Gamma Multiplicities in a Multiplying Sample for the Assay of Nuclear Materials

The multiplicities, or factorial moments, of the distribution of the number of neutrons emerging from a fissile sample can be used to identify and quantify fissile isotopes, in particular even-N isotopes of transuranic elements. In fact, the spontaneously emitted source neutrons can induce further fissions in the sample, thereby changing the number distributions of the neutrons leaving the sample, and therefore their multiplicities. The multiplicities increase monotonically with sample mass, hence the measurement of the multiplicities can be used to quantify the sample mass.Analytical expressions for multiplicities that include induced fission effects have been derived for neutrons in the past. These expressions are given as functions of the probability of induced fission per neutron, and have been investigated both by Monte Carlo methods and in experiments using thermal neutron detectors. The object of this paper is to derive analytical formulae for the multiplicities of the gamma photons emitted by both spontaneous and induced fissions, and to perform a quantitative analysis. In addition, neutron and gamma multiplicities are calculated by Monte Carlo simulation using a modified version of the MCNP-PoliMi code. Good agreement is found between the analytical formulae and the Monte Carlo results. The results show the potential advantage of using gamma multiplicities when compared to neutron multiplicities: their higher quantitative values may, in principle, have the effect of leading to a larger sensitivity on the sample mass when compared to the analysis based on neutrons alone

The Statistics of the Number of Neutron Collisions prior to Absorption

We propose a simple analytical model to describe the statistics of the number of collisions undergone by fast neutrons during slowing down until they are absorbed. We assume that the moderator is homogeneous and account for scattering and absorption, but do not consider thermalization. Although the problem cannot be solved in a compact form, a simple recurrent formula provides the solution in a very transparent way. The model can be readily evaluated numerically, and the results are in excellent agreement with the corresponding Monte Carlo simulations. Both the mean number and the variance of the number of collisions are calculated. The results are discussed and compared with the classical case of neutron slowing down to or past a given energy in a moderating medium without absorption

Diagnostics Of Detector Tube Impacting With Wavelet Techniques

A neutron noise based method is proposed for the detection of impacting of detector tubes in BWRs. The basic idea relies on the assumption that non-stationary transients (e.g. fuel box vibrations) may be induced at impacting. Such short-lived transients are difficult to detect by spectral analysis methods. However, their presence in the detector signal can be detected by wavelet analysis. A simple wavelet technique, the so-called Haar transform, is suggested for the detection of impacting. Tests of the proposed method have been performed with success on both simulated data with controlled impacting as well as with real measurement data. The simulation model as well as the results of the wavelet analysis are reported in this paper. The source codes written in MATLAB ® are available at a public ftp site. The necessary information to reproduce the simulation results is also reported. 1. INTRODUCTION There have been several methods proposed and tested in the past for detecting the impac..

The effect of capture gammas, photofission and photonuclear neutrons to the neutron-gamma Feynman variance-to-mean ratios (neutron, gamma and total)

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

The Inclusion of Photofission, Photonuclear, (n, xn), (n, n \u27 x gamma), and (n, x gamma) Reactions in the Neutron-Gamma Feynman-Alpha Variance-to-Mean Formalism

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

Derivation of pulsed Feynman- and Rossi-alpha formulae including delayed neutrons

In previous works, the authors have developed an effective solution technique for calculating the pulsed Feynman- and Rossi-alpha formulae.Through derivation of these formulae, it was shown that the technique can easily handle various pulse shapes of the pulsed neutron source.Furthermore, it was also shown that both the deterministic (i.e.{} synchronizing with the pulsing of neutron source) and stochastic (non-synchronizing) Feynman-alpha formulae can be obtained with this solution technique.However, for mathematical simplicity and the sake of insight, the formal derivation was performed in a model without delayed neutrons.In this paper, to demonstrate the robustness of the technique, the pulsed Feynman- and Rossi-alpha formulae were re-derived by taking one group of delayed neutrons into account.The results show that the advantages of this technique are retained even by inclusion of the delayed neutrons.Compact explicit formulae are derived for the Feynman- and Rossi-alpha methods for various pulse shapes and pulsing methods

Developments in Core-Barrel Motion Monitoring and Applications to the Ringhals PWR Units

Core-barrel motion (CBM) surveillance and diagnostics, based on the amplitude of the peaks of the normalized auto power spectral densities (APSDs) of the ex-core neutron detectors, have been performed and continuously developed in Sweden and were applied for monitoring of the three PWR units, Ringhals 2 to 4. From 2005, multiple measurements were taken during each fuel cycle, and these revealed a periodic behavior of the 8-Hz peak of the beam-mode motion: the amplitude increases within the cycle and returns to a lower value at the beginning of the next cycle. The work reported in this paper aims to clarify the physical reason for this behavior. A combination of a mode separation method in the time domain and a nonlinear curve fitting procedure of the frequency spectra revealed that two types of vibration phenomena contribute to the beam-mode peak. The lower frequency peak around 7 Hz in the ex-core detector APSDs corresponds to the CBM, whose amplitude does not change during the cycle. The higher frequency peak around 8 Hz arises from the individual vibrations of the fuel assemblies, and its amplitude increases monotonically during the cycle. This paper gives an account of the work that has been made to veri,b, the above hypothesis

Determination of the subcriticality level using the Cf-252 source-detector method

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

Determination of the subcriticality level using the Cf-252 source-detector method

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