Structure-Dependent Doppler Broadening Using a Generalized Thermal Scattering Law

The thermal scattering law (TSL), i.e., S(α,β), represents the momentum and energy exchange phase space for a material. The incoherent and coherent components of the TSL correlate an atom’s trajectory with itself and/or with other atoms in the lattice structure. This structural information is especially important for low energies where the wavelength of neutrons is on the order of the lattice interatomic spacing. Both thermal neutron scattering as well as low energy resonance broadening involve processes where incoming neutron responses are lattice dependent. Traditionally, Doppler broadening for absorption resonances approximates these interactions by assuming a Maxwell–Boltzmann distribution for the neutron velocity. For high energies and high temperatures, this approximation is reasonable. However, for low temperatures or low energies, the lattice structure binding effects will influence the velocity distribution. Using the TSL to determine the Doppler broadening directly introduces the material structure into the calculation to most accurately capture the momentum and energy space. Typically, the TSL is derived assuming cubic lattice symmetry. This approximation collapses the directional lattice information, including the polarization vectors and associated energies, into an energy-dependent function called the density of states. The cubic approximation, while valid for highly symmetric and uniformly bonded materials, is insufficient to capture the true structure. In this work, generalized formulation for the exact, lattice-dependent TSL is implemented within the Full Law Analysis Scattering System Hub (FLASSH) using polarization vectors and associated energies as fundamental input. These capabilities are utilized to perform the generalized structure Doppler broadening analysis for UO2.

LOW TEMPERATURE EFFECTS ON PWR FUEL ASSEMBLY CRITICALITY CALCULATIONS

One of the parameters affecting the neutron multiplication factor keff of a system containing fissile material is the system temperature. Therefore, the effect of temperature on criticality safety analyses is an area of international interest. In this context, the Working Party on Nuclear Criticality Safety (WPNCS) of the OECD Nuclear Energy Agency (NEA) formed a subgroup to define and execute a code-to-code comparison benchmark to investigate the effect of temperature on keff for PWR fuel assemblies. Two configurations of a generic water-moderated PWR fuel assembly were analysed at different temperatures between 233 K and 588 K, and with different assembly burnups. Based on this benchmark, GRS performed an additional study to investigate the impact of the moderator densities, the neutron reaction cross sections and the thermal scattering data on keff separately. The benchmark results show the expected decrease of keff with temperature and a considerable jump in keff at the phase transition of the moderator. The additional investigation demonstrates that the jump in keff is mainly caused by the change of the moderator density due to the phase transition. The change of the thermal scattering data due to the phase transitions leads to a similar but smaller jump in keff. Furthermore, the actual impact of the different parameters on keff depend strongly on the considered fuel assembly configuration.

DEVELOPMENT OF NEURAL THERMAL SCATTERING (NeTS) MODULES FOR REACTOR MULTI-PHYSICS SIMULATIONS

Modern multi-physics codes, often employed in the simulation and development of thermal nuclear systems, depend heavily on thermal neutron interaction data to determine the space-time distribution of fission events. Therefore, the computationally expensive analysis of such systems motivates the advancement of thermal scattering law (TSL) data delivery methods. Despite considerable improvements on past strategies, current implementations are limited by trade-offs between speed, accuracy, and memory allocation. Furthermore, many of these implementations are not easily adaptable to additional input parameters (e.g., temperature), relying instead on various interpolation schemes. In this work, a novel approach to this problem is demonstrated with a neural network trained on beryllium oxide thermal scattering data generated by the FLASSH nuclear data code of the Low Energy Interaction Physics (LEIP) group at North Carolina State University. Using open-source deep learning libraries, this approach maps a unique functional form to the S(α,β,T) probability distribution function, providing a continuous representation of the TSL across the input phase space. For a given material, the result is a highly accurate, neural thermal scattering (NeTS) module that enables rapid sampling and execution with minimal memory requirements. Moreover, extension of the NeTS phase space to other parameters of interest (e.g., pressure, radiation damage) is highly possible. Consequently, NeTS modules for different materials under various conditions can be stored together in material “lockers” and accessed on-the-fly to generate problem specific cross-sections.

NEW VALIDATION OF SI CROSS-SECTION USING SILICA SAND

Silicon cross-sections, being important for a criticality safety of final spent fuel disposals, were recently reevaluated within the IAEA INDEN project. Similarly, the thermal Scattering Law matrix for silicon dioxide, which is also important for criticality safety, was also reevaluated in the ENDF/B-VIII.0 library. Due to these reasons, a series of validation experiments with silica sand were performed at the LR-0 reactor. This paper describes these validation experiments, which used two different amounts of silica sand placed in the core. The first part of validation was carried out as critical experiments in order to benefit from the suitability of integral experiments for validation. The second part -fast neutron spectrum measurement in the sand -was performed in order to obtain knowledge of its characteristics and its agreement with a calculation. The results showed significant improvement of the Thermal Scattering Law matrix for silicon dioxide available in the ENDF/B-VIII.0 library. They also showed that the new INDEN evaluation of silicon cross-sections, together with its description in the ENDF/B-VIII.0 gives disagreement rate closest to the experiments carried out without silica sand insertions. The spectrum measurement showed that the calculations of fast neutron spectra in the sand show only slight differences between different evaluations of silicon cross-sections. However, the fast neutron spectrum is not dependent on the Thermal Scattering Law. The calculated spectra show relatively good agreement with the measurement.

THERMAL SCATTERING LAW ENDF LIBRARIES FOR LIQUID FLIBE

Several advanced nuclear reactor concepts have been proposed in the past few years where FLiBe molten salt represents a major constituent of the core. In this case, neutrons produced in fission slow down and moderate in FLiBe (a eutectic with a mixture of 2:1 ratio of LiF and BeF2) until they reach low energies (i.e, below 1 eV). At that stage, the thermalization process becomes dominant and the neutrons achieve a quasi-equilibrium energy state that is dependent on the temperature of the moderator. In neutronic simulations, the description of neutron thermalization is captured using the thermal scattering law (TSL), i.e., S(α,β), of the material in which low energy neutrons are interacting. S(α,β) defines the energy-momentum phase space that is available for an incoming low energy neutron. In addition, it is directly proportional to the double differential thermal neutron scattering cross section. In this work, the TSL of molten salt FLiBe is developed based on a generalized density of excitation states (GDOS) derived from atomic trajectories generated using classical molecular dynamics (MD) simulations that were performed with the LAMMPS code. The MD simulations utilized a Born-Mayer type atomic potential function that was verified to reproduce the properties of FLiBe including density and viscosity. The FLASSH code was used to evaluate the TSL’s ENDF File 7 in a temperature range extending from 773 K to 1673 K. In addition, ACE type cross section libraries are produced and tested with the objective of contributing the data to the National Nuclear Data Center for inclusion in the ENDF/B-VIII database.

Impact of H in H2O thermal scattering data on depletion calculation: k∞, nuclide inventory and decay heat

The impact of the H in H2O thermal scattering data are calculated for burnup quantities, considering models of a UO2 pincell with DRAGON and SERPENT. The Total Monte Carlo method is applied, where the CAB model parameters are randomly varied to produce sampled (random) LEAPR input files for NJOY. A large number of burnup calculations is then performed, based on the random thermal scattering data. It is found that the impact on k∞ is relatively small (less than 35 pcm), as for nuclide inventory (less than 1% at 50 MWd/kgU) and for decay heat (less than 0.4%). It is also observed that the calculated probability density functions indicate strong non-linear effects.