify accuracy and resolve outstanding issues, particularly with reference to the opacity project (OP). Among the improvements incorporated are: (i) large-scale Breit–Pauli R -matrix calculations for complex atomic systems including fine structure, (ii) convergent close coupling wave function expansions for the ( e + ion) system to compute oscillator strengths and photoionization cross sections, (iii) open and closed shell iron ions of interest in astrophysics and experiments, (iv) a treatment for plasma broadening of autoionizing resonances as function of energy-temperature-density dependent cross sections, (v) a ‘top-up’ procedure to compare convergence with R -matrix calculations for highly excited levels, and (vi) spectroscopic identification of resonances and bound ( e + ion) levels. The present R -matrix monochromatic opacity spectra are fundamentally different from OP and lead to enhanced Rosseland and Planck mean opacities. An outline of the work reported in other papers in this series and those in progress is presented. Based on the present re-examination of the OP work, opacities of heavy elements might require revisions in high temperature-density plasma sources.

Pradhan, A. K. (ORCID:0000000187753643)↗

(U) A General-Purpose Code for Correlated Sampling Using Batch Statistics with MCNP6 for Fixed-Source Problems

Correlated sampling can be used to reduce the uncertainty of a difference of tallies by taking advantage of the negative covariance term in the sandwich formula. Booth first showed how correlated sampling can be applied with batch statistics using MCNP’s tally fluctuation chart (TFC) to reduce the uncertainty of a difference of tallies in fixed-source problems. Booth presented a problem in which a 1273% uncertainty in a difference was reduced to 8% by accounting for correlations. Researchers He and Su recently studied correlated sampling using the TFC in MCNP version 5. They determined that the code did not print enough digits in the TFC tally means for accurate batch statistics in some cases. After modifying the source code, they concluded that “correlated sampling can yield a standard deviation of about one magnitude smaller than that predicted by the direct, un-correlated simulation when the changes in system response are small (say about 1%), which is equivalent to saving in CPU time by a factor of 100. Such saving [sic] becomes less significant as the change in system response becomes larger.” He and Su provided the formulas needed to apply batch statistics to compute the correlated uncertainty of a difference of tallies. In this report, we follow up on their work by providing the formulas needed to apply batch statistics to compute the correlated uncertainty of a ratio of tallies and of a difference of two tallies divided by a third tally. We extend these formulas to differences and ratios of ratios. These formulas are applied to reduce the uncertainty associated with calculating a relative sensitivity. He and Su did not investigate the accuracy of their correlated sampling uncertainty estimates. We use their test problems and evaluate the accuracy of the uncertainty estimates by comparing with results obtained from random sampling, and, in simple cases, with theoretical values of the “exact” uncertainties. We find that the uncertainties obtained from batch statistics are accurate as long as at least 100 batches are used. We present a new computer code, COSUBS (COrrelated Sampling Using Batch Statistics), that reads MCNP6 TFCs and applies correlated sampling using batch statistics for the tally combinations that the user specifies. COSUBS is a very general tool that compares all TFCs for a base case and one or two perturbed cases. It computes uncertainties for ratios if given only a base case. This report is organized as follows. The equations to apply batch statistics to the difference of random tallies are reviewed in Sec. II. Section III presents the equations for applying batch statistics to a ratio of random tallies; this is useful for computing relative sensitivities using a one-sided finite difference and the relative sensitivity using the differential operator method. Section IV presents the equations for applying batch statistics to a difference of two random tallies divided by a third; this is useful for computing a relative sensitivities using a central difference. Section V presents the equations for applying batch statistics to a difference of two ratios with four random tallies. Section VI presents the equations for applying batch statistics to a one-sided finite difference estimate of the relative sensitivity of a ratio (this uses four random tallies). Section VII presents the equations for applying batch statistics to a central difference estimate of the relative sensitivity of a ratio (this uses six random tallies). Section VIII presents the equations for applying batch statistics to a sum of random tallies. Section IX discusses how to apply batch statistics using MCNP6. Section X presents COSUBS, describing its command-line options and logic. Sections XI through XVI present numerical results for various test problems. Section XVII is a summary and conclusions. Appendix A derives the theoretical Monte Carlo tally variance given certain assumptions; these variances are used to verify the batch statistics for some of the problems. Appendix B lists the MCNP6 input for the unperturbed example problem. Appendix C presents modifications made to MCNP6.3 to support this work.

97 MATHEMATICS AND COMPUTING↗

A summary of the mechanical properties data developed in FY 2023 by ANL, INL and ORNL to support the data package development for the A709 Code Case

This report provides the status of tensile, creep, fatigue, and creep-fatigue testing to date conducted at Argonne National Laboratory, Idaho National Laboratory, and Oak Ridge National Laboratory to generate the data package required to qualify Alloy 709 in American Society of Mechanical Engineers, Boiler and Pressure Vessel Code, Section III, Division 5. The Division 5 Class A Alloy 709 Code Case requires data generated from a minimum of three commercial heats. Extensive mechanical properties data have been generated on two commercial heats, and some initial test data have been generated from the third commercial heat. The room temperature tensile test results for the three commercial heats met the specification minimum of the American Society of Mechanical Engineers, Boiler and Pressure Vessel Code, Section II, Part A, SA-213/SA-213M for Grade TP310MoCbN (UNS S31025) seamless tubing. These three commercial heats of Alloy 709 are suitable for generating the code case data.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗

Structural design challenges and implications for high temperature concentrating solar power receivers

High operating temperatures along with diurnal cycling and high operating stresses bring many material and engineering challenges for concentrated solar power (CSP) receivers. Current design rules in ASME Boiler and Pressure Vessel (B&PV) Code for high temperature structural components were not intended for CSP components. The paper reviews the design rules in several sections of ASME B&PV Code in terms of their applicability in designing high temperature CSP receivers. With some restrictions and modifications, the conditions assumed in the design rules in Section III, Division 5 of ASME B&PV Code are found to closely resemble the loading conditions of CSP receiver, including accounting for the interaction between creep and fatigue damage. Further, the paper applies the proposed design rules to an external tubular receiver design and discusses several lessons learned from the design study. The creep damage accumulation due to high thermal stresses resulting from circumferentially non-uniform flux distribution is found to control the design of CSP receivers. Several mitigation actions to improve the design life of receivers are also discussed.

14 SOLAR ENERGY↗

A Structural Design Approach Tailored for the Rapid Preliminary Design of Microreactor Components

High-temperature microreactors can play a role in developing reliable, portable energy sources for off-grid remote locations, microgrid concepts, and industrial process heat. Portability and passive safety criteria tend to skew microreactor structural component designs toward complex geometries, high thermal stresses, and design bases with large numbers of startup/shutdown cycles. Current design rules, as typified by Section III of the American Society of Mechanical Engineers (ASME) Boiler & Pressure Vessel Code, are less than optimal for these conditions, particularly for preliminary component designs where developers need to rapidly consider a large number of potential component configurations. This paper presents a design method targeted toward rapid, efficient evaluation of preliminary component designs using modern finite element analysis. The new method retains key connections with the ASME Code rules and design data while streamlining the design approach. This paper presents the design method, several verification examples illustrating the similarities and differences between the new method and the current ASME rules, and the application of the new approach to the evaluation of a test article mimicking key features of a heat pipe–cooled microreactor.

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗

Thermal Aging Effects on the Yield and Tensile Strength of 9Cr-1Mo-V (Grade 91)

The long-term exposure of 9Cr-1Mo-V (Grade 91) steel to elevated temperature can have a significant effect on reducing its yield and tensile strength. The yield and tensile strength changes, in turn, have potential implications to the assurance of the integrity of components constructed with this material over their design or intended lifetime. The ASME Boiler & Pressure Vessel Code (BPVC), Section III, Division 5 (III-5, high temperature reactors) provides tabulated reduction factors for Grade 91 yield and tensile strength as a function of exposure temperature and time up to 300,000 h. ASME BPVC III-5 s intent to extend these factors to an exposure duration of 500,000 h, the lack of available historic information to support the existing factors, and the recent development of a physics-based prediction model for ASME BPVC application are prime motivation for this study. This work describes results of the conventional time-temperature Hollomon–Jaffe parameter, strength reduction ratio prediction method using an updated, extensive Grade 91 unaged and related aged material strength database. The method, previously used by Oak Ridge National Laboratory in its evaluation of Grade 91 and likely used in development of the existing BPVC III-5 reduction factors, provides strength reduction ratio predictions useful for general component fitness-for-service assessments and for computing BPVC III-5 reduction factors as defined. Specific reduction factors to 500,000 h at 650 °C applicable to ASME BPVC III-5 are computed from the strength reduction ratios.

36 MATERIALS SCIENCE↗

Critical Evaluation of a Novel Analysis Technique for Assessment of Printed Circuit Heat Exchangers in High-Temperature Nuclear Service

Application of printed circuit heat exchangers (PCHEs) to very high-temperature reactors (VHTRs) requires mechanical performance assessment methodologies. The PCHE morphology consists of thousands of millimeter-scale channels, for enhanced thermal efficiency, enclosed in a meter-scale PCHE core. PCHE geometry under thermomechanical creep-fatigue transients results in multi-axial interactions between its different segments, such as channeled core, walls, and headers. These global-level interactions influence the local channel-level responses. Hence, developing a PCHE performance assessment methodology, following the ASME Code, Section III, Division 5 provisions, is a critical gap to be filled. There is no analysis or design methodology available in ASME Code to assess a PCHE for its global and local level performances under high temperature and pressure loadings. This paper critically evaluates a recently proposed two-step analysis technique to estimate global interactions and local channel-level responses of PCHEs. In this novel analysis technique, the channeled PCHE core is replaced with orthotropic solid blocks of representative stiffness properties for the global thermomechanical analysis. Here, subsequent channel scale submodel analysis with detailed channel geometry, loading, and elastic-perfectly plastic (EPP) material model estimates the local responses for PCHE performance assessment. This paper critically evaluates this novel technique for its effectiveness in PCHE performance assessment. Finite element (FE) models imitating various analysis issues are developed, and FE analysis results are scrutinized. An important outcome of this study is the validation of the novel two-step PCHE analysis technique for application to the performance assessment of PCHEs in VHTRs.

42 ENGINEERING↗

AN INITIAL ASSESSMENT OF THE CREEP-RUPTURE STRENGTHS FOR WELDMENTS WITH ALLOY 800H BASE METAL AND ALLOY 617 FILLER METAL

In Section III, Division 5 of the American Society of Mechanical Engineers Boiler and Pressure Vessel Code, Alloy 800H is qualified for elevated-temperature nuclear construction for temperatures up to 760°C (1,400°F) and a maximum service life of 300,000 hours. There are two permissible filler metals for Alloy 800H weldments specified in Division 5: ENiCrFe-2 (Alloy A) and ERNiCr-3 (Alloy 82). Low creep-rupture strengths of these weldments at the upper limits of the qualified temperatures and service lives may restrict the design envelope for elevated-temperature nuclear construction with Alloy 800H. As a result, an alternative filler metal is desired to improve the creep-rupture strengths of Alloy 800H weldments for the qualified temperatures and service lives. This work investigates an overmatched filler metal. Specifically, a weldment with Alloy 800H base metal and Alloy 617 filler metal fabricated by semiautomated gas tungsten arc welding is investigated. A scoping creep-rupture test program was conducted of cross-weld specimens at temperatures ranging from 750 to 1,000°C (1,292 to 1,832°F). Preliminary results on the creep-rupture strengths of the Alloy 800H weldment with Alloy 617 filler metal do not show significant improvement compared to the filler metals currently qualified in Division 5 for Alloy 800H weldments. Consequently, work is in progress to investigate a matching filler metal.

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗

Interim Mechanical Properties Data from FY2022 ORNL Testing of A709 with Precipitation Treatment for ASME Code Case Data Package

A collaborative research and development effort in support of the Alloy 709 Code Case qualification in the American Society of Mechanical Engineers Boiler and Pressure Vessel Code, Section III, Division 5, High Temperature Reactors is being conducted at the US Department of Energy’s Oak Ridge National Laboratory, Idaho National Laboratory, and Argonne National Laboratory. A recent assessment on the Alloy 709 development and testing effort concluded that the mechanical properties of Alloy 709 with the precipitation treatment continued to outperform those of Type 316 stainless steel. The assessment also affirmed the recommendation for its Code qualification. This report provides the detailed integrated data generated to date on the two commercial heats of Alloy 709 in plate product form with precipitation treatment condition that were used as the basis for this assessment. Oak Ridge National Laboratory has continued to perform a subset of the Code Case testing for tensile properties, creep rupture, fatigue, and creep-fatigue. This report also updates the key Alloy 709 Code Case testing status and results in FY 2022 at Oak Ridge National Laboratory.

36 MATERIALS SCIENCE↗