Method for determining the amount of plutonium in the presence of curium by passive neutron counting

Abstract

To provide a method for determining the amount of plutonium in the presence of curium by a passive neutron measurement method.SOLUTION: Measuring the electrical pulse train using a radiation detection system and determining a first number and a second number of secondary pulse coincidences between the electrical pulses in a first time window and a second time window, wherein the first time window and the third time window are selected such that the number of secondary pulse coincidences relating to plutonium is larger than the number of secondary pulse coincidences relating to curium in one of the first time window and the third time window and smaller than the number of secondary pulse coincidences relating to curium in the other window; The plutonium quantity is determined by applying a non-linear regression model having a total number of pulses, a first number of secondary pulse coincidences, and a second number of secondary pulse coincidences, the model being pre-trained on a set of simulation values.SELECTED DRAWING: Figure 3

Description

[Technical Field]

[0001] The present invention relates to the field of passive neutron metrology for the characterization of radioactive waste or nuclear material (whether solid or in solution). More precisely, the invention relates to the metrology of coincidence counting of neutrons and gamma particles produced by spontaneous fission, with the aim of determining the mass of plutonium in packages of radioactive waste, in samples of nuclear material (ingots, powder containers, fuel pellets or rods, machining scrap or any other form), or even in solutions of nuclear material (spent fuel reprocessing process). [Background technology]

[0002] in radioactive waste packaging and nuclear materials 242 Cm and 244 The presence of Cm can lead to a substantial overestimation of the amount of plutonium present. 242 More frequently present than Cm (half-life 162 days) 244 For example, Cm (half-life 18.1 years) 244 Spontaneous fission neutron yield of Cm (ns -1 .g -1 ) is the primary neutron emitter from spontaneous fission of plutonium 240 As a result, the presence of curium in the waste package is likely to be related to the even-numbered isotopes of plutonium ( 238,240,242 Pu, but for simplicity, the main emitter 240 This can obscure the neutron signal produced by spontaneous fission of Pu (which refers only to Pu). 240 Pu equivalent mass (all isotopes) 238,240,242 The risk of overestimation is very high, due to the high uncertainty in the assessment of the total mass of plutonium from the mass that would result in the emission of the same number of neutrons as Pu, which is important for determining the mass of fissile material (isotopes) for example when verifying criticality safety standards or in material audits. 239 and 241Pu) or when managing radioactive waste storage facilities (initial acceptance criteria and long-term alpha activity, in particular isotope 239 and 240 In cases of this kind, it is not feasible to use ab initio information (i.e., information not derived from measurements but provided by the owner of the nuclear material or the waste producer) on the relative proportions of plutonium and curium, since even small uncertainties in these mass ratios would lead to excessive errors in the estimate of the amount of plutonium.

[0003] Despite the presence of curium in radioactive waste or nuclear material, there are two types of counting methods to accurately estimate the mass of plutonium: active neutron counting or passive neutron counting.

[0004] Active neutron counting is based on the use of pulsed neutron generators. This method, described in Reference

[10] , is currently the preferred solution, since it allows achieving a sufficiently high ratio between the signal (prompt neutrons from fission induced in plutonium and also in uranium) and background noise (mainly due to passive, spontaneous fission of curium). However, active counting involves much higher technical constraints and costs than passive counting. In particular, the price of the neutron generator is high and depends on the required emission level; in addition, its ownership and use require regulatory approval, which in detail requires special operator training, radiation protection measures (radiation-shielded rooms) and physical protection of the equipment (dual-use items), and audits of the tritium sources it contains.

[0005] For this reason, it is less expensive to investigate methods based on passive neutron counting.

[0006] The vast majority of passive neutron measurement facilities intended to characterize plutonium (nuclear materials, radioactive waste packages, processing fluids, etc.) by detecting the spontaneous fission neutrons emitted simultaneously are equipped with 3He gas proportional counters, as they are highly sensitive to thermal neutrons and less sensitive to gamma rays.

[0007] In certain cases, the unwanted presence of curium, a very powerful neutron emitter due to spontaneous fission, leads to a very significant overestimation of the amount of plutonium.

[0008] Currently, there are two main passive neutron counting methods implemented with 3He detectors to assess plutonium mass in the presence of curium, both of which are based on the fact that curium isotopes emit more neutrons from spontaneous fission than plutonium isotopes (average 2.72 vs. 2.16, due to different multiplicity distributions - see reference [4]).

[0009] These methods are based on the use of pulse coincidence counts in a pulse train measured by a detector: in a time window of a given size starting from the arrival time of a pulse, N or more pulse coincidences (N is a strictly positive integer) are detected for each pulse when N-1 further pulses are detected in that time window.

[0010] The first evaluation method using passive neutron counting consists of evaluating the ratio between the number of true secondary pulse coincidence counts corresponding to a pair of neutrons and the total number of pulse counts. This method is described in reference [5] and is generally used in measurement facilities that do not have very high detection efficiency or any neutron multiplicity counting system.

[0011] In this first method, 244In the presence of Cm, a significant increase in the ratio between true pulse coincidence and total pulse counts can be observed. However, this ratio is known to vary as the inverse of the apparent neutron detection efficiency. Therefore, any uncontrolled decrease in apparent efficiency (e.g., if the waste package contains elements that slow down and then absorb neutrons, or if the instrumentation contains only moderator elements that make neutron detection more difficult when the instrumentation includes an absorber such as cadmium in front of the detector) can be erroneously attributed to the presence of curium. Thus, this method generally does not allow for accurate estimation of the amount of plutonium in the presence of curium, but only provides qualitative information about the likelihood of its presence and the associated risk of overestimating the plutonium mass.

[0012] The second evaluation method using passive neutron counting consists in measuring the neutron multiplicity, in particular the ratio between the number of true second-pulse coincidence counts (called doublets) and the number of true third-pulse coincidence counts (called triplets). This second method is described, for example, in references [1] and [8].

[0013] This second method also 244 Cm and 240 We also exploit the difference between the probability distributions of the number of neutrons emitted by spontaneous fission of Pu (the two main emitters are Cm and Pu). The ratio between the triplet and doublet counts is 240 More than Pu 244 Cm, which in principle makes it possible to distinguish between the two. Reference [1] states that 244 The maximum atomic fraction of Cm, i.e., on the order of 0.1%, 244 Cm and 240[8] points out that it is conceivable to assess the amount of plutonium up to its maximum mass ratio with Pu. However, the implementation of this method requires the use of neutron measurement equipment with a very large number of 3He counters (up to five rings of 40 3He counters surrounding a 100 liter waste drum) in order to achieve a very high detection efficiency (number of counts per emitted neutron) of 30%-40% and therefore a statistically usable number of triplet counts. However, as also pointed out in Reference [8], in the majority of cases, particularly in the case of radioactive waste packages where matrix effects reduce the detection efficiency and where the ratio between the masses of Cm and Pu can reach several percent, this method, as mentioned above, is not feasible. 244 It only provides qualitative information about the risk that exists for Cm.

[0014] The patent application published by the applicant under EP 3 835 831 A1 relates to a method for counting plutonium by the passive detection method of neutron coincidence counting, which uses plastic PVT scintillators (PVT is the abbreviation for polyvinyltoluene, such detectors are sensitive to fast neutrons) instead of 3He detectors, mainly because the latter are too costly and sensitive to accidental coincidences (much longer coincidence window). The proposed method is based on selecting the coincidence window in time so that the arrival times of the three detected particles (neutrons and prompt gamma particles) are taken into account when counting triplets, with the aim of better discriminating between triplets resulting from spontaneous fission and those resulting from various parasitic reactions, such as the (α,n) reaction, but also from elastic and inelastic scattering, which give rise to crosstalk and therefore to undesired coincidences. However, this method 244 The estimation error regarding the existence of Cm is not taken into account. [Prior art documents] [Patent documents]

[0015] [Patent Document 1] European Patent Application Publication No. 3 835 831 A1 [Non-patent literature]

[0016] [Non-Patent Document 1] B.Perot et al,“The characterization of radioactive waste:a critical review of techniques implemented or under development at CEA,France”,EPJ Nuclear Sci.Technol.Volume 4,2018 [Non-patent document 2] N. Ensslin, “Passive Nondestructive Assay of Nuclear Materials”, 1991 [Non-patent document 3] JB Porcher, T. Lambert, N. Saurel, H. Schoech, L. Tondut, C. Passard, G. Granier “Dossier de Recommandations pour l'Optimisation des Mesures Neutroniques Passives”, Rapport CEA, 2013, ISSN 0429-3460 [Non-patent document 4] DHBeddingfield, APBelian, “Detection of Cm-244 in Plutonium-Bearing Wastes at Reprocessing Facilities”, Los Alamos National Laboratory, 2004 [Non-patent document 5] Patrick MJ Chard et al., “Field Examples of Waste Assay Solutions for Curium-Contaminated Wastes”, ICEM2009-16259 Summary of the Invention [Problem to be solved by the invention]

[0017] Therefore, where the prior art does not allow it, i.e. 244 Cm and 240 In nuclear materials or radioactive waste drums, when the mass ratio between Pu and 244 In the presence of Cm 240 There is a need for a method to accurately estimate the amount of Pu by passive neutron coincidence counting. Furthermore, there is a need for a method to accurately estimate the amount of Pu by fission products or activation products ( 137 Cs, 60 Parasitic gamma contributions due to ions such as Co must be avoided because the plastic scintillators used in the detectors are sensitive to this type of radiation. [Means for solving the problem]

[0018] The present invention provides a novel method for determining plutonium mass by passive neutron counting, which uses the technique described in EP 3 835 831 A1 but improves it in the presence of curium.

[0019] To this end, the present invention utilizes a nonlinear regression model that includes multiple explanatory variables, the explanatory variables being the number of true coincidences of various orders counted in two different time intervals, the magnitude of these time intervals being such that in one the contribution of plutonium is different (higher or lower) than the contribution of curium, and in the other the opposite is true.

[0020] In the remainder of this description, the number of true second-order pulse coincidences is also referred to as doublets, and the number of true third-order pulse coincidences is also referred to as triplets.

[0021] Taking into account two time intervals and calculating the doublets and triplets associated with training a non-linear regression model parameterized by explanatory variables calculated for these two separate intervals makes it possible, in contrast to prior art methods, to better characterize the plutonium mass in the presence of curium.

[0022] One subject of the present invention is a method for determining the amount of plutonium in a radioactive sample in the presence of curium, comprising the steps of: - measuring the train of electrical pulses using a radiation detection system comprising a plurality of detectors arranged around the sample, the detectors capable of generating electrical pulses in response to the detection of radioactive particles; - determining a first number and a second number of secondary pulse coincidences between electrical pulses sent by the detector in a first time window and a second time window, respectively, - the second time window consists of a concatenation of the first time window and the third time window; - selecting the first time window and the third time window such that the number of secondary pulse coincidences related to plutonium is greater than the number of secondary pulse coincidences related to curium in one of the first time window and the third time window, and is less than the number of secondary pulse coincidences related to curium in the other window. - determining the amount of plutonium by applying a nonlinear regression model having as parameters the total number of pulses measured, the first number of secondary pulse coincidences, and the second number of secondary pulse coincidences, the model being pre-trained on a set of simulated values ​​obtained using the numerical model. The method includes:

[0023] According to one detailed aspect of the invention, the second time window is selected to incorporate pulse pairs corresponding to radiation of type (γ,n) and (n,n) and to exclude pulse pairs corresponding to radiation of type (γ,γ).

[0024] In one variant of embodiment, the method according to the invention comprises: - determining a first number and a second number of third pulse coincidences between electrical pulses sent by the detector in a first time window and in a second time window, respectively; - the nonlinear regression model further comprises the first and second numbers of third-order pulse coincidences as parameters. Further includes:

[0025] In one variant of embodiment, the method according to the invention comprises: - determining a first number of tertiary pulse coincidences between electrical pulses sent by the detector such that the time difference between the first and second pulses is within a first time window and the time difference between the second and third pulses is within a first time window; - determining a second number of tertiary pulse coincidences between electrical pulses sent by the detector such that the time difference between the first and second pulses falls within a second time window and the time difference between the second and third pulses falls within a second time window, - the nonlinear regression model further comprises the first and second numbers of third-order pulse coincidences as parameters. Further includes:

[0026] According to a detailed aspect of the invention, the second time window is selected to include triplets of pulses corresponding to radiation of type (γ,n,n) and (n,n,n) and to exclude triplets of pulses corresponding to radiation of type (γ,γ,γ).

[0027] According to one detailed aspect of the invention, the first time window is equal to [10ns;20ns], the second time window is equal to [10ns;60ns] and the third time window is equal to [20ns;60ns].

[0028] According to one detailed aspect of the invention, the first time window is equal to [20ns;60ns], the second time window is equal to [10ns;60ns] and the third time window is equal to [10ns;20ns].

[0029] Another subject of the present invention is a system for determining the amount of plutonium in a radioactive sample in the presence of curium, comprising a plurality of detectors arranged around the sample and capable of generating an electrical pulse in response to the detection of a radioactive particle, and a computer configured to carry out the steps of the method according to the invention.

[0030] According to one detailed aspect of the invention, each detector includes an organic plastic scintillator made from polyvinyl toluene (PVT).

[0031] Other features and advantages of the present invention will become more clearly apparent from the following description taken in conjunction with the accompanying drawings, in which: [Brief explanation of the drawings]

[0032] [Figure 1] 1 shows a first schematic diagram of a passive neutron measurement system according to an embodiment of the present invention; [Figure 2] 1 shows a second schematic diagram of a passive neutron measurement system according to an embodiment of the present invention; [Figure 3] 1 shows a flowchart detailing steps of an embodiment of a method for determining the amount of plutonium according to one embodiment of the present invention; [Figure 4a] An example of the determination of coincidence counts for a pulse train is shown; [Figure 4b] We present a table of the distribution of multiplicity degrees for the example in Figure 4a; [Figure 5] An example of a Rossi alpha curve is shown below: [Figure 6] An example of a plot of the energy spectrum of spontaneous fission neutrons of 244Cm and 240Pu is shown below: [Figure 7] Rossi alpha curves for 244Cm and 240Pu are shown, respectively; [Figure 8] Illustrates a first example of an estimation of the mass of 240Pu using a first type of nonlinear regression model; [Figure 9] Illustrates a first example of the estimation of the mass of 240Pu using a second type of nonlinear regression model; [Figure 10] Illustrates a first example of the estimation of the mass of 240Pu using the third type of nonlinear regression model; [Figure 11] Illustrates a second example of the estimation of the mass of 240Pu using a second type of nonlinear regression model; [Figure 12] Illustrates another example of estimating the mass of 240Pu using the fourth type of nonlinear regression model; [Figure 13] 1 illustrates the calculation of the number of third-order pulse coincidences by time selection based on a two-dimensional histogram according to prior art principles; [Figure 14] 10 illustrates another example of estimating the mass of 240Pu using a fifth type of nonlinear regression model. DETAILED DESCRIPTION OF THE INVENTION

[0033] FIG. 1 shows a simplified schematic diagram of a passive neutron measurement system according to one embodiment of the present invention.

[0034] In this non-limiting example, the measurement system includes four detectors, each including a PVT plastic scintillator S1-S4 and a photomultiplier tube P1-P4. The number of detectors may be greater than this, for example, equal to 10 or 16.

[0035] The measurement system also includes a computer 2 connected to the photomultiplier tubes P1-P4 via an analog-to-digital converter 3. The system 1 may also include a human-machine interface module 4, for example a monitor for displaying the measurement results.

[0036] 2 shows another example of a schematic diagram of a passive neutron measurement system, in this case comprising 16 detectors 203 based on PVT plastic scintillators. The system further comprises a tubular lead shield 201 arranged inside the detectors and a drum 202 in which the sample is placed. The system rests on a support pallet 204. In one variant of the embodiment, the lead shield 201 may be omitted or its thickness may be adjusted to the intensity of the gamma rays emitted by the sample to be analyzed.

[0037] The measurement system according to the present invention comprises a PVT plastic scintillator (without neutron-gamma ray discrimination capability) as described in the patent application referenced in [2].

[0038] The measurement system preferably uses a plastic scintillator made of polyvinyltoluene (PVT) and does not use a 3He detector for the following reasons.

[0039] 3He detectors have a time constant of the order of tens of microseconds, corresponding to the time it takes for the detector to thermalize, whereas plastic scintillators directly detect fast neutrons, with a time constant of the order of tens of nanoseconds. References [2] and [3] use this property to suppress the number of random coincidences and to separate the plutonium signal from parasitic gamma-ray sources (the presence of fission or activation products in the measurement object) and neutron sources ( 241 Am or 238 This distinguishes between signals from (α,n) reactions on light nuclei, such as oxygen in plutonium oxide, in the presence of strong α emitters, such as Pu.

[0040] FIG. 3 shows a flow chart detailing the steps of an embodiment of a method for determining the amount of plutonium in the presence of curium in a sample using the system illustrated in FIGS.

[0041] The method begins with step 301 of measuring coincidences, which is performed for a given sample using the system described above. Each detector includes a photomultiplier tube capable of sending an electrical signal representative of the light signal generated in the plastic scintillator. This electrical signal is recorded for each detector. At the end of this measurement step, a train of pulses is obtained, each pulse characterized by at least its arrival time and its emitted energy.

[0042] In step 302, the number of secondary coincidences is determined from the pulse train measured in step 301 for two specific time windows selected in a manner described below.

[0043] In step 303, optionally the number of third-order coincidences is also determined for the same time window as in step 302.

[0044] Finally, in step 304, a nonlinear regression model is run, which has been trained to determine the amount of plutonium present in the sample based on three parameters: the total number of pulses and the two numbers of second-order coincidences determined in step 302; or five parameters: the three parameters mentioned above and the two numbers of third-order coincidences determined in step 303.

[0045] FIG. 4 a illustrates, in one example, the principle of determining the number of Nth pulse coincidences for a measured pulse train 400 .

[0046] According to well-known principles, more particularly described in reference [5], there exists an Nth pulse coincidence when, for a given pulse with arrival time t0, there are N-1 other pulses in a time window of given size whose beginnings coincide with time t0. The number N can range from 0 to N d -1 (N d is the number of detectors in the system).

[0047] In the example of Figure 4a, the time window has a size of 100 ns, and zeroth or first order coincidences (no other pulses in the window) as well as first and second order multiplicities (one and two further pulses in the window, respectively) are identified.

[0048] Furthermore, in this figure a distinction is made between the so-called R+A window (R+A is the acronym for Real+Accidental), which applies to all measured pulses, and the so-called A window (A is the acronym for Accidental), which corresponds to random coincidence counts for a time window located beyond a certain time delay, set equal to approximately 10 times the detection time of the neutrons in the system. In the example of Figure 4a, this time delay is equal to 1000 ns.

[0049] To determine the number of Nth coincidences, first, we first determine the multiplicity M for N, which varies from 0 to a predefined maximum integer value max. N The number of multiplicity orders is determined. A distribution of multiplicity orders is obtained as provided in the table of FIG. 4b for the detailed example of FIG. 4a. From this distribution, the k-th factorial moment is determined, which is defined by the following relation:

number

[0050] The numbers of true first, second and third order coincidences - also called singlets, doublets and triplets (S, D and T) - are then given by the following formulas (see references [5] and [7]): S=(R+A)0=(A)0 D = (R + A)1 - (A)1

number

[0051] FIG. 5 shows an example of a Rossi alpha curve that produces a histogram of the number of secondary pulse coincidences as a function of the value of the time window.

[0052] In other words, this histogram is obtained by measuring the arrival time of the next pulse at each detection. The example in Figure 5 shows a detection system consisting of a PVT plastic scintillator. 240 Pu was obtained from the plutonium source.

[0053] In this graph, a first time window [10-60] ns corresponding to counting true + random coincidences and a second time window [260-310] ns corresponding to counting the number of random coincidences are identified.

[0054] In the time interval [0~10]ns, the second-order coincidence counts corresponding to the γγ pair are concentrated. In the time interval [10~60]ns, the second-order coincidence counts corresponding to the γn and nn pairs are concentrated.

[0055] To be able to accurately quantify plutonium in the presence of curium, it is proposed to count the number of secondary pulse coincidences using two separate time intervals.

[0056] Specifically, the present invention provides: 244 Cm and 240 This is based on the difference in the energy spectrum of spontaneous fission neutrons between Pu and Cr.

[0057] Figure 6 shows 240 Pu and 244 The energy spectra 601 and 602 of spontaneous fission neutrons of Cm are shown.

[0058] This figure shows the emission probability in the energy ranges [0.2-2] MeV and [2-7] MeV. 240 Pu (curve 601) and 244 Cm (curve 602).

[0059] Figure 7 shows 240 Pu(701) and 244 A comparison of the Rossi α curves for given values ​​of doublets measured in the time window [10-60] ns between Cm(702) and Cm(702) is shown.

[0060] Figure 7 shows the average arrival times of fission neutrons and gamma particles after their initial detection, depending on the speed of the neutrons (several cm.ns depending on their energy). -1 ) compared to the velocity of gamma particles (30 cm.ns -1 ) is faster, so the first detection is generally that of gamma particles.

[0061] There is a first peak corresponding to the detection of pairs of gamma particles, followed by a "bump" corresponding to the detection of pairs involving at least one neutron, where the velocity of the neutron varies with the square root of its energy, so the shape is comparable to the spectrum in Figure 6. Looking at Figure 7, we see that in the window [20-60] ns, and also in the window [10-20] ns, there is a 240 Pu and 244 It can be seen that there is a large difference between Cm and spontaneous fission. Thus, the probability of detecting neutrons resulting from spontaneous fission is 240 Compared to Pu 244 It is observed that for Cm, the trend reverses between 20 and 60 ns. Specifically, curves 701 and 702 intersect at approximately time t=20 ns.

[0062] More specifically, for the numerical example in Figure 7, 240For a plutonium sample and a curium sample each containing an equivalent mass of Pu, respectively, for the same number of coincidences over the entire window [10-60] ns, the values ​​of the number of true second-order coincidences for the two time intervals are presented in the table below.

[0063] [Table 1]

[0064] By exploiting this difference in contributions in two separate time windows, 244 In samples in the presence of Cm 240 It is now possible to improve predictions of Pu mass using nonlinear regression models.

[0065] Specifically, as demonstrated below: 240 The contribution of Pu is 244 a first time window that is larger than the contribution of Cm, and 244 The contribution of Cm 240 By considering a second time window larger than the contribution of Pu as a parameter in the nonlinear regression model, 240 This allows for improved prediction of Pu's mass.

[0066] The exact boundary between these two time windows (here equal to 20 ns) is determined experimentally by looking for the best compromise in terms of performance, for example by testing different time windows and by comparing the predictions of the obtained regression models.

[0067] For example, two time windows correspond to two elements. 240 Pu and 244 The ratio of the number of coincidences in each of the Cm windows may be defined to be greater than a first predetermined threshold in one of the windows and less than a second predetermined threshold in the other window. 244 Cm and 240The ratio of the contribution between Pu and Zn is equal to 1.04 in the window [10~20] ns and 0.97 in the window [20~60] ns.

[0068] Step 304 of the method of the present invention involves executing a pre-trained nonlinear regression model to determine a plurality of parameters based on the number of coincidences. 240 This involves determining the mass or amount of Pu.

[0069] The model may be, for example, a multiple linear least squares regression model or an artificial neural network as described in Reference

[11] , or more generally, any trainable model that can be trained to predict the amount of plutonium based on multiple measurements of the number of pulse coincidences.

[0070] 8, 9 and 10 illustrate the prediction results obtained with a Monte Carlo-based nonlinear regression model for simulated data corresponding to a source composed of plutonium and curium.

[0071] The number of settings is determined by three variable parameters: 244 Cm and 240 The mass of Pu, and 60 This corresponds to a full factorial experimental design with a Co source activity (emitting two correlated gamma rays at 1173 keV and 1332 keV). A full factorial design with a large number of settings for the above values ​​is used as a learning database to train a predictive model. Once the model has been trained on this database, it can be used to generate predictions from new measurements made on new, unknown samples. 240 The Pu mass can be estimated.

[0072] The training data is at least 244 Cm and 240The mass of Pu and the values ​​of the explanatory variables of the model (total number of pulses, number of coincidences in two separate intervals) are given. Training data can be measured on multiple samples using the apparatus illustrated in Figures 1 and 2, or simulated with a Monte Carlo particle transport code as described in Reference [9].

[0073] Figure 8 shows the graph for a regression model with only the total number of pulses (also called singlets S) and the number of secondary pulse coincidences counted in a single time window equal to [10-60] ns (also called doublets D) as inputs. 240 The predicted results (y-axis) are shown as a function of the measured mass of Pu.

[0074] As can be seen from Figure 8, the predicted results are highly dispersed and do not match the actual measured values ​​well. 244 Cm and 240 This is due to the fact that in the whole window [10-60] ns where Pu has the same number of second-order coincidences, the model is unable to discriminate between the plutonium and curium contributions.

[0075] Figure 9 shows the predicted results when the model has as input three parameters in this case: the total number of pulses, the first number of true secondary pulse coincidences counted in a first time window equal to [10-20] ns, and the second number of true secondary pulse coincidences counted in a second time window equal to [10-60] ns.

[0076] FIG. 10 alternatively shows the predicted results when the model has three parameters as inputs: the total number of pulses, a first number of true secondary pulse coincidences counted in a first time window equal to [20-60] ns, and a second number of true secondary pulse coincidences counted in a second time window equal to [10-60] ns.

[0077] Figures 9 and 10 show that in the regression model, three explanatory variables, i.e., D[10-20]ns and D[10-60]ns etc. (see Figure 9), or D[20-60]ns and D[10-60]ns etc. (see Figure 10), are used to consider singlets in one and doublets in the other counted in two separate coincidence windows, resulting in a higher accuracy than when using a single window D[10-60]ns (Figure 8). 240 This shows that much better predictions of Pu's mass are possible.

[0078] Specifically, the predicted values ​​are much closer to the measured values ​​in Figures 9 and 10, regardless of the amount of curium, compared to Figure 8. This result is related to the separation of the explanatory variables into two separate windows: the overall window and windows with a larger influence of plutonium or curium.

[0079] The results shown in Figures 8-10 were obtained with simulated data for a point source of plutonium and curium located in the center of a 118 L drum filled with cellulose of density 0.3. To evaluate the influence related to the multiplication effect as a result of induced fission, which becomes significant for plutonium masses above 100 g, a second experimental design with 124 setups was simulated for a sphere of PuO2 powder of density 3, again located in the center of the same organic matrix.

[0080] The variable simulated in this second experimental design was the volume of the PuO2 powder sphere, which is proportional to the total mass of plutonium, 240 The mass of Pu and 244 It was related to the mass of Cm.

[0081] Figure 11 shows the prediction results obtained with the same regression model with as inputs the total number of pulses, the first number of secondary pulse coincidences counted in a first time window equal to [10-20] ns, and the second number of secondary pulse coincidences counted in a second time window equal to [10-60] ns.

[0082] In Figure 11, although the performance of the regression model is worse than that of Figures 9 and 10, the 240 For the Pu equivalent mass, due to the multiplication effect, the performance of the model with the three explanatory variables mentioned above (S, D[10~20]ns and D[10~60]ns) is nevertheless still entirely acceptable for practical applications.

[0083] More generally, the value of the time interval over which doublets are counted depends on the detection device in question and on the distance between the sample and the detector.

[0084] The intervals chosen as inputs for the regression model are more generally those between two elements. 240 Pu and 244 Two consecutive time intervals in which one of the Cm contributes more than the other, and vice versa.

[0085] We now describe another embodiment of the present invention, in which the regression model has five input parameters, namely the three parameters S, D[10-20]ns and D[10-60]ns described above and two other parameters, namely a first number of third pulse coincidences counted in a first time window equal to [10-20]ns and a second number of third pulse coincidences counted in a second time window equal to [10-60]ns.

[0086] The regression model, consisting of these five explanatory variables, allows the influence of the multiplication effect on the estimation of plutonium mass, which is significant for plutonium masses above 100 g, to be significantly reduced.

[0087] Specifically, using these third-order coincidence counts, 244 Cm and 240 This allows for better utilization of the neutron multiplicity difference between Pu and Zn. Therefore, a regression model with five explanatory variables evaluated in one window of 10-20 ns and another window of 10-60 ns was used. 240It is possible to obtain a better prediction of the mass of Pu.

[0088] Figure 12 shows the prediction results obtained with the model with the five variables mentioned above.

[0089] In one variation of the embodiment, the number of third-order pulse coincidences may be determined using a two-dimensional histogram of third-order coincidences.

[0090] 13 illustrates such a histogram 1300 constructed from a pulse train 1301. The histogram corresponds to every combination 1302 of three coincidence pulses, with the time interval between the first two pulses plotted on the axis Δ 2-1 and the time interval between the second and third pulses is plotted on the axis Δ 3-2 It is plotted on.

[0091] The number of secondary pulse coincidences is calculated by the region of interest (ROI) in the histogram. net The region may be determined by summing the values ​​of , where the region is defined by the desired time window.

[0092] According to reference [3], this area of ​​interest is related to: ROI net =(ROI raw -A C )-(A Δ2-1 -A C )-(A Δ3-2 -A C ) A C is the common accidental region of the histogram 1300; A Δ2-1 is the accidental region along the first axis of the histogram; A Δ3-2 is the accidental region along the second axis of the histogram; and ROI raw corresponds to the area where counting is performed in a given time window) is calculated by

[0093] Therefore, in a similar way as described above, the two explanatory variables of the number of third-order coincidences determined for the two time windows [10-20] ns and [10-60] ns are used to calculate the ROI from this histogram 1300. net may be determined by calculation of

[0094] FIG. 14 shows the prediction results obtained with a model with five variables when the number of third-order coincidences is calculated using the histogram of FIG.

[0095] In summary, the nonlinear regression model implemented in step 304 of the method according to the invention may have three or five explanatory variables.

[0096] The first three variables are - total number of pulses, which corresponds to the number of first-order coincidences (singlets); - a first number of secondary coincidences (doublets) calculated in a first time window selected such that the plutonium contribution is greater than or less than the curium contribution; and - a first number of second coincidences (doublets) calculated in a second time window corresponding to the concatenation of the first time window and the third time window, such that the respective contributions of plutonium and curium are the inverse of those in the first time window; is.

[0097] The two additional variables are - a first number (triplet) of third-order coincidences calculated in a first time window; and - the first number (triplet) of third-order coincidences calculated in the second time window, The number of third-order coincidences may be calculated directly from the pulse train (triplets) or through the creation of a two-dimensional histogram (ROI net ) is.

[0098] For example, the first time window is [10 to 20] ns, the second time window is [10 to 60] ns, and the third time window is [20 to 60] ns.

[0099] Alternatively, the first time window is [20 to 60] ns, the second time window is [10 to 60] ns, and the third time window is [10 to 20] ns.

[0100] References [1] DHBeddingfield, APBelian, “Detection of Cm-244 in Plutonium-Bearing Wastes at Reprocessing Facilities”, Los Alamos National Laboratory, 2004. [2] V. Bottau, R. De Stefano, C. Carasco, C. Eleon, B. Perot, “Method for radiation detection comprising neutron-gamma discrimination and corresponding system”, European Patent Application Publication No. 3 835 831 A1. [3] V. Bottau, C. Carasco, B. Perot, C. Eleon, R. De Stefano, L. Isnel, I. Tsekhanovich, “Detection of Fission Coincidences With Plastic Scintillators for the Characterization of Radioactive Waste Drums”, TNS IEEE, volume 69, issue 4, 2022. [4] N. Ensslin, “Passive Nondestructive Assay of Nuclear Materials”, 1991. [5] J-B Porcher, T. Lambert, N. Saurel, H. Schoech, L. Tondut, C. Passard, G. Granier “Dossier de Recommandations pour l’Optimisation des Mesures Neutroniques Passives”, Rapport CEA, 2013, ISSN 0429-3460. [7] N. Ensslin, “Application Guide to Neutron Multiplicity Counting”, LA-13442-M, UC-700, November 1998. [8] Patrick M J Chard et al., “Field Examples of Waste Assay Solutions for Curium-Contaminated Wastes”, ICEM2009-16259. [9] S.A. Pozzi, E. Padovani, M. Marseguerra, “MCNP-PoliMi, a Monte-Carlo code for correlation measurements”, Nuclear Instruments and Methods in Physics Research, A 513(2003)550-558.

[10] B. Perot et al, “The characterization of radioactive waste: a critical review of techniques implemented or under development at CEA, France”, EPJ Nuclear Sci. Technol. Volume 4, 2018.

[11] Pedregosa, et al., “Scikit-learn: Machine learning in Python.” Journal of Machine Learning Research, 2825-2830, 2011.

Explanation of Symbols

[0101] 1 System 2. Computer 3 Analog-to-Digital Converter 4 Human Machine Interface Module 201 Lead shielding 202 Drums 203 Detector 204 Support Pallet 301 Measure coincidence counts 302 Determine the doublet 303 Determine the triplet 304 Run a regression model 400 pulse train 601,602 curve 701,702 curve 1300 Histogram 1301 Pulse train 1302 Combination of three coincidence pulses S1~S4 PVT plastic scintillator P1~P4 Photomultiplier tube

Claims

1. 1. A method for determining the amount of plutonium in a radioactive sample in the presence of curium, comprising: - measuring (301) the train of electrical pulses using a radiation detection system comprising a plurality of detectors arranged around the sample and capable of generating electrical pulses in response to the detection of radioactive particles; - determining (302) a first number and a second number of secondary pulse coincidences between said electrical pulses sent by said detector, in a first time window and in a second time window, respectively, - said second time window consists of a concatenation of said first time window and a third time window; - selecting the first time window and the third time window such that the number of secondary pulse coincidences related to plutonium is greater than the number of secondary pulse coincidences related to curium in one of the first time window and the third time window, and is less than the number of secondary pulse coincidences related to curium in the other window; determining (304) the amount of plutonium by applying a non-linear regression model having as parameters the total number of pulses measured, the first number of secondary pulse coincidences, and the second number of secondary pulse coincidences, the model having been pre-trained on a set of simulated values ​​obtained using a numerical model; A method comprising:

2. 2. The method of claim 1, wherein the second time window is selected to incorporate pulse pairs corresponding to (γ,n) and (n,n) type radiation and to exclude pulse pairs corresponding to (γ,γ) type radiation.

3. - determining (303) a first number and a second number of tertiary pulse coincidences between the electrical pulses sent by the detector in the first time window and in the second time window, respectively; 3. The method for determining the amount of plutonium according to claim 1 or 2, further comprising: - the non-linear regression model further comprises as parameters the first and second numbers of tertiary pulse coincidences.

4. determining (303) a first number of tertiary pulse coincidences between the electrical pulses sent by the detector such that the time difference between the first and second pulses is included in the first time window and the time difference between the second and third pulses is included in the first time window; determining (303) a second number of tertiary pulse coincidences between the electrical pulses sent by the detector such that the time difference between the first and second pulses is included in the second time window and the time difference between the second and third pulses is included in the second time window; 3. The method for determining the amount of plutonium according to claim 1 or 2, further comprising: a method in which the non-linear regression model further comprises the first and second numbers of tertiary pulse coincidences as parameters.

5. 5. The method for determining the amount of plutonium according to claim 3 or 4, wherein the second time window is selected to include triplets of pulses corresponding to radiation of the (γ, n, n) and (n, n, n) types and to exclude triplets of pulses corresponding to radiation of the (γ, γ, γ) type.

6. 6. The method for determining the amount of plutonium according to claim 1, wherein the first time window is equal to [10 ns; 20 ns], the second time window is equal to [10 ns; 60 ns], and the third time window is equal to [20 ns; 60 ns].

7. 6. The method for determining the amount of plutonium according to claim 1, wherein the first time window is equal to [20 ns; 60 ns], the second time window is equal to [10 ns; 60 ns], and the third time window is equal to [10 ns; 20 ns].

8. 8. A system for determining the amount of plutonium in a radioactive sample in the presence of curium, the system comprising: a plurality of detectors arranged around the sample, the detectors being capable of generating an electrical pulse in response to the detection of a radioactive particle; and a computer configured to carry out the steps of the method of any one of claims 1 to 7.

9. 9. The system for determining plutonium content as recited in claim 8, wherein each detector includes an organic plastic scintillator made of polyvinyl toluene (PVT).

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