Source-driven Systems Research Articles

Time-dependent Green's function generation with Monte Carlo for transient analysis of source-driven systems

The transient analysis of nuclear reactors is an important issue from a safety point of view. The deterministic methods, by considering different approximations, are extensively used to solve the neutron transport equations. Nowadays, by the continuous increase of computational resources, the feasibility of utilization of pure Monte Carlo methodology in the nuclear reactor transient analysis, without using different approximations, is being increased. In the present work, a detailed Dynamic Monte Carlo (DMC) methodology is developed and employed to investigate the transient analysis of source driven nuclear systems. Analytically solvable time and space and time dependent problems are introduced and solved to verify variance reduction tools used in the DMC methodology. Then, the DMC method is utilized to generate time dependent Green's functions for transient analysis of the source-driven systems (SDSs) studied in literature. The equilibrium and post perturbation transient responses of source driven systems are obtained by utilizing the Green's functions generated for those systems. The newly developed novel method is applied to different transient benchmark problems of SDSs. The performance and validity of the proposed method are discussed through qualitative and quantitative comparisons with the results given for the test and benchmark problems.

Secondary-Source Core Reload Modeling with VERA

The CASL reactor simulation package VERA has been adapted to provide high-fidelity simulation capabilities for modeling source range detector response during subcritical reactor configurations. New features include the activation and shuffling of secondary-source assemblies, use of burned fuel neutron emission data from the ORIGEN depletion solver to the MPACT deterministic neutron transport solver, allowance of user-defined sources in MPACT based on material composition, ability to solve the subcritical source-driven system with neutron multiplication using the MPACT diffusion solver, and transfer of the calculated fission source from MPACT to the continuous-energy Monte Carlo solver Shift for final detector response evaluation using the CADIS methodology for variance reduction. These new capabilities were benchmarked against Watts Bar Unit 1 plant operating data for the first few fuel loading steps and were found to demonstrate excellent agreement with the measured data.

Coarse Mesh Rebalance Acceleration of Fission Source Iteration for Subcritical Source-Driven Systems

Coarse mesh rebalance (CMR) method is formulated for the acceleration of fission source iteration (FSI) in the multigroup transport theory analysis of subcritical source-driven systems. The within-group equations are solved by diamond-differenced SN method and CMR has been employed also for the acceleration of scattering source iterations. By numerical experiments, carried out in spherical geometry, stability and performance characteristics of the proposed acceleration are determined and assessed. Systems containing a central nonmultiplying source region and an outer multiplying blanket region are considered. CMR is stable provided that the number of coarse mesh regions in the blanket is in a stability interval between a minimum and a maximum value, irrespective of the fine mesh used in SN calculations. Maximum acceleration is obtained for an optimum number of blanket coarse mesh regions which is also independent of the fine mesh. Both the width of the stability interval and the optimum speed-up ratio (execution time ratio of the unaccelerated run to the accelerated one) increases as the system becomes optically thicker. If we let the system approach criticality by increasing the blanket size, the number of FSIs increases dramatically if no acceleration is employed. For such slightly subcritical systems, very high speed-up ratios are obtained with CMR acceleration whose performance is independent of the criticality level.

An Analytical Solution for the Two-Group Diffusion Theory Analysis of Multiregion Source-Driven Systems

An analytical solution of the two-group diffusion equations is derived for multiregion source-driven subcritical systems in spherical geometry. An analytical formulation for the calculation of the effective multiplication factor is also presented. Using typical two-group cross sections characterizing source, buffer, and blanket regions, parameters such as neutron amplification, source efficiency, and blanket fast flux peaking factor are calculated. The criticality solution is utilized to calculate the effective multiplication factor and the neutron source efficiency. The dependency of the calculated global parameters on design variables like the source, buffer, blanket thicknesses, and subcriticality level is studied. Thin source regions result in very high neutron amplification, at the expense of high blanket fast flux peaking factors. If a buffer region is put between the source and the blanket regions, flux peaking could be reduced at the expense of reduced neutron amplification. If the subcriticality level can be reduced without jeopardizing safety, the neutron amplification increases and the fast flux peaking is reduced.

Experimental validation of unique combination numbers for third- and fourth-order neutron correlation factors of zero-power reactor noise

ABSTRACT Zero-power reactor noise is useful for subcriticality measurements. Based on the nuclear reactor physics and the theory of neutron detection, this paper theoretically clarifies that the third- and fourth-order neutron correlation factors and can be expressed as functions of the second-order neutron correlation factor . In particular, if the neutron-counting gate width is sufficiently large, the saturation values and are almost equal to the unique combination numbers, ‘3’ and ‘15,’ for a source-driven subcritical system, where the subcriticality is less than 10,000 pcm. These unique combination numbers, ‘3’ and ‘15,’ for and were validated using actual zero-power reactor noise measurements carried out at the Kyoto University Criticality Assembly. In this study, the estimation of statistical errors and correlations between different gate widths owing to the bunching method was achieved by the moving block bootstrap method. For a sufficiently long measured reactor noise in a steady and unperturbed state, a statistical test for the evaluation of the critical state and the absolute measurement of subcriticality can be carried out by statistically quantifying the difference between the measurement value of and the unique combination number.

Analysis of KUCA measurements by the reactivity monitoring MAρTA method

A recently developed method for the continuous reactivity monitoring in nuclear reactors and in subcritical source-driven systems is applied for the interpretation of flux measurements carried out in the KUCA facility. The scope of the work is to validate the method using real experimental data. The method is based on general mathematical properties of the differential equations constituting the point kinetic model. Several pulsed experiments performed in different system configurations and using different source target materials are analysed. The results are compared with the classic area ratio method. A good agreement is obtained when the space-energy transient following the source shut-down dies out and when the system sets on a point-like evolution. The results prove the suitability of the proposed method for application to the reactivity monitoring of source-driven systems.

Importance weighting of local flux measurements to improve reactivity predictions in nuclear systems

Abstract The reactivity monitoring is a key aspect for the safe operation of nuclear reactors, especially for subcritical source-driven systems. Various methods are available for both off-line and on-line reactivity determination from direct measurements carried out on the reactor. Usually the methods are based on the inverse point kinetic model applied to signals from neutron detectors and results may be severely affected by spatial and spectral effects. Such effects need to be compensated and correction procedures have to be applied. In this work, a new approach is proposed, by using the full information from different local measurements to generate a global signal through a proper weighting of the signals provided by single neutron detectors. A weighting techique based on the use of the adjoint flux proves to be efficient in improving the prediction capability of inverse techniques. The idea is applied to the recently developed algorithm, named MAρTA, that can be used in both off-line and on-line modes.

A method for the continuous monitoring of reactivity in subcritical source-driven systems

The reactivity monitoring in subcritical accelerator-driven systems is a key aspect for the development of this technology. In this work, an inverse method for the determination of the system reactivity from the analysis of flux and power signals, based on the point kinetic approach, is applied to source-driven systems. The features of the algorithm specific to the application to subcritical assemblies are identified, and the sensitivity to the integral parameters characterizing the system is discussed. The technique is applied to different transient situations, simulated by neutronic codes adopting point kinetics and multigroup diffusion, and its accuracy in the presence of localized spatial and spectral phenomena is assessed. Different approaches for the reduction of the uncertainties introduced by the experimental noise are proposed and compared.

The Langevin Approach to Reactor Noise in Accelerator-Driven Systems

Reactor noise in accelerator-driven systems (ADSs) is different from that in critical or radioactive source-driven subcritical systems because of the periodically pulsed source and its non-Poisson character. In two earlier papers, we developed a theory of ADS reactor noise, incorporating these features. The non-Poisson character of the source does not permit the use of the forward Kolmogorov equation or the Bartlette formula, two commonly used techniques in traditional noise theory. The method used in these papers was a probability-generating function combined with the linear character of the reactor noise in zero-power systems. In this paper we develop the Langevin approach to reactor noise in ADSs. Apart from being simpler, the Langevin approach allows treatment of feedback effects arising in ADSs with significant power as well as other noise sources, if any. We demonstrate that it is possible to obtain the correct expressions for various noise descriptors using this approach. The method is then applied to treat correlated non-Poisson pulsed sources with a finite pulse width including delayed neutrons. The present paper complements and expands our earlier discussions of ADS reactor noise.

Exact-to-precision generalized perturbation theory for source-driven systems

Presented in this manuscript are new developments to perturbation theory which are intended to extend its applicability to estimate, with quantifiable accuracy, the exact variations in all responses calculated by the model with respect to all possible perturbations in the model's input parameters. The new developments place high premium on reducing the associated computational overhead in order to enable the use of perturbation theory in routine reactor design calculations. By way of examples, these developments could be employed in core simulation to accurately estimate the few-group cross-sections variations resulting from perturbations in neutronics and thermal-hydraulics core conditions. These variations are currently being described using a look-up table approach, where thousands of assembly calculations are performed to capture few-group cross-sections variations for the downstream core calculations. Other applications include the efficient evaluation of surrogates for applications that require repeated model runs such as design optimization, inverse studies, uncertainty quantification, and online core monitoring. The theoretical background of these developments applied to source-driven systems and supporting numerical experiments are presented in this manuscript. Extension to eigenvalue problems will be presented in a future article.

Feynman-Alpha and Rossi-Alpha Formulas with Delayed Neutrons for Subcritical Reactors Driven by Pulsed Non-Poisson Sources with Correlation between Different Pulses

Through our earlier papers, we have shown that reactor noise in accelerator-driven systems (ADS) is different from that in critical or radioactive source-driven subcritical systems due to periodically pulsed source and its non-Poisson character. We have developed a theory of reactor noise for ADS, taking into account the non-Poisson character of the source. Various noise descriptors, such as Rossi-alpha, Feynman-alpha (or variance to mean), power spectral density, and cross power spectral density, have been derived for a periodically pulsed source, including correlation between different pulses and finite pulses of different shapes. For mathematical simplicity, the theory was restricted to the case of prompt neutrons only. Recently, we extended the theory to the delayed neutron case and derived Feynman-alpha and Rossi-alpha formulae by considering the source to be a periodically pulsed non-Poisson source, without correlations between different pulses. The present paper extends the treatment to account for the possibility of correlations between pulses. Feynman-alpha and Rossi-alpha formulas are derived by considering the source to be a periodic sequence of delta function non-Poisson pulses, with exponential correlations.

Integral parameters in source-driven systems

Integral parameters can give useful information on the physical properties of a multiplying system. However, various theoretical problems are encountered when trying to introduce them in a consistent way for source-driven systems. Many questions also arise for their experimental estimation. After some general considerations, the paper presents comparisons of numerical results obtained in different approaches and by the application of inverse methods to localized neutron flux signal detections. Results presented refer to the Yalina Booster experimental facility, which constitutes an excellent challenging test for the models and methods, being a neutronically, spatially and spectrally decoupled system. Some considerations on the usefulness of such parameters for kinetic analyses and to qualify the system characteristics are also included in the paper, analyzing both highly and loosely coupled configurations.

Feynman-Alpha and Rossi-Alpha Formulas with Delayed Neutrons for Subcritical Reactors Driven by Pulsed Non-Poisson Sources

In our earlier papers, we developed a theory of reactor noise for accelerator-driven systems (ADSs). It was shown that reactor noise in ADSs is different from that in critical or radioactive source-driven subcritical systems because of the periodically pulsed source and its non-Poisson character. Various noise descriptors, such as Rossi alpha, Feynman alpha (or variance to mean), power spectral density, and cross-power spectral density, were derived, for a periodically pulsed source, including correlation between different pulses and finite pulses of different shapes. Throughout the work we restricted ourselves to the case of prompt neutrons only. In the present paper, we extend the theory to the delayed neutron case. Feynman-alpha and Rossi-alpha formulas are derived by considering the source to be a periodically pulsed non-Poisson source, without correlations between different pulses. Each pulse is assumed to be a delta function. The calculations are carried out in the time domain that leads to closed-form expressions for these descriptors.

Pulsed neutron source measurements in the subcritical ADS experiment YALINA-Booster

A subcritical zero-power source-driven coupled core, the YALINA-Booster, has been constructed for experimental investigations of neutron kinetics of source-driven systems. In this study, the reactivity of two subcritical configurations has been determined by the area ratio method. The prompt neutron decay constants have been evaluated through slope fitting of the prompt neutron decay as well as through the pulsed Rossi-α method. It is shown that the slope fitting method and the pulsed Rossi-α method give stable results whereas the area ratio method results show spatial dependence. The reasons for the spatial spread are addressed.

Comparative assessment of methods for the reactivity measurement in subcritical systems by pulsed experiments

Abstract The determination of the subcriticality level for source-driven systems is an important problem that can be handled by several deterministic methods developed for the interpretation of flux signals in pulsed experiments. The paper compares the performance of several methods for different physical characteristics of the system considered and for different durations of the source pulse. The effects of the subcriticality level and of the experimental uncertainty are also investigated. Furthermore, an analysis of the influence of spatial effects is carried out. The study gives some indications on the most suitable method in a specific experimental configuration pointing out at the situations where non-conservative evaluations of the reactivity can be expected, i.e. when the system effective multiplication constant is underestimated.

Neutronics safety analysis in severe transients of the dual-cooled waste transmutation blanket for the FDS-I

The conceptual design of the fusion-driven subcritical system FDS-I with the multifunctional subcritical dual-cooled waste transmutation (DWT) blanket proposed as a middle step toward the final application of fusion energy was presented previously. Safety is a key concern for the innovative conceptual system. The potential safety characteristic is expected as one of the advantages of FDS-I for the transmutation and incineration of nuclear waste compared with the critical reactor. With the intent of evaluating the inherent and passive safety features of FDS-I, the reactivity coefficients (e.g. the coolant density/void effect and the Doppler feedback), which are similar to those in critical reactors, and the kinetics quantities (e.g. neutron generation time and β eff), which are influenced by the external neutron source of the source-driven system, are calculated and analyzed. In addition, the specific transient scenarios for FDS-I, which show the effects of the source power perturbation on the safety parameters, is presented.

Effects of neutron source characteristics in direct and adjoint problems for subcritical systems

The phase space configuration of the neutron source in a subcritical source-driven system has important effects on its physical behaviour. This paper analyses three important aspects: the role of the time and space dispersion of the source neutrons in the simulation of pulsed experiments; the effect of the source characteristics on significant integral parameters for subcritical systems, such as effective multiplication constant and source multiplication; the effect of the choice of the neutron detector (adjoint source) on the neutron importance and, consequently, on integral parameters such as the neutron effective lifetime. The results presented show the importance of a proper treatment of the source phenomena, which always appear relevant.

Point Genetics: A New Concept to Assess Neutron Kinetics

Point genetic equations are introduced. These equations are similar to the well-known point kinetic equations but characterize and couple individual fission generations in subcritical systems. Point genetic equations are able to describe dynamic behavior of source-driven subcritical systems on shorter timescales than is possible with point kinetic equations. Point genetic parameters can be used as a first-order characterization of the system and can be calculated using standard Monte Carlo techniques; the implementation in other calculational schemes seems straightforward. A Godiva sphere is considered to show the applicability of the point genetic equations in describing a detector response on short timescales. For this system the point genetic parameters are calculated and compared with reference calculations. Typical dynamic source behavior is considered by studying a transient in which the neutron source energy decreases from 20 to 1 MeV. For all cases studied, the point genetic equations are compared to full space-time kinetic solutions, and it is shown that point genetics performs well.

Some Features of Spatial Neutron Kinetics for Multiplying Systems

The paper considers some physical aspects of the neutron space kinetics of critical and source-driven subcritical systems. The possibility of introducing some indicators to qualify the spatial nature of neutronic transients is investigated. It is shown theoretically and then proved by numerical examples that the separation of the eigenvalues of the mathematical operator defining the problem can be taken as a good indicator of the importance of space effects in time-dependent conditions. To obtain good physical insight into the phenomena, paradigmatically simple configurations are considered, and whenever possible, a fully analytical approach is used. The presented results evidence the limits of applicability of classic simplified models for transient analyses, such as point kinetics. In a second part, the paper considers the open problem of the choice of the weighting function to be used either for the generation of the kinetic parameters of pointlike models or for the exploitation of quasi-static procedures, analyzing comparatively the effect of different options on the results of transient calculations.

Application of the Multipoint Method to the Kinetics of Accelerator-Driven Systems

The mathematical foundations of the multipoint method are illustrated and the method is developed for the neutron kinetics of multiplying systems to treat physical situations in which spatial and spectral effects can play an important role in transient conditions, and hence the classical point-kinetic model can become inadequate. In the present paper the method is specifically developed for source-driven systems, through a proper adaptation of the factorization-projection technique used to derive other classic kinetic models. The results presented for some test cases show the advantages that can be attained with respect to the standard point model, even when treating relevant spatial and spectral transients. It is then shown how the technique can be inserted into a quasi-static framework.