Solar neutron transport in the earth's atmosphere
Solar neutron transport in Earth atmosphere from neutron spectral measurements
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Solar neutron transport in Earth atmosphere from neutron spectral measurements
Neutron transport equation in five dimensional tensor form, applying finite differencing by integration method via use of divergence theorem
Monte Carlo (MC) neutron transport provides detailed estimates of radiological quantities within fission reactors. This involves tracking individual neutrons through a computational geometry. CPU-based MC codes use multiple polymorphic tracker types with different tracking algorithms to exploit the repeated configurations of reactors, but virtual function calls have high overhead on the GPU. The Shift MC code was modified to support GPU-based tracking with three strategies: dynamic polymorphism with virtual functions, static polymorphism, and a single tracker type with tree-based acceleration. On the Frontier supercomputer these methods achieve 77.8%, 91.2%, and 83.4%, respectively, of the tracking rate obtained using a specialized tracker optimized for rectilinear-grid-based reactors. This indicates that all three methods are suitable for typical reactor problems in which tracking does not dominate runtime. The flexibility of the single tracker method is highlighted with a hexagonal-grid microreactor problem, performed without hexagonal-grid-specific tracking routines, providing a 2.19× speedup over CPU execution.
High energy neutron transport calculated using one dimensional discrete ordinates code with anisotropic scattering, comparing results with nucleon transport code calculations
The method of nearby problems (MNP) is a solution verification technique that does not require the use of multiple spatial grids. To estimate spatial discretization error without requiring a high-fidelity spatial grid, an analytical curve fit is interpolated from the numerical solution. The residual between the curve fit solution and numerical solution is calculated and added as an additional source term to the governing equation. The nearby solution is estimated using the updated source term and boundary conditions to remain consistent with the curve fit interpolation. The nearby solution can be compared to the curve fit solution as a discretization error estimation while using a single spatial grid. Without the use of higher fidelity spatial grids, the MNP is able to approximate the spatial discretization error, a facet of solution verification. The application of the method of nearby problems is presented for one- and two-dimensional neutron transport problems for both fixed source and criticality problems on the spatial variable. The fixed source results demonstrate the effectiveness of nearby problems for spatial error identification using the discrete ordinates method. Criticality results are shown to identify area of high spatial error for the C5G7 problem as well as for the discrete ordinates solver. A novel approach of combining the capabilities of Monte Carlo with the discrete ordinates nearby problems is presented for one- and two-dimensional fixed source problems. In conclusion, the MNP demonstrates its effectiveness at identifying spatial error on a single structured grid with a wide variety of neutron transport problems.
Time dependent monoenergetic neutron transport in finite slab with finite reflectors
Accurate reconstruction of the neutron flux distribution within a reactor core is essential for safe and efficient reactor operation. Traditional power shape synthesis in Light Water Reactors relies on hundreds of in-core detectors. However, this approach becomes impractical for Advanced Reactors and Microreactors due to limited space and harsh environments. To address this challenge, we propose a data-driven methodology that combines high-fidelity modeling with real-time ex-core sensor measurements, enabling the reconstruction of core power distribution while minimizing the reliance on intrusive in-core instrumentation. This project began in FY24 and achieved two initial milestones: (1) the definition of a three-year development plan for a Digital Twin framework and (2) the development of high-fidelity neutronics models of the Purdue University Reactor One (PUR-1) using both MCNP6 and OpenMC. The PUR-1 reactor, a zero-power facility, was selected due to its suitability for neutronics-focused modeling and the availability of experimental data for validation. Both models were benchmarked using neutron flux measurements obtained from irradiated gold foils, which were strategically placed within the core during a dedicated campaign in July 2024. This report marks the continuation and completion of those foundational tasks. The OpenMC model has been refined (improved geometric accuracy, expanded cross-section libraries, and refined sampling) and validated using additional experimental data. An updated sensor design—based on quadrupole configuration—was designed to measure both ex-core flux and its spatial gradient. These measurements will serve as inputs to a neural network-based reconstruction algorithm. Finally, the methodology was demonstrated on a two-dimensional test case representative of the heterogeneous material composition of the PUR-1 reactor core. A neural network implementation of the Kirchhoff-Helmholtz integral equation was employed to solve the boundary value problem using peripheral sensor measurements. The preliminary results confirm the strong potential of the proposed approach for accurate and minimally invasive neutron flux reconstruction.
Neutron flux per unit energy induced in atmosphere by solar neutrons computed as function of atmospheric depth compared to cosmic ray induction
Monte Carlo criticality transport codes, which rely on the power iteration procedure, are a fundamental tool for nuclear criticality safety practitioners in assessing the neutron multiplication factor (k eff ) for problems involving fissile material. In these calculations, ensuring the convergence of both the fission source distributions and the k eff estimate for accurate results is crucial. However, a converged k eff estimate does not necessarily mean the fission source distribution is also converged because the fission source and flux distribution may continue to evolve even after k eff convergence. Therefore, most Monte Carlo transport criticality codes now offer various diagnostic tests to assess fission source convergence in addition to the k eff convergence by analyzing the trends of these quantities over multiple generations.
On August 30, 2024, the National Nuclear Data Center (NNDC) released the ENDF/B-VIII.1 nuclear data library [1]. The library was released in the standard Evaluated Nuclear Data File (ENDF) format.
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A description of the FASTER-III program for Monte Carlo Carlo calculation of photon and neutron transport in complex geometries is presented. Major revisions include the capability of calculating minimum weight shield configurations for primary and secondary radiation and optimal importance sampling parameters. The program description includes a users manual describing the preparation of input data cards, the printout from a sample problem including the data card images, definitions of Fortran variables, the program logic, and the control cards required to run on the IBM 7094, IBM 360, UNIVAC 1108 and CDC 6600 computers.
Solution of neutron transport equation in heavy gas in plane geometry in case of infinite medium and constant total cross section
Computer program computes transport of neutrons and gamma rays in complex geometries and fluxes averaged over specified regions and surfaces of the geometry.
The theory used in FASTER-III, a Monte Carlo computer program for the transport of neutrons and gamma rays in complex geometries, is outlined. The program includes the treatment of geometric regions bounded by quadratic and quadric surfaces with multiple radiation sources which have specified space, angle, and energy dependence. The program calculates, using importance sampling, the resulting number and energy fluxes at specified point, surface, and volume detectors. It can also calculate minimum weight shield configuration meeting a specified dose rate constraint. Results are presented for sample problems involving primary neutron, and primary and secondary photon, transport in a spherical reactor shield configuration.
An analytic benchmark with continuous-energy cross sections was previously derived to validate criticality calculations. Here, to extend the utility of the analytic benchmark to verify the implementation of $\bar{ν}$ and prompt fission neutron spectrum (PFNS) uncertainty propagation methods, new simplified forms that are dependent on the incident (fission-causing) neutron energy, as well as the outgoing neutron energy for the PFNS, are introduced in this work. The analytical forms for the flux and adjoint flux are derived for the extended benchmark and used to determine the 𝑘-eigenvalue sensitivity to $\bar{ν}$ and PFNS. The 𝑘-eigenvalue uncertainty due to $\bar{ν}$ and PFNS is calculated for the analytic benchmark using simplified$\bar{ν}$ and PFNS representations based on the ENDF-B/VIII.0 239 Pu evaluation. Because of the low sensitivity of the analytic benchmark to the physical PFNS, a nonphysical high-sensitivity PFNS is also presented.
This work studies the impact of explicit and homogenized modeling approaches on the multiphysics simulation of TRistructural ISOtropic (TRISO) fuel compacts in prismatic High Temperature Gas Reactors (HTGRs) and the silver release predictions. TRISO fuel compacts exhibit complex double heterogeneity that significantly affects heat conduction, neutron transport, and fission products release. In this work, we use Cardinal, a multiphysics tool based on the Multiphysics Object-Oriented Simulation Environment (MOOSE) framework, to couple neutron transport and heat conduction. OpenMC is used for neutron transport and the MOOSE heat transfer module is used for the heat conduction. Then, we use BISON for the silver release predictions. Two different modeling approaches—explicit modeling of individual TRISO particles and homogenized representation using effective thermal properties—are compared at high TRISO packing fractions (20% and 40%) across varying power densities. Results demonstrate that homogenization significantly under-predicts peak temperatures, for the case of high power/TRISO, there is a difference of 83.73 K in the maximum temperature. Additionally, homogenization underestimates the silver release predictions compared to explicit modeling. Specifically, the temperature and power density differences lead to significant differences in silver release predictions. This work demonstrates the importance of accurately modeling heterogeneity of the TRISO particles to reliably predict fission product release and assess reactor safety margins.
This report describes how to produce reference solutions for the equilibrium core search of pebble bed reactors using the pyrates Python library. The pyrates library uses the kugelpy methodology to perform running-in calculations to reach an equilibrium core. This approach relies on full-core Monte Carlo neutron transport calculations and the shifting of fuel pebble inventory through the reactor to simulate pebble movement in the core from one step to the next of a running-in scenario. In addition to the use of Serpent for the Monte Carlo neutron transport calculations, as part of this work, updates for the use of the Shift Monte Carlo code were integrated into the official pyrates GitHub repository. Comparisons of running-in simulations for a generic pebble bed reactor produced by using pyrates with Serpent and Shift are shown. Although consistent trends are shown between the use of the two Monte Carlo codes, the limiting factor in either calculation is the computation time due to the need to perform several hundred full-core neutron transport calculations before an equilibrium core is reached.