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Gamma-ray spectrometry is widely applied in several science fields, and in particular in non-destructive gamma scanning and gamma emission tomography of irradiated nuclear fuel. Often, a collimator is used in the experimental setup, to selectively interrogate a region of interest in the fuel. For the optimization of instrument design, as well as for planning measurement campaigns, predictive models for the transmitted gamma-ray intensity through the collimator are needed. Commonly, Monte Carlo radiation transport tools are used for accurate prediction of gamma-ray transport, however, the long computation time requirements when used in low-efficiency experimental setups present challenges. In this work, the full-energy peak intensity transmitted through a rectangular collimator slit was examined. A uniform planar surface source emitting isotropically was considered, and the rate of photons reaching an ideal counter plane on the opposite side of the collimator was evaluated by analytical integration. To find a closed-form primitive function, some idealizations were required, and thereby parametric models were obtained for the optical field of view, dependent on slit dimensions (length, height and width) and source-to-collimator distance. It was shown that the count rate in the detector is independent of the collimator-to-source distance. For contributions from outside the optical field of view, where a closed-form expression cannot be found, instead fast numerical integration methods were proposed. The results were validated using the Monte Carlo code MCNP6.2. For the analytical method, deviations were larger, the shorter the collimator, with up to 25% of underestimation obtained for the shortest examined collimator of 10 cm length. However, the longer the collimator, the better the observed agreement. This accuracy is deemed to be sufficient for instrument design and measurement planning, where often the order of magnitude of the count rate is not a priori known. For the numerical method, the results showed an agreement within 3% for all evaluated collimator settings. The methods are planned for use in iterative optimization routines in the design of Gamma Emission Tomography devices, as well as for the prediction of gamma spectra obtained in the planning of fuel inspections. An application of the proposed method was demonstrated in spectrum prediction for a short cooling-time fuel rod test from the Halden reactor.

The paper describes a data library containing material composition of spent nuclear fuel. The data is extracted from burnup and depletion calculations with the Serpent2 code. The simulations were done with a PWR fuel pin cell geometry, for both initial UO2 and MOX fuel load for a wide range of initial enrichments (IE) or initial plutonium content (IPC), discharge burnup (BU) and cooling time (CT). The fuel library contains the atomic density of 279 nuclides (fission products and actinides), the total spontaneous fission rate, total photon emission rate, activity and decay heat at 789,406 different BU, CT, IE configurations for UO2 fuel and at 531,991 different BU, CT, IPC configurations for MOX fuel. The fuel library is organized in a publicly available comma separated value file, thus its further analysis is possible and simple.

Nondestructive gamma-ray spectrometry of nuclear fuel is routinely performed in axial gamma scanning devices and more recently with gamma emission tomography. Following the irradiation of a fresh nuclear fuel with high intensity neutron flux in a nuclear reactor core, a great number of gamma-emitting radionuclides are created. These can be utilized for gamma spectrometric techniques. However, due to the high density and atomic number of the nuclear fuel, self-attenuation of gamma-rays is a challenge, which requires attenuation correction in order to perform accurate analysis of the source activity in the fuel. In this study, the degradation of the gamma-ray mass attenuation with burnup was investigated and, in addition, a predictive model was created by investigating the attenuation change at various gamma energies caused by the burnup of the nuclear fuel. This model is intended for use by spectrometry practitioners inspecting nuclear fuel. To this aim, the energy-dependent gamma-ray mass-attenuation coefficients were investigated as a function of burnup for UOX, and three MOX fuels having different initial Pu contents. The Serpent 2 reactor physics code was used to simulate the burnup history of the fuel pins. The nuclide inventory of the Serpent 2 output is combined with the NIST XCOM database to calculate the mass attenuation coefficients. The mass attenuation coefficient of the fuel was found to decrease with the fuel burnup, in the range of a few percent, depending on the burnup and gamma energy. Also, a theoretical burnup dependent swelling model was imposed on fuel density to see how linear attenuation coefficient of fuel material is changed. Furthermore, greater effect may be expected on the transmitted intensity, where a simulation study of a PWR assembly revealed that the contribution from the inner rods in a scanned fuel assembly increased by tens of percent compared to the one with non-irradiated fresh fuels, when shielded by the outer rods of the assembly. A sensitivity analysis was performed in order to test the effect of a number of geometrical and operational reactor parameters that were considered to potentially effect the mass attenuation coefficient. Finally, a simple-to-use predictive model was constructed providing the mass-attenuation coefficient [cm2/g] of fuel as a function of burnup [MWd/kgHM] and initial Pu content [wt%]. The resulting predictive model was optimized by using the nonlinear regression method.

Applying Higher Order Campbelling methods in neutron flux monitoring with fission chambers is advantageous due to their capabilities to suppress the impact of unwanted noises and signal contributions (such as gamma radiation). This work aims to verify through experimental results that the basic assumptions behind the Higher Order Campelling methods are valid in critical reactors. The experiments, reported in this work, were performed at the MINERVE reactor in Cadarache. It is shown that the calibration of a fission chamber and the associated electronic system is possible in higher order mode. With the use of unbiased cumulant estimators and with digital processing, it is shown that over a wide count rate range, accurate count rate estimation can be achieved based on signal samples of a few ms, which is a significant progress compared to similar experimental results in the literature. The difference between the count rate estimated by pulse counting and by the Higher Order Campelling is less than 4%. The work also investigates the possibility of monitoring transient events. For this purpose, a control rod drop event was followed in Higher Order Campbelling mode.

International audience; This paper investigates, through numerical simulations, the performance of a signal analysis method by which a high temperature fission chamber can be used over a wide range of count rates. Results reported in a previous paper (Elter et al., 2015 [I]) indicated that the traditional Campbell method and the pulse mode cannot provide a sufficient overlap at medium count rates. Hence the use of the so-called Higher Order Campbell (HOC) methods is proposed and their performance is investigated. It is shown that the HOC methods can guarantee the linearity (i.e. correctness) of the neutron flux estimation over a wide count rate, even during transient conditions. The capabilities of these methods for suppressing parasitic noise (originating from various sources) are verified.

The detectors of the neutron flux monitoring system of the foreseen French GEN-IV sodium-cooled fast reactor (SFR) will be high temperature fission chambers placed in the reactor vessel in the vicinity of the core. The operation of a fission chamber over a wide-range neutron flux will be feasible provided that the overlap of the applicability of its pulse and Campbelling operational modes is ensured. This paper addresses the question of the linearity of these two modes and it also presents our recent efforts to develop a specific code for the simulation of fission chamber pulse trains. Our developed simulation code is described and its overall verification is shown. An extensive quantitative investigation was performed to explore the applicability limits of these two standard modes. It was found that for short pulses the overlap between the pulse and Campbelling modes can be guaranteed if the standard deviation of the background noise is not higher than 5% of the pulse amplitude. It was also shown that the Campbelling mode is sensitive to parasitic noise, while the performance of the pulse mode is affected by the stochastic amplitude distributions.

The signals of fission chambers are traditionally evaluated with Campbelling methods at medium count rates. Lately there has been a growing interest in the extension of Campbelling methods to cover a wider range of count rates. These methods are applied to measure the neutron flux in the stationary state of the reactor. However, there has not been any attempt to generalize these techniques for transient reactor states. This short note is devoted to a discussion of this question. It is shown through analytic and numerical calculations that for practical reasons the traditional, stationary Campbelling methods can be applied for transient scenarios as well. (C) 2016 Elsevier B.V. All rights reserved.

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.

This paper reviews a new real-time measurement instrument dedicated for online neutron monitoring with fission chambers in nuclear reactors. The instrument implements the higher order Campbelling methods and self-monitoring capabilities on an open source development board. The board includes an CPU/FPGA System on a Chip. The feasibility of the measurement instrument was tested both in laboratory with a signal generator and in the Minerve reactor. It is shown that the instrument provides reliable and robust count rate estimation over a wide reactor power range based on the third order statistics of the fission chamber signal. In addition, the system is able to identify whether the measured count rate change is due to the malfunction of the detector or due to the change in the neutron flux. The applied self-monitoring method is based on the spectral properties of the fission chamber signal. During the experimental verification, the considered malfunction was the change of the polarization voltage.

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.