Singular eigenfunction solution of the monoenergetic neutron transport equation for finite radially reflected critical cylinders.
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Westfall, R. M.↗
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FASTER 3: A generalized-geometry Monte Carlo computer program for the transport of neutrons and gamma rays. Volume 2: Users manual
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.
Jordan, T. M.↗
TRANSPORT THEORY OF NEUTRONS IN HEAVY GAS IN PLANE GEOMETRY. I. THE INFINITE MEDIUM AND CONSTANT TOTAL CROSS-SECTION
Solution of neutron transport equation in heavy gas in plane geometry in case of infinite medium and constant total cross section
REACTOR CONTROL↗
Monte Carlo program for the transport of neutrons and gamma rays
Computer program computes transport of neutrons and gamma rays in complex geometries and fluxes averaged over specified regions and surfaces of the geometry.
Jordon, T. M.↗
Griffin: A MOOSE-based reactor physics application for multiphysics simulation of advanced nuclear reactors
Griffin is a Multiphysics Object-Oriented Simulation Environment (MOOSE) based reactor physics application for multiphysics simulations of advanced reactor designs jointly developed by Idaho National Laboratory and Argonne National Laboratory. This paper summarizes the motivation, significance, architecture, design, and features of Griffin. Griffin offers flexible and extensible features to address the challenges associated with advanced reactor designs. These features range from fundamental particle transport to specific reactor physics tasks. The features cover a wide range including on-the-fly and traditional two-step cross-section generation methods, steady-state and transient transport solvers suitable for both heterogeneous and homogeneous models, high-fidelity depletion where thousands of isotopes can be tracked and low-fidelity depletion characterized by burnup, etc. The most fundamental aspect that sets Griffin apart from other reactor analysis codes is that it is developed based on the MOOSE framework. A modular development approach is strongly enforced, with multiphysics being an essential element considered since the beginning of Griffin’s development. Griffin links various MOOSE physics modules and couples to other MOOSE-based applications and non-MOOSE-based applications for multiphyiscs simulations. Griffin includes three modules: ISOXML for preparing and managing multigroup cross sections, radiation transport for solving the neutron transport equation, and reactor analysis for user-oriented reactor physics analysis functionalities. Griffin uses various finite element methods for spatial discretization, multigroup approximation for energy discretization and discrete ordinates method, spherical harmonics expansion method, and diffusion approximation for streaming direction discretization to solve the neutron transport equation. Griffin’s flexibility is evidenced through Griffin’s various applications to fast reactor, high-temperature reactor, pebble bed reactor, molten salt reactor, and microreactor designs. Griffin development follows the software quality assurance procedure for MOOSE-based applications and with software requirements consistent with the ASME NQA-1 standard. Griffin has been adopted into the reactor analysis system for the U.S. NRC and is in use at U.S. companies, universities and national laboratories.
97 MATHEMATICS AND COMPUTING↗
FASTER 3: A generalized-geometry Monte Carlo computer program for the transport of neutrons and gamma rays. Volume 1: Summary report
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.
Jordan, T. M.↗
An Analytic Benchmark for Neutron Boltzmann Transport with Downscattering—Part IV: PFNS and $\bar{ν}$ Uncertainty Propagation
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.
73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
Multiphysics simulation of TRISO fuel compacts and the effects of homogenization on silver release predictions
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.
11 - NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗
Nonlinear light-output calibration of the oxygenated xylene scintillators used in OMEGA neutron time-of-flight spectrometers
Neutron time-of-flight (nTOF) spectrometers are essential instruments for measuring and evaluating the performance of inertial confinement fusion implosions. The neutron spectrometers utilized for the OMEGA laser include two liquid-based scintillators, each consisting of a large volume filled with xylene that is coupled to four photomultiplier tubes. Analysis of the signal from these detectors requires detailed knowledge of the scintillator’s light output, which is needed to fit the nTOF spectrum, from which the neutron energy spectrum is informed. The light output is nonlinearly proportional to the neutron energy, which, in turn, affects the interpretation of the neutron energy spectrum from a TOF signal. A recent campaign on OMEGA was performed to calibrate the xylene detectors and infer the shape of the light-output curve. The campaign utilized materials with increasing Z placed in the OMEGA target chamber to initiate scattering events with the 14 MeV fusion neutrons. This process leads to the production of backscatter neutrons of varying energies that appear as peaks in the nTOF data. Simulations using a neutron transport code were combined with the measured deuterium–tritium neutron yields to calculate the expected backscattered neutron yields from the well-known scattering cross sections of each material. Furthermore, the neutron-energy dependent light output of the scintillator inferred from the experiment is compared to the light-output curve simulated with a neutron transport code for the following neutron energies: 1.5, 2.5, 6, and 14 MeV.
47 OTHER INSTRUMENTATION↗
Coupled Reactor and Engine Nuclear Thermal Propulsion Modeling Methodology
The design and development process of a Nuclear Thermal Propulsion (NTP) system requires extensive multiphysics modeling to couple the neutron physics and thermal feedback effects to determine the reactor’s power shape. Propulsion system performance codes utilize this power shape to determine NTP key performance parameters. While the power shape is heavily dependent on the temperature profile and geometry of the reactor, many analyses either assume a constant power shape, or use neutronics analysis to determine a power shape for a specific reactor configuration. The development of a coupling interface for a propulsion system performance code and a Monte Carlo neutron transport code (OpenMC) allows for the reactor power shape to be calculated in an iteration loop. The interface utilizes a file share system to transfer geometry dimensions, temperatures, and material identifiers to OpenMC, which is used to perform a neutron transport simulation of a design like the government Testing Reference Design reactor. The interface is then able to post-process the results from OpenMC and use the same file share system to share a power shape and other important neutron transport parameters to the system performance code. Initial results show that neglecting the changes to power shape when comparing reactor configurations can yield inaccurate results. Furthermore, utilizing propellants other than hydrogen gas can cause significant changes to the power shape, and thus, the thermal performance of a specific reactor design. This methodology is being expanded to allow for multiple families of NTP reactors to be analyzed, including block moderator, particle bed, and NERVA-derived reactors.
multiphysics coupling↗
Coupled Reactor and Engine Nuclear Thermal Propulsion Modeling Methodology
The design and development process of a Nuclear Thermal Propulsion (NTP) system requires extensive multiphysics modeling to couple the neutron physics and thermal feedback effects to determine the reactor’s power shape. Propulsion system performance codes utilize this power shape to determine NTP key performance parameters. While the power shape is heavily dependent on the temperature profile and geometry of the reactor, many analyses either assume a constant power shape, or use neutronics analysis to determine a power shape for a specific reactor configuration. The development of a coupling interface for a propulsion system performance code and a Monte Carlo neutron transport code (OpenMC) allows for the reactor power shape to be calculated in an iteration loop. The interface utilizes a file share system to transfer geometry dimensions, temperatures, and material identifiers to OpenMC, which is used to perform a neutron transport simulation of a design like the government Testing Reference Design reactor. The interface is then able to post-process the results from OpenMC and use the same file share system to share a power shape and other important neutron transport parameters to the system performance code. Initial results show that neglecting the changes to power shape when comparing reactor configurations can yield inaccurate results. Furthermore, utilizing propellants other than hydrogen gas can cause significant changes to the power shape, and thus, the thermal performance of a specific reactor design. This methodology is being expanded to allow for multiple families of NTP reactors to be analyzed, including block moderator, particle bed, and NERVA-derived reactors.
multiphysics coupling↗
Demonstration of Monte Carlo Reference Equilibrium Core Solutions for Pebble Bed Reactors Using Shift in kugelpy
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.
22 GENERAL STUDIES OF NUCLEAR REACTORS↗
Demonstration of Monte Carlo Reference Equilibrium Core Solutions for Pebble Bed Reactors Using Shift in kugelpy
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.
22 GENERAL STUDIES OF NUCLEAR REACTORS↗
Structural Aspects of Neutron Survival Probabilities
The neutron survival probability (and related quantities including probabilities of extinction and initiation) is a central element of the broader stochastic theory of neutron populations and finds application in fields including reactor start-up, analysis of reactor power bursts and criticality accidents, and safeguards. In a full neutron transport formulation, the equation governing the single-neutron survival probability is a backward or adjoint-like integro-partial differential equation with the added complexity of being highly nonlinear. Analogous formulations of this equation exist in the context of many approximate theories of neutron transport, with the point kinetics formulation having received significant theoretical attention since the 1940s. This work continues this tradition by providing a novel analysis of the single-neutron survival probability equation using the tools of boundary layer theory. The analysis reveals that the “fully dynamic” solution of the single-neutron survival probability equation—and some key probability distributions derived from it—may be cast as a singular perturbation around the underlying quasi-static single-neutron probability of initiation. In this perturbation solution, the expansion parameter is the ratio of the neutron generation time to a macroscopic time scale characterizing the overall system evolution; this interpretation illuminates some of the fundamental structural aspects of neutron survival phenomena.
97 MATHEMATICS AND COMPUTING↗
Experimental observation and integrated modelling of proton-beryllium fusion in He and D plasmas at JET
Validated integrated modelling of JET ITER-like wall experiments in which fusion performance is driven by reactions between fast ions and intrinsically present metal wall impurities is presented. A steady-state L-mode plasma with dominant proton-beryllium fusion and neutron yields of up to ≈ 6·10 13 s -1 is developed in He and D, via radiofrequency heating of a H minority. The fusion drive is unambiguously confirmed by the neutral particle analyser, fast ion loss detector, and γ-ray diagnostics. Experiments are analysed via an integrated modelling framework, developed to model the two-stage proton beryllium-fusion chain and produce high-fidelity fusion product source terms. The modelling chain comprises TRANSP and JETTO for plasma core modelling, LOCUST for full orbit product tracking and collisional slowing-down, DRESS to resolve two- and three-body fusion kinematics, and MCNP for neutron transport calculations. Modelling shows that the primary 9 Be(p,n) 9 B reaction is the dominant neutron emitter at naturally present concentrations of beryllium in these experiments. The yield contribution of secondary reactions between fusion products and beryllium, 9 Be(d,n) 10 B and 9 Be(α,n) 12 C, is found to be negligible. The proton-deuteron knock-on effect in D plasmas is modelled, which is calculated to contribute ≈ 25% to the total neutron yield. For both He and D discharges the total computed neutron rates match fission chamber (FC) measurements within the combined experimental and computational uncertainty, with an average discrepancy of ≈ ± 20%. Realistic proton-beryllium neutron sources are propagated through JET’s MCNP neutron transport model which shows that 235 U FCs’ response is sensitive to p–Be source changes, with up to ≈ 10% variation compared to a D–D neutron source. We show that the high-energy tail of the fast proton minority can be studied with multi-foil neutron activation. The framework is also applied to the study of interactions between fast protons and boron impurities, of relevance to ITER. We calculate that in JET conditions a significant alpha source with DT-like energies could be generated through 11 B(p, α)2α fusion, and detected via γ-emission in secondary interactions between fast alphas and boron. The work represents an important step towards validating predictive integrated modelling capabilities for non-standard fusion reactions.
JET↗
Preliminary Investigation of Target keff Search for Fuel Feed in MSRs
Fluid fuel molten salt reactor (MSR) concepts may achieve continuous-at-power operation with continuous or batch fresh fuel feed to counter reactivity loss from fuel burnup and fission product buildup. Accurate modeling and simulation of MSRs requires consideration of online fuel feed during depletion as well as a capability to determine the required feed amount to maintain a target multiplication factor (keff). As a first step supporting a full implementation of a new search capability into the SCALE code system’s TRITON reactor physics and depletion sequence, a preliminary investigation was performed to identify the best approach for a critical feed search capability considering computation time and accuracy. Using a simple iterative approach in which initial feed amounts were guessed based on previous depletion steps, the main drivers of computation time were found as the Monte Carlo neutron transport settings and the applied tolerance for the target keff. In the applied model, with tight convergence criteria (keff convergence to 8 pcm and a tolerance of ±15 pcm), the critical search calculation required twice the number of neutron transport calculations compared to a depletion calculation without critical search. In contrast, with a relaxed tolerance of ±50 pcm, the overall computation time for the critical search for merely increased by 30-40%. Further studies will be performed before implementing the critical search capability into TRITON.
Faulkner, Jonathon [ORNL]↗
(U) A Code System for Cross-Section Uncertainty Propagation for PARTISN
A rudimentary code system has been developed for propagating neutron cross-section uncertainties to response uncertainties using the PARTISN multigroup discrete-ordinates neutron transport code. The code system uses the first-order sandwich rule with sensitivities computed using SENSMG and covariances computed using NJOY. Databases of reaction cross sections and covariances using ENDF/B-VIII.0 data in the LANL standard 30-group structure have been precalculated. The final uncertainty in a k eff example problem compares well with the result from TOFFEE, a similar code that propagates neutron cross-section uncertainties to response uncertainties using the MCNP6 Monte Carlo neutron transport code. Presently, neither code system propagates uncertainties in $\overline{v}$, $\overline{μ}$, or χ, and neither code system propagates nuclide-nuclide covariances
73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
Computational attributes of the integral form of the equation of transfer
Difficulties can arise in radiative and neutron transport calculations when a highly anisotropic scattering phase function is present. In the presence of anisotropy, currently used numerical solutions are based on the integro-differential form of the linearized Boltzmann transport equation. This paper, departs from classical thought and presents an alternative numerical approach based on application of the integral form of the transport equation. Use of the integral formalism facilitates the following steps: a reduction in dimensionality of the system prior to discretization, the use of symbolic manipulation to augment the computational procedure, and the direct determination of key physical quantities which are derivable through the various Legendre moments of the intensity. The approach is developed in the context of radiative heat transfer in a plane-parallel geometry, and results are presented and compared with existing benchmark solutions. Encouraging results are presented to illustrate the potential of the integral formalism for computation. The integral formalism appears to possess several computational attributes which are well-suited to radiative and neutron transport calculations.
Frankel, J. I.↗