Applying machine learning methods for the analysis of two-dimensional mass spectra

In a measurement of isomeric yield-ratios in fission, the Phase-Imaging Ion-Cyclotron-Resonance technique, which projects the radial motions of ions in the Penning trap (JYFLTRAP) onto a position-sensitive micro-channel plate detector, has been applied. To obtain the yield ratio, that is the relative population of two states of an isomer pair, a novel analysis procedure has been developed to determine the number of detected ions in each state, as well as corrections for the detector efficiency and decay losses. In order to determine the population of the states in cases where their mass difference is too small to reach full separation, a Bayesian Gaussian Mixture model was implemented. The position-dependent efficiency of the micro-channel plate detector was calibrated by mapping it with 133 Cs+ ions, and a Gaussian Process was trained with the position data to construct an efficiency function that could be used to correct the recorded distributions. The obtained numbers of counts of excited and ground-state ions were used to derive the isomeric yield ratio, taking into account decay losses as well as feeding from precursors.

Nuclear data adjustment using Bayesian inference, diagnostics for model fit and influence of model parameters

The mathematical models used for nuclear data evaluations contain a large number of theoretical parameters that are usually uncertain. These parameters can be calibrated (or improved) by the information collected from integral/differential experiments. The Bayesian inference technique is used to utilize measurements for data assimilation. The Bayesian approximation is based on the least-square or Monte-Carlo approaches. In this process, the model parameters are optimized. In the adjustment process, it is essential to include the analysis related to the influence of model parameters on the adjusted data. In this work, some statistical indicators such as the concept of Cook’s distance; Akaike, Bayesian and deviance information criteria; effective degrees of freedom are developed within the CONRAD platform. Further, these indicators are applied to a test case of 155Gd to evaluate and compare the influence of resonance parameters.

Influence of nuclear data parameters on integral experiment assimilation using Cook’s distance

Nuclear data used in designing of various nuclear applications (e.g., core design of reactors) is improved by using integral experiments. To utilize the past critical experimental data to the reactor design work, a typical procedure for the nuclear data adjustment is based on the Bayesian theory (least-square technique or Monte-Carlo). In this method, the nuclear data parameters are optimized by the inclusion of the experimental information using a Bayesian inference. The selection of integral experiments is based on the availability of well-documented specifications and experimental data. Data points with large uncertainties or large residuals (outliers) may affect the accuracy of the adjustment. Hence, in the adjustment process, it is very important to study the influence of experiments as well as of the prior nuclear data on the adjusted results. In this work, the influence of each individual reaction (related to nuclear data) is analyzed using the concept of Cook’s distance. First, JEZEBEL (Pu239, Pu240 and Pu241) integral experiment is considered for data assimilation and then the transposition of results on ASTRID fast reactor concept is discussed.

Fitting a defect non-linear model with or without prior, distinguishing nuclear reaction products as an example

Fitting a parametrized function to data is important for many researchers and scientists. If the model is non-linear and/or defect, it is not trivial to do correctly and to include an adequate uncertainty analysis. This work presents how the Levenberg-Marquardt algorithm for non-linear generalized least squares fitting can be used with a prior distribution for the parameters and how it can be combined with Gaussian processes to treat model defects. An example, where three peaks in a histogram are to be distinguished, is carefully studied. In particular, the probability r₁ for a nuclear reaction to end up in one out of two overlapping peaks is studied. Synthetic data are used to investigate effects of linearizations and other assumptions. For perfect Gaussian peaks, it is seen that the estimated parameters are distributed close to the truth with good covariance estimates. This assumes that the method is applied correctly; for example, prior knowledge should be implemented using a prior distribution and not by assuming that some parameters are perfectly known (if they are not). It is also important to update the data covariance matrix using the fit if the uncertainties depend on the expected value of the data (e.g., for Poisson counting statistics or relative uncertainties). If a model defect is added to the peaks, such that their shape is unknown, a fit which assumes perfect Gaussian peaks becomes unable to reproduce the data, and the results for r₁ become biased. It is, however, seen that it is possible to treat the model defect with a Gaussian process with a covariance function tailored for the situation, with hyper-parameters determined by leave-one-out cross validation. The resulting estimates for r₁ are virtually unbiased, and the uncertainty estimates agree very well with the underlying uncertainty.

Total Monte Carlo evaluation for dose calculations

Total Monte Carlo (TMC) is a method to propagate nuclear data (ND) uncertainties in transport codes, by using a large set of ND files, which covers the ND uncertainty. The transport code is run multiple times, each time with a unique ND file, and the result is a distribution of the investigated parameter, e.g. dose, where the width of the distribution is interpreted as the uncertainty due to ND. Until recently, this was computer intensive, but with a new development, fast TMC, more applications are accessible. The aim of this work is to test the fast TMC methodology on a dosimetry application and to propagate the (56)Fe uncertainties on the predictions of the dose outside a proposed 14-MeV neutron facility. The uncertainty was found to be 4.2 %. This can be considered small; however, this cannot be generalised to all dosimetry applications and so ND uncertainties should routinely be included in most dosimetry modelling.

Neutron tomography of axially symmetric objects using 14 MeV neutrons from a portable neutron generator

In nuclear boiling water reactor cores, the distribution of water and steam (void) is essential for both safety and efficiency reasons. In order to enhance predictive capabilities, void distribution assessment is performed in two-phase test-loops under reactor-relevant conditions. This article proposes the novel technique of fast-neutron tomography using a portable deuterium-tritium neutron generator to determine the time-averaged void distribution in these loops. Fast neutrons have the advantage of high transmission through the metallic structures and pipes typically concealing a thermal-hydraulic test loop, while still being fairly sensitive to the water/void content. However, commercially available fast-neutron generators also have the disadvantage of a relatively low yield and fast-neutron detection also suffers from relatively low detection efficiency. Fortunately, some loops are axially symmetric, a property which can be exploited to reduce the amount of data needed for tomographic measurement, thus limiting the interrogation time needed. In this article, three axially symmetric test objects depicting a thermal-hydraulic test loop have been examined; steel pipes with outer diameter 24 mm, thickness 1.5 mm, and with three different distributions of the plastic material POM inside the pipes. Data recorded with the FANTOM fast-neutron tomography instrument have been used to perform tomographic reconstructions to assess their radial material distribution. Here, a dedicated tomographic algorithm that exploits the symmetry of these objects has been applied, which is described in the paper. Results are demonstrated in 20 rixel (radial pixel) reconstructions of the interior constitution and 2D visualization of the pipe interior is demonstrated. The local POM attenuation coefficients in the rixels were measured with errors (RMS) of 0.025, 0.020, and 0.022 cm(-1), solid POM attenuation coefficient. The accuracy and precision is high enough to provide a useful indication on the flow mode, and a visualization of the radial material distribution can be obtained. A benefit of this system is its potential to be mounted at any axial height of a two-phase test section without requirements for pre-fabricated entrances or windows. This could mean a significant increase in flexibility of the void distribution assessment capability at many existing two-phase test loops.

Correction for dynamic bias error in transmission measurements of void fraction

Dynamic bias errors occur in transmission measurements, such as X-ray, gamma, or neutron radiography or tomography. This is observed when the properties of the object are not stationary in time and its average properties are assessed. The nonlinear measurement response to changes in transmission within the time scale of the measurement implies a bias, which can be difficult to correct for. A typical example is the tomographic or radiographic mapping of void content in dynamic two-phase flow systems. In this work, the dynamic bias error is described and a method to make a first-order correction is derived. A prerequisite for this method is variance estimates of the system dynamics, which can be obtained using high-speed, time-resolved data acquisition. However, in the absence of such acquisition, a priori knowledge might be used to substitute the time resolved data. Using synthetic data, a void fraction measurement case study has been simulated to demonstrate the performance of the suggested method. The transmission length of the radiation in the object under study and the type of fluctuation of the void fraction have been varied. Significant decreases in the dynamic bias error were achieved to the expense of marginal decreases in precision.

Neutron emission spectroscopy results for internal transport barrier and mode conversion ion cyclotron resonance heating experiments at JET

The effect of ion cyclotron resonance heating (ICRH) on (3He)D plasmas at JET was studied with the time of flight optimized rate (TOFOR) spectrometer dedicated to 2.5 MeV dd neutron measurements. In internal transport barrier (ITB) plasma experiments with large 3He concentrations (X(3He)>15%) an increase in neutron yield was observed after the ITB disappeared but with the auxiliary neutral beam injection and ICRH power still applied. The analysis of the TOFOR data revealed the formation of a high energy (fast) D population in this regime. The results were compared to other mode conversion experiments with similar X(3He) but slightly different heating conditions. In this study we report on the high energy neutron tails originating from the fast D ions and their correlation with X(3He) and discuss the light it can shed on ICRH-plasma power coupling mechanisms.