| 1. |
- al-Dbissi, Moad, 1994, et al.
(författare)
-
Conceptual design and initial evaluation of a neutron flux gradient detector
- 2022
-
Ingår i: Nuclear Instruments and Methods in Physics Research, Section A: Accelerators, Spectrometers, Detectors and Associated Equipment. - : Elsevier BV. - 0168-9002. ; 1026
-
Tidskriftsartikel (refereegranskat)abstract
- Identification of the position of a localized neutron source, or that of local inhomogeneities in a multiplying or scattering medium (such as the presence of small, strong absorbers) is possible by measurement of the neutron flux in several spatial points, and applying an unfolding procedure. It was suggested earlier, and it was confirmed by both simulations and pilot measurements, that if, in addition to the usually measured scalar (angularly integrated) flux, the neutron current vector or its diffusion approximation (the flux gradient vector) is also considered, the efficiency and accuracy of the unfolding procedure is significantly enhanced. Therefore, in support of a recently started project, whose goal is to detect missing (replaced) fuel pins in a spent fuel assembly by non-intrusive methods, this idea is followed up. The development and use of a dedicated neutron detector for within-assembly measurements of the neutron scalar flux and its gradient are planned. The detector design is based on four small, fiber-mounted scintillation detector tips, arranged in a rectangular pattern. Such a detector is capable of measuring the two Cartesian components of the flux gradient vector in the horizontal plane. This paper presents an initial evaluation of the detector design, through Monte Carlo simulations in a hypothetical scenario.
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| 2. |
- al-Dbissi, Moad, 1994, et al.
(författare)
-
Identification of diversions in spent PWR fuel assemblies by PDET signatures using Artificial Neural Networks (ANNs)
- 2023
-
Ingår i: Annals of Nuclear Energy. - 0306-4549 .- 1873-2100. ; 193
-
Tidskriftsartikel (refereegranskat)abstract
- Spent nuclear fuel represents the majority of materials placed under nuclear safeguards today and it requires to be inspected and verified regularly to promptly detect any illegal diversion. Research is ongoing both on the development of non-destructive assay instruments and methods for data analysis in order to enhance the verification accuracy and reduce the inspection time. In this paper, two models based on Artificial Neural Networks (ANNs) are studied to process measurements from the Partial Defect Tester (PDET) in spent fuel assemblies of Pressurized Water Reactors (PWRs), and thus to identify at different levels of detail whether nuclear fuel has been replaced with dummy pins or not. The first model provides an estimation of the percentage of replaced fuel pins within the inspected fuel assembly, while the second model determines the exact configuration of the replaced fuel pins. The two models are trained and tested using a dataset of Monte-Carlo simulated PDET responses for intact spent PWR fuel assemblies and a variety of hypothetical diversion scenarios. The first model classifies fuel assemblies according to the percentage of diverted fuel with a high accuracy (96.5%). The second model reconstructs the correct configuration for 57.5% of the fuel assemblies available in the dataset and still retrieves meaningful information of the diversion pattern in many of the misclassified cases.
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| 3. |
- al-Dbissi, Moad, 1994, et al.
(författare)
-
On the use of neutron flux gradient with ANNs for the detection of diverted spent nuclear fuel
- 2024
-
Ingår i: Annals of Nuclear Energy. - 0306-4549 .- 1873-2100. ; 204
-
Tidskriftsartikel (refereegranskat)abstract
- One of the main tasks in nuclear safeguards is regular inspections of Spent Nuclear Fuel (SNF) assemblies to detect possible diversions of special nuclear material such as 235U and 239Pu. In these inspections, characteristic signatures of SNF such as emissions of neutrons and gamma rays from the radioactive decay, are measured and their consistency with the declared assemblies is verified to ensure that no fuel pins have been removed. Research in this field is focused on both the development of detection equipment and methods for the analysis of the acquired measurement data. In this paper, the use of the neutron flux gradient, which is not considered in regular SNF verification, is investigated in combination with the scalar neutron flux as input to artificial neural network models for the quantification of fuel pins in SNF assemblies. The training and testing of these ANN models rely on a synthetic dataset that is generated from Monte Carlo simulations of a typical intact pressurized water reactor assembly and with different patterns of fuel pins replaced by dummy pins. The dataset consists of unique scenarios so that the ANN can be assessed over “unknown” cases that are not part of the learning phase. Results show that the neutron flux gradient is advantageous for a more accurate reconstruction of diversions within SNF assemblies.
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| 4. |
- Anderson, Johan, 1973, et al.
(författare)
-
Derivation and quantitative analysis of the differential self-interrogation Feynman-alpha method
- 2012
-
Ingår i: European Physical Journal Plus. - : Springer Science and Business Media LLC. - 2190-5444. ; 127:2, s. 1-6
-
Tidskriftsartikel (refereegranskat)abstract
- A stochastic theory for a branching process in a neutron population with two energy levels is used to assess the applicability of the differential self-interrogation Feynman-alpha method by numerically estimated reaction intensities from Monte Carlo simulations. More specifically, the variance to mean or Feynman-alpha formula is applied to investigate the appearing exponentials using the numerically obtained reaction intensities.
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| 5. |
- Anderson, Johan, 1973, et al.
(författare)
-
Derivation and quantitative analysis of the differential self-interrogation Feynman-alpha method
- 2011
-
Ingår i: Proceedings 52nd INMM Conference 17-21 July, Palm Desert, CA, USA (2011).
-
Konferensbidrag (refereegranskat)abstract
- A stochastic theory for a branching process in a neutronpopulation with two energy levels is used to assess theapplicability of the differential self-interrogation Feynman-alpha method by numerically estimated reaction intensities from Monte Carlo simulations. More specifically, the variance to mean or Feynman-alpha formula is applied to investigate the appearing exponentials using the numerically obtained reaction intensities.
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| 6. |
- Anderson, Johan, 1973, et al.
(författare)
-
On the Feynman-alpha formula for fast neutrons
- 2011
-
Ingår i: Proceedings 33rd ESARDA 16-20 May, Budapest, Hungary (2011).
-
Konferensbidrag (refereegranskat)abstract
- In this contribution, a stochastic theory for a branching process in a neutron population with two energy levels is investigated. In particular, a variance to mean or Feynman-alpha formula is derived in this generalized scenario using the Kolmogorov forward or master equation theory for the probabilities in a system with a compound Poisson source.
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| 7. |
- Anderson, Johan, 1973, et al.
(författare)
-
Two-point theory for the differential self-interrogation Feynman-alpha method
- 2012
-
Ingår i: European Physical Journal Plus. - : Springer Science and Business Media LLC. - 2190-5444. ; 127:8, s. 1-9
-
Tidskriftsartikel (refereegranskat)abstract
- 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.
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| 8. |
- Andersson, Tell, et al.
(författare)
-
Development and application of core diagnostics and monitoring for the Ringhals PWRs
- 2003
-
Ingår i: Progress in Nuclear Energy. - 0149-1970. ; 43:1-4, s. 35-41
-
Tidskriftsartikel (refereegranskat)abstract
- Noise analysis and reactor diagnostics have been applied at the Ringhals PWRs for a long time. Through a collaboration with the Department of Reactor Physics, Chalmers University of Technology, methods for treating new problems were elaborated, and known methods were developed further to make them more effective or to suit specific applications. All these methods were tested in real measurements, and many of them have been used routinely afterwards. In this paper two particular new methods are described in detail: 1) the determination of the axial position of control rods from the axial shape of the neutron flux with neural network methods, and 2) the use of gamma thermometers for the determination of the MTC and for core flow estimation.
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| 9. |
- Avdic, Senada, et al.
(författare)
-
Item identification with a space-dependent model of neutron multiplicities and artificial neural networks
- 2023
-
Ingår i: Nuclear Instruments and Methods in Physics Research, Section A: Accelerators, Spectrometers, Detectors and Associated Equipment. - 0168-9002. ; 1057
-
Tidskriftsartikel (refereegranskat)abstract
- A method of calculating the neutron multiplicity rates (singles, doubles and triples rates), based on transport theory, was developed by us recently. The model treats the full 3-D spatial transport and multiplication of neutrons, accounting also for the shape of the item and the spatial distribution of the source, in one-speed theory. For a given item and its source distribution, the model can predict the multiplicity rates more precisely than the point model, on which traditional neutron multiplicity counting is based. However, so far it has not been investigated how the enhanced accuracy of the calculated multiplicity rates (i.e. the solution of the direct task) can be used to estimate the parameters of interest of the measurement item, primarily the fission rate (the solution of the inverse task). Unlike for the point model, the multiplicity rates under the extended scheme can only be given numerically, as solutions of integral transport equations, and hence an analytical inversion of the formulae is not possible. In this work it is investigated how machine learning methods, primarily the use of artificial neural networks, which only need numerical values of the solution of the direct task (the multiplicity rates), can be used for this purpose. It is shown that for numerical test items containing a mixture of 239Pu and 240Pu, the fraction of the latter varying between 4% and 25%, one can extract the masses of both isotopes from a properly trained network.
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| 10. |
- Avdic, Senada, et al.
(författare)
-
Unfolding sample parameters from neutron and gamma multiplicities using artificial neural networks.
- 2009
-
Ingår i: ESARDA Bulletin. - 0392-3029. ; :43, s. 21-29
-
Tidskriftsartikel (refereegranskat)abstract
- Expressions for neutron and gamma factorial momentshave been known in the literature. The neutronfactorial moments have served as the basis of constructinganalytic expressions for the detection ratesof singles, doubles and triples, which can be used tounfold sample parameters from the measured neutronmultiplicity rates. The gamma factorial momentscan also be extended into detection rates of multiplets,as well as the combined use of joint neutronand gamma multiplicities and the corresponding detectionrates. Counting up to third order, there arenine auto- and cross factorial moments.Adding the gamma counting to the neutrons introducesnew unknowns, related to gamma generation,leakage, and detection. Despite of having more unknowns,the total number of independent measurablemoments exceeds the number of unknowns. On theother hand, the structure of the additional equationsis substantially more complicated than that of theneutron moments, hence the analytical inversion ofthe gamma moments alone is not possible.We suggest therefore to invert the non-linear systemof over-determined equations by using artificialneural networks (ANN), which can handle both thenon-linearity and the redundancies in the measuredquantities in an effective and accurate way. The useof ANN is successfully demonstrated on the unfoldingof neutron multiplicity rates for the sample fissionrate, the leakage multiplication and the ratio.The analysis is further extended to unfold also thegamma related parameters. The stability and robustnessof the ANNs is further investigated to verify theapplicability of the method. The ANN approach enablesextraction of additional important informationon the fissile sample compared to the application ofthe analytical method.
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| 11. |
- Baeten, P., et al.
(författare)
-
Determination of the subcriticality level using the Cf-252 source-detector method
- 2010
-
Ingår i: Annals of Nuclear Energy. - : Elsevier BV. - 0306-4549 .- 1873-2100. ; 37:5, s. 740-752
-
Tidskriftsartikel (refereegranskat)abstract
- Measurement and monitoring of reactivity in a subcritical state, e.g. during the loading of a power reactor, has a clear safety relevance. The methods currently available for the measurement of k(eff) in stationary subcritical conditions should be improved as they refer to the critical state. This is also very important in the framework of ADS (accelerator driven systems) where the measurement of a subcritical level without knowledge of the critical state is looked for. An alternative way to achieve this is by mean of the Cf-252 source-detector method. The method makes use of three detectors inserted in the reactor: two "ordinary" neutron detectors and one Cf-252 source-detector which contains a small amount of Cf-252 that introduces neutrons in the system through spontaneous fission. By observing fissions through the detection system and correlating the signals of the three detectors, the reactivity rho (and hence the multiplication factor k) can be determined. Before the actual measurements took place, a suitable data acquisition system was realized in order to process the signals and compute the auto and cross power spectral densities. The measurements were then performed in the VENUS reactor, using the Cf-252 source-detector and two BF3 neutron detectors. The multiplication factor was determined using the Cf source method and compared with measurements using other methods and with computational results (Monte Carlo simulations). The Cf method was benchmarked at a UOX core to other experimental methods that used the critical state as reference and to calculations. Afterwards, the Cf source technique was analyzed in a MOX core to study the possible impact of a significant intrinsic source on the results. This benchmarking gives the possibility to validate the Cf method as a reliable technique for the measurement of subcritical levels in steady state and for cores with an intrinsic source like MOX or burnt fuel cores. (C) 2010 Elsevier Ltd. All rights reserved.
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| 12. |
- Chernikova, Dina, 1982, et al.
(författare)
-
A direct method for evaluating the concentration of boric acid in a fuel pool using scintillation detectors for joint-multiplicity measurements
- 2013
-
Ingår i: Nuclear Instruments and Methods in Physics Research, Section A: Accelerators, Spectrometers, Detectors and Associated Equipment. - : Elsevier BV. - 0168-9002. ; 714, s. 90-97
-
Tidskriftsartikel (refereegranskat)abstract
- The present investigations are aimed at the development of a direct passive non-intrusive method for determining the concentration of boric acid in a spent fuel pool using scintillation detectors with the purpose of correcting joint-multiplicity measurement results. The method utilizes a modified relation between two gamma lines with energy of 480 keV and 2.23 MeV, respectively. The gamma line at 480 keV belongs to the thermal neutron capture in boron. The 2.23 MeV gamma line characterizes the capture of thermal neutrons in hydrogen. Thus, the relation between them can reveal the concentration of the boron in the fuel pool. In order to test this method, first MCNPX and MCNP-PoliMi simulations were performed. Then, based on the results of Monte Carlo simulations, the method was verified by an experimental study with a 241Am-Be source and EJ-309 scintillation detectors. The concentration of boron in water varied from 1550 ppm to 4000 ppm. The results of these tests are provided in the paper and they show that the spectral ratio between these two lines can in principle be used to determine the boron content.
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| 13. |
- Chernikova, Dina, 1982, et al.
(författare)
-
A general analytical solution for the variance-to-mean Feynman-alpha formulas for a two-group two-point, a two-group one-point and a one-group two-point cases
- 2014
-
Ingår i: European Physical Journal Plus. - : Springer Science and Business Media LLC. - 2190-5444. ; 129:11, s. Art. no. 259-
-
Tidskriftsartikel (refereegranskat)abstract
- This paper presents a full derivation of the variance-to-mean or Feynman-alpha formula in a two-energy-group and two-spatial-region treatment. The derivation is based on the Chapman-Kolmogorov equation with the inclusion of all possible neutron reactions and passage intensities between the two regions. In addition, the two-group one-region and the two-region one-group Feynman-alpha formulas, treated earlier in the literature for special cases, are extended for further types and positions of detectors. We focus on the possibility of using these theories for accelerator-driven systems and applications in the safeguards domain, such as the differential self-interrogation method and the differential die-away method. This is due to the fact that the predictions from the models which are currently used do not fully describe all the effects in the heavily reflected fast or thermal systems. Therefore, in conclusion, a comparative study of the two-group two-region, the two-group one-region, the one-group two-region and the one-group one-region Feynman-alpha models is discussed.
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| 14. |
- Chernikova, Dina, 1982, et al.
(författare)
-
Application of the two-group - one-region and two-region - one-group Feynman-alpha formulas in safeguards and accelerator-driven system (ADS)
- 2013
-
Ingår i: Proceeding of ESARDA meeting 2013.
-
Konferensbidrag (refereegranskat)abstract
- The applicability of the two-group (one-region) and two-region (one-group) Feynman-alpha (variance to mean) formulas was assessed with regards to applications in safeguards and accelerator-driven system (ADS) considered as an option for transmutation of nuclear wastes. Since two-group calculations with the master equation technique when both thermal and fast fissions are included, have not been performed earlier, investigation of this problem has a methodological value of its own. The potential applications of the two-group - one-region and two-region - one-group Feynman-alpha approaches in nuclear safeguards were evaluated and compared to the results of Monte-Carlo simulations.
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| 15. |
- Chernikova, Dina, 1982, et al.
(författare)
-
Derivation of two-group two-region Feynman-alpha formulas and their application to Safeguards and accelerator-driven system (ADS)
- 2013
-
Ingår i: Proceeding of INMM 54th Annual Meeting.
-
Konferensbidrag (refereegranskat)abstract
- The theory of the Feynman-alpha method was extended to two-energy groups and two-regions by the use of the Chapman - Kolmogorov equation with complete description of various processes including all reaction intensities for neutrons. This paper presents a full derivation of the variance to mean formula with the forward approach, as well as quantitative evaluation of the formula with regards to applications in safeguards and accelerator-driven system. The quantitative assessment was made through MCNPX and MCNP-PoliMi simulations. The motivation for this work is related to the fact that the traditional one-group (and one-region) variance to mean formula was elaborated and used for thermal systems in which the thermal flux and the lifetime of thermal neutrons dominates. However, this approach does not fully describe the fast neutron systems, as well as heavily reflected thermal systems, since the effects of the reflector play a significant role in the latter. Thus, a two-group two-point master equation approach might lend the possibility of treating a fast multiplying material surrounded with a reflector in a more accurate way, by treating the counts separately in the fast and the thermal groups (or in the fissile and reflector regions). Investigation of this problem has a methodological value of its own since, for example, two-group calculations with the master equationtechnique when both thermal and fast fissions are included, have not been performed earlier.
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| 16. |
- Chernikova, Dina, 1982, et al.
(författare)
-
Testing a direct method for evaluating the concentration of boron in a fuel pool using scintillation detectors, and a 252Cf and an 241Am-Be source
- 2013
-
Ingår i: Proceeding of ESARDA meeting 2013.
-
Konferensbidrag (refereegranskat)abstract
- The present investigations are aimed at the development and testing of a direct non-destructive method for evaluating the concentration of boron in a fuel pool using scintillation detectors. The method uses a modified ratio between two gamma lines with energy of 480 keV and 2.23 MeV. These lines belong to the capture of a thermal neutron in boron and hydrogen, respectively. The relation between them can reveal the concentration of boron in the fuel pond.The method proposed was tested in a laboratory experiment with a 252Cf and an 241Am-Be source. EJ-309 liquid scintillation detectors were used for measurements of gamma spectra. The concentration of boron in water varied from 1550 ppm to 4200 ppm. The optimization and test studies were performed via MCNPX simulations.The results of these tests are provided in the present paper and they show that the boron content in water can be determined through using the characteristics of gamma lines with energy of 480 keV and 2.23 MeV.
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| 17. |
- Chernikova, Dina, 1982, et al.
(författare)
-
Testing of small detectors with glass rod light guides for multiplicity measurement purposes
- 2012
-
Ingår i: Proceedings of The 53nd Annual Meeting of the Institute of Nuclear Materials Management.
-
Konferensbidrag (övrigt vetenskapligt/konstnärligt)abstract
- In this paper we investigate the applicability of small scintillators with glass rod lightguides to measure both neutrons and gamma rays from the sample. Experimental test ofthese detectors and their suitability for the task can be performed at Lund University usingnatural uranium rods, therefore the MCNPX simulation set-up corresponds to the Lund con-figuration. The long-term goal of this research is to develop a method of joint-multiplicitycounting for fuel evaluation into a technology capable of quantifying plutonium in the fuelpool, where a lot of factors, such as presence of neutron absorbers (boron acid), can affect al-most all parameters, such as multiplication etc. Therefore, part of the present investigationswas devoted to the development of a direct method for determination of the concentrationof boron acid in the fuel pool using scintillation detectors with further correction of mea-surement results. For this purpose we suggest a method which utilizes a relation betweengamma lines with energy of 480 keV and 2.23 MeV for the direct evaluation of concentrationof boron acid in water. Test results of the new method, and an answer to questions regardingthe ability to measure both neutron and gamma rays using small scintillation detectors withglass rod light guides are provided in this paper.
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| 18. |
- Chernikova, Dina, 1982, et al.
(författare)
-
The effect of capture gammas, photofission and photonuclear neutrons to the neutron-gamma Feynman variance-to-mean ratios (neutron, gamma and total)
- 2015
-
Ingår i: Mathematics and Computations, Supercomputing in Nuclear Applications and Monte Carlo International Conference, M and C+SNA+MC 2015, Nashville, United States, 19-23 April 2015. - 9781510808041 ; 2, s. 1040-1051
-
Konferensbidrag (refereegranskat)abstract
- Two versions of the neutron-gamma variance-to-mean (Feynman-alpha) formula for separate gamma detection and total neutron-gamma detection were recently derived and evaluated by Chernikova, et. al. [1]. However, the neutrons and gammas emitted in a photofission reaction or the release of gammas in certain thermal neutron capture reactions were not included in the theoretical models of Chernikova, et. al. [1]. In this paper, in order to evaluate the influence of these type of reactions to the values the neutron-gamma Feynman variance-to-mean ratios (neutron, gamma and total), we derive the enhanced Feynman-alpha formulae for separate neutron, gamma detection and total neutron-gamma detections. The theoretical derivation is based on the Chapman-Kolmogorov equation with inclusion of general reactions, photofission and capture gammas. The quantitative evaluation of the effect of capture gammas and photonuclear neutrons to the neutron-gamma Feynman variance-to-mean ratios (neutron, gamma and total) is done by using reaction intensities obtained from MCNPX simulations. The new enhanced formulas and their impact to the final values of different variance-to-mean ratios are the main subject of the discussion in the present paper.
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| 19. |
- Chernikova, Dina, 1982, et al.
(författare)
-
The Inclusion of Photofission, Photonuclear, (n, xn), (n, n ' x gamma), and (n, x gamma) Reactions in the Neutron-Gamma Feynman-Alpha Variance-to-Mean Formalism
- 2017
-
Ingår i: Nuclear Science and Engineering. - 0029-5639 .- 1943-748X. ; 185:1, s. 206-216
-
Tidskriftsartikel (refereegranskat)abstract
- This paper sets up a formalism that is sufficiently general to describe the effects of photofission, photonuclear, (n, xn), (n, n?x?), and (n, x?) reactions on the neutron-gamma Feynman-alpha variance-to-mean ratios. Such a formalism is obtained using the Chapman-Kolmogorov (master) forward equation for the above-mentioned set of nuclear reactions. Thereafter, the issue of estimating reaction intensities for gammas in the master equation is highlighted by the paper. As an example, a quantitative evaluation of reaction intensities is given for a case when (n, ?), photonuclear, and (n, 2n) reactions are relevant for the system. However, an evaluation of the influence of these types of reactions to the values of the Feynman variance-to-mean ratios is not within the scope of this paper. Overall, the results obtained in this paper are intended to give an extended systematic framework for the study of the neutron- and gamma-based nondestructive assay problems in nuclear reactor applications and materials control.
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| 20. |
- Chernikova, Dina, 1982, et al.
(författare)
-
The neutron-gamma Feynman variance to mean approach: Gamma detection and total neutron-gamma detection (theory and practice)
- 2015
-
Ingår i: Nuclear Instruments and Methods in Physics Research, Section A: Accelerators, Spectrometers, Detectors and Associated Equipment. - : Elsevier BV. - 0168-9002. ; 782, s. 47-55
-
Tidskriftsartikel (refereegranskat)abstract
- 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 particular importance for detectors of either gamma photons or deleclors sensitive to both neutron and gamma radialion. If applied to a plastic or liquid deleclor, he total neutron-gamma detection Feynman-Y expression corresponds Lo a situation where no discrimination is made between neutrons and gamma parlicles. The gamma variance Lo mean formulas are useful when a detector of only gamma radialion is used or when working with a combined neutron-gamma deleclor at high count rates. The theoretical derivation is based on the Chapman-Kolmogorov equation with the inclusion of general reactions and corresponding 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 Cf-252-source. In addition, the variance to mean ratios, neutron, gamma and total neutron-gamma are evaluated experimentally for a weak Cf-252 neutron-gamma source, a Cs-137 random gamma source and a Na-22 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-alpha formulas.
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| 21. |
- Degweker, S. B., et al.
(författare)
-
Extension of the invariant embedding method for the calculation of particle fluctuations
- 2009
-
Ingår i: International Conference on Mathematics, Computational Methods and Reactor Physics 2009, M and C 2009; Saratoga Springs, NY; United States; 3 May 2009 through 7 May 2009. - 9781615673490 ; 2, s. 925-938
-
Konferensbidrag (refereegranskat)abstract
- Invariant embedding theory is an alternative formulation of particle transport theory. So far the method has exclusively been used for calculating first moments, i.e. expectations. The present paper extends the method to treat fluctuations. A probability balance equation is derived in the traditional invariant embedding approach from which equations for the first and second order densities are derived. It is shown that only the equations for the first order densities are non-linear, while subsequent order densities obey linear equations. With the method, correlations between particles at two different energies and angles, or the higher moments of the emitted multiplicity distribution, such as the variance, from a target bombarded by incident particles can be determined. The approach is illustrated by a simple forward backward scattering model. The possibility of applying the method to finite sized slabs and spheres is also discussed.
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| 22. |
- Degweker, S. B., et al.
(författare)
-
Stochastic Invariant Imbedding Theory for a Distributed Internal Source
- 2011
-
Ingår i: Nuclear Science and Engineering. - 0029-5639 .- 1943-748X. ; 168:3, s. 248-264
-
Tidskriftsartikel (refereegranskat)abstract
- Invariant imbedding theory is an alternative formulation of particle transport theory. Until very recently, this theory was used only for deterministic calculations, i.e., for calculations of the first moment of the particle distribution. In a previous paper we set up a probability balance equation in the invariant imbedding approach. An equation was also obtained for the probability generating functional (pgfl) of reflected particles from which equations for the first- and second-order densities were derived. The approach was illustrated by a simple forward-backward scattering model with and without incorporating energy dependence to describe sputtering due to an external source of energetic particles on a medium. In this paper we extend these results to the case of a distributed internal source of particles. Among the possible applications, we discuss the problem of internal sputtering. We derive equations for the pgfl and the first- and second-order densities and show their connection with the external source problem. We treat the finite slab problem in addition to the semi-infinite slab geometry considered in our previous paper.
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| 23. |
- Degweker, Shashikant, 1956, et al.
(författare)
-
Stochastic equations in the invariant imbedding formulation of particle transport
- 2009
-
Ingår i: Annals of Nuclear Energy. - : Elsevier BV. - 0306-4549 .- 1873-2100. ; 36:8, s. 1108-1119
-
Tidskriftsartikel (refereegranskat)abstract
- Invariant imbedding theory is an alternative formulation of particle transport theory. Although stochasticfoundations of invariant imbedding have been known from the beginnings, the method itself has so farexclusively been used for calculating first moments, i.e. expectations. The present paper attempts toset up a probability balance equation in the invariant imbedding approach from which equations forthe first and second order densities are derived. It is shown that only the equations for the first order densitiesare non-linear, while subsequent order densities obey linear equations. This is expected to considerablysimplify solution to those problems which involve second order density calculations whereinvariant imbedding techniques may be profitably used. Examples of such quantities are the varianceor correlations between particles detected at two different energies or angles or the higher momentsof the emitted multiplicity distribution such as the variance from a target bombarded by incident particles.One possible area of application of our equations is non-destructive estimation of fissile material bythe active neutron assay technique. Another area is the study of particle cascade development in sputteringand positron backscattering from surfaces. The approach is illustrated by a simple forward–backwardscattering model for these two problems.
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| 24. |
- Demaziere, Christophe, 1973, et al.
(författare)
-
2-D 2-group neutron noise simulator and its application to anomaly localisation
- 2001
-
Ingår i: Proc. Int. Mtg. Mathematical Methods for Nuclear Applications (M&C2001). - 0894486616
-
Konferensbidrag (refereegranskat)abstract
- This paper presents a so-called neutron noise simulator, essentially an algorithm to calculate the dynamic transfer function, and its use in a procedure allowing to locate a noise source from the neutron detector readings. The noise simulator relies on the two-group diffusion approximation in 2-D. Benchmarking of this calculator versus analytical solutions showed that the finite difference discretisation scheme used in the simulator was accurate in case of homogeneous cores and a central noise source. The localisation algorithm was found to give correct results as long as one single noise source exists in the core and when the transfer function from the removal cross-section noise to the thermal neutron noise was used. Applying this localisation procedure to the Forsmark-1 BWR (Sweden) when a local instability event occurred (cycle 16) pointed out, via the use of an appropriate set of detectors, a region close to where an unseated fuel element was discovered.
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| 25. |
- Demaziere, Christophe, 1973, et al.
(författare)
-
A phenomenological model for the explanation of a strongly space-dependent Decay Ratio
- 2003
-
Ingår i: Proc. Int. Mtg. Nuclear Mathematical and Computational Sciences (M&C2003). - 0894486748
-
Konferensbidrag (refereegranskat)abstract
- It is commonly believed that the Decay Ratio (DR), a parameter characterizing the stability of Boiling Water Reactors (BWRs), is a space-independent parameter of the reactor, i.e. it is independent of which Local Power Range Monitor (LPRM) is used in the core to perform the evaluation. This paper shows that the presence of several simultaneous types or sources of instability with different stability properties and different space dependence renders the DR also space-dependent, and even strongly space dependent. Two cases were investigated: the case of a local instability (i.e. one induced by a local noise source) coexisting with a global instability (in-phase oscillations), and the case of two local instabilities (noise sources). The results of these calculations were compared to the Forsmark-1 channel instability event, where strongly space-dependent decay ratios had been found in the measurements. Good adequacy was found between the DR model applied to the Forsmark-1 event and the corresponding measured DR. The fact that one single noise source in the core does not allow explaining a non-homogeneous DR suggests that in the case of Forsmark-1, at least two types or sources of instability had to be present in the core at the same time. According to the results obtained in this paper, these could be either a local and a global instability, or two local ones.
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| 26. |
- Demaziere, Christophe, 1973, et al.
(författare)
-
Analysis of an MTC noise measurement performed in Ringhals-2 using gamma-thermometers and in-core neutron detectors
- 2003
-
Ingår i: Progress in Nuclear Energy. - 0149-1970. ; 43:1-4, s. 57-66
-
Tidskriftsartikel (refereegranskat)abstract
- A noise measurement in the Swedish Ringhals-2 PWR was performed in January 2002 by using twelve gamma-thermometers and two in-core neutron detectors, all located on the same axial level in the reactor. The gamma-thermometers are very versatile tools since they allow estimating the core-averaged moderator temperature noise throughout the core. This core-averaged temperature noise was then used to estimate the MTC by noise analysis, via a new MTC noise estimator. It was shown that whatever the location of the neutron detector might be, the MTC is always correctly estimated by this new MTC noise estimator, without any calibration to a known value of the MTC prior to the noise measurement. For the purpose of comparisons, the MTC was also estimated by using a single gamma-thermomemeter and a single core-exit thermocouple, together with an in-core neutron detector. In such cases, the WC was systematically underestimated, with a stronger bias for the core-exit thermocouple than for the gamma-thermometer. This shows that the main reason of the MTC underestimation by noise analysis in all the experimental work until now was due to the radially non-homogeneous temperature noise throughout the core. The resulting deviation from point-kinetics of the reactor response has a negligible effect.
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| 27. |
- Demaziere, Christophe, 1973, et al.
(författare)
-
Determination of the MTC by noise analysis methods
- 2003
-
Ingår i: Proc. Annual Mtg. Nuclear Technology 2003 (JK2003).
-
Konferensbidrag (refereegranskat)abstract
- Determination of the moderator temperature coefficient (MTC) in pressurised water reactors has been the matter of interest for a long time. The MTC should be within certain limits at all times; it should be negative, but its absolute value should not exceed a certain limit either. Since the MTC changes continuously during the fuel cycle with burnup and the corresponding change in the boron concentration in the water, a monitoring of its value is necessary. The traditional methods that are used to measure the MTC are time consuming and expensive. The noise based methods are more flexible but so far they were rather inaccurate with a systematic underestimation of the MTC. In recent work we have pointed out that the main weakness of the noise based method is the poor knowledge of the driving source, by measuring the temperature fluctuations only in one radial point whereas those fluctuations are highly spacedependent. The problems of the noise method can be eliminated or largely improved if the core average temperature is used instead of the local temperature, leading to an improved noise estimator. This fact was confirmed by us in detailed numerical simulations. The new estimator was also tested in measurements at an operating plant. In the Swedish Ringhals-2 PWR, 12 strings of gamma thermometers are permanently installed. In the frequency range of interest to the MTC, i.e. within 0.1 - 1 Hz, these sensors act as pure noise thermocouples, measuring the temperature fluctuations of the cold junction which is in the coolant. With the signals of the gamma thermometers the fluctuations of the core averaged temperature can be estimated accurately. A full measurement was performed in 2002 with gamma thermometers taken in all 12 radial points at one axial elevation, 2 in-core neutron detectors, and one core exit thermocouple. The purpose of the present paper is to report on these measurements. It was shown that with the suggested noise estimator, based on the core average temperature fluctuations, the correct value of the MTC was obtained, by comparison to SIMULATE calculations. It was seen that using only one in-core gamma thermometer the estimated value of the MTC was in significant error, and using one single core exit thermocouple yielded a yet larger error. The performance of the new MTC estimator was also investigated in view of some parameters of the evaluation such as the FFT procedure used and the neutronic weight function used in the core averaging of the temperature. Some further improvement of the method is also touched upon.
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| 28. |
- Demaziere, Christophe, 1973, et al.
(författare)
-
Development of a method for measuring the MTC by noise analysis and its experimental verification in Ringhals-2
- 2004
-
Ingår i: Nuclear Science and Engineering. - 0029-5639 .- 1943-748X. ; 148:1, s. 1-29
-
Tidskriftsartikel (refereegranskat)abstract
- This paper deals with the estimation of the moderator temperature coefficient of reactivity (MTC) by noise analysis. The current noise analysis-based MTC measurement, relying on the cross correlation between the neutron noise measured by a single in-core neutron detector and the local temperature noise given by a single core-exit thermocouple located at the top of the same fuel assembly, or of a neighboring fuel assembly, is not accurate. The MTC is systematically underestimated by a factor of 2 to 5 compared to its design-predicted value. A theoretical study shows that, in case of nonhomogeneous moderator temperature noise, the core-averaged moderator temperature noise should be used for the MTC estimation. The new estimation method can reach up to 3% accuracy as compared with the results of core calculations for the Swedish Ringhals-2 pressurized water reactor (PWR). We show via noise measurements performed at the Ringhals-2 PWR that the moderator temperature noise is actually radially strongly heterogeneous and loosely coupled. The new MTC noise estimator is demonstrated to provide an accurate MTC evaluation, with the core-averaged moderator temperature noise estimated via the use of many radial in-core gamma-thermometers. More important, different forms of weighting functions are suggested to calculate the core-averaged moderator temperature noise. This new MTC noise estimator, which is nonintrusive and free of calibration, can therefore be applied to monitor the MTC throughout the cycle.
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| 29. |
- Demaziere, Christophe, 1973, et al.
(författare)
-
Development of a method for measuring the MTC by noise analysis and its experimental verification in Ringhals-2
- 2002
-
Ingår i: Proc. Int. Mtg. New Frontiers of Nuclear Technology: Reactor Physics, Safety and High-Performance Computing (PHYSOR2002). - 0894486721
-
Konferensbidrag (refereegranskat)abstract
- This paper deals with the estimation of the Moderator Temperature Coefficient of reactivity (MTC) by noise analysis. Previous experimental investigations showed that the MTC was systematically underestimated by a factor of two to five compared to its design-predicted value. In these measurements, the MTC was always determined by cross-correlating the neutron noise provided by a single in-core neutron detector with the local temperature noise given by a single core-exit thermocouple located at the top of the same fuel assembly, or of a neighbouring fuel assembly. It is shown in this paper via a noise measurement performed at the Swedish Ringhals-2 Pressurised Water Reactor (PWR) that the moderator temperature noise is radially strongly heterogeneous. Such a non-homogeneous temperature noise is proven theoretically to explain why the MTC was always underestimated in the previous experimental work when only the local temperature was used. A new MTC noise estimator, relying on the core-averaged moderator temperature noise, is thus proposed. This new estimator is demonstrated to provide an accurate MTC evaluation, as long as the radial structure of the moderator temperature noise can be measured. In the case of Ringhals-2, such in-core temperature measurements are carried out by Gamma-Thermometers (GTs), which in the frequency range of interest for the MTC investigation by noise analysis are working as ordinary thermocouples. This method, which is non-intrusive and free of calibration, can therefore be applied to monitor the MTC throughout the cycle.
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| 30. |
- Demaziere, Christophe, 1973, et al.
(författare)
-
Estimation of the Moderator Temperature Coefficient (Analysis of an MTC measurement using boron dilution method)
- 2000
-
Ingår i: Proc. Int. Topl. Mtg. Nuclear Plant Instrumentation, Controls, and Human-Machine Interface Technologies (NPIC&HMIT 2000).
-
Konferensbidrag (refereegranskat)abstract
- The boron dilution method is analyzed, which is widely used for Moderator Temperature Coefficient (MTC) measurement in Pressurized Water Reactors (PWRs). Data were taken from the measurement of the at-power MTC at the PWR Unit 4 of the Ringhals Nuclear Power Plant (Sweden) during fuel cycle 16 at 300 ppm. Detailed calculations were made to estimate all reactivity effects. Calculations were performed with the static code SIMULATE-3, and error limits were also estimated. The analysis showed that the contribution from the Doppler correction was almost negligible, whereas the reactivity correction due to effects other than the Doppler and the boron effects were surprisingly significant. It was found that the uncertainty associated with the boron dilution method could be larger than previously expected.
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| 31. |
- Demaziere, Christophe, 1973, et al.
(författare)
-
Evaluation of the boron dilution method for Moderator Temperature Coefficient measurements
- 2002
-
Ingår i: Nuclear Technology. - 0029-5450 .- 1943-7471. ; 140:1, s. 147-163
-
Tidskriftsartikel (refereegranskat)abstract
- A measurement of the at-power moderator temperature coefficient (MTC) at the pressurized water reactor Unit 4 of the Ringhals Nuclear Power Plant (Sweden) during fuel cycle 16 is analyzed. The measurement was performed when the boron concentration decreased under 300 ppm in the reactor coolant system, by using the boron dilution method. Detailed calculations were made to estimate all reactivity effects taking place during such a measurement. These effects can only be accounted for through static core calculations that allow calculating contributions to the reactivity change induced by the moderator temperature change. All the calculations were performed with the Studsvik Scandpower SIMULATE-3 code. Analysis of the measurement showed that the contribution of the Doppler effect (in the fuel) was almost negligible, whereas the reactivity effects due to other than the Doppler fuel coefficient and the boron change were surprisingly significant. It was concluded that due to the experimental inaccuracies, the uncertainty associated with the boron dilution method could be much larger than previously expected. The MTC might then be close to -72 pcm/oC, whereas the main goal of the measurement is to verify that the MTC is larger (less negative) than this threshold. The usefulness of the boron dilution method for MTC measurements can therefore be questioned.
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| 32. |
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| 33. |
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| 34. |
- Demaziere, Christophe, 1973, et al.
(författare)
-
Investigation of the validity of the point-kinetic approximation for subcritical heterogeneous systems in 2-group diffusion theory for measurement of the reactivity in ADS
- 2005
-
Ingår i: Proc. Int. Conf. Nuclear Energy Systems for Future Generation and Global Sustainability (GLOBAL2005). - 4890471332
-
Konferensbidrag (refereegranskat)abstract
- In this paper, calculations are performed on a 2-D heterogeneous reflected subcricital system to determine the spatial distribution of the neutron noise induced by fluctuations of a neutron source located in the middle of the core. Likewise, the point-kinetic component of the neutron noise is determined and compared to the actual neutron noise. It is found that close to the source, the amplitude of the actual neutron noise is larger than its point-kinetic component, while smaller close to the core periphery. For increasing core subcriticalities and/or decreasing frequencies, the deviation of the reactor response from point-kinetics becomes smaller. Based on these observations, the source modulation method is considered for the evaluation of the core subcriticality, since this method is based on point-kinetics. Although the reactor response only deviates slightly from point-kinetics in practical cases such as for an ADS (i.e. a deeply subcritical medium), the reactivity estimated from the source modulation technique significantly deviates from its actual value. Small deviations of the reactor response from point-kinetics lead to large inaccuracies in the estimation of the reactivity, whereas perfect agreement with point-kinetics leads to a pathological case where the formula for estimating the reactivity is ill-posed. Therefore, the source modulation technique seems to be of limited applicability.
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| 35. |
- Demaziere, Christophe, 1973, et al.
(författare)
-
Numerical tools applied to power reactor noise analysis
- 2009
-
Ingår i: Progress in Nuclear Energy. - : Elsevier BV. - 0149-1970. ; 51:1, s. 67 - 81
-
Tidskriftsartikel (refereegranskat)abstract
- In order to be able to calculate the space- and frequency-dependent neutron noise in real inhomogeneous systems intwo-group theory, a code was developed for the calculation of the Greens function (dynamic transfer function) of such systems. This paper reports on the development as well as the test and application of the numerical tools employed. The code developed yields the space-dependence of the fluctuations of the neutron flux induced by fluctuating properties of the medium in the 2-group diffusion approximation and in a two-dimensional representation of heterogeneous systems, for both critical systemsand non-critical systems with an external source. Someapplications of these tools to power reactor noise analysis are then described, including the unfolding of the parameters of the noise source from the induced neutron noise, measured at a few discrete locations throughout the core. Other concrete applications concern the study of the space-dependence of the Decay Ratio in Boiling Water Reactors, the noise-based estimation of the Moderator Temperature Coefficient of reactivity in Pressurized Water Reactors, the modeling of the beam- and shell-mode core-barrel vibrations in Pressurized Water Reactors, and the investigation of the validity of the point-kinetic approximation in subcritical systems driven by an external source.In most of these applications, calculations performed using thecode are compared with at-power plant measurements. Power reactornoise analysis applications of the above type, i.e. coremonitoring without disturbing plant operation, is of particularinterest in the framework of the extensive program of poweruprates worldwide.
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| 36. |
- Demaziere, Christophe, 1973, et al.
(författare)
-
Numerical tools applied to power reactor noise analysis
- 2006
-
Ingår i: Proc. 5th Int. Topl. Mtg. Nuclear Plant Instrumentation, Controls, and Human Machine Interface Technology (NPIC&HMIT 2006), Albuquerque, New Mexico, USA, November 12-16, 2006, American Nuclear Society. - 0894480510
-
Konferensbidrag (refereegranskat)abstract
- In this paper, the development of numerical tools allowing the determination of the neutron noise in power reactors is reported. These tools give the space-dependence of the fluctuations of the neutron flux induced by fluctuating properties of the medium in the 2-group diffusion approximation and in a 2-dimensional representation of heterogeneous systems. Some applications of these tools to power reactor noise analysis are then described. These applications include the unfolding of the noise source from the resulting neutron noise measured at a few discrete locations throughout the core, the study of the space-dependence of the Decay Ratio in Boiling Water Reactors, the noise-based estimation of the Moderator Temperature Coefficient of reactivity in Pressurized Water Reactors, the modeling of shell-mode core barrel vibrations in Pressurized Water Reactors, and the investigation of the validity of the point-kinetic approximation in subcritical systems.
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| 37. |
- Demaziere, Christophe, 1973, et al.
(författare)
-
On the possibility of the space-dependence of the stability indicator (decay ratio) of a BWR
- 2005
-
Ingår i: Annals of Nuclear Energy. - : Elsevier BV. - 0306-4549 .- 1873-2100. ; 32:12, s. 1305-1322
-
Tidskriftsartikel (refereegranskat)abstract
- A model is proposed for the explanation of the space-dependence of the so-called decay ratio (DR) which is used to quantify the stability properties of boiling water reactors (BWRs). The study was prompted by the observation of a strongly space-dependent decay ratio in an instability event at the Swedish Forsmark-1 BWR. Prior to that event, the space-dependence of the DR was neither observed, nor assumed possible in the theoretical models of instability. The model proposed here is based on a previous suggestion by one of the authors on how to model the estimation of the DR in case of two different types of oscillations (instabilities) being present in the core simultaneously. The model was earlier only used in a space-independent form, but here its applicability is extended such that space-dependence of the oscillations is also accounted for, by using a noise simulator. The investigations show that the DR, as determined by the individual LPRMs (neutron detectors) at different positions, can be strongly space-dependent if at least two different oscillations with differing DR and space-dependence exist in the core simultaneously. The observed space-dependence of the DR in the Forsmark case can be reconstructed by the model.
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| 38. |
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| 39. |
- Demaziere, Christophe, 1973, et al.
(författare)
-
Study of the MTC estimation by noise analysis in 2-D heterogeneous systems
- 2003
-
Ingår i: Progress in Nuclear Energy. - 0149-1970. ; 43:1-4, s. 313-319
-
Tidskriftsartikel (refereegranskat)abstract
- The effect of a heterogeneous distribution of the temperature noise on the MTC estimation by noise analysis is investigated. This investigation relies on 2-group diffusion theory, and all the calculations are performed in a 2-D realistic heterogeneous core. It is shown, similarly to the 1-D case, that the main reason of the MTC underestimation by noise analysis compared to its design-predicted value lies with the fact that the temperature noise might not be homogeneous in the core, and therefore using the local temperature noise in the MTC noise estimation gives erroneous results. A new MTC estimator, which was previously proposed for 1-D 1-group homogeneous cases and which is able to take this heterogeneity into account, was extended to 2-D 2-group heterogeneous cases. It was proven that this new estimator is always able to give a correct MTC estimation with an accuracy of 3%. This small discrepancy comes from the fact that the reactor does not behave in a point-kinetic way, contrary to the assumptions used in the noise estimators. This discrepancy is however quite small.
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| 40. |
- Demaziere, Christophe, 1973, et al.
(författare)
-
Theoretical investigation of the MTC noise estimate in 1-D homogeneous systems
- 2002
-
Ingår i: Annals of Nuclear Energy. - 0306-4549 .- 1873-2100. ; 29:1, s. 75-100
-
Tidskriftsartikel (refereegranskat)abstract
- In this paper, the accuracy of the noise-based determination of the moderator temperature coefficient (MTC) is investigated theoretically and quantitatively. It is known from earlier work that the noise method systematically underestimates the MTC. In this paper, it is found that the main reason for the underestimation lies with the radial incoherence of the temperature fluctuations. The deviation of the reactor response from point-kinetics is another possible reason, but it was found to play a quite insignificant role. The theory of neutron noise, induced by spatially random perturbations is elaborated and by its help the inaccuracy (bias) of the noise based MTC estimation was quantitatively investigated. It was found that a relatively short correlation length of the temperature fluctuations, which is in agreement with experimental evidence, can explain the observed underestimation of the MTC by the noise method.
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| 41. |
- Demaziere, Christophe, 1973, et al.
(författare)
-
Theoretical investigation of the MTC noise estimate in 1-D homogeneous systems
- 2000
-
Ingår i: Proc. 28th Informal Mtg. Reactor Noise (IMORN-28).
-
Konferensbidrag (refereegranskat)abstract
- Two possible reasons of the MTC underestimation by noise analysis are investigated: the deviation from point-kinetics of the reactor response, and the effect of randomly distributed (both in time and in space) noise sources. The strong deviation of the MTC noise estimate from its actual value is found to be mainly due to the heterogeneous structure of the temperature noise. The spatial heterogeneous temperature noise distribution gives both a smaller (space independent) reactivity effect, and a smaller (space dependent) cross-power spectrum density between neutron and temperature noise, in comparison with homogeneous noise sources, on which the MTC definition relies.
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| 42. |
- Demaziere, Christophe, 1973, et al.
(författare)
-
Theory of neutron noise induced by spatially randomly distributed noise sources
- 2000
-
Ingår i: Proc. Int. Mtg. Advances in Reactor Physics and Mathematics and Computation into the Next Millennium (PHYSOR2000). - 0894486551
-
Konferensbidrag (refereegranskat)abstract
- In this paper the neutron noise, induced by spatially randomly distributed noise sources is investigated. The prime example of such a case is the neutron noise induced by temperature fluctuations in a PWR core, where the temperature fluctuations in the separate channels (radial positions) are only weakly correlated and their space dependence can only be specified in a statistical sense. Solutions are given for the auto- and cross-spectra of the neutron noise, in terms of the spatial cross-spectra of the noise source (temperature fluctuations). The spatial structure of the neutron noise spectrum is investigated quantitatively as a function of the frequency and the correlation length of the perturbation. The validity of the point kinetic approximation is also investigated. It is found that in the low frequency limit, point kinetics dominates even if the noise source correlation length is zero, i.e. the noise source is completely uncorrelated in space. On the other hand, in systems of realistic sizes and at plateau frequencies, i.e. at around a few Hz, noticeable deviations occur from point kinetics if the source correlation length is much smaller than the system size. The magnitude of this deviation is only a few percents at plateau frequencies in the present 1-D model, but by extrapolation it can be expected to be much larger in realistic 2-D calculations. This latter result bears importance for the determination of the moderator temperature coefficient (MTC) with noise methods, where usually a point kinetic core response is assumed in the evaluation of measurements.
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| 43. |
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| 44. |
- Dykin, Victor, 1985, et al.
(författare)
-
Investigation of the space-dependent noise induced by propagating density fluctuations
- 2010
-
Ingår i: International Conference on the Physics of Reactors 2010, PHYSOR 2010. - 9781617820014 ; 2, s. 963-978
-
Konferensbidrag (övrigt vetenskapligt/konstnärligt)abstract
- The space-dependent behavior of neutron noise induced by a propagating perturbation, represented by the fluctuations of the absorbtion cross section propagating with the coolant of a PWR, is investigated in a one-dimensional one-group approach. The general space-frequency problem is solved for this specific noise source with the help of Greens function technique. All calculations are made in the frame of first-order perturbation theory. The solution is investigated for a different frequencies and system sizes. The limits of point-kinetic and space-dependent behaviour were investigated. An interesting interference phenomenon was found between the point kinetic and the pure space dependent components of the noise for certain combinations of the frequency and system size. The results bear a significance for the dynamics of Molten Salt Reactors (MSR), which will be reported on in a companion paper.
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| 45. |
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| 46. |
- Dykin, Victor, 1985, et al.
(författare)
-
Qualitative and quantitative investigation of the propagation noise in various reactor systems
- 2014
-
Ingår i: Progress in Nuclear Energy. - : Elsevier BV. - 0149-1970. ; 70, s. 98-111
-
Tidskriftsartikel (refereegranskat)abstract
- 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.
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| 47. |
- Dykin, Victor, 1985, et al.
(författare)
-
Remark on the neutron noise by propagating perturbations in a MSR
- 2014
-
Ingår i: Proceedings of the International Conference on Physics of Reactors, PHYSOR 2014.
-
Konferensbidrag (refereegranskat)abstract
- The neutron noise induced by propagating perturbations in a bare 1-D Molten Salt Reactor (MSR) model is calculated and analyzed using one-group diffusion theory. The neutron noise for different noise sources of which two have not been accounted for, corresponding to the fluctuations of the fission and absorption cross sections as well as to the fuel velocity is calculated and the results are qualitatively compared. Unlike in previous work, the solution is obtained through the matrix Green's function of the flux and precursor equations being kept separate. It is shown that in the case when the noise is represented by the fluctuations of the fission cross-section, the noise source attains a complex structure which is different from that in traditional reactors. On the other hand, in the cases investigated, despite all qualitative differences in the noise calculation procedure as well as in the structure of the noise source, it turns out that the noise induced by the absorption and the fission cross sections follow a similar behaviour. In addition, it is observed that the inclusion of the fluctuations in the fuel velocity examined in this paper slightly suppresses the total neutron noise for low frequency region i.e. below ∼ 2 Hz but on the other hand it enhances the latter one by one of order of magnitude for high frequencies i.e. above ∼ 2 Hz compared to the effect of other noise sources. The results contribute to the understanding and interpretation of the neutron noise in MSRs.
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| 48. |
- Dykin, Victor, 1985, et al.
(författare)
-
Remark on the neutron noise induced by propagating perturbations in an MSR
- 2016
-
Ingår i: Annals of Nuclear Energy. - : Elsevier BV. - 0306-4549 .- 1873-2100. ; 90, s. 93-105
-
Tidskriftsartikel (refereegranskat)abstract
- The neutron noise induced by propagating perturbations in a simple model of a Molten Salt Reactor (MSR) is calculated and analyzed using one/two-group diffusion theory. The novelty, as compared to previous works, is that the noise source includes also the fluctuations of the fission cross sections and the fluid velocity, in addition to the previous case when only the fluctuations of the absorption cross section were accounted for. Another novelty is that the solution is obtained through the matrix Green's function of the flux and precursor equations, these two being kept separate. Inclusion of each of these two new noise sources leads to a structure of the noise source, and hence also that of the neutron noise, which is conceptually different from the case when only the fluctuations of the absorption cross sections are treated, with some surprising features. The use of the matrix Green's function is advantageous to understand the new features, and it helps to point out some new aspects of the neutron noise even in traditional systems, which have not been noticed before. The results contribute to the understanding and interpretation of the neutron noise in MSRs. (C) 2015 Elsevier Ltd. All rights reserved.
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| 49. |
- Dykin, Victor, 1985, et al.
(författare)
-
Remark on the role of the driving force in BWR instability
- 2009
-
Ingår i: Annals of Nuclear Energy. - : Elsevier BV. - 0306-4549 .- 1873-2100. ; 36:10, s. 1544-1552
-
Tidskriftsartikel (refereegranskat)abstract
- Simple models of BWR instability, used e.g. in understanding the role of the various oscillation modes inthe overall stability of the plant, assume that each oscillation mode can be described by a second ordersystem (a damped harmonic oscillator) driven by a white noise driving force. Change of the decay ratio(DR) of the observed signal is, as a rule, associated with the changing of the parameters of the dampedoscillator, mainly its damping coefficient, and is interpreted in terms of the change of the stability ofthe system. However, conceptually, one cannot exclude cases when the change of the response of a drivendamped oscillator is due to the change of the properties of the driving force. In this work we investigatethe effect of a non-white driving force on the behaviour of the system. A question of interest is howchanges of the spectrum of the driving force influence the observed autocorrelation function (ACF) ofthe resulting signal. Hence we calculate the response of a damped harmonic oscillator driven by anon-white driving force, corresponding to the reactivity effect of propagating density fluctuations intwo-phase flow. It is shown how in some special cases such a driving force, when interpreting the neutronnoise as if induced by a white noise driving source, can lead to an erroneous conclusion regarding thestability of the system. It is also concluded that in the practically interesting cases the effect of the coloureddriving force, arising from propagating density fluctuations, is negligible.
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| 50. |
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