Benchmarking the invariant embedding method against analytical solutions in model transport problems

The purpose of this paper is to demonstrate the use of the invariant embedding method in a few model transport problems for which it is also possible to obtain an analytical solution. The use of the method is demonstrated in three different areas. The first is the calculation of the energy spectrum of sputtered particles from a scattering medium without absorption, where the multiplication (particle cascade) is generated by recoil production. Both constant and energy dependent cross-sections with a power law dependence were treated. The second application concerns the calculation of the path length distribution of reflected particles from a medium without multiplication. This is a relatively novel application, since the embedding equations do not resolve the depth variable. The third application concerns the demonstration that solutions in an infinite medium and in a half-space are interrelated through embedding-like integral equations, by the solution of which the flux reflected from a half-space can be reconstructed from solutions in an infinite medium or vice versa. In all cases, the invariant embedding method proved to be robust, fast, and monotonically converging to the exact solutions

Diagnóstico de las vibraciones del barrilete y de los elementos combustibles en los PWRs de Ringhals, Suecia

El diagnóstico de las estructuras internas de los PWR, en particular del barrilete del núcleo y su soporte se pueden realizar por medio del análisis de las señales de los detectores de neutrones extra-nucleares. Se han elaborado varios procedimientos que se han usado en diversas plantas en todo el mundo [1], [2]. El objetivo es la vigilancia de la integridad de la estructura del núcleo y la detección temprana y la cuantificación de signos de fatiga, desgaste, etc en las diferentes estructuras tales como el muelle, la placa de sujeción del barrilete del núcleo, etc. Esta vigilancia se ha venido realizando en las tres unidades PWR 2, 3 y 4 de la central sueca de Ringhals desde 1970. Durante las últimas dos décadas el trabajo se ha llevado a cabo en el contexto de un contrato de colaboración entre la Universidad de Chalmers y Ringhals. Esta actividad de colaboración ha consistido tanto en el desarrollo de nuevos métodos, la mejora de éstos así como su aplicación continuada para diagnóstico, vigilancia, incluyendo un análisis de tendencia a lo largo del tiempo. Este trabajo describe el desarrollo realizado en los últimos años con un énfasis especial en los tres últimos

Energy Correlation of Prompt Fission Neutrons

In all cases where neutron fluctuations in a branching process (such as in multiplicity measurements) are treated in an energy dependent description, the energy correlations of the branching itself (energy correlations of the fission neutrons) need to be known. To date, these are not known from experiments. Such correlations can be theoretically and numerically derived by modelling the details of the fission process. It was suggested earlier that the fact that the prompt neutrons are emitted from the moving fission targets, will influence their energy and angular distributions in the lab system, which possibly induces correlations. In this paper the influence of the neutron emission process from the moving targets on the energy correlations is investigated analytically and via numerical simulations. It is shown that the correlations are generated by the random energy and direction distributions of the fission fragments. Analytical formulas are derived for the two-point energy distributions, and quantitative results are obtained by Monte-Carlo simulations. The results lend insight into the character of the two-point distributions, and give quantitative estimates of the energy correlations, which are generally small

Two-Group Theory of the Feynman-Alpha Method for Reactivity Measurement in ADS

The theory of the Feynman-alpha method, which is used to determine the subcritical reactivity of systems driven by an external source such as an ADS, is extended to two energy groups with the inclusion of delayed neutrons. This paper presents a full derivation of the variance to mean formula with the inclusion of two energy groups and delayed neutrons. The results are illustrated quantitatively and discussed in physical terms

Comments on the stochastic characteristics of fission chamber signals

This paper reports on theoretical investigations of the stochastic properties of the signal series of ionisation chambers, in particular fission chambers. First, a simple and transparent derivation is given of the higher order moments of the random detector signal for incoming pulses with a non homogeneous Poisson distribution and random pulse heights and arbitrary shape. Exact relationships are derived for the higher order moments of the detector signal, which constitute a generalisation of the so-called higher order Campbelling techniques. The probability distribution of the number of time points when the signal exceeds a certain level is also derived. Then, a few simple pulse shapes and amplitude distributions are selected as idealised models of the detector signals. Assuming that the incoming particles form a homogeneous Poisson process, explicit expressions are given for the higher order moments of the signal and the number of level crossings in a given time interval for the selected pulse shapes

Qualitative and quantitative investigation of the propagation noise in various reactor systems

The space-dependent neutron noise, induced by propagating perturbations (propagation noise for short) is investigated in a one-dimensional homogeneous model of various reactor systems. By using two-group theory, the noise in both the fast and the thermal group is calculated. The purpose is to investigate the dependence of the properties of the space-dependent fast and thermal propagation noise on the static neutron spectrum as well as on the presence of the fluctuations of several cross sections. The motivation for this study arose in connection with recent work on neutron noise in molten salt reactors (MSR) with propagating fuel of various compositions. Some new features of the induced noise were observed, but it was not clear whether these were due to the propagating perturbation alone, or to the propagation of the fuel and hence that of the delayed neutron precursors. The present study serves to clarify the significance of the spectral properties of the different cores through calculating the propagation noise in four different reactor systems, as well as considering the influence of the perturbation of the various cross sections. By comparing the results with those obtained in MSR, the effect of the moving fuel on the propagation noise is clarified. It is shown that in fast systems the noise in the fast group is much larger than in the thermal group and hence can gain diagnostic importance. It is also shown that the coexistence of several cross section fluctuations leads to qualitatively and quantitatively new characteristics of the noise, hence it is important to model the effect of e.g. temperature fluctuations of the coolant in a proper way. (C) 2013 Elsevier Ltd. All rights reserved

A time and frequency domain analysis of the effect of vibrating fuel assemblies on the neutron noise

[EN] The mechanical vibrations of fuel assemblies have been shown to give rise to high levels of neutron noise, triggering in some circumstances the necessity to operate nuclear reactors at a reduced power level. This work analyses the effect in the neutron field of the oscillation of one single fuel assembly. Results show two different effects in the neutron field caused by the fuel assembly vibration. First, a global slow variation of the total reactor power due to a change in the criticality of the system. Second, an oscillation in the neutron flux in-phase with the assembly vibration. This second effect has a strong spatial dependence that can be used to localize the oscillating assembly. This paper shows a comparison between a time-domain and a frequency-domain analysis of the phenomena to calculate the spatial response of the neutron noise. Numerical results show a really close agreement between these two approaches.This project has received funding from the Euratom research and training programme 2014-2018 under grant agreement No 754316. Also, this work has been partially supported by Spanish Ministerio de Economia y Competitividad under project BES-2015-072901 and financed with the help of a Primeros Proyectos de Investigation (PAID-06-18), Vicerrectorado de Investigacitin, Innovation y Transferencia of the Universitat Politecnica de Valencia (UPV).Vidal-Ferràndiz, A.; Carreño, A.; Ginestar Peiro, D.; Demazière, C.; Verdú Martín, GJ. (2020). A time and frequency domain analysis of the effect of vibrating fuel assemblies on the neutron noise. Annals of Nuclear Energy. 137:1-12. https://doi.org/10.1016/j.anucene.2019.107076S112137Akcasu, Z. (1958). General Solution of the Reactor Kinetic Equations without Feedback. Nuclear Science and Engineering, 3(4), 456-467. doi:10.13182/nse58-a25482Antonopoulos-Domis, M. (1976). Reactivity and neutron density noise excited by random rod vibration. Annals of Nuclear Energy, 3(9-10), 451-459. doi:10.1016/0306-4549(76)90030-xDemaziere, C. (2006). Analysis methods for the determination of possible unseated fuel assemblies in BWRs. International Journal of Nuclear Energy Science and Technology, 2(3), 167. doi:10.1504/ijnest.2006.010713Demazière, C. (2011). CORE SIM: A multi-purpose neutronic tool for research and education. Annals of Nuclear Energy, 38(12), 2698-2718. doi:10.1016/j.anucene.2011.06.010Demazière, C., & Andhill, G. (2005). Identification and localization of absorbers of variable strength in nuclear reactors. Annals of Nuclear Energy, 32(8), 812-842. doi:10.1016/j.anucene.2004.12.011Demazière, C., Dykin, V., & Jareteg, K. (2017). Development of a point-kinetic verification scheme for nuclear reactor applications. Journal of Computational Physics, 339, 396-411. doi:10.1016/j.jcp.2017.03.020Demazière, C., & Pázsit, I. (2009). Numerical tools applied to power reactor noise analysis. Progress in Nuclear Energy, 51(1), 67-81. doi:10.1016/j.pnucene.2008.01.010Ginestar, D., Verdú, G., Vidal, V., Bru, R., Marín, J., & Muñoz-Cobo, J. L. (1998). High order backward discretization of the neutron diffusion equation. Annals of Nuclear Energy, 25(1-3), 47-64. doi:10.1016/s0306-4549(97)00046-7Hébert, A. (1985). Application of the Hermite Method for Finite Element Reactor Calculations. Nuclear Science and Engineering, 91(1), 34-58. doi:10.13182/nse85-a17127Jonsson, A., Tran, H. N., Dykin, V., & Pázsit, I. (2012). Analytical investigation of the properties of the neutron noise induced by vibrating absorber and fuel rods. Kerntechnik, 77(5), 371-380. doi:10.3139/124.110258Kronbichler, M., & Kormann, K. (2012). A generic interface for parallel cell-based finite element operator application. Computers & Fluids, 63, 135-147. doi:10.1016/j.compfluid.2012.04.012Larsson, V., & Demazière, C. (2009). Comparative study of 2-group and diffusion theories for the calculation of the neutron noise in 1D 2-region systems. Annals of Nuclear Energy, 36(10), 1574-1587. doi:10.1016/j.anucene.2009.07.009Olmo-Juan, N., Demazière, C., Barrachina, T., Miró, R., & Verdú, G. (2019). PARCS vs CORE SIM neutron noise simulations. Progress in Nuclear Energy, 115, 169-180. doi:10.1016/j.pnucene.2019.03.041Park, J., Lee, J. H., Kim, T.-R., Park, J.-B., Lee, S. K., & Koo, I.-S. (2003). Identification of reactor internals’ vibration modes of a Korean standard PWR using structural modeling and neutron noise analysis. Progress in Nuclear Energy, 43(1-4), 177-186. doi:10.1016/s0149-1970(03)00021-0Pázsit, I. (1988). Control-rod models and vibration induced noise. Annals of Nuclear Energy, 15(7), 333-346. doi:10.1016/0306-4549(88)90081-3Pázsit, I., & Th.Analytis, G. (1980). Theoretical investigation of the neutron noise diagnostics of two-dimensional control rod vibrations in a PWR. Annals of Nuclear Energy, 7(3), 171-183. doi:10.1016/0306-4549(80)90082-1Pázsit, I., & Glöckler, O. (1983). On the Neutron Noise Diagnostics of Pressurized Water Reactor Control Rod Vibrations. I. Periodic Vibrations. Nuclear Science and Engineering, 85(2), 167-177. doi:10.13182/nse83-a27424Ravetto, P. (1997). Reactivity oscillations in a point reactor. Annals of Nuclear Energy, 24(4), 303-314. doi:10.1016/s0306-4549(96)00066-7Sunde, C., Demazière, C., & Pázsit, I. (2006). Calculation of the Neutron Noise Induced by Shell-Mode Core-Barrel Vibrations in a 1-D, Two-Group, Two-Region Slab Reactor Model. Nuclear Technology, 154(2), 129-141. doi:10.13182/nt06-1Tran, H.-N., Pázsit, I., & Nylén, H. (2015). Investigation of the ex-core noise induced by fuel assembly vibrations in the Ringhals-3 PWR. Annals of Nuclear Energy, 80, 434-446. doi:10.1016/j.anucene.2015.01.045Vidal-Ferràndiz, A., Carreño, A., Ginestar, D., & Verdú, G. (2019). A Block Arnoldi Method for the SPN Equations. International Journal of Computer Mathematics, 1-22. doi:10.1080/00207160.2019.1602768Vidal-Ferrandiz, A., Fayez, R., Ginestar, D., & Verdú, G. (2014). Solution of the Lambda modes problem of a nuclear power reactor using an h–p finite element method. Annals of Nuclear Energy, 72, 338-349. doi:10.1016/j.anucene.2014.05.026Vidal-Ferràndiz, A., Fayez, R., Ginestar, D., & Verdú, G. (2016). Moving meshes to solve the time-dependent neutron diffusion equation in hexagonal geometry. Journal of Computational and Applied Mathematics, 291, 197-208. doi:10.1016/j.cam.2015.03.040Viebach, M., Bernt, N., Lange, C., Hennig, D., & Hurtado, A. (2018). On the influence of dynamical fuel assembly deflections on the neutron noise level. Progress in Nuclear Energy, 104, 32-46. doi:10.1016/j.pnucene.2017.08.010Weinberg, A. M., & Schweinler, H. C. (1948). Theory of Oscillating Absorber in a Chain Reactor. Physical Review, 74(8), 851-863. doi:10.1103/physrev.74.85

Börtönzsúfoltság kontra nemzetállamok

The authors provide an overview of prison overcrowding in Europe, and the European Court of Human Right’s jurisprudence in the field.A szerzők áttekintést nyújtanak a börtönök túlzsúfoltságáról Európában, valamint az Emberi Jogok Európai Bíróságának ezen a területen folytatott ítélkezési gyakorlatáról

Two-point theory for the differential self-interrogation Feynman-alpha method

A Feynman-alpha formula has been derived in a two region domain pertaining the stochastic differential self-interrogation (DDSI) method and the differential die-away method (DDAA). Monte Carlo simulations have been used to assess the applicability of the variance to mean through determination of the physical reaction intensities of the physical processes in the two domains. More specifically, the branching processes of the neutrons in the two regions are described by the Chapman - Kolmogorov equation, including all reaction intensities for the various processes, that is used to derive a variance to mean relation for the process. The applicability of the Feynman-alpha or variance to mean formulae are assessed in DDSI and DDAA of spent fuel configurations.Comment: 15 pages, 5 figures. Submitted to EPJ Plu

The neutron-gamma Feynman variance to mean approach: gamma detection and total neutron-gamma detection (theory and practice)

Two versions of the neutron-gamma variance to mean (Feynman-alpha method or Feynman-Y function) formula for either gamma detection only or total neutron-gamma detection, respectively, are derived and compared in this paper. The new formulas have a particular importance for detectors of either gamma photons or detectors sensitive to both neutron and gamma radiation. If applied to a plastic or liquid scintillation detector, the total neutron-gamma detection Feynman-Y expression corresponds to a situation where no discrimination is made between neutrons and gamma particles. The gamma variance to mean formulas are useful when a detector of only gamma radiation is used or when working with a combined neutron-gamma detector at high count rates. The theoretical derivation is based on the Chapman-Kolmogorov equation with inclusion of general reactions and passage intensities for neutrons and gammas, but with the inclusion of prompt reactions only. A one energy group approximation is considered. The comparison of the two different theories is made by using reaction intensities obtained in MCNPX simulations with a simplified geometry for two scintillation detectors and a 252Cf-source enclosed in a steel container. In addition, the variance to mean ratios, neutron, gamma and total neutron-gamma, are evaluated experimentally for a weak 252Cf neutron-gamma source in a steel container, a 137Cs random gamma source and a 22Na correlated gamma source. Due to the focus being on the possibility of using neutron-gamma variance to mean theories for both reactor and safeguards applications, we limited the present study to the general analytical expressions for Feynman-Y formulas