The paper analyses the neutron data and covariance matrixes, which are crucial for the computational prediction of neutronic characteristics of fast neutron reactors with uranium-plutonium fuel and currently available in the state-of-the-art versions of evaluated nuclear data libraries: ENDF/B-VIII, JENDL-5, TENDL 2021, JEFF 4T1. The newly obtained covariance data are compared to the data that was presented in the Russian evaluated nuclear data library BROND 3.1. A simplified model of a fast neutron reactor with mixed dense nitride uranium-plutonium fuel and heavy liquid metal coolant was used to calculate the spread in neutronic performance values and their uncertainties due to neutron data using different evaluated nuclear data libraries for the following characteristics: effective multiplication factor, effective delayed neutron fraction, Doppler reactivity coefficient, breeding ratio and gain, reactivity margin for fuel burnup and other fuel burnup characteristics. It has been observed that, on the whole, the uncertainties of the reactor functionals have decreased when estimated using state-of-the-art versions of evaluated neutron data libraries, compared to previous releases of those libraries. The paper also examines changes in target accuracies for predicting the main neutronic characteristics of fast neutron reactors over the past decades, as well as evaluates the requirements for neutron data uncertainties to achieve the recently declared target accuracies. The main findings of this study are presented in two aspects: first, in terms of the effects evaluated neutron data from different libraries have on the accuracy of calculations for the key neutronic characteristics of fast reactors; and second, in terms of the potential for improving the accuracy of predicted neutronic characteristics of fast reactors by considering the results of reactor physics measurements.

evaluated neutron data, uncertainties, covariance matrices, fast neutron reactor, sensitivity coefficient, uncertainty, data assimilation

Estimating the uncertainty and accuracy of computational predictions regarding the neutronic performance of nuclear reactors, radiation protection, and external fuel cycle technologies necessitates data on the uncertainties associated with the interactions of neutrons and material nuclei. The current state of knowledge regarding neutron data and their uncertainties is represented in various national libraries of evaluated neutron data for general applications: BROND 3.1 (Russian Federation, 2016), ENDF/B-VIII (USA, 2018), JENDL-5 (Japan, 2021), JEFF 3.3 and JEFF 4T1 (European Union, 2017, 2022 test version), and TENDL 2021 (IAEA, 2021). In the context of designing fast neutron reactors, evaluated neutron data play a crucial role in determining the accuracy of computational predictions for key reactor neutronic characteristics. These characteristics are essential for optimizing reactor core layouts, nuclear fuel refueling strategies, and the parameters of external fuel cycle technologies.

For several decades, working groups of the OECD’s Nuclear Energy Agency (NEA), in collaboration with the Nuclear Data Section of the International Atomic Energy Agency (IAEA), have been engaged in analyzing and assessing the impact of uncertainties in neutron data on the accuracy of computational predictions for the neutronic performance of Generation IV nuclear reactors (WPEC Subgroup 46). The ultimate goal of this analysis is to establish both the achieved and target accuracies for computational predictions of reactor neutronic characteristics, as well as to identify priorities for updating neutron data. This updating is crucial for enhancing the accuracy and reliability of computational predictions for the performance of innovative facilities under design (Cabellos et al. 2023).

The increasing demands for cost-effectiveness and safety in the design of Generation IV reactor systems necessitate periodic revisions of both the target accuracy for computational predictions of essential neutronic characteristics and the required accuracy of neutron data. These revisions aim to make accuracy requirements more stringent and are informed by the accumulation of experimental information, as well as the development of computational models, methods, and tools. The target and achieved accuracies for calculating key neutronic performance data related to fast reactors are summarized in Table 1. The “current state” reflects the results of generalizing estimates obtained from the OECD NEA working groups.

Using a simplified model of a heavy liquid metal-cooled fast reactor (LFR) with nitride uranium-plutonium fuel, key neutronic characteristics have been calculated based on the current versions of evaluated neutron data libraries. These characteristics include the effective multiplication factor (k_eff), Doppler reactivity factor (Δρ_D), burnup reactivity margin (Δρ_burn), effective fraction of delayed neutrons (β_eff), breeding ratio (BR), and other fuel burnup characteristics. Additionally, the nuclear data uncertainty has been estimated based on the results of integrated measurements from the BFS-61 critical assemblies (DICE, IDAT), which possess similar neutronic properties. The ONIX code (Andrianov et al. 2023a, 2023b) was utilized to solve the inverse problem of defining the requirements for cross-sections of neutron interactions with actinide nuclei. This analysis assumes that the neutron data should ensure a target accuracy for the effective multiplication factor (k_eff) calculation of the considered LFR model at a level no greater than 0.2%.

The simplified cylindrical LFR model, utilizing lead coolant and nitride uranium-plutonium fuel, consists of a homogeneous mixture containing 33 wt. % uranium-plutonium fuel, 60 wt. % lead, and 7 wt. % iron. The volume fractions of these materials are comparable to those of the BFS-61 model and are surrounded by a reflector made up of 88 wt. % lead and 12 wt. % iron (Bychkov et al. 2024). The plutonium composition in the fuel is sourced from open literature, with the plutonium content assumed to be 13 wt. % and the concentration of ²³⁵U in depleted uranium set at 0.2% (Balovnev et al. 2021). The core height is specified to be 110 cm, while the radius is determined based on criticality conditions. The thickness of both the end and side reflectors is selected to ensure that neutron escape from the core is consistent with that of the standard LFR model. The fuel life of 900 effective days (without refueling) has been calculated for operation at a rated thermal power level of 700 MW. During the computational simulation, no partial refueling mode was implemented, and the refueling interval duration was assumed to be 150 effective days, with a 30-day outage at the end of each refueling interval.

For the neutronic calculations, a precision code equipped with a built-in module for calculating variations in nuclide composition was employed. The NUCLEX and NUDAPS codes were utilized to estimate the neutronic performance uncertainties due to nuclear data uncertainties. These codes incorporate a functional approach to assess both nuclear data and technological uncertainties in the calculated characteristics, utilizing sensitivity coefficients and variant calculations based on the generation of random input data samples (Andrianov et al. 2022, 2023c).

Table 2 presents the ranges of values and uncertainties associated with nuclear data for the key neutronic characteristics (k_eff, ∆ρ_D, ∆ρ_burn, β_eff, BR and fuel burnup characteristics) of the LFR model under consideration. These were calculated using various evaluated neutron data libraries, including BROND 3.1, ENDF/B-VIII, JENDL-5, TENDL 2021, and JEFF 4T. Table 3 outlines the uncertainties related to the nuclear data for the LFR model’s fuel composition at the end of cycle (EoC), estimated at 900 days using the NUCLEX code. This estimation is based on uncertainty data for one-group neutron cross-sections obtained from the NUDAPS system, which utilizes covariance data from different evaluated nuclear data libraries.

Overall, the values of the reactor functional uncertainties estimated using the considered library versions were lower than those derived from earlier versions (see Andrianova et al. 2014, for example). Notably, uncertainties in neutron cross-sections were documented in the 2010 and 2011 library versions in two sections: MF32 (uncertainties of resonance parameters) and MF33 (uncertainties of cross-sections for energies above 0.2 MeV). In the most recent library versions, data on uncertainties in the resonance region have been consolidated into the MF33 section, covering a large number of groups (approximately 1000). However, the MF32 section for ²³⁸U, which was necessary for estimating uncertainties in resonance self-shielding and Doppler effects, has been removed from the nuclear data files. None of the analyzed libraries provide data on uncertainties for nitrogen neutron reaction cross-sections, with the exception of the JENDL-5 library, which includes covariance data for the (n, p) cross-section.

The estimates indicate a preserved spread of 0.7% between the k_eff values obtained from the ENDF/B-VIII and JEFF 4T libraries. The maximum spread across all analyzed libraries is 1%, which corresponds to the uncertainties associated with nuclear data estimated using the current versions of non-Russian evaluated nuclear data libraries, ranging from 0.84% to 0.95%. The k_eff uncertainty due to nuclear data uncertainties for the initial state, estimated using the BROND 3.1 library, is significantly higher at 1.5%, primarily attributed to uncertainties in the capture cross-section and inelastic neutron scattering on ²³⁸U nuclei.

The variation in estimates for one-group cross-sections of neutron interactions with actinide nuclei is notably high, exceeding 50% for the capture cross-sections of Am and Cm. Nonetheless, this variation is comparable to the uncertainties employed in the latest versions of non-Russian evaluated nuclear data libraries. The uncertainties presented in the BROND 3.1 library appear to be underestimated for several minor actinides.

As the core temperature increases, there are no changes in the uncertainties associated with neutron cross-sections, nor are there changes in uncertainties related to the dilution cross-section. Previously, information on the uncertainties of the self-shielding effect was included in the MF32 section, which, as mentioned earlier, has been excluded from the current versions of non-Russian evaluated nuclear data libraries. Consequently, the reactor functional uncertainties in both cold and hot states will remain the same. The spectral component of uncertainty for one-group neutron cross-sections of actinides is minimal, not exceeding 0.3% for capture cross-sections and 0.1% for fission cross-sections.

There is a notable variation in the data on delayed neutrons across non-Russian evaluated nuclear data libraries, with the maximum spread in the β_eff value reaching 19%. The statistical uncertainty of the Monte Carlo calculation is approximately 2σ ~ 9%, highlighting the necessity of adjusting the uncertainty for this parameter through integrated measurements. The minimum values of β_eff for both the initial state and at the end of the cycle (900 days) correspond to the calculations from the JENDL library.

Although the overall values of reactor functional uncertainties estimated using updated library versions have decreased compared to those derived from earlier versions, the uncertainties in reactor functionals due to nuclear data remain higher than what is required by reactor facility design engineers. This underscores the need for a thorough assessment of the accuracy of computational predictions for reactor performance. Such assessments should take into account a coupled analysis of accumulated experimental data from measurements conducted at critical assemblies (k_eff, β_eff, reactivity effects, spectral indices, etc.) as well as from research and power reactors, particularly focusing on post-irradiation experiments.

The estimated accuracy of computational simulations for neutronic processes is informed by the results of reactor physics experiments (Usachev and Bobkov 1980). Publicly accessible data regarding these reactor physics experiments can be found in the OECD NEA’s international handbooks on evaluated criticality benchmark experiments (ICSBEP) and evaluated reactor physics benchmark experiments (IRPhE) (DICE, IDAT). An analysis of the information and data derived from measurements at various critical assemblies leads to the conclusion that the BFS-61 critical assembly is the closest match to the LFR model under consideration.

Three critical configurations of BFS-61, composed of heterogeneous reactor materials (plutonium, depleted uranium, graphite, and lead), were employed in a series of measurements aimed at studying the neutronic performance of a lead-cooled reactor facility. These measurements focused on critical parameters, reactivity coefficients, and ratios of fission and capture reaction rates for various materials, including structural and fuel materials as well as minor actinides. The BFS-61 assemblies featured a standard core layout but differed in the composition of the side reflector: BFS-61-0 had a three-layer side reflector made of lead, steel, and depleted uranium dioxide; BFS-61-1 utilized a double-layer reflector of lead and depleted uranium dioxide; and BFS-61-2 incorporated a bottom-layer reflector of depleted uranium dioxide.

The uncertainties in posterior reactor functionals, attributed to nuclear data uncertainties (with the results of integral measurements considered), were estimated using the ONIX code (Andrianov et al. 2023b). Prior estimates – defined in this paper as the uncertainties in neutronic functionals arising from the variability in neutron-nuclei interaction characteristics derived from evaluated nuclear data files –a re contrasted with posterior estimates. The uncertainties in posterior reactor functionals incorporate the results of integrated measurements taken at critical assemblies with neutronic properties similar to those of the target facilities. Fig. 1 illustrates both prior and posterior estimates for reactor functional uncertainties related to nuclear data uncertainties, as well as the variance in calculated values obtained from different sets of evaluated neutron data.

Figure 1. 

Values of k_eff prior to (red) and after (blue) adjustments of neutron data for experiments a. BFS-61-0; b. BFS-61-1; c. BFS-61-2, and d. the LFR model based on BROND 3.1 (BR), ENDF/B-VIII (EN), JENDL-5 (JL), TENDL 2021 (TL) and JEFF 4T (JF) libraries (– experimental values of k_eff, – – – measurement uncertainties ± 1 σ).

The figure demonstrates that adjusting neutron constants within their uncertainty limits can effectively reduce discrepancies between calculations and experimental results for the integrated experiments considered. Consequently, this adjustment leads to a decrease in both the uncertainties of reactor functionals due to nuclear data uncertainties for target systems and the spread among values derived from various evaluated neutron data libraries.

The adjustment of nuclear constants results in reduced discrepancies between calculations and experimental data, as well as smaller calculation uncertainties. This adjustment leads to a shift in the neutronic performance values and their associated uncertainties for the LFR model under consideration. Prior to the adjustment, the spread in nuclear constants for the k_eff calculations of the BFS-61-0 experiments ranged from 0.6% to 0.8%. In contrast, the spread in the k_eff calculations (beginning of cycle, cold) for the LFR model was approximately 1%. After the adjustment, this spread decreased to 0.2% to 0.4% for the BFS-61 and to 0.6% for the LFR model, respectively.

Furthermore, the uncertainties in k_eff due to nuclear data uncertainties were significantly reduced following the adjustment: for BFS-61, they decreased from 0.8%–0.9% to 0.25%, while for the LFR model, the uncertainties diminished from 0.8%–1.5% to a range of 0.3%–0.4%. It is noteworthy that different neutron data libraries exhibit negligible differences in terms of quality, as they generally yield similar discrepancies between calculations and experiments, as well as comparable calculation uncertainties.

Tables 4, 5 present data on the estimated posterior uncertainties for criticality—taking into account the results of integrated measurements—at both the beginning and end of the cycle. Additionally, they include the fuel composition uncertainties calculated for different libraries at the end of the cycle, as applied to the LFR model under consideration.

Since the 1970s, the need to update neutron data for fast reactor calculations has evolved, driven by the increasing demand for greater accuracy in computational predictions of key reactor characteristics. Early studies (Usachev and Bobkov 1980) assessed both the achieved and required accuracies of neutron data, establishing these based on the conditions necessary to meet target accuracies for calculating the BR and k_eff, set at 2% and 1%, respectively, for sodium-cooled fast reactors utilizing uranium-plutonium oxide fuel (see Table 1).

In these calculations, diagonalized matrices of neutron constant uncertainties were employed (solving a conditional nonlinear optimization problem) without directly considering the energy cross-correlations among cross-sections. As a result, the required accuracies of neutron data determined through this method may be regarded as overestimated. For instance, in reference Manokhin and Usachev 1984, the necessary uncertainties for the one-group fission cross-sections of ²³⁹Pu and ²⁴¹Pu, which were estimated to ensure a k_eff uncertainty of 1%, were reported as 4% and 8%, respectively.

Later studies (Working Party 2008) demonstrated that directly accounting for energy cross-correlations among actinide neutron cross-sections – determined from actual experimental data – significantly improved the criticality uncertainty estimation for sodium-cooled fast reactors and lead-cooled fast reactors. This approach enabled a criticality calculation accuracy of 0.3% to 0.4%, even when the one-group fission cross-sections for ²³⁹Pu and ²⁴¹Pu were set at 5% and 10%, respectively. This finding underscores the importance of accurately considering the correlation properties of neutron data uncertainties when estimating the target accuracies of reactor parameters.

Table 6 presents data on the currently achieved accuracies of one-group actinide neutron cross-sections (averaged with a neutron spectrum for the LFR model). These estimates are based on the latest versions of various non-Russian evaluated nuclear data libraries, including ENDF/B-VIII.0, JEFF-3.3, JENDL-4.0, and TENDL-2019, as well as the Russian BROND-3.1 library. Since the estimates for covariance matrices—and, consequently, for one-group neutron cross-sections – vary significantly, Table 6 provides both the average values of uncertainties and the range of values for one-group cross-sections calculated using the libraries in question. The required accuracies (see Table 6) were obtained by solving the inverse problem for determining target accuracies using the ONIX code, under the assumption that neutron constants must ensure a k_eff calculation accuracy for the LFR model of no more than 0.2% (Andrianov et al. 2023a, 2023b).

As shown in Table 6, the uncertainties of neutron cross-sections for the actinides most critical to the estimation of k_eff calculation accuracy for LFRs, identified as “required” in the 1984 study, have now been achieved thanks to advancements in experimental techniques and neutron data estimation. Consequently, the current a priori uncertainty for LFR k_eff – estimated based on covariance matrices of neutron data uncertainties without incorporating the results of integrated measurements – aligns with the 1984 target uncertainty of approximately 1%. However, given that the presently required k_eff calculation accuracy for LFRs utilizing uranium-plutonium fuel is around 0.2% to 0.3%, the achieved accuracies in neutron data cannot be regarded as being sufficient.

The key observations regarding the current study can be summarized from two perspectives: 1) the effects of evaluated neutron data from different libraries on the accuracy of calculating key neutronic characteristics of LFRs, and 2) the potential for improving the accuracy of computational predictions for LFR neutronic performance by incorporating integrated measurement results.

Using a simplified model of a heavy liquid metal-cooled fast reactor (LFR) with dense uranium-plutonium fuel, an analysis was conducted to assess the effects of various evaluated neutron data libraries (ENDF/B-VIII, JENDL-5, TENDL-2021, JEFF-4T1, BROND-3.1) on the accuracy of calculating key neutronic characteristics. The results indicate that uncertainties in determining essential reactor functional – such as the effective multiplication factor, effective fraction of delayed neutrons, Doppler reactivity effect, breeding ratio, and burnup reactivity margin – have decreased compared to the results obtained with earlier versions of these libraries. This improvement highlights progress in neutron data evaluation.

An analysis of the target calculation accuracy for LFR neutronic performance, as declared over the past decades, reveals the necessity for further enhancements in the accuracy of evaluated neutron data. This paper evaluates the requirements for neutron data accuracy needed to achieve the stated target accuracy.

To improve the accuracy of computational predictions for LFR neutronic performance, it is crucial to incorporate the results of integral measurements. This approach enables the validation and refinement of both computational models and evaluated neutron data libraries. Key factors in enhancing the reliability and safety of advanced LFR reactors include continued research in neutron data evaluation, upgrades to computational codes, and the execution of new, highly informative integral experiments.

The research was supported by a grant from the Russian Science Foundation (project number: 23-29-10154).