Multiplying System Research Articles

Integral experiments with a cylindrical multiplying system of metal plutonium

Integral experiments with a cylindrical multiplying system of metal plutonium

Optimal fissile distribution in multiplying systems: Illustrative examples with Monte Carlo simulation and Pontryagin’s maximum principle

In multiplying systems, such as nuclear reactors and criticality experiments, it is desirable to place the fissile material in the optimal or ‘best’ way to reduce the critical mass of the system as well as to achieve uniform fuel burnup. This paper considers two methods, namely Pontryagin’s maximum principle (PMP) and Monte Carlo (MC) perturbation for estimating a minimum critical mass configuration. These methods are applied to an elementary multizone model of a pressurized water reactor (PWR) and a criticality experiment to estimate the minimum critical mass. It is found that while two-group diffusion theory with PMP predicts a minimum critical mass, more detailed MC simulations with MCNP5 show a consistent reduction in critical mass when fissile fuel is placed in inner zones. Such a distribution reduces the fissile material requirement but is undesirable due to the higher power peaking. MC simulations show that for a three-zone model of the KORI 1 PWR, a uniform fissile distribution gives criticality for 1.09 atomic percent (at.%) enrichment, whereas non-uniform fissile distribution (0.6, 1.6, 0.6 at.%) reduces the critical mass by 14%. The changes found from MC simulations were subsequently predicted from first- and second-order derivative sampling. It was found that substantial computational savings can be achieved for large-scale optimization problems. In the case of a criticality experiment, MC derivative sampling was also used to estimate optimal fissile distribution for minimizing the critical mass.

Towards a highly efficient and unbiased population-control algorithm for kinetic Monte Carlo simulations

Population-control methods are key to non-stationary Monte Carlo simulations of multiplying systems: they prevent either the unbounded growth or the disappearance of neutrons, occurring respectively in supercritical and subcritical conditions; furthermore, they contribute to an efficient allocation of computational resources by addressing the unbalance between the neutron and the precursor populations. In this paper, we present two alternative populationcontrol algorithms: the legacy implementation in TRIPOLI-4®, the Monte Carlo code developed at CEA, and an improved version that is currently under investigation, based on the use of a simplified point-kinetics solver. We assess the performance of these methods through the simulation of a $2.2 step reactivity insertion in a fast system (Flattop-Pu), leading to an increase of the neutron population by a factor 200, which is benchmarked against point kinetics. We show that the new implementation not only suppresses the slight bias that was present in the legacy method due to a stochastic normalization factor, but also outperforms the previous algorithm in terms of variance reduction and improvement of the figure of merit.

Verification of Feynman-α formula including the effect of delayed neutrons

The Feynman-Y function formulas, including the effect of delayed neutrons with point kinetics approximation, have been widely investigated. The formula that considers the prompt-prompt correlation and neglects the prompt-delayed correlation was well-established in the past. Although the formulas that consider the prompt-delayed correlation have been proposed, their verification has not yet been presented because the correlation is too small to be quantitatively identified. Using the joint detection probability based on a heuristic approach, this study derives the Feynman-Y function formula that considers prompt-delayed correlation. The formula is verified by comparing it with a Monte Carlo simulation. The prompt-delayed correlation effect is discussed using numerical examples. The correlation effect is negligible in most subcritical multiplying systems. However, the effect becomes increasingly significant as the multiplying system approaches criticality.

‘Openness in Action’ Early Steps in Cosmic Phenomenology

‘Openness in Action’ Early Steps in Cosmic Phenomenology

Investigation of the AGN-201M Research Reactor’s Unique Dominance Ratio

The dominance ratio is the ratio of the first higher-order mode eigenvalue of a system to the fundamental eigenvalue, k1/k0. It can be used to determine how well coupled the neutrons in a multiplying system are, as well as the computational difficulty of the power iteration method in a Monte Carlo simulation. The purpose of this study is to investigate the University of New Mexico’s (UNM’s) AGN-201M reactor’s unusually low dominance ratio of 0.632. The AGN-201M reactor is a small, thermal spectrum reactor located at the UNM. It is moderated by polyethylene, reflected by graphite, and uses fuel comprised of uranium microspheres embedded in polyethylene plates that are separated by an aluminum baffle. The investigation included a parametric study of the reactor’s fuel geometry, fuel density, and reflector thickness to examine their impact on the reactor’s dominance ratio. In addition, neutronically similar systems were examined to identify common causes for systems with low dominance ratios. The reason for the small dominance ratio of the AGN-201M reactor when compared to large thermal reactors was determined to be because of its size and fuel plate composition. The reflector’s effect on the dominance ratio is small in comparison to the other factors but was found to have a nonzero effect. Furthermore, the AGN-201M was found to have a significantly lower dominance ratio than systems with which it shares a very high ( > 95%) degree of neutronic similarity. However, the two most similar systems were close in size to the core of the AGN-201M reactor and were moderated with polyethylene as well.

Multiplication Factor for Subcritical Multiplying System and the Efficiency of Source Neutrons

Multiplication Factor for Subcritical Multiplying System and the Efficiency of Source Neutrons

Depletion calculation of subcritical system with consideration of spontaneous fission reaction

ABSTRACT Modification of the Monte Carlo depletion calculation code OpenMC was performed to enable the depletion calculation of the subcritical neutron multiplying system. With the modified code, it became possible to evaluate the quantity of short half-life fission products from spontaneous and induced fissions in the subcritical system. As a preliminary study, it was applied to the fuel debris storage canister filled with nuclear materials and spontaneous fission nuclides. It was confirmed that the code could successfully provide a quantity of short half-life fission products (FPs) over time and provide the relationship between the activity ratio of 88Kr to 135Xe and effective neutron multiplication factor of the canister.

ЭКСПЕРИМЕНТЫ ПО ИССЛЕДОВАНИЮ ТЕМПЕРАТУРНОГО ЭФФЕКТА РЕАКТИВНОСТИ В ПЛУТОНИЕВЫХ РАЗМНОЖАЮЩИХ СИСТЕМАХ БЕЗ ОТРАЖАТЕЛЯ

The article presents the investigation into reactivity and critical parameters affected by temperature changes in cylindrical and spherical space-effective multiplying systems (MS) of plutonium in α-phase without reflector during integral critical experiments. The experiments were performed in “Zababakhin All-Russia Research Institute of Technical Physics” on a critical assembly stand FKBN-2. Brief description of the experimental set up is provided. During the experiments, the multiplication factors and decay constant of the prompt neutrons were determined at a fixed gap between MS parts and different MS temperatures. Values of MS critical gap at different MS temperatures were established experimentally. The change in MS reactivity is initiated by energy release under the plutonium isotopes alpha-decay. As a result, the change in MS temperature during the experiments without its forced regulation may reach ~40 °C. It is proposed to consider this temperature effect when specifying experimental results including error estimation. The obtained experimental data were used to estimate the temperature coefficients of reactivity. The work results are applied to create benchmark models of the multiplying systems.

ЭКСПЕРИМЕНТЫ ПО ИССЛЕДОВАНИЮ ПРОХОЖДЕНИЯ НЕЙТРОНОВ ЧЕРЕЗ СЛОИ ГИДРИДА ЛИТИЯ-7 В УРАНОВОЙ РАЗМНОЖАЮЩЕЙ СИСТЕМЕ С ПРИМЕНЕНИЕМ МЕТОДА НЕЙТРОННО-АКТИВАЦИОННОГО АНАЛИЗА

The paper provides the precision experimental results on fission spectrum neutrons transmission through lithium hydride layers-7 with neutron activation analysis. The experiments were performed in Zababakhin All-Russia Research Institute of Technical Physics” on a critical assembly stand FKBN 2. A cylindrical multiplying system (MS) made of high enriched uranium was used as a source of fission spectrum neutrons. Activation integrals of neutron activation detectors (NADs) located at different points of the composite lithium-7 hydride reflector face-mounted on the cylindrical uranium MS were determined in the experiments. NADs based on nickel, indium, titanium, aluminum and copper were used. NADs of different types were exposed to radiation at power ~25-30 W during 1-1,5 hours. Nickel NAD was used as a monitor. Activation integrals absolute measurement error was determined by a certified technique and ranged from ~4 to ~8 % (2σ). Relative measurement error was determined by statistical accuracy, instrument peaks software processing correctness and was found not to exceed 5,4 % (2σ). Using the data obtained, spectral indices (the ratio of the normalized values of the activation integrals of various detectors types to the one of nickel detector), which provide information on the neutron spectrum were determined.

The heuristically-based generalized perturbation theory

The generalized perturbation method is described relevant to ratios of bi-linear functionals of the real and adjoint neutron fluxes of critical multiplying systems. Simple linear analysis for optimization and sensitivity studies are then feasible relative to spectrum and space-dependent quantities, such as Doppler and coolant void reactivity effects in fast reactors.

On the Issue of Stability and Safety of the Superbooster, a Pulsed Neutron Source

A high-intensity pulsed neutron source can be constructed according to the principle of a superbooster, i.e., a neutron multiplying system of the neutron-generating target of the proton accelerator with proton energy of about 1 GeV in the subcritical reactivity modulation system. Usually, superboosters are considered to be safe and reliable nuclear facilities. However, as indicated in this paper, a powerful superbooster may prove to be less stable in operation than a pulsed reactor. Therefore, the problems of its safety call for close study.

Third order adjoint sensitivity analysis of reaction rate responses in a multiplying nuclear system with source

Until recently, the 2nd-order sensitivities of reactor physics model responses to the nuclear data characterizing the respective model were impractical to compute exactly and exhaustively, because of the so-called “curse of dimensionality.” Hence, the effects of the 2nd-order sensitivities on the uncertainties produced in responses by the uncertain nuclear data have been routinely neglected. Recently, the author has developed a general 2nd-order adjoint sensitivity analysis methodology which overcame the “curse of dimensionality” to perform the first-ever complete computation of the exact 21,976 first-order, and 482,944,576 s-order sensitivities for a OECD/NEA reactor physics benchmark response to the uncertain nuclear data that characterize the neutron transport computational model of this benchmark. In particular, the numerical results obtained for the benchmark’s leakage response with respect to the benchmark’s group-averaged isotopic total cross sections indicated that, contrary to the widely held belief that the 2nd-order response sensitivities in reactor physics systems are negligible, the opposite turned out to be the case, i.e., many of the 2nd-order sensitivities were orders of magnitude larger than the corresponding 1st-order ones. Consequently, neglecting the 2nd-order sensitivities would cause very large non-conservative errors by under-reporting the response variance and erroneously reporting its expected value.The fact that a large number of 2nd-order response sensitivities are significantly larger than the 1st-order sensitivities has motivated the development of the general expressions presented in this work for the efficient and exact computation of the 3rd-order response sensitivities of reaction rate responses to nuclear data for subcritical reactor physics systems modeled by the neutron transport equation. The mathematical results derived in this work are currently implemented in production-oriented three-dimensional neutron transport code systems to enable the computation of 3rd-order sensitivities of reactor physics systems, commencing with the OECD/NEA benchmark mentioned above.

New variants of Bennett variance method with correlation indices for reducing delayed-neutron contribution

The Feynman-alpha method has been frequently employed to measure the subcriticality of a neutron multiplying system through determination of the prompt neutron decay constant. This method, however, often encounters a difficulty with unstable multiplying systems where the neutron population is temporally varying and drifting owing to perturbations due to removal or replacement of fuels and absorbers. In the unstable multiplying systems, the delayed-neutron contribution is remarkably enhanced and makes it difficult to extract the prompt neutron decay constant from the prompt-neutron contribution. The linear difference filter methods that are variants of the Bennett variance one were hence developed to mitigate this kind of difficulty by reducing the delayed-neutron contribution. In the present study, further new variants are proposed. It is shown that the present methods with correlation indices consisting of more than three successive gates can reduce the delayed-neutron contribution more effectively than the conventional ones.

Second-order adjoint sensitivity analysis of a general ratio of functionals of the forward and adjoint fluxes in a multiplying nuclear system with source

In the present work, the Second-Order Adjoint Sensitivity Analysis Methodology (2nd-ASAM) is applied to a generic multiplying subcritical nuclear system comprising a non-fission neutron source in order to compute efficiently and exactly all of the 1st- and 2nd-order functional derivatives (“sensitivities”) of a system response with respect to the system’s many parameters. The system response is defined to be a ratio of two general nonlinear functionals of the forward and adjoint particle fluxes, while the system parameters include isotopic number densities, microscopic cross sections, fission spectrum parameters, neutron sources, and detector response functions. Such ratios of functionals represent the most general models for quantities of fundamental importance in reactor physics, including eigenvalues, ratios of reaction rates and forward/adjoint flux-weighted multi-group cross sections. The exact expressions obtained in this work will be used in subsequent works to perform a large-scale sensitivity analysis of a polyethylene-reflected plutonium metal sphere experimental benchmark to the nuclear data characterizing this benchmark, comprising 21,976 first-order sensitivities and 482,944,576 second-order sensitivities.

Verification of the ROSFOND/ABBN nuclear data based on the OECD/NEA benchmark on criticality safety of mox-fueled systems

The paper presents the results of a computational analysis of the OECD/NEA benchmark conducted to estimate the accuracy of the critical safety parameters of multiplying MOX-fueled systems. The computational test is a set of 15 spherical multiplying systems that differ in their compositions and geometries. According to the test conditions, the keff values of the analyzed systems are unknown in advance. As part of the computational analysis of the test involving national codes and nuclear data libraries, along with the keff calculations, it is also necessary to estimate the a priori (due to the accuracy of the nuclear data used) and a posteriori (based on the accumulated experimental information) errors in the calculated keff values. Based on the benchmark, an updated version of the ROSFOND/ABBN-RF nuclear data was tested. The results of estimating the a priori and a posteriori errors in keff using the INDECS system for the proposed test models are presented. The analysis of the calculated data shows that (1) the observed spread in the keff values obtained from the Russian ROSFOND library and foreign evaluated nuclear data libraries (ENDF/B-VII.0, JEFF-3.2, JENDL-4.0) varies from –0.3 up to 0.8%; and (2) the deviation of the calculation results in the keff values obtained from the ROSFOND library and its group version, ABBN-RF, does not exceed 0.1%. The average a priori error in keff for all the tested options of multiplying systems is about 1% and, taking into account the selected set of experimental criticality data for MOX-fueled systems, including experiments at the BFS facilities, the average a posteriori error in keff can be reduced to 0.3%. The performed estimations confirm the high accuracy of the ROSFOND/ABBN-RF nuclear data for calculating the critical safety parameters of multiplying MOX-fueled systems.

An analytical approach to bifurcations and stability in simplified mathematical models of nuclear reactors

Asymptotic analytical methods are applied to study some problems related with bifurcations (both local and global) and stability in three simple mathematical models of nuclear reactors.The first case is a reactor which is subcritical at rest and driven by a distributed external neutron source. Under suitable conditions in the temperature feedback reactivity, the mathematical model predicts a static global bifurcation with three critical states, two stable and one unstable, with the possibility of a runaway. The dynamics of this system is studied, in a framework of slow manifold theory, by methods of restricted nonlinear modal analysis, and the results of a digital simulation are summarized. The model could be modified and extended to study the space time dynamics of sub-critical multiplying systems driven by external neutron sources (neutron beams produced by accelerators).The second case is related with in phase and out of phase xenon oscillations in large thermal reactors. The known subcritical Hopf bifurcation that appears in the context of global mode oscillations is revisited. After applying a nonlinear modal analysis to the mathematical model, a normal form is derived by an averaging method. Approximate analytical formulae for the radii of the unstable limit cycles and for the trajectories of the state variables in a neighborhood of the bifurcation point are obtained.The third case is a non-trivial modification and development of a simple mathematical model intended to describe certain mechanical kinetic effects stemming from a possible coupling of nuclear, thermal and mechanical vibration processes. We show that, under suitable conditions, a dynamic supercritical Hopf bifurcation in the reactor power appears in the framework of our modified model. A normal form is derived by an averaging method. Analytical formulae for the radii of the stable limit cycles and the trajectories of the state variables in a neighborhood of the bifurcation are given.

Application of the Second-Order Comprehensive Adjoint Sensitivity Analysis Methodology to Compute First- and Second-Order Sensitivities of Flux Functionals in a Multiplying System with Source

This work presents an application of the Second-Order Adjoint Sensitivity Analysis Methodology (2nd-ASAM) to the neutron transport Boltzmann equation that models a multiplying subcritical system comprising a nonfission neutron source to compute efficiently and exactly all of the first- and second-order functional derivatives (sensitivities) of a detector’s response to all of the model’s parameters, including isotopic number densities, microscopic cross sections, fission spectrum, sources, and detector response function. As indicated by the general theoretical considerations underlying the 2nd-ASAM, the number of computations required to obtain the first and second orders increases linearly in augmented Hilbert spaces as opposed to increasing exponentially in the original Hilbert space. The results presented in this work are currently being implemented in several production-oriented three-dimensional neutron transport code systems for analyzing specific subcritical systems.

Second-order sensitivities of a general functional of the forward and adjoint fluxes in a multiplying nuclear system with source

This work presents an application of the Second-Order Adjoint Sensitivity Analysis Methodology (2nd-ASAM) to compute efficiently and exactly all of the 1st- and 2nd-order functional derivatives (“sensitivities”) of a generic scalar-valued response to parameters for a multiplying subcritical system comprising a non-fission neutron source. The response is defined to be a nonlinear functional of the forward and adjoint particle fluxes while the system parameters include isotopic number densities, microscopic cross sections, fission spectrum, sources, and detector response functions. As indicated by the general theoretical considerations underlying the 2nd-ASAM, the number of computations required to obtain the 1st- and 2nd-order increases linearly in augmented Hilbert spaces as opposed to increasing exponentially in the original Hilbert space. This unique feature provides the fundamental reason for the unmatched efficiency of the 2nd-ASAM for computing exactly all of the 1st- and 2nd-order responses sensitivities to model parameters. The results presented in this work are currently being implemented in several production-oriented three dimensional neutron transport code systems for analyzing specific subcritical systems.

Second-order sensitivity and uncertainty analysis of the Roussopoulos-functional for a subcritical multiplying nuclear system with source

The Roussopoulos-functional has long been used for selecting trial functions for the forward and adjoint fluxes when computing reaction rates in nuclear systems and/or particle detector responses, because this functional was considered in previous works and textbooks to be accurate to second-order in variations of the model’s forward and adjoint fluxes. However, by applying the Second-Order Adjoint Sensitivity Analysis Methodology (2nd-ASAM), this work shows that the first-order sensitivities of the Roussopoulos-functional to the system’s parameters (including isotopic number densities, microscopic cross sections, fission spectrum, forward and adjoint sources) are not identically zero. This means that the Roussopoulos-functional is not accurate to second-order in the flux variations if the system parameters are imprecisely (rather than perfectly well) known, as is invariably the case in practice. This work also illustrates the application of the 2nd-ASAM for computing efficiently the correct expressions of the second-order sensitivities of the Roussopoulos-functional to model parameters. The results presented in this work indicate the correct path for future possible uses of the Roussopoulos-functional for performing sensitivity and uncertainty analyses of both forward and inverse problems in nuclear systems.