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

Abstract

The invention relates to a method for determining the amount of plutonium in a radioactive sample in the presence of curium, comprising the following steps: measuring (301) an electrical pulse train by means of a radiation detection system, determining (302) a first number and a second number of second order pulse coincidence between the electrical pulses delivered by the detector, respectively,-the second time window consisting of a union of the first time window and a third time window, the first time window and the third time window are selected such that the number of second order pulses associated with plutonium is higher in one of the first time window and the third time window than the number of second order pulses associated with curium and lower in the other window than the number of second order pulses associated with curium; -determining (304) the amount of plutonium by applying a non-linear regression model having as parameters: the total number of measured pulses, a first number of second order pulse coincidence and a second number of second order pulse coincidence, said model being pre-trained on a set of simulated values obtained using a numerical model.

Description

Technical Field

[0001] This invention relates to the field of passive neutron measurement for characterizing radioactive waste or nuclear materials (whether in solid or in solution). More specifically, it relates to measuring the coincidence of neutrons and gamma particles generated by spontaneous fission, with the aim of determining the mass of plutonium in radioactive waste packages, nuclear material samples (ingots, powder containers, fuel pellets or rods, processing waste, or any other form), or nuclear material solutions (used in processes for reprocessing spent fuel). Background Technology

[0002] Radioactive waste packages and nuclear materials 242 Cm and 244 The presence of Cm may lead to a significant overestimation of the amount of plutonium contained therein. Specifically, with 244 Taking Cm as an example, 244 Cm ratio 242 Cm is more frequently present (half-life of 18.1 years), while 242 Cm disappears quickly (half-life is 162 days). 244 Spontaneous fission neutron yield of Cm (ns) -1 .g -1 )Compare 240 The concentration of curium (Pu, the primary emitter of neutrons from spontaneous plutonium fission) is approximately 10,000 times higher. Therefore, the presence of curium in the waste package may potentially mask the presence of even-numbered isotopes of plutonium (Pu). 238,240,242 Pu, but for simplicity, only the main emitter will be referenced. 240 The neutron signal generated by the spontaneous fission of Pu. In this case, it comes from... 240 The equivalent mass of Pu (will be emitted with all isotopes) 238,240,242 Assessing the total mass of plutonium (which has as many neutrons as Pu) becomes highly uncertain and carries a very high risk of overestimation. This raises problems in various ways, such as when validating critical safety criteria or when auditing nuclear materials to determine their fissile mass (isotopes). 239 Pu and 241 Pu), or when managing radioactive waste storage sites (initial acceptance criteria and long-term alpha activity, especially regarding isotopes). 239 Pu and 240 In this type of case, it is not feasible to use non-empirical information about the relative proportions of plutonium and curium (i.e., information provided by nuclear material owners or waste producers that is not obtained through measurement), because even a small amount of uncertainty in that mass ratio can introduce too much error into the estimation of the amount of plutonium.

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

[0004] Active neutron measurements are based on the use of a pulsed neutron generator. The method described in reference

[10] is the currently recommended solution as it allows obtaining a sufficiently high ratio between the signal (fast neutrons induced in plutonium, but also in uranium, fissions) and the background noise (passive mainly, due to spontaneous fissions of curium). However, active measurements require much more technical constraints and costs than passive measurements. In particular, the price of the neutron generator is high and depends on the emission level required; moreover, its possession and use are limited by regulatory authorities, in particular the need for specific operator training, radiation protection means (radiation cell) and physical protection of the device (dual use item) and the tritium source it contains to be audited.

[0005] For these reasons, research has been conducted on methods based on passive neutron measurements, which are cheaper.

[0006] The vast majority of passive neutron measurement facilities aimed at characterizing plutonium (nuclear material, radioactive waste packages, treatment solutions, etc.) are equipped with 3He gas proportional counters, as they are very sensitive to thermal neutrons and less sensitive to gamma radiation, by detecting spontaneously emitted fission neutrons in a coincident manner.

[0007] In some cases, the presence of unwanted curium leads to a very significant overestimation of the amount of plutonium, as curium is a very intense neutron emitter by spontaneous fission.

[0008] Currently, there are two main passive neutron measurement methods, which make use of 3He detectors to evaluate the mass of plutonium in the presence of curium, both based on the fact that curium isotopes emit more neutrons by spontaneous fission than plutonium isotopes (2.72 on average against 2.16, with different diversity distributions - see reference [4]).

[0009] These methods are based on the measurement of coincidences of pulses in a burst measured by the detector. When, in a given size time window starting at the time of arrival of a pulse, N-1 additional pulses are detected in that time window, an Nth or higher order pulse coincidence is detected for each pulse, where N is a strict positive integer.

[0010] The first method of evaluation by passive neutron measurement consists in evaluating the ratio between the number of counts corresponding to 2nd order true pulse coincidences of neutron pairs and the total number of counts of pulses. This method, described in reference [5], is generally used in measurement facilities that do not have a very high detection efficiency or in measurement facilities that do not have any neutron diversity counting system.

[0011] In this first method, in the presence of 244 Cm, a significant increase in the ratio between the number of counts of true pulse coincidences and the total number of counts of pulses can be observed. However, this ratio varies as the inverse of the apparent neutron detection efficiency. Therefore, any uncontrolled decrease in the apparent efficiency, such as in the case of a waste package containing elements that slow down and then absorb neutrons, or containing only slowing-down elements, making it more difficult to detect neutrons when the measuring facility contains an absorber such as cadmium in front of the detector, can be wrongly attributed to the presence of curium. This method therefore generally does not allow the amount of plutonium to be accurately estimated in the presence of curium, and only provides qualitative information about the possible presence of curium, and the associated risk of overestimation of the plutonium mass.

[0012] A second method of evaluation by passive neutron measurement consists in the measurement of the neutron diversity, in particular the ratio between the number of counts of 2ndorder true pulse coincidences (called pairs) and the number of counts of 3rdorder true pulse coincidences (called triplets). This second method is described, for example, in references [1] and [8].

[0013] This second method also takes advantage of the difference between the probability distributions of the number of neutrons emitted by spontaneous fission of 244 Cm and 240 Pu (the two main emitters of Cm and Pu). 244 Cm is higher than 240 Pu, which in principle makes it possible to distinguish between them. Reference [1] shows that it is possible to envisage evaluating the amount of plutonium with a maximum atomic fraction of 244 Cm of 1000 ppm, i.e. a mass of 244 Cm and 240 Pu of the order of 0.1%. However, the implementation of this method requires the use of a neutron measurement facility equipped with a very large number of 3He counters (up to 5 turns of 40 3He counters around a 100-litre waste drum) in order to obtain a very high detection efficiency (number of counts per emitted neutron) of 30% to 40% and thus a statistically exploitable number of triplet counts. However, in most cases, in particular in the presence of matrix effects in the radioactive waste packages that reduce the detection efficiency and the ratio between the masses of Cm and Pu can reach a few percent, this method, as mentioned above, only provides qualitative information about the risk of the presence of 244 Cm, as also shown in reference [8].

[0014] Applicant's patent application published as EP 3835831 A1 relates to a method for measuring plutonium by passive detection of neutron coincidence with a plastic PVT scintillator (PVT stands for polyvinyltoluene, such a detector is sensitive to fast neutrons) instead of a 3He detector, mainly because of the high cost of 3He detectors and their sensitivity to accidental coincidences (longer coincidence window). The proposed method is based on a time selection of the coincidence window in order to take into account the arrival times of the three detected particles (neutron and fast gamma particles) when counting triplets in order to better discriminate triplets due to spontaneous fission from triplets due to various parasitic reactions such as (a,n) reactions, but also triplets due to elastic and inelastic scattering producing crosstalk and thus unwanted coincidences. However, this method does not take into account the estimation errors related to the presence of Cm. 244 Cm.

[0015] There is therefore a need for a method for accurately estimating the quantity of plutonium in the presence of Cm in a barrel of nuclear material or radioactive waste, via passive measurement of neutron coincidence, when the prior art does not allow it, i.e. when 244 Cm and 240 the ratio between the masses of plutonium and Cm is greater than 0.1%. 244 Cm. 240 Pu. Moreover, since the plastic scintillator used in the detector is sensitive to this type of radiation, it is necessary to avoid the parasitic gamma contribution due to fission or activation products that can be present in the object to be measured (for example 137 Cs, 60 Co). SUMMARY

[0016] The present invention provides a new method for determining the mass of plutonium by passive neutron measurement, which uses the technique described in EP 3835831 A1 but improves it in the presence of Cm.

[0017] To this end, the invention uses a non-linear regression model with a plurality of explanatory variables, the explanatory variables being the number of real coincidences of each order counted in two different time intervals, the size of these time intervals being designed so that in one of the time intervals the contribution of plutonium is different (higher or lower) than the contribution of Cm, while in the other time interval the opposite is true.

[0018] In the remainder of the description, the number of real coincidences of order 2 is also referred to as binary coincidences. The number of real coincidences of order 3 is also referred to as triplets.

[0019] Contrary to the methods of the prior art, the pairs and triplets associated with the training of a non-linear regression model, parameterized by the explanatory variables calculated for the two different intervals, are calculated considering two time intervals, which allows a better characterization of the plutonium mass in the presence of curium.

[0020] One subject of the application is a method for determining the amount of plutonium in the presence of curium in a radioactive sample, the method comprising the steps of:

[0021] - measuring the electrical pulse train by 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 a radioactive particle,

[0022] - determining, in a first time window and in a second time window, a first number and a second number of 2nd order pulse coincidences between the electrical pulses delivered by the detectors, respectively,

[0023] - the second time window consisting of the union of the first time window and a third time window,

[0024] - the first time window and the third time window being chosen so that the number of 2nd order pulse coincidences related to plutonium is higher in one of the first time window and the third time window than the number of 2nd order pulse coincidences related to curium, and lower in the other window than the number of 2nd order pulse coincidences related to curium,

[0025] - determining the amount of plutonium by applying a non-linear regression model having as parameters the total number of pulses measured, the first number of 2nd order pulse coincidences and the second number of 2nd order pulse coincidences, the model being pre-trained on a set of simulated values obtained using a numerical model.

[0026] According to one particular aspect of the application, the second time window is chosen so as to include pairs of pulses corresponding to (γ, n) and (n, n) type radiation and to exclude pairs of pulses corresponding to (γ, γ) type radiation.

[0027] In one variant of the embodiment, the method according to the application further comprises the steps of:

[0028] - determining, in a first time window and in a second time window, a first number and a second number of 3rd order pulse coincidences between the electrical pulses delivered by the detectors, respectively;

[0029] - the non-linear regression model further having as parameters the first number and the second number of 3rd order pulse coincidences.

[0030] In one variant of the embodiment, the method according to the application further comprises the steps of:

[0031] - determining a first number of 3-order pulse coincidences between the electrical pulses delivered by the detectors, such that the time difference between the first and second pulses is contained in a first time window, and the time difference between the second and third pulses is contained in the first time window,

[0032] - determining a second number of 3-order pulse coincidences between the electrical pulses delivered by the detectors, such that the time difference between the first and second pulses is contained in a second time window, and the time difference between the second and third pulses is contained in the second time window,

[0033] - said non-linear regression model further has as parameters said first and second numbers of 3-order pulse coincidences.

[0034] According to one particular aspect of the invention, the second time window is chosen so as to include pulse triplets corresponding to (y, n, n) and (n, n, n) types of radiation, and to exclude pulse triplets corresponding to (y, y, y) type of radiation.

[0035] According to one particular aspect of the invention, 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].

[0036] According to one particular aspect of the invention, 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].

[0037] Another subject of the invention is a system for determining the amount of plutonium in the presence of curium in a radioactive sample, the system comprising a plurality of detectors arranged around said sample and capable of generating electrical pulses in response to the detection of a radioactive particle, and a computer configured to perform the steps of the method according to the invention.

[0038] According to one particular aspect of the invention, each detector comprises an organic plastic scintillator made of polyvinyltoluene (PVT). BRIEF DESCRIPTION OF DRAWINGS

[0039] Other features and advantages of the invention will become more apparent upon reading the following description, the description being read in conjunction with the accompanying drawings.

[0040] [ Figure 1 ] shows a first schematic view of a passive neutron measurement system according to one embodiment of the invention;

[0041] [ Figure 2Fig. 2 shows a second schematic view of a passive neutron measurement system according to one embodiment of the application;

[0042] [ Figure 3 ] Fig. 3 shows a flow chart detailing the implementation steps of a method for determining the amount of plutonium according to one embodiment of the application;

[0043] [ Figure 4a ] Fig. 4 shows one example of determining coincidences of a pulse train;

[0044] [ Figure 4b ] Fig. 5 shows a distribution table of the diversity order of the examples of Figure 4a ;

[0045] [ Figure 5 ] Fig. 6 shows one example of a Rossi-alpha curve;

[0046] [ Figure 6 ] Fig. 7 shows one example of a plot of the energy spectrum of spontaneous fission neutrons of 244 Cm and 240 Pu;

[0047] [ Figure 7 ] Fig. 8 shows the Rossi-alpha curve of 244 Cm and 240 Pu, respectively;

[0048] [ Figure 8 ] Fig. 9 shows a first example of estimating the mass of 240 Pu using a first type of non-linear regression model;

[0049] [ Figure 9 ] Fig. 10 shows a first example of estimating the mass of 240 Pu using a second type of non-linear regression model;

[0050] [ Figure 10 ] Fig. 11 shows a first example of estimating the mass of 240 Pu using a third type of non-linear regression model;

[0051] [ Figure 11 ] Fig. 12 shows a second example of estimating the mass of 240 Pu using a second type of non-linear regression model;

[0052] [ Figure 12 ] Fig. 13 shows another example of estimating the mass of 240 Pu using a fourth type of non-linear regression model;

[0053] [ Figure 13 ] Fig. 14 shows the calculation of the 3rd order pulse coincidence counts versus time selection based on a 2-dimensional histogram according to prior art principles;

[0054] [ Figure 14 This illustrates the estimation using a fifth type of nonlinear regression model. 240 Another example of the quality of Pu. Detailed Implementation

[0055] Figure 1 A simplified schematic diagram of a passive neutron measurement system according to one embodiment of the present invention is shown.

[0056] In this non-limiting example, the measurement system includes four detectors, each comprising a PVT plastic scintillator S1-S4 and a photomultiplier P1-P4. The number of detectors can be higher, for example, equal to 10 or 16.

[0057] The measurement system also includes a computer 2 connected to photomultipliers P1-P4 via an analog-to-digital converter 3. System 1 may also include a human-machine interface module 4, such as a monitor on which the measurement results are displayed.

[0058] Figure 2 Another example of a passive neutron measurement system, including 16 detectors 203 based on PVT plastic scintillators, is shown in schematic diagram. The system also includes a tubular lead screen 201 disposed inside the detectors and a container 202 in which the sample is disposed. The system rests on a support tray 204. In a variation of the embodiment, the lead screen 201 may be omitted, or its thickness may be customized to match the intensity of gamma radiation emitted by the sample to be analyzed.

[0059] The measurement system according to the invention is equipped with a PVT plastic scintillator (without neutron-gamma distinction), as described in the cited patent application [2].

[0060] The measurement system preferably uses a plastic scintillator made of polyvinyl toluene (PVT) instead of a 3He detector for the following reasons.

[0061] The 3He detector has a time constant on the order of tens of microseconds, corresponding to the time required for neutron thermalization, unlike plastic scintillators which directly detect fast neutrons and have time constants on the order of tens of nanoseconds. This property is used in references [2] and [3] to limit the number of accidental coincidences and to distinguish between plutonium signals and parasitic gamma sources (in the presence of fission or activation products in the analyte) and neutron sources (in the presence of strong alpha emitters, such as...). 241 Am or 238 In the case of Pu, the signal is obtained from the (α,n) reaction in the photonucleus of oxygen in, for example, plutonium oxide.

[0062] Figure 3 Detailed explanation is shown via Figure 1 and 2A flowchart of the implementation steps of the method for determining the amount of plutonium in the presence of ccurie in a sample is shown.

[0063] The method starts with a measurement step 301, which is performed by the system described above on a given sample. Each detector comprises a photomultiplier able to deliver an electrical signal which is a representation of the optical 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 being characterized at least by its arrival time and by its radiation energy.

[0064] In step 302, from the train of pulses measured in step 301, the number of 2-order coincidences is determined for two specific time windows selected in a manner explained below.

[0065] In step 303, the number of 3-order coincidences is optionally also determined for the same time windows as in step 302.

[0066] Finally, in step 304, a non-linear regression model is executed, training the model to determine the amount of plutonium present in the sample on the basis of three parameters: the total number of pulses determined in step 302, and the two numbers of 2-order coincidences; or on the basis of five parameters: the three preceding parameters, and the two numbers of 3-order coincidences determined in step 303.

[0067] In one example, Figure 4a The principle of determining the number of N-order pulse coincidences of a measured train of pulses 400 is illustrated.

[0068] According to known principles described in particular in reference [5], an N-order pulse coincidence exists when, for a given pulse with arrival time t0, there are N-1 other pulses present in a given size time window starting in coincidence with time t0. The number N varies from 0 to N d -1, with N d being the number of detectors in the system.

[0069] In the example of Figure 4a , the time window has a size of 100 ns, and it has been identified the diversity of 0-order or 1 -order coincidences (no other pulse in the window), and the diversity of 1 -order and 2-order (1 and 2 additional pulses in the window, respectively).

[0070] In addition, in the figure, a so-called R+A window (R+A is the acronym for Real + Accidental) has been distinguished, which applies to all the measured pulses, and a so-called A window (A is the acronym for Accidental), which corresponds to accidental coincidences located outside a time window exceeding a certain time delay, which is set equal to about 10 times the neutron detection time in the system. InFigure 4a In the example, the time delay is equal to 1000ns.

[0071] To determine the number of N-order coincidences, we first determine the diversity M of N as it varies from 0 to a predefined maximum integer value max. N The quantity. Obtain the distribution of diversity order, such as in... Figure 4a In a specific example Figure 4b The table provides the information. Based on this distribution, determine the k-th order factorial moment defined by the following relation:

[0072]

[0073] in

[0074] (R+A) k and (A) k These are the k-th factorial moments of the (R+A) and (A) distributions, respectively;

[0075] M N (R+A) and M N (A) represents the order N of the diversity of the distributions (R+A) and (A), respectively; and

[0076] "max" is the order of maximum diversity, which is, for example, equal to the number of detectors in the system.

[0077] The number of true correspondences of orders 1, 2, and 3, also known as untuples, doubletuples, and triplets (S, D, and T), are then given by the following equations (see references [5] and [7]):

[0078] S=(R+A)0=(A)0

[0079] D=(R+A)1-(A)1

[0080]

[0081] S is the total number of pulses in the pulse train.

[0082] Figure 5 An example of a Rossi-alpha curve is shown, which produces a histogram of the number of second-order impulse coincidences as a function of the value of a time window.

[0083] In other words, for each detection, the histogram is obtained by measuring the arrival time of the next pulse. Figure 5 The embodiments in the example utilize 240 The plutonium source was obtained in a detection system composed of PVT plastic scintillators.

[0084] In the graph, a first time window [10-60] ns corresponding to the count of true + unexpected matches and a second time window [260-310] ns corresponding to the count of the number of unexpected matches have been identified.

[0085] In the time interval [0-10] ns, the second-order symbols corresponding to the γγ pairs are concentrated. The time interval [10-60] ns corresponds to the γn and nn pairs.

[0086] To enable accurate quantization of plutonium in the presence of curium, a method using two distinct time intervals to count the number of second-order pulse coincidences was proposed.

[0087] Specifically, the present invention is based on 244 Cm and 240 The difference between the energy spectra of spontaneous fission neutrons in Pu.

[0088] Figure 6 It shows 240 Pu and 244 The energy spectrum of spontaneous fission neutrons in Cm, 601, 602.

[0089] This figure shows the emission probabilities in the energy ranges [0.2–2] MeV and [2–7] MeV. 240 Pu (curve 601) and 244 There are significant differences between Cm (curve 602).

[0090] Figure 7 It shows in 240 Pu(701) and 244 Comparison of Rossi-alpha curves for given values ​​of the binary tuple measured within a time window of [10-60] ns between Cm(702).

[0091] Figure 7 The figure shows the average arrival times of the fission neutrons and gamma particles after the first detection, which is typically the detection of gamma particles due to their velocity (30 cm·ns). -1 The velocity is higher than that of a neutron (a few cm·ns). -1 (This depends on its energy).

[0092] There is a first peak corresponding to the detection of gamma particle pairs, followed by a "bump" corresponding to the detection of pairs involving at least one neutron, the shape of which is similar to... Figure 6 The spectrum in the neutrons has a fairly consistent shape because the velocity of a neutron varies with the square root of its energy. Figure 7 It can be seen from this that 240 Pu and 244There is a significant difference between Cm in the number of 2nd order coincidences in the window [20-60] ns and in the window [10-20] ns. Thus, with 240 Pu, the contribution of Cm is higher in the window of coincidences between 10 and 20 ns compared to the contribution of Pu. This trend is reversed between 20 and 60 ns. In particular, the curves 701, 702 cross approximately at time t = 20 ns. 244 A higher probability of neutrons caused by spontaneous fission being detected is observed for Cm, this trend being reversed between 20 and 60 ns. In particular, the curves 701, 702 cross approximately at time t = 20 ns.

[0093] More particularly, for Figure 7 a numerical example, the values of the number of 2nd order real coincidences are given in the following table for the two time intervals, for plutonium samples and curium samples each containing an equivalent mass of 400 g of 240 Pu, for the same number of coincidences in the total window [10-60] ns.

[0094] 240 Pu (400 g) ​ <![CDATA[ 244 Cm (400 g of 240 Pu eq )]]> D[10-20] ns 286155 299059 D[20-60] ns 553343 535718

[0095] By exploiting this difference in contribution in the two different time windows, it is possible to improve the prediction of the mass of 244 Pu in the sample in the presence of 240 Cm by means of a non-linear regression model.

[0096] In particular, a first time window in which the contribution of 240 Pu is greater than the contribution of 244 Cm and a second time window in which the contribution of 244 Cm is greater than the contribution of 240 Pu are considered as parameters of the non-linear regression model, which allows to improve the prediction of the mass of 240 Pu, as will be explained below.

[0097] The exact boundaries between the two time windows, here equal to 20 ns, are determined experimentally, by searching for the best compromise in terms of performance, for example by testing various time windows and by comparing the predictions of the regression models obtained.

[0098] For example, the two time windows can be defined so that the ratio of the respective number of coincidences of the two elements 240 Pu and 244 Cm is higher than a first predefined threshold in one of the windows and lower than a second predefined threshold in the other window. In the above example, 244 Cm and 240 Pu is equal to 1.04 in the window [10-20] ns and to 0.97 in the window [20-60] ns.

[0099] Step 304 of the method according to the invention includes executing a previously trained nonlinear regression model to determine based on a plurality of coincidence parameters. 240 The quality or quantity of Pu.

[0100] The model is, for example, a multilinear least squares regression model or an artificial neural network as described in reference

[11] , or more generally any trainable model capable of learning to predict the amount of plutonium based on multiple measurements of the number of impulse coincidences.

[0101] Figure 8 , 9 Figures 1 and 10 show the prediction results obtained using a nonlinear regression model based on the Monte Carlo method for simulated data corresponding to sources composed of plutonium and curium.

[0102] The number of configurations corresponds to a full factorial design with three variable parameters, namely... 244 Cm and 240 Pu's quality and 60 The activity of the Co source (emitting two correlated gamma rays at 1173 keV and 1332 keV). A full factorial design including a large number of configurations of the above values ​​was used as a learning database for training the predictive model. Once the model has been trained on this database, it can be used to estimate based on new measurements taken on new, unknown samples. 240 PU quality.

[0103] At least the training data should be given. 244 Cm and 240 The quality of the Pu and the values ​​of the model's explanatory variables (total number of impulses, coincidence number in two different intervals). Training data can be obtained using... Figure 1 and Figure 2 The device shown measures on multiple samples, or can be simulated using Monte Carlo particle transport codes as described in reference [9].

[0104] Figure 8 The graph shows the regression model. 240 The predicted result (y-axis) of the quality of Pu is a function of the actual value of the regression model, which has only the total number of impulses (also known as the unary S) and the number of second-order impulse coincidences counted in a single time window of [10-60] ns (also known as the binary D) as input.

[0105] from Figure 8 As can be seen, the predicted results are highly dispersed and do not closely match the actual values. This is because the model cannot distinguish between the contributions of plutonium and curium across the entire window [10-60] ns, where... 244 Cm and 240Pu has the same number of second-order symbols.

[0106] Figure 9 The prediction results are shown when the model has the following three parameters as input: total number of impulses, first number of second-order true impulse coincidences counted in a first time window equal to [10-20] ns, and second number of second-order true impulse coincidences counted in a second time window equal to [10-60] ns.

[0107] or, Figure 10 The prediction results are shown when the model has the following three parameters as input: total number of impulses, first number of second-order true impulse coincidences counted in a first time window equal to [20-60] ns, and second number of second-order true impulse coincidences counted in a second time window equal to [10-60] ns.

[0108] Figure 9 and Figure 10 This illustrates considering three explanatory variables in the regression model: one is the unary variable, and the other is in two different conformation windows, such as D[10-20]ns and D[10-60]ns (see...). Figure 9 ), or D[20-60]ns and D[10-60]ns (see Figure 10 The tuples counted in the three explanatory variables allow for a higher yield than using a single window D[10-60]ns( Figure 8 (better when) 240 Pu quality prediction.

[0109] Specifically, with Figure 8 Compared to China, Figure 9 or Figure 10 The predicted values ​​are closer to the actual values, regardless of the amount of curium. This result involves dividing the explanatory variables into two distinct windows: the entire window and a window in which either plutonium or curium has a greater influence.

[0110] Figures 8 to 10 The results shown were obtained using data from point source simulations of plutonium and curium located at the center of a 118L barrel filled with cellulose at a density of 0.3. To assess the effects related to the multiplication effect as a result of induced fission (which becomes significant for plutonium masses greater than 100g), a second experimental design with 124 configurations was simulated for PuO2 powder spheres at a density of 3, with the PuO2 powder spheres still located at the center of the same organic matrix.

[0111] In this second experimental design, the simulated variable is the volume of the PuO2 powder spheres, which is related to the total mass of plutonium. 240 Pu's quality and 244 It is related to the quality of Cm.

[0112] Figure 11 The prediction results obtained with the same regression model having as input the total number of pulses, a first number of 2-order pulse coincidences counted in a first time window equal to [10-20] ns and a second number of 2-order pulse coincidences counted in a second time window equal to [10-60] ns are shown.

[0113] Although in Figure 11 a degradation of the performance of the regression model on the results of Figure 9 and 10 was observed, for plutonium masses greater than 100 g, due to the multiplication effect, the performance of the model having 3 of the above explained variables (S, D[10-20] ns and D[10-60] ns) is still fully acceptable for practical applications. 240 Pu equivalent masses, due to the multiplication effect, the performance of the model having 3 of the above explained variables (S, D[10-20] ns and D[10-60] ns) is still fully acceptable for practical applications.

[0114] More generally, the numerical value of the time interval in which the pairs are counted depends on the detection device in question and on the distance between the sample and the detector.

[0115] The intervals chosen as input of the regression model are more generally two consecutive time intervals, in which the two elements 240 Pu and 244 Cm contribute more than the other, and vice versa.

[0116] Another embodiment of the application will now be described, in which the regression model has 5 input parameters: the 3 above parameters S, D[10-20] ns and D[10-60] ns and 2 other parameters, namely a first number of 3-order pulse coincidences counted in a first time window equal to [10-20] ns and a second number of 3-order pulse coincidences counted in a second time window equal to [10-60] ns.

[0117] The regression model consisting of these 5 explained variables allows the influence of the multiplication effect, which is significant for plutonium masses greater than 100 g, to be greatly limited on the estimation of the plutonium mass.

[0118] In particular, the use of 3-order coincidences makes it possible to better exploit the difference in neutron diversity between 244 Cm and 240 Pu. It is thus possible to obtain a better prediction of the mass of 240 Pu with a regression model having 5 explained variables evaluated in one time window between 10 and 20 ns and 5 explained variables evaluated in another time window between 10 and 60 ns.

[0119] Figure 12The prediction results obtained with the model with the 5 variables described above are shown.

[0120] In one variant of the embodiment, the number of 3-order pulse coincidences can be determined by a 2-dimensional histogram of 3-order coincidences.

[0121] Figure 13 This histogram 1300 is illustrated constructed from the pulse train 1301. The histogram represents each combination of 3 coincident pulses 1302, the time interval between the first two pulses is plotted on the axis 2-1 above, and the time interval between the second and third pulses is plotted on the axis 3-2 above.

[0122] The number of 2-order pulse coincidences can be determined by summing the values of a region of interest ROI net of the histogram, which is defined by the desired time windows.

[0123] According to reference [3], this region of interest is given by the following relation:

[0124] ROI net = (ROI raw - A C ) - (A Δ2-1 - A C ) - (A Δ3-2 - A C )

[0125] A C is the common accidental region of the histogram 1300;

[0126] A Δ2-1 is the accidental region along the first axis of the histogram;

[0127] A Δ3-2 is the accidental region along the second axis of the histogram; and

[0128] ROI raw corresponds to the region where counts occur in the given time windows.

[0129] Thus, in a similar way as described above, two explanatory variables of the number of 3-order coincidences determined for the two time windows [10-20] ns and [10-60] ns can be determined via the calculation of ROI net from this histogram 1300.

[0130] Figure 14 The prediction results obtained with the model with the 5 variables described above are shown. Figure 13

[0131] ​In summary, the non-linear regression model performed in step 304 of the method according to the application can have 3 or 5 explanatory variables.

[0132] The first three variables are:

[0133] - the total number of pulses, which corresponds to the number of coincidences of order 1 (unary);

[0134] - a first number of coincidences of order 2 (binary) calculated in a first time window chosen so that the contribution of plutonium is greater than or less than the contribution of curium; and

[0135] - a first number of coincidences of order 2 (binary) calculated in a second time window corresponding to the concatenation of the first time window and the third time window, so that the respective contributions of plutonium and curium are reversed with respect to the first time window.

[0136] The two additional variables are:

[0137] - a first number of coincidences of order 3 (ternary) calculated in the first time window; and

[0138] - a first number of coincidences of order 3 (ternary) calculated in the second time window,

[0139] - the number of coincidences of order 3 can be calculated directly from the pulse trains (ternary) or via the construction of a two-dimensional histogram (ROI net ).

[0140] For example, the first time window is [10-20] ns, the second time window is [10-60] ns, and the third time window is [20-60] ns.

[0141] Alternatively, the first time window is [20-60] ns, the second time window is [10-60] ns, and the third time window is [10-20] ns.

[0142] References

[0143] [1] D. H. Beddingfield, A. P. Belian, “Detection of Cm-244 in Plutonium-Bearing Wastes at Reprocessing Facilities”, Los Alamos National Laboratory, 2004.

[0144] [2] V. Bottau, R. De Stefano, C. Carasco, C. Eleon, B. Perot, “Method for radiation detection comprising neutron-gamma discrimination and corresponding system”, patent application EP 3 835 831 Al.

[0145] [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.

[0146] [4] N. Ensslin, “Passive Nondestructive Assay of Nuclear Materials”, 1991.

[0147] [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.

[0148] [7] N. Ensslin, “Application Guide to Neutron Multiplicity Counting”, LA-13442-M, UC-700, November 1998.

[0149] [8] Patrick M J Chard et al., “Field Examples of Waste Assay Solutions for Curium-Contaminated Wastes”, ICEM2009-16259.

[0150] [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.

[0151]

[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.

[0152]

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

Claims

1. A method for determining the amount of plutonium in a radioactive sample in the presence of curium, the method comprising the steps of: measuring (301) a train of electrical pulses by a radiation detection system, the radiation detection system comprising a plurality of detectors arranged around the sample and capable of generating electrical pulses in response to detecting radioactive particles, determining (302) a first number and a second number of 2nd order pulse coincidences between the electrical pulses delivered by the detectors in a first time window and a second time window, respectively, the second time window consisting of the union of the first time window and a third time window, the first and third time windows being chosen so that the number of 2nd order pulse coincidences related to plutonium is higher in one of the first and third time windows than the number of 2nd order pulse coincidences related to curium and lower 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 and second number of 2nd order pulse coincidences, the model being pre-trained on a set of simulated values obtained using a numerical model.

2. The method for determining the amount of plutonium according to claim 1, wherein, the second time window being chosen so as to include pulse pairs corresponding to (y,n) and (n,n) types of radiation and to exclude pulse pairs corresponding to (y,y) types of radiation.

3. The method for determining the amount of plutonium according to any of the preceding claims, further comprising the steps of: determining (303) a first number and a second number of 3rd order pulse coincidences between the electrical pulses delivered by the detectors in the first and second time windows, respectively; the non-linear regression model further having as parameters the first and second number of 3rd order pulse coincidences.

4. The method for determining the amount of plutonium according to any of claims 1 and 2, further comprising the steps of: determining (303) a first number of 3rd order pulse coincidences between the electrical pulses delivered by the detectors so that a time difference between a first pulse and a second pulse is included in the first time window and a time difference between the second pulse and a third pulse is included in the first time window, determining (303) a second number of 3rd order pulse coincidences between the electrical pulses delivered by the detectors so that the time difference between the first pulse and the second pulse is included in the second time window and the time difference between the second pulse and the third pulse is included in the second time window, the non-linear regression model further having as parameters the first and second number of 3rd order pulse coincidences.

5. The method for determining the amount of plutonium according to any one of claims 3 and 4, wherein, the second time window being chosen so as to include triplets of pulses corresponding to (y,n,n) and (n,n,n) types of radiation and to exclude triplets of pulses corresponding to (y,y,y) types of radiation.

6. The method for determining the amount of plutonium according to any of the preceding claims, 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. The method for determining the amount of plutonium according to any one of claims 1 to 5, 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. A system for determining the amount of plutonium in a radioactive sample in the presence of americium, the system comprising a plurality of detectors arranged around the sample and capable of generating an electrical pulse in response to detecting a radioactive particle, and a computer configured to perform the steps of the method according to any of the preceding claims.

9. The system for determining the amount of plutonium of claim 8, wherein, Each detector comprises an organic plastic scintillator made of polyvinyltoluene (PVT).

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