Cross-section Adjustment Research Articles

Nuclear cross-section adjustment based on the 2-D/1-D transport code KYADJ

The theoretical basis for the nuclear cross-section adjustment in the 2-D method of characteristics (MOC) and 1-D SN coupling sensitivity and uncertainty analysis code KYADJ is developed. The energy-dependent sensitivity coefficients are produced by the sensitivity analysis using the 3-D fine flux and adjoint flux based on the first-order perturbation theory. Not only can the sensitivity coefficients be used to estimate the uncertainty of the effective multiplication factor caused by the measurement uncertainties of nuclear cross-section data, but also they can be implemented in the cross-section adjustment according to the Bayes’ theorem and the generalized linear-least-squares method (GLLSM). The cross-section adjustment aims to promote nuclear data evaluations, code verifications, and data validations. In this paper, the adjustment method is verified by the light water reactor (LWR) benchmarks: the MOX pin-cell and the PB-2 assembly cases from the UAM benchmarks. The virtual experimental value is assumed to be the target value of the cross-section adjustment. The results show that the GLLSM can reduce the differences between the calculated and experimental (C/E) values remarkably. All the relative variations of cross-sections for the adjustment are given according to the information of the (C/E) value, the sensitivity coefficients, and the prior uncertainties. The posteriori uncertainties are given, which demonstrates the decrease of the uncertainties.

MAVEN‐IUVS Observations of the CO2+ UV Doublet and CO Cameron Bands in the Martian Thermosphere: Aeronomy, Seasonal, and Latitudinal Distribution

AbstractWe analyze two Martian years of dayglow measurements of the CO Cameron bands and the CO2+ ultraviolet doublet (UVD) at 298–299 nm with the Imaging UltraViolet Spectrograph on board the Mars Atmosphere and Volatile EvolutioN (MAVEN) orbiter. We show that the altitude and the brightness of the two emissions peaks are strongly correlated, although data were collected over a wide range of latitudes and seasons. Averaged limb profiles are presented and compared with numerical simulations based on updated calculations of the production of the CO (a3Π) and the CO2+ (B 2Σ) states. The model simulations use the solar flux directly measured on board MAVEN with the Extreme Ultraviolet Monitor and the neutral densities provided by the Mars Climate Database version 5.3, adapted to the conditions of the observations. We show that the altitude and the shape of the sample limb profiles are well reproduced using the Mars Climate Database neutral atmosphere. The simulated peak intensities of the CO2+ UVD and Cameron bands are in good agreement considering the uncertainties on the excitation cross sections and the calibration of the Imaging Ultraviolet Spectrograph (IUVS) and Extreme Ultraviolet Monitor instruments. No significant adjustment of the electron impact cross section on CO2 to produce the a3Π state is needed. Seasonal‐latitudinal maps of the Cameron and UVD peak altitude observed during two Martian years show variations as large as 23 km. Model simulations of the amplitude of these changes are in fair agreement with the observations except during the southern summer dust period (Ls = 270–320°) when the calculated rise of the dayglow layer is underestimated.

Synchronous screening-and-optimization of nano-engineered blood pressure-drop using rapid robust non-linear Taguchi profiling

Atherosclerosis induces abnormal blood-flow patterns in coronary arteries mainly because of the irregular accumulation of fibrofatty plaque on the artery walls. Morphological alterations of the wall-surface attributes downgrade vascular elasticity, which compromises the normal blood-pressure gradient behavior by sporadically interfering with the effective-flow cross-section adjustment. An iron-oxide booster has been recently studied as a potential nano-particle treatment to regulate an elevated blood-pressure condition. Taguchi-type multi-factorial experimentation rapidly generates small and dense datasets in order to expedite arterial flow screening/optimization predictions. The optimal blood pressure-drop performance is investigated against four vital controlling factors. We show that tracking down inherently complex blood-flow phenomena often entails the elucidation of non-linear and messy data structures. Translating such data demands robust and agile techniques to decipher governing relationships while guarding against spurious effects from uncertainty asymmetry. We also show that by using distribution-free profiling, we may synchronously accomplish the screening and optimization tasks more accurately in comparison to other competing techniques. Illustrating our technique on a chemical engineering paradigm, we found that out of the four investigated factors only the blood behavior index to be strongly influential. A blood behavior index setting of 0.5, which is below the normal physiological limit, minimizes the blood pressure drop at an optimal value of 385 Pa/m. The proposed methodology demonstrates how the required sampling size may be further reduced, thus making the study even more economically and practically efficient. This was shown to be achieved without relinquishing important information about the dominant phenomena, hence rendering our solution to be also lean and agile.

Generalized formulation of extended cross-section adjustment method based on minimum variance unbiased linear estimation

ABSTRACT By introducing a new assumption of linear estimation, we derive a new formulation of the extended cross-section adjustment (EA) method, which minimizes the variance of the design target core parameters. The new formulation is derived on the basis of minimum variance unbiased estimation with no use of the assumption of normal distribution. In this formulation, we found that EA has infinitely many solutions as the adjusted cross-section set. The new formulation of EA can represent all the possible solutions minimizing the variance of the design target core parameters and includes a special case identical to the classical Bayesian EA method, which was derived on the basis of the Bayes theorem under the assumption of normal distribution. Moreover, we prove that the special case minimizes not only the variance of the design target core parameters but also the variance of the nuclear data. Meanwhile, we show that the new assumption of linear estimation is consistent with the Kalman filter and demonstrate that we can formulate similarly the extended bias factor method, the conventional cross-section adjustment method, and the regressive cross-section adjustment method with no use of the assumption of normal distribution.

Dissimilar Friction Stir Butt Welding of Aluminum and Copper with Cross-Section Adjustment for Current-Carrying Components

Manufacturing dissimilar joints of aluminum and copper is a challenging task. However, friction stir welding (FSW) was found to be a suitable technique to produce aluminum–copper joints. Due to different electrical conductivities between aluminum and copper, an adjustment of the cross-section is required to realize electrical conductors free of resistive losses. Taking this into account, this paper presents initial results on the mechanical and electrical properties of friction stir butt welded aluminum and copper blanks having thicknesses of 4.7 mm and 3 mm, respectively. Three different approaches were investigated with the aim to produce sound welds with properties similar to those of the used base materials. Friction stir welding has been conducted at a welding speed of 450 mm/min. Subsequently, the welded specimens were subjected to metallographic analysis, tensile testing, and measurements of the electrical conductivity. The ultimate tensile force of the best joints was about 10 kN, which corresponds to joint efficiencies of approximately 72% of the aluminum base material. The analysis of electrical joint properties led to very promising results, so that the potential of FSW of Al–Cu butt joints with sheets having different thicknesses could be confirmed by the investigations carried out.

Cross-section adjustment in the fast energy range on the basis of an Asymptotic Progressing nuclear data Incremental Adjustment (APIA) methodology

The data assimilation benchmark launched by the “Subgroup 33” on ‘‘Methods and issues for the combined use of integral experiments and covariance data’’ of the Working Party on Evaluation Cooperation (WPEC) of the OECD Nuclear Energy Agency Nuclear Science Committee is investigated by means of a recently proposed Asymptotic Progressing nuclear data Incremental Adjustment (APIA) technique. More specifically, two distinct APIA simulations having a different sequence are compared on the basis of the deterministic code system ERANOS. The analysis mainly uses a priori cross-sections along with covariance data in 33 groups both stemming from the TENDL evaluation. This basic nuclear data, which is preprocessed before the APIA methodology is used, is consistent in terms of (1) data source and (2) combined processing on the basis of the Total Monte Carlo method. The similar a posteriori cross-sections being provided, largely avoiding conflicts between partial adjustments as a result of the individual incremental assimilation steps are indicative of consistent adjustments according to a previous study. Correspondingly, the TENDL inelastic scattering cross-sections of 238U and 23Na would need some reductions essentially as a consequence of the assimilation of ZPPR9 experimental data. Another important result of the study is that there is a markedly trend of improvement for the a posteriori as against the a priori ratios of computed (C) to experimental values especially as regards the central 238U fission reaction rate per atom relative to the central 235U fission reaction rate per atom, and also as regards sodium coolant density effects; independently of the APIA sequence, the a posteriori C-values in most cases lie within the one-sigma experimental uncertainty or just a little outside, and the resulting reduced uncertainties of the a posteriori as against the a priori C-values are found correspondingly smaller than the experimental uncertainties. It appears that a suitable adjustment would likely require as a basis the use of consistent cross-sections and covariance data.

Uncertainty quantification of criticality in solid-moderated and -reflected cores at Kyoto University Critical Assembly

ABSTRACT Uncertainty quantification is conducted for the criticality of excess reactivity and control rod worth obtained at the Kyoto University Critical Assembly (KUCA). By combining SRAC2006 and MARBLE code systems, the sensitivity coefficients of the cross sections for aluminum-27 (27Al) comprising mainly of core components are large in the solid-moderated and -reflected cores (A cores) at KUCA. Also, the uncertainty is dominant in the uranium-235 isotope by the covariance data of JENDL-4.0, and a quantitative value is about 150 pcm induced by the JENDL-4.0 data library in the KUCA A cores, whereas the covariance data of 27Al are not prepared in JENDL-4.0. Moreover, the effect of decreasing uncertainty is obtained by applying the cross-sectional adjustment method to the uncertainty analyses. From the results, a series of uncertainty quantifications is expected to clarify the uncertainty of sub-criticality in accelerator-driven system experiments with spallation neutrons in the KUCA A cores.

235U elastic cross-section adjustment in criticality benchmarks – Comparison between JENDL-4.0 and ENDF/-VII.1

The main aim of this study is to estimate the uncertainty on the multiplication factor (keff) caused by the elastic cross-section uncertainty of the 235U nucleus, and the adjustment of this cross-section using the generalized linear-least squares method. For this purpose, the sensitivity matrix of keff with respect to 235U elastic cross section in the two nuclear evaluations ENDF/B-VII.1 and JENDL-4.0, has been assessed in several thermal, intermediate and fast benchmarks; which have been taken from the International Handbook of Evaluated Criticality Safety Benchmark Experiments (IHECSBE). The selection of these benchmarks is based on chi-square statistic test (χ2) that measures the statistical weight of deviations between calculus and experience results of the integral parameters caused by uncertainty in differential data. In this statistical test the sensitivity and covariance matrices are used. The sensitivity matrix has been calculated by the adjoint-weighted perturbation technique of the multi-purpose Monte Carlo code MCNP6.1. The 235U elastic covariance matrix has been generated in 44 neutron energy groups by the ERRORJ module of the nuclear data processing system NJOY99. The prior and posterior uncertainties on the keff, the adjusted elastic cross-section of the 235U and covariance matrix have been estimated using FORTRAN 95 code developed in our laboratory based on the generalized linear-least squares method.The results obtained show that: the 235U elastic cross-sections taken from JENDL-4.0 requires an adjustment which can reach 6% in 0–100 keV, 4.5% in 100 keV–625 keV and 2.5% in 625 keV–0.5 MeV, while those from ENDF/B-VII.1 needs an adjustment which can reach 5% in 0–100 keV, 3% in 100 keV-625 keV and 1% in 625 keV–0.5 MeV interval. The adjusted cross-section in the two evaluations ameliorates the posterior calculated keff with respect to the experimental keff. Also the posterior covariance matrix decreases the nuclear uncertainty of the adjusted keff.

Dimension-reduced cross-section adjustment method based on minimum variance unbiased estimation

ABSTRACT A new formulation of the cross-section adjustment methodology with the dimensionality-reduction technique has been derived in the light of the fact that it is often used under the condition of ill-posed problem, where the number of integral experimental quantities is less than the number of adjusted nuclear data parameters. This new formulation is proposed as the dimension-reduced conventional cross-section adjustment method (DRCA). The derivation of DRCA is based on the minimum variance unbiased estimation (MVUE), and the assumption of normal distribution is not used. The result of DRCA depends on a user-defined matrix that determines the dimension-reduced feature subspace. We examined three variations of DRCA, namely, DRCA1, DRCA2, and DRCA3, which employ (1) the nuclear data covariance matrix as the user-defined matrix, (2) the sensitivity coefficient matrix postmultiplied by the nuclear data covariance matrix, and (3) the sensitivity coefficient matrix, respectively. Mathematical investigation and numerical verification revealed that DRCA2 is equivalent to the currently widely used cross-section adjustment method. Moreover, DRCA3 is found to be identical to the cross-section adjustment method based on MVUE, which has been proposed in the previous study.

Cross section adjustment for fast reactor design: ATCROSS code and its application

For a competitive design of a fast reactor core in the Republic of Korea, the conventional cross section adjustment approach was chosen as a promising method to improve prediction accuracy of target core parameters. The new ATCROSS code has been developed which together with the APSTRACT code could serve as effective computational systems in the future SFR design. The determination of cross section uncertainty propagation on evaluated final parameter was implemented into these codes. As a result, the potential impact of inaccurate quantities in evaluated nuclear data, such as microscopic cross sections, can be determined and quantified.The results of uncertainty analyses performed for the Korean PGSFR reactor are in a good accordance with those already published for the similar designs; thus the calculated target cross section uncertainties could be seen as realistic. The uncertainty of keff induced by cross section data reaches approximately 2%. The uncertainty induced by cross section data for fuel temperature and loss of coolant reactivity feedback effects reach 6% and 13%, respectively. These uncertainties may be reduced by applying the conventional cross section adjustment method in conjunction with sufficient amount of high-quality experimental data. The first application of conventional cross section method to PGSFR core design is introduced in the paper.

A new cross section adjustment method of removing systematic errors in fast reactors

A new cross section adjustment method has been derived in which systematic errors in measured data and calculated results of neutronics characteristics are estimated and removed in the adjustment. Bias factors which are the ratio between measured data and calculated results are used to estimate systematic errors. The difference of the bias factors from unity is caused generally by systematic errors and stochastic errors. Therefore by determining whether the difference is within the total stochastic errors of measurements and calculations, systematic errors are estimated. Since stochastic errors are determined for individual confidence levels, systematic errors are also dependent to the confidence levels. The method has been applied to cross section adjustments using 589 measured data obtained from fast critical assemblies and fast reactors. The adjustments results are compared with those of the conventional adjustment method. Also the effect of the confidence level to the adjusted cross sections is discussed.

Sensitivity and Uncertainty Analyses of Lead Sample Reactivity Experiments at Kyoto University Critical Assembly

Sensitivity and uncertainty analyses of lead (Pb) isotope cross sections are conducted with the use of sample reactivity experiments at the Kyoto University Critical Assembly (KUCA). With the combined use of the SRAC2006 and MARBLE code systems, attempts are made to precisely examine the contributions of the reactions and energy regions of Pb isotope cross sections to reactivity based on the covariance data of JENDL-4.0. Moreover, the effect of decreasing uncertainty is discussed in terms of the accuracy of sample reactivity by applying the cross-section adjustment method to the uncertainty analyses. From the results of the sensitivity and uncertainty analyses, the reliability of Pb isotope cross sections, such as the Pb isotope covariance data of JENDL-4.0, is compared with the JENDL-3.3, ENDF/B-VII.0, and JEFF-3.1 libraries. Additionally, the numerical results reveal the applicability of the sensitivity and uncertainty analyses to the thermal neutron spectrum cores, such as the KUCA core, and demonstrate the improvement in the calculation results generated by the cross-section adjustment.

Influence of alluvial cover and lithology on the adjustment characteristics of semi-alluvial bedrock channels

A growing body of research has focused on evaluating the adjustment characteristics of semi-alluvial channels containing proximate bedrock, mixed, and alluvial sections. Active orogens have been the focus of most empirical field-based studies with comparatively less focus on semi-alluvial bedrock channels located in other regions. In this study, we present an inventory of channel geometry data collected from semi-alluvial bedrock channels in Ontario and Québec, Canada, which are not subject to tectonic uplift. Data were sourced from a variety of physiographic settings, permitting evaluation of the influence of alluvial cover, lithology, and gradient on cross-sectional channel form. Our results show no substantial difference in channel width or scaling behaviour amongst bedrock, mixed, and alluvial channels included in our study, except for sedimentary bedrock channels virtually bare of alluvial cover that represent a uniquely wide, distinct subgroup. Channel gradient does not appear to exhibit any observable control on channel width amongst our study rivers, suggesting that sedimentary bedrock channels form a distinct subgroup because of lithology. Comparatively, the widths of our bedrock channels formed in igneous/metamorphic bedrock are comparable to the widths of mixed channels and alluvial channels for a given discharge and drainage area. Our findings also suggest that cross-sectional adjustment of sedimentary bedrock channels is achieved through lateral erosion of the channel banks and downward erosion of the channel bed, whereas cross-sectional adjustment of igneous/metamorphic bedrock is primarily achieved through downward erosion of the bed with limited lateral erosion of the banks.

New approaches to provide feedback from nuclear and covariance data adjustment for effective improvement of evaluated nuclear data files

A critical examination of the role of uncertainty assessment, target accuracies, role of integral experiment for validation and, consequently, of data adjustments methods is underway since several years at OECD-NEA, the objective being to provide criteria and practical approaches to use effectively the results of sensitivity analyses and cross section adjustments for feedback to evaluators and experimentalists in order to improve without ambiguities the knowledge of neutron cross sections, uncertainties, and correlations to be used in a wide range of applications and to meet new requirements and constraints for innovative reactor and fuel cycle system design. An approach will be described that expands as much as possible the use in the adjustment procedure of selected integral experiments that provide information on “elementary” phenomena, on separated individual physics effects related to specific isotopes or on specific energy ranges. An application to a large experimental data base has been performed and the results are discussed in the perspective of new evaluation projects like the CIELO initiative.

Cross-section adjustment methods based on minimum variance unbiased estimation

ABSTRACTOn the basis of the minimum variance approach, the unified formulation for three types of the cross-section adjustment methods has been derived in a straightforward way without assuming the normal distribution. These methods are intended to minimize the variances of the predicted target core parameters, the adjusted cross-section set, and the calculated integral experimental values. The first and the second methods are found to be slightly different from the extended and the conventional cross-section adjustment methods based on the Bayesian approach with the normal distribution assumption, respectively. However, they become equivalent in some cases and results. The third method is a new method, which is necessary from the viewpoint of the symmetry of the formulation. In addition, it is verified by numerical calculations that the derived formulation gives the minimized variances as intended. The derivation procedure proposed in the present paper is potentially applicable to developing more sophisticated cross-section adjustment methods because of the less assumptions on the probability density function.

Application of the “best representativity” method to a PWR fuel calculation using the critical experiments at the Toshiba NCA facility

To judge the applicability of a critical experiment, it is necessary to confirm the similarities of the experiment with actual reactor conditions or equipment. The concept of the “representativity factor” has been well adopted since the late 1970’s, particularly for fast breeder reactors (FBRs) and future reactor studies. In our previous study, we extended this concept to the design of a light water reactor (LWR) system, and derived mathematical formulas for a new numerical evaluation method to correct a physical property of a target system. This method is different from the cross-section adjustment method and the bias factor method. For the first qualification of the method, sample calculations were carried out to correct the effective neutron multiplication factor through critical experiments at the Toshiba Nuclear Critical Assembly (NCA) facility.We also compared the result with that of the Product of Exponentiated experimental values method (PE method) of the extended bias factor methods. A good agreement was observed.The purpose of this study was to demonstrate the applicability of the method to the infinite neutron multiplication factor. Using the method and three kinds of critical experiments of NCA, calculations were performed to correct the infinite neutron multiplication factor of a pressurized water reactor (PWR) fuel assembly. Under combination of NCA critical experiments, the representativity factor became closer to unity. Simultaneously, a correction of the infinite multiplication factor was realized. Results were firstly compared among different combinations of experiments. Comparisons with the results of other calculation methods were also conducted. Whole results were explained with physical considerations.

A-priori and A-posteriori Covariance Data in Nuclear Cross Section Adjustments: Issues and Challenges

In order to provide useful feedback to evaluators a set of criteria are established for assessing the robustness and reliability of the cross section adjustments that make use of integral experiment information. Criteria are also provided for accepting the “a posteriori” cross sections, both as new “nominal” values and as “trends”. Some indications of the use of the “a posteriori” covariance matrix are indicated, even though more investigation is needed to settle this complex subject.

Use and Impact of Covariance Data in the Japanese Latest Adjusted Library ADJ2010 Based on JENDL-4.0

The current status of covariance applications to fast reactor analysis and design in Japan is summarized. In Japan, the covariance data are mainly used for three purposes: (1) to quantify the uncertainty of nuclear core parameters, (2) to identify important nuclides, reactions and energy ranges which are dominant to the uncertainty of core parameters, and (3) to improve the accuracy of core design values by adopting the integral data such as the critical experiments and the power reactor operation data. For the last purpose, the cross section adjustment based on the Bayesian theorem is used. After the release of JENDL-4.0, a development project of the new adjusted group-constant set ADJ2010 was started in 2010 and completed in 2013. In the present paper, the final results of ADJ2010 are briefly summarized. In addition, the adjustment results of ADJ2010 are discussed from the viewpoint of use and impact of nuclear data covariances, focusing on 239Pu capture cross section alterations. For this purpose three kind of indices, called “degree of mobility,” “adjustment motive force,” and “adjustment potential,” are proposed.

Applications of Integral Benchmark Data

The International Reactor Physics Experiment Evaluation Project (IRPhEP) and the International Criticality Safety Benchmark Evaluation Project (ICSBEP) provide evaluated integral benchmark data that may be used for validation of reactor physics/nuclear criticality safety analytical methods and data, nuclear data testing, advanced modeling and simulation, and safety analysis licensing activities. The handbooks produced by these programs are used in over 30 countries. Five example applications are presented in this paper: (a) use of IRPhEP data in uncertainty analyses and cross-section adjustment, (b) uncertainty evaluation methods for reactor core design at Japan Atomic Energy Agency using reactor physics experimental data, (c) application of benchmarking data to a broad range of criticality safety problems, (d) cross-section data testing with ICSBEP benchmarks, and (e) use of the International Handbook of Evaluated Reactor Physics Benchmark Experiments to support the power industry.

Channel bifurcation and adjustment on the upper Yadkin River, North Carolina (USA)

The bifurcation of river flow around large stable islands, also known as anabranching, represents a distinctive form of river adjustment that is uncommon in the Appalachian Piedmont province of the eastern U.S. Within this province, highly localized river branching similar to classical anabranching forms exists in one area near the foot of the Blue Ridge Escarpment. This paper examines channel form and processes along a reach of the upper Yadkin River in North Carolina (USA) before and after a flood-induced division of its flow into two subparallel branches, both of which remain active 35years later. The research draws on aerial photograph analyses, channel surveying, and observations of inset channel benches, flood frequency analysis, and discharge monitoring and modeling to analyze planform history and to track and explain changes in newly excised and losing channels along the bifurcated reach. The characterization of this branched reach resembles some descriptions of gravel-dominated laterally active anabranching, although the match is imperfect. Reductions in valley slope and confinement and the presence of local valley constrictions near the base of the escarpment steeplands have been conducive to long-term sedimentation and a greater likelihood of branching. A period of relatively rapid cross section adjustment occurred on both branches soon after bifurcation, and this may have permitted the losing branch to remain open. Well-stratified benches currently observed along the losing branch are interpreted to be largely the late product of a waning early major adjustment phase and moderate, recent, and perhaps ongoing variations in flow division and appear to be not fully adjusted to prevailing discharges. Coarse benches along the newly excised branch are better-adjusted inset floodplain fragments created primarily by lateral migration and point accretion. Patterns of benchfull flow frequency variation are interpreted to indicate that the flow bifurcation ratio has been neither static nor monotonically changing in recent decades. Further exploration of branching in this environment, otherwise dominated by single-thread meandering patterns, is of importance for a variety of management and ecological concerns.