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Deterministic modelling of the SPERT IV reactor transients using the multi-physics capability of WIMS

The ANSWERS WIMS reactor physics code is being developed for whole core multi-physics modelling. The established neutronics capability for lattice calculations has recently been extended to be suitable for whole core modelling of Small Modular Reactors (SMRs). A whole core transport, SP3 or diffusion flux solution is combined with fuel assembly resonance shielding. An integrated thermal hydraulic solver permits temperature and density variations to feedback to the neutronics calculation. This capability can be applied to both steady state and time dependent transient problems. Nuclear reactor design and safety case development requires assessment of a range of reactor transients, to inform both normal operation limitations and accident scenario analysis. This paper presents new methodology developed in WIMS to couple the core neutronics to the integrated core thermal hydraulics solver for the simulation of reactor transients in whole core models. To support the validation of the multi-physics capability of WIMS, this capability has been applied to the reactivity insertion transient experiments performed in the plate fuelled SPERT-IV reactor. This study employs WIMS using the whole core solver MERLIN, which calculates the time-dependent flux distribution and magnitude, coupled to ARTHUR, which solves for the time-dependent thermal hydraulics solution, and provides thermal feedback via the cross sections generated by GEOM, which performs resonance shielding calculations and generates cross section data for the plate geometry. This spatial kinetics model, with dynamic cross section generation, allows for variations in the temperature and neutron flux profile with time.

21 SPECIFIC NUCLEAR REACTORS AND ASSOCIATED PLANTS↗

Collisional simulations of the modulator section in coherent electron cooling

The first section of any coherent electron cooling (CeC) system is the modulator, where the density of the electron beam is modulated by the copropagating ion beam. This density modulation is a result of Coulomb collisions between the individual particles of the two beams. The pairwise, stochastic part of the interactions impacts the overall performance of the CeC process. We present the first simulations of the density modulations of the electron beams from a collisional picture of the dynamics, considering the proof-of-principle CeC experiments at Brookhaven National Laboratory. These simulations were performed using PHAD, which is the first efficient, large-scale collisional numerical method in beam physics that we have previously developed and benchmarked. Realistic beam distributions and external fields have been optimized to provide strong modulation signals necessary for variations of coherent electron cooling systems. Cooling performance limits and potential collisionless simulation pitfalls are pointed out. Published by the American Physical Society 2024

43 PARTICLE ACCELERATORS↗

Tracking Radioactive Isotopes in HVAC and Application for Hot Cell Analyses - 20155

In recent years, the surge in the number of isotope production facilities under design has increased the need to analyze isotope migration in facility Heating, Ventilation, and Air Conditioning (HVAC) during normal operations and accident scenarios. These facilities are used to produce isotopes for medical, security, and industrial applications and as such are subject to license and regulatory requirements 10CFR20, 10CFR30, 10CFR50, and 10CFR70. GOTHIC, a general-purpose thermal-hydraulics software package, includes the ability to model isotopic tracers, radioactive decay and isotope migration as well as HEPA and charcoal filters for isotope retention. A GOTHIC model was developed by Zachry Nuclear Engineering (ZNE) to examine the effect of negative room pressure, HEPA filtration, and HVAC fluctuations on radiation areas, hot cells and gloveboxes. Radioactive tracers were used to simulate the concentration of spills within contaminated areas, track the migration of isotopes of interest, and determine the isotopic retention and buildup on facility HEPA filters. A variety of isotopes with concern to dose (e.g., Kr-85, Sr-90, I-131, etc.), including their decay and progeny, are included in the analysis. Negative pressures are maintained in the regions of interest by a representative central HVAC system equipped with a volumetric fan that exhausts to the environment after a series of isolation valves and HEPA filters. GOTHIC is an industry trusted tool for providing engineering solutions for a variety of applications, including fission product tracking, aerosol and particulate transport and ventilation assessments. The software provides an integrated analysis environment that includes a graphical user interface (GUI) for constructing analysis models, a numerical solver that includes parallel processing capabilities and a post-processor for evaluating simulation results. It solves the conservation equations for mass, momentum and energy for multicomponent, multi-phase flow in lumped parameter and multi-dimensional geometries (1, 2, or full 3D), including the effects of turbulence, diffusion and buoyancy. It has been developed and maintained under a Quality Assurance program in compliance with the requirements of 10CFR50 Appendix B and applicable portions of ASME NQA-1 since 1995. GOTHIC has been used for assessing both forced and natural convection conditions for a wide range of applications, including: - Tracking concentration of hazardous gases and chemicals for habitability and safety assessments - Determining ventilation and filtration requirements and optimizing location and arrangement of these systems - Room heat-up, including diverse and Flexible coping strategies for Extended Loss of AC Power (FLEX/ELAP) - Equipment Qualification (EQ) A distinctive feature of GOTHIC is the ability to track many different fields/substances in a simulation, including user defined tracer elements, in the liquid, vapor and droplet fields as well as surfaces and filters. This capability allows GOTHIC to model fission product transport and release or the removal of particulates or harmful toxins from exhaust gases using a spray scrubber or other types of filtration systems. GOTHIC also includes models for engineered equipment, such as fans, filters, charcoal filters, dryers/demisters, dampers, etc. The aerosols and other filtered material are removed or accumulated in these components. The range of aerosol and radiological applications that GOTHIC has been used for includes: - Source Term: Primary Coolant (Equilibrium) Activity; Non-Water Coolant Source/Leakage. - Conditions for Iodine Re-evolution: Sump/Suppression Pool Conditions and pH; - RWST Conditions and pH. - Isotope Removal Mechanisms: Containment Sprayed and Unsprayed Region Mixing; Charcoal Filter Heating due to Iodine decay. - Radionuclide Transport and Decay: Post-LOCA Release in containment; Transport between connected Compartments and vent systems; Groundwater transport of radionuclides. - Non-Newtonian Fluid modeling for sludge, waste tanks, etc. ADAMS ML071581053 (titled 'Best Practice Guidelines for the use of CFD in Nuclear Reactor Safety Applications') poses guidelines for applying single phase CFD codes in nuclear reactor safety problems and GOTHIC is listed as a 'tool for 3D flows' and 'dispersal and deposition of radionuclides.' The Nuclear Quality Assurance (NQA) pedigree of GOTHIC is an important aspect for applications in the nuclear industry. The fundamental tracer models (convective transport, molecular and turbulent diffusion, removal mechanisms, etc.) have been verified using analytical solutions and validated against applicable separate effects tests. Also, GOTHIC has been benchmarked to many integrated effects tests, including Phebus FP (Fission Product). GOTHIC gives good agreement for the buildup and decay of fission products in Phebus Test 3. The model developed by ZNE demonstrates GOTHIC's applicability and acceptability for use in analyzing the migration and retention of radioactive isotopes and their progeny in normal operation and accident scenario analyses for isotope production facilities, hot cells, and gloveboxes. The tracer activities calculated by GOTHIC can then be used in downstream radiation transport and shielding codes like RADTRAD-NAI{sup C}, MCNP{sup R}, and MicroShield{sup R} to determine on-site and of-site doses. (authors)

12 MANAGEMENT OF RADIOACTIVE AND NON-RADIOACTIVE W↗

Analysis of SCALE Criticality and Sensitivity Calculations for Reflected HEU Cylinders

The SCALE code package offers multiple nuclear data libraries and sensitivity and uncertainty (S/U) methods supporting and derived from Monte Carlo (MC) transport. The CSAS and TSUNAMI-3D sequences use KENO MC, utilizing either continuous-energy (CE) cross sections or multigroup (MG) cross section libraries. TSUNAMI-3D has two CE calculational methods: the iterated fission probability (IFP) method, and the Contribution-Linked eigenvalue sensitivity/Uncertainty estimation via Tracklength importance CHaracterization (CLUTCH) method. Previous work has shown poor agreement between CLUTCH and confirmatory direct perturbation calculations in specific applications (e.g., fissionable and polyethylene reflectors). The HEU-MET-FAST-084 (HMF-084) International Criticality Safety Benchmark Evaluation Project evaluation consists of 27 cylindrical highly enriched uranium metal cores with 14 unique reflector materials of 0.5 and 1 in. thicknesses. Included in this list of reflector materials are natural uranium and polyethylene. This work utilized SCALE 6.2.4 models of the HMF-084 evaluation, with additional non-physical configurations to test both the MG bias and CLUTCH functionality across a variety of reflector material thicknesses. The evaluation’s use of concentric cylinders allowed for examination of several MG self-shielding methods: infinite homogenous, cylindrical, and spherical. The results indicate that the use of polyethylene reflectors with CLUTCH is not fundamentally impossible but sensitive to geometry. The poor performance of CLUTCH with fissionable reflectors was reaffirmed. The 2 in. and greater polyethylene-reflected calculations demonstrate the necessity of using the 302-group library for fast systems. The nickel MG bias was substantial, as discussed in a companion paper, as were cobalt and iron.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

Reduced-order modeling for efficient cross section library development in high-temperature gas reactor pebble-bed depletion analysis

Accurate modeling of running-in and equilibrium conditions in pebble-bed reactors (PBRs) requires precise microscopic multigroup neutron cross sections. In Griffin, deterministic neutronics calculations rely on multivariate interpolation over large cross section libraries, resulting in significant memory usage and performance bottlenecks. This work, together with a companion paper on Griffin integration, explores reduced-order models (ROMs) to replace interpolation with lightweight surrogates. Several ROM techniques are benchmarked, with deep neural networks (DNNs) demonstrating superior memory efficiency, scalability, and predictive accuracy. A total of 295 DNNs were trained to build a comprehensive isotope library, integrated into Griffin through a custom LibTorch interface for depletion analysis. Initial results demonstrate that DNN-based ROMs drastically reduce memory demands while preserving accuracy, enabling finer tabulations and additional state variables without overhead. In conclusion, the framework also supports online cross section generation and real-time DNN updates through transfer learning, improving fidelity by capturing self-shielding and evolving nuclide compositions during burnup.

22 - GENERAL STUDIES OF NUCLEAR REACTORS↗

Performance Improvements of the Griffin Solvers in FY24

The Griffin code is a MOOSE-based reactor physics application jointly developed by Idaho National Laboratory and Argonne National Laboratory under the Department of Energy Office of Nuclear Energy Nuclear Energy Advanced Modeling and Simulation Program. This fiscal year, we have made significant efforts to improve the performance of transport solver options and cross-section generation for the efficient use of Griffin in advanced reactor applications. For the HFEM-PN solver, the residual evaluations of HFEM kernels were optimized by utilizing the pre- computed averaged cross sections for individual elements. Numerical integration involving the evaluation of basis functions at quadrature points was bypassed by facilitating precomputed element mass matrices for response matrices. Red-black iterations were improved by introducing a new generalized minimum residual based solver. The memory usage of response matrix storage was significantly reduced by applying basis function rotations on interfaces and calculating volumetric odd-parity moments on the fly. Additionally, the adjoint flux and transient calculation capabilities of the HFEM-PN solver were successfully implemented and verified using the TWIGL benchmark problem. For the DFEM-SN solver, memory footprint and computation time were significantly reduced by not treating angular flux vectors as the MOOSE nonlinear system vectors. Specifically for IQS, scalar adjoint weighting was introduced to further eliminate angular adjoint flux storage in the MOOSE auxiliary system. It was demonstrated through the three-dimensional Advanced Burner Test Reactor core problem that the memory usage for transient calculations with the IQS method was reduced by over 7.5× compared to before the optimizations. For the self-shielding application programming interface, a new double-heterogeneity treatment method, named the Bell Function-Based Analytic Two-Region Slowing Down Method, was developed to efficiently flux-volume homogenize TRISO particles with the matrix. Additionally, optimizations were made to hyper- fine group (HFG) slowing down calculations by pretabulating collision probability coefficients and grouping isotopes, significantly reducing the computational time for calculating scattering sources per HFG. Lastly, the pin power reconstruction module was extended to account for temporal behavior in a microreactor analysis problem, specifically for a control drum transient. Verification tests for each of these improvements demonstrated significant performance enhancements and memory reduction.

22 - GENERAL STUDIES OF NUCLEAR REACTORS↗

Manifold Learning-Based Polynomial Chaos Expansions for High-Dimensional Surrogate Models

In this work we introduce a manifold learning-based method for uncertainty quantification (UQ) in systems describing complex spatiotemporal processes. Our first objective is to identify the embedding of a set of high-dimensional data representing quantities of interest of the computational or analytical model. For this purpose, we employ Grassmannian diffusion maps, a two-step nonlinear dimension reduction technique which allows us to reduce the dimensionality of the data and identify meaningful geometric descriptions in a parsimonious and inexpensive manner. Polynomial chaos expansion is then used to construct a mapping between the stochastic input parameters and the diffusion coordinates of the reduced space. An adaptive clustering technique is proposed to identify an optimal number of clusters of points in the latent space. The similarity of points allows us to construct a number of geometric harmonic emulators which are finally utilized as a set of inexpensive pretrained models to perform an inverse map of realizations of latent features to the ambient space and thus perform accurate out-of-sample predictions. Thus, the proposed method acts as an encoder-decoder system which is able to automatically handle very high-dimensional data while simultaneously operating successfully in the small-data regime. The method is demonstrated on two benchmark problems and on a system of advection-diffusion-reaction equations which model a first-order chemical reaction between two species. In all test cases, the proposed method is able to achieve highly accurate approximations which ultimately lead to the significant acceleration of UQ tasks.

42 ENGINEERING↗

Performing k eff Validation of As-Loaded Criticality Safety Calculations Using UNF-ST&DARDS: Applicable Experiment Selection [Slides]

This presentation discusses the UNF-ST&DARDS which performs many analyses for as-loaded SNF canisters, including criticality safety, shielding, thermal-hydraulic, and containment. It also discusses the experiment selection based on c k assessment of similarity and that the c k value of 0.8 or greater considered applicable for validation. 11 PWR SNF canisters (MPC-32) are used in this work. 1 model represents a failed fuel assembly as fresh, per the design basis and the remaining 10 models represent all 32 assemblies with depleted fuel. In conclusion, critical experiment selection can be performed with S/U techniques for as-loaded canisters in UNF-ST&DARDS. Sufficient benchmark experiments exist to support validation and additional MOX experiments that are a good match for commercial SNF would be a benefit to provide independent data. The presentations states that S/U techniques identify different pools of experiments for different systems and that the process is amenable to automation within UNF-ST&DARDS.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

Radio frequency mixing modules for superconducting qubit room temperature control systems

As the number of qubits in nascent quantum processing units increases, the connectorized RF (radio frequency) analog circuits used in first generation experiments become exceedingly complex. The physical size, cost, and electrical failure rate all become limiting factors in the extensibility of control systems. We have developed a series of compact RF mixing boards to address this challenge by integrating I/Q quadrature mixing, intermediate frequency/LO (local oscillator)/RF power level adjustments, and direct current bias fine tuning on a 40 × 80 mm 2 four-layer printed circuit board with electromagnetic interference shielding. The RF mixing module is designed to work with RF and LO frequencies between 2.5 and 8.5 GHz. The typical image rejection and adjacent channel isolation are measured to be ~27 dBc and ~50 dB. By scanning the drive phase in a loopback test, the module short-term amplitude and phase linearity are typically measured to be 5 ×10 -4 (V pp /V mean ) and 1 ×10 -3 radian (pk-pk). The operation of the RF mixing board was validated by integrating it into the room temperature control system of a superconducting quantum processor and executing randomized benchmarking characterization of single and two qubit gates. We measured a single-qubit process infidelity of 9.3(3) × 10 -4 and a two-qubit process infidelity of 2.7(1) × 10 -2 .

47 OTHER INSTRUMENTATION↗

FY22 Year End Report of Delivery Environments Predictive Capabilities Use in Analysis of SRP Programs

As was established in a previous milestone report for FY20, W-13 continues to be tasked with analyses that require knowledge of in-flight environments and require an in-house capability to generate such environments. To this end, FY21 work included obtaining and benchmarking the use of such tools for an in-house capability. With these tools available for analysis tasks, FY22 work has been to continue the development of analysis for Responsive Development Experiment (ReDX) flights in the Stockpile Responsiveness Program (SRP). While no flights were executed in FY22 that leveraged internal flight analysis., this report shows that both CBAERO and TAOS were used in W-13 under the Delivery Environments Program for the FY22 milestone in order to predict the flight environments of ReDX flight 3 and determine preliminary environments of the Calypso flight vehicle which includes a deployable heat shield.

42 ENGINEERING↗

Pulsed-Neutron Experiments at the Inherently Safe Subcritical Assembly

The pulsed neutron technique is a powerful, dynamic method to assay the reactivity of a multiplying system. This work presents the novel application of the pulsed neutron technique to the Inherently Safe Subcritical Assembly, an experimental configuration accepted by the International Criticality Safety Benchmark Evaluation Project Handbook. The experiments were replicated with COG11.3, a continuous-energy Monte Carlo code. The pulsed neutron data were analyzed using the Sjöstrand and Gozani area-ratio methods and by extracting the prompt neutron decay constant. Subsequent static k-eigenvalue and 𝛼-eigenvalue simulations were also performed for the same configurations. Neutron detector dead-time effects from the experiments were corrected using the Backwards Extrapolation Method and shown to have a negligible impact on the estimated reactivities. The results highlight that capturing time-dependent effects like delayed neutron precursor buildup are essential to accurately reproduce experimental results. They also highlight the importance of shielding the detectors from generator source neutrons in deeply subcritical configurations.

21 SPECIFIC NUCLEAR REACTORS AND ASSOCIATED PLANTS↗

LA17-V-InverseRadTransportProblem-PD2Kb. Final Project Report

In the inverse radiation transport problem, a radiation signal emanating from an unknown object is used to reconstruct geometric and material parameters of the object , e.g., the mass of special nuclear material (SNM), the isotopic composition of the SNM (e.g., the enrichment of 235U), the thickness of shielding, etc. The inverse radiation transport problem is one of the most fundamental and important in the emergency response mission, and has been addressed in previous NA-22 and NA-42/84 investments by using derivative-free optimization methods. Our project was aimed at (i) consolidating previous work by applying polynomial chaos expansion (PCE) for reducing significantly the number of forward model simulations required by derivative-free optimization methods; (ii) developing a general-purpose framework and stand-alone software for solving the inverse radiation transport problem by applying a new “predictive modeling” methodology (predictive modeling of coupled multi-physics systems, PM_CMPS) which enables the fusing of experimental and computational information; and (iii) developing several benchmarks (for unscattered gamma rays) for demonstrating the quantification of non-Gaussian features (e.g., skewness and kurtosis, which characterize asymmetries and long tails) of response distributions by deterministically and efficiently propagating parameter uncertainties (covariances and higher-order moments, where available) using high-order sensitivities computed by the recently developed comprehensive adjoint sensitivity analysis methodology (C-ASAM). With regard to (i), application of PCE, the most significant accomplishment of this project was an implementation of PCE into INVERSE that significantly reduced computation time for the DiffeRential Evolution Adaptive Metropolis (DREAM) and Differential Evolution (DE) methods. For inverse transport problems with measurements of neutron leakage, neutron multiplication, and neutron-induced gamma-rays, the solution times for the DREAM and DE methods were reduced by factors of 30-300, reducing run times from hours to minutes while maintaining the same accuracy as the standard (non-PCE) DREAM and DE. Speedups were further improved by exploring sparse grid quadrature sets using the Toolkit for Adaptive Stochastic Modeling and Non-Intrusive ApproximatioN (Tasmanian) toolset. An initial exploration of sparse grids indicated that further speedups factors of 5-10 are obtainable. The implementation of PCE in INVERSE is not in a form that users can easily access. With regard to (ii), solving the inverse problem using a predictive modeling paradigm, the most significant accomplishment of this project were the derivation and implementation of adjoint-based second derivatives in neutron and photon transport theory. There are two codes that compute these derivatives. SENSPG computes them for uncollided gamma rays and SENSMG computes them for neutron leakage. SENSMG is open-source code available on github. Other significant accomplishments included a stand-alone code, MULTI-PRED, that implements the predictive modeling paradigm, along with a detailed manual. The code was implemented in the existing INVERSE code for inverse problems, but a head-to-head comparison of inverse methods was not achieved. We also derived and implemented the capability to compute sensitivities for multiplicity measurements into the SENSMG code, and this capability was used in a data assimilation application, but it was not used for solving inverse problems. With regard to (iii), developing benchmarks to demonstrate the importance of high-order sensitivity and uncertainty analysis, the most significant accomplishment of this project were two test problems that showed how important second-order sensitivities are.

07 ISOTOPE AND RADIATION SOURCES↗

SCALE 6.2.4 Validation: Reactor Physics

This report is the third volume in a report series documenting the validation of SCALE 6.2.4, which is used herein with ENDF/B-VII.1 libraries, for nuclear criticality safety, reactor physics, and radiation shielding applications. This report focuses on validating SCALE capabilities that affect reactor physics applications. The experimental data used as basis for validation consists of measurement data for nuclide inventory, decay heat, and full-core experiments and include the following: 1. radiochemical assay measurements of 40 nuclides of importance to burnup credit, decay heat, and radiation shielding in 169 light-water reactor (LWR) spent nuclear fuel samples that cover burnups up to 70 GWd/MTU and initial enrichments up to 4.9% 235 U; 2. full-assembly decay heat measurements for 236 LWR assemblies with: a. initial fuel enrichments up to 4% 235 U, b. assembly burnups of 5–51 GWd/MTU, and c. cooling times after discharge in the 2- to 27-year range (of importance to spent nuclear fuel storage, transportation, and disposal); and 3. pulse fission irradiations for fissionable materials at cooling times of interest to severe accident analyses (<10 5 s). Validation examples for full-core analysis are based on startup experiments for the Watts Bar Nuclear Unit 1 (WBN1) pressurized water reactor (PWR) and two high-temperature gas-cooled reactor (HTGR) benchmarks for the HTR-10 pebble bed and the prismatic HTTR reactor.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗

Improvements to the Modeling of the TREAT Reactor and Experiments

This paper summarizes the latest improvements and lessons learned from the modeling and simulation of the transient test reactor at Idaho National Laboratory using the MAM- MOTH reactor physics application. MAMMOTH is a MOOSE-based, Finite Element Method application that specializes in the analysis of the spatial dynamics behavior of nuclear reactors. Since early 2018 several transient tests have been conducted at TREAT, thus providing the opportunity to apply and benchmark modern modeling and simulation tools. MAMMOTH was used to provide predictions of the power coupling factor between the core and the experiment for various experiments. Even though the power coupling factor predictions agree very well with the experimental data, within the bounds of the experimental uncertainty, one shortcoming was the underprediction of the total energy deposited in the core and in the experiment. Determination of the sources for this discrepancy are ongoing, but several key problems have been identified and resolved, thus providing valuable insights for future research. This paper discusses several of these lessons learned. First, the heat capacity data for the TREAT fuel has some significant problems due to limitations of the measurement techniques used circa 1960s. The sensitivity of the peak power and the total energy deposition to various representations of the heat capacity is approximately 5%. Second, the effects of the biological shield and thermal column on the modeling of the core are non-negligible, since they affect the mean generation time and the effective reflection of neutrons back into the core, which is suspected to be important during the core heat up. Matching the reactor period resolves the fact that the reduced spatial domain used in the MAMMOTH model underpredicts the mean generation time. The neutron reflection from these regions is marginally improved with the use of an albedo boundary condition. Third, modeling of the control rod movement with a multi-scheme method is introduced and its current limitations are exposed. Fourth, we explore the effects of using a homogenized model with Superhomogenization equivalence and how that differs from fully heterogeneous simulations. Finally, the energy condensation effects for this graphite core are significant. Solutions with 10 and 26 energy groups show the benefits of using a finer coarse group structure.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗

Improvement and Verification of Online Cross Section Generation Capability of Griffin for TRISO-fueled Reactors

Griffin, a MOOSE-based reactor multiphysics code jointly developed by Idaho National Laboratory and Argonne National Laboratory under the DOE Office of Nuclear Energy’s NEAMS program, has pursued the development of an online multigroup cross section generation capability for a few years to enable high-fidelity, problem-dependent neutronics analyses of advanced thermal reactors. Recent advancements in Griffin’s online multigroup cross section generation capability have significantly improved the accuracy, robustness, and efficiency of self-shielding calculations for both prismatic and pebble-bed TRISO-fueled reactor applications. Key developments include a unified fuel self-shielding method applicable to both TRISO and annular compact/spherical shell fuel zone geometries; an advanced Dancoff Category-based Equivalence Theory using a bell function for non-fuel resonance treatment, achieving more than an order-of-magnitude speedup compared to the Tone method; an on-the-fly multigroup equivalence approach to mitigate group condensation errors; and a streaming correction method for pebble-bed homogenization. A proof-of-concept demonstration of on-the-fly group condensation with consistent P0 transport correction was also achieved. The method reproduced direct fine-group solutions with excellent accuracy (eigenvalue errors within 10 pcm and pin-power differences within 0.5%), but due to performance limitations of the current fixed-source solver, improvements to solver efficiency will be addressed in future work. Verification tests were performed on graphite-moderated TRISO-fueled two-dimensional core benchmark problems representing gas-cooled microreactors, heat pipe-cooled microreactors, gas-cooled pebble-bed reactors, and fluoride salt-cooled high-temperature reactors. Across all cases, Griffin showed excellent agreement with Serpent2 continuous energy Monte Carlo solutions: eigenvalue errors within 200 pcm, pin-power root-mean-square errors within 2%, and control rod and drum worth errors less than 2%. It should be noted that, for the benchmark problem, cross section generation contributed less than 3% of the total simulation times. These results demonstrate that Griffin’s online cross section generation capability delivers accurate and efficient reactor physics solutions across a wide spectrum of TRISO-fueled advanced reactor designs. With further improvements to the fine-group fixed-source solver and planned extensions to depletion, transients, and coupled neutron–gamma transport, Griffin will be well-positioned to become a powerful and comprehensive tool for advanced reactor analysis.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗

Gerischer Electrochemistry Today

Semiconductor photoelectrochemistry is a dynamic and interdisciplinary field at the forefront of research in solar fuels, energy conversion, and catalysis. Here, this Perspective captures the collective insights from the second Gerischer Electrochemistry Today Symposium, held at Colorado State University in Fort Collins, CO, in August 2024, which convened leading researchers, early-career scientists, and industry partners to define the critical next steps for the field. Through interactive sessions, technical talks, panel discussions, and training initiatives─including a Semiconductor Electrochemistry Bootcamp─the symposium emphasized three pillars of advancement: (i) facilitating the exchange of new ideas in semiconductor electrochemistry and charge separation; (ii) fostering the development of future researchers, research topics, and participation in the semiconductor workforce; and (iii) building community. This Energy Focus distills key themes from the meeting and identifies major knowledge gaps in the following areas: mechanisms of charge separation and recombination, role of defects and disorder, dynamic and operando characterization methods, interfacial chemistry and surface passivation, theoretical and modeling limitations, and standardization and benchmarking. The inclusive and collaborative structure of the symposium enabled the generation of this comprehensive report that will serve as a roadmap for fundamental and applied research in the rapidly evolving field of semiconductor electrochemistry over the next decade.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Performance assessment of PHITS simulations for the inverse-kinematic p( 7 Li,n) 7 Be reaction based on fast-neutron measurements with a diamond detector

The inverse-kinematics p( 7 Li,n) 7 Be reaction produces forward-focused neutron emission, offering enhanced usable flux and reduced shielding requirements. Reliable simulation of such neutron fields is essential for the development of compact accelerator-based neutron sources. In this study, a PHITS-based simulation framework for the reaction was experimentally assessed using fast-neutron measurements. Forward-directed neutrons were measured with a diamond neutron detector and quantitatively compared with simulations with newly prepared IK-Frag cross-section file based on the proton-induced reaction data in ENDF/B-VIII.1, TENDL-2023, and JENDL-4.0/HE. Measurements and simulations were performed for incident 7 Li 3+ energies ranging from 15.0 to 25.0 MeV using a 50 μm-thick polypropylene target. For all conditions, the PHITS-based simulation framework reproduced the deposited energy spectra at the correct order of magnitude. The comparison of deposited energy spectra in the diamond detector showed high correlation coefficients across all investigated energies, indicating reasonable agreement in spectral shape between simulations and measurements. This work represents an initial step toward establishing a benchmark for PHITS simulations of the inverse kinematic reaction between an incident lithium-ion and a proton target.

43 PARTICLE ACCELERATORS↗

Synergistic learning with multi-task DeepONet for efficient PDE problem solving

Multi-task learning (MTL) is an inductive transfer mechanism designed to leverage useful information from multiple tasks to improve generalization performance compared to single-task learning. It has been extensively explored in traditional machine learning to address issues such as data sparsity and overfitting in neural networks. In this work, we apply MTL to problems in science and engineering governed by partial differential equations (PDEs). However, implementing MTL in this context is complex, as it requires task-specific modifications to accommodate various scenarios representing different physical processes. To this end, we present a multi-task deep operator network (MT-DeepONet) to learn solutions across various functional forms of source terms in a PDE and multiple geometries in a single concurrent training session. We introduce modifications in the branch network of the vanilla DeepONet to account for various functional forms of a parameterized coefficient in a PDE. Additionally, we handle parameterized geometries by introducing a binary mask in the branch network and incorporating it into the loss term to improve convergence and generalization to new geometry tasks. Our approach is demonstrated on three benchmark problems: (1) learning different functional forms of the source term in the Fisher equation; (2) learning multiple geometries in a 2D Darcy Flow problem and showcasing better transfer learning capabilities to new geometries; and (3) learning 3D parameterized geometries for a heat transfer problem and demonstrate the ability to predict on new but similar geometries. Finally, our MT-DeepONet framework offers a novel approach to solving PDE problems in engineering and science under a unified umbrella based on synergistic learning that reduces the overall training cost for neural operators.

42 ENGINEERING↗