A method for neutron flux distribution inversion based on PGNAA technology

Abstract

The present invention discloses a method for inverting neutron flux distribution based on the PGNAA technology. This method utilizes the characteristics of the in-situ radioactivity and high penetrability of neutron-induced gamma rays in the PGNAA technology. Intervals are divided according to the neutron field distribution to be analyzed, and a gamma-ray detector array is set around the neutron field. Gamma-ray volume sources are set in each interval based on Monte Carlo simulation. The response factors between each gamma-ray volume source and the detector array are obtained through simulation calculation, that is, the response function of the detector to the gamma-ray volume sources in each interval, and a response matrix is established. The gamma-ray detector array is used to collect the neutron-induced gamma rays in the materials within the neutron field, and inversion calculation is carried out in combination with the response matrix obtained through simulation calculation to obtain the neutron flux in each interval of the neutron field, and thus the neutron flux distribution of the neutron field can be obtained. The present invention effectively reduces the interference effects of gamma-ray background and strong radiation field on neutron measurement in the traditional method, and the measurement of neutron flux distribution inversion is simple and has high accuracy.

Description

Technical Field

[0001] The present invention belongs to the field of neutron physics, and particularly relates to a method for inverting neutron flux distribution based on PGNAA technology. Background Art

[0002] To meet the development goals of sustainability, safety, reliability, and economy, the reactor system is constantly undergoing technological updates and iterations. The existing major advanced reactor types under development include liquid sodium-cooled fast neutron reactor (SFR), liquid lead-cooled fast neutron reactor (LFR), very high temperature reactor (VHTR), supercritical pressure water-cooled reactor (SCWR), gas-cooled fast neutron reactor (GFR), molten salt liquid reactor (MSR), etc. However, these advanced reactor types generally require extreme reaction conditions, such as extremely high temperature, and the existing in-core measurement systems cannot meet the requirements of real-time measurement of the neutron field in the advanced reactor core.

[0003] The conventional neutron flux monitoring method for reactors is to insert a self-powered detector through an opening in the reactor body for monitoring. This detector is expensive, complex to operate, requires regular replacement, and will greatly affect the structural strength of the reactor body. In addition, when the instrument is used in the reactor, an opening needs to be made in the cladding and placed in the reactor, and the opening will have a great impact on the safety performance of the cladding. Moreover, when facing the fourth-generation reactors such as high-temperature gas-cooled reactors, the complex environment of high temperature and high pressure in the reactor will have a great interference on the measurement accuracy of the instrument and the measurement method.

[0004] The instrument based on the nuclear reaction method is also sensitive to gamma rays in the neutron-gamma mixed radiation field, so the measurement result is greatly affected by gamma ray interference.

[0005] The currently developed out-of-reactor detection methods are mainly based on neutron transport theory, directly detecting neutrons outside the reactor for inverting neutron flux distribution. However, the above methods are complex, have poor accuracy, and low feasibility, and cannot meet the measurement requirements of advanced nuclear reactors.

[0006] The existing commonly used absolute measurement method is nuclear activation method. The measurement accuracy of the nuclear activation method is restricted by the purity of the activation foil, the half-life of the nuclide, the accuracy of the cross-section, etc. Secondly, this method needs to wait for the activation foil to be irradiated and then analyzed and measured, and cannot realize the on-line real-time measurement of neutron information and flux distribution, and the detection efficiency is relatively low.

[0007] Prompt Gamma-ray Neutron Activation Analysis (PGNAA) is a nuclear analysis technique that has many advantages over other analysis techniques in the field of measurement and analysis, including high penetrability, non-destructiveness, in-situ emission, and high analysis accuracy. The PGNAA technique mainly utilizes prompt gamma rays. When neutrons interact with matter, radiation capture and inelastic scattering reactions occur, and characteristic energy gamma rays are emitted within an extremely short time (less than 10 - 14 s), and by obtaining the gamma-ray energy spectrum through a photon detector, most nuclides and their contents can be qualitatively and quantitatively identified. Therefore, it is expected to develop a new method for inverting neutron flux distribution based on the PGNAA technique by using the neutron information provided by neutron-induced gamma rays, which can effectively realize the computational inversion of neutron flux distribution. Summary of the Invention

[0008] In order to overcome the shortcomings and deficiencies of the prior art, the purpose of the present invention is to provide a method for inverting neutron flux distribution based on the PGNAA technique.

[0009] The present invention is implemented as follows. A method for inverting neutron flux distribution based on the PGNAA technique includes the following steps:

[0010] S1. Construct a neutron field model based on Monte Carlo simulation software, and construct a corresponding PGNAA experimental platform, including a neutron source, a gamma-ray detector array, and structural materials within the neutron field, and divide the neutron field into intervals;

[0011] S2. Set gamma-ray volume sources in each interval, and obtain the response factors between each gamma-ray volume source and the detector array through simulation calculation or experimental testing, that is, the response function of the detector to the gamma-ray volume sources in each interval, and establish a response matrix;

[0012] S3. Set the neutron source to perform Monte Carlo simulation calculation or experimental testing. Neutrons undergo radiation capture or inelastic scattering reactions with the structural materials within the neutron field, generating prompt gamma rays with characteristic energies. Use the gamma-ray detector array to obtain the corresponding gamma-ray energy spectrum, and thus calculate the net count of the prompt gamma-ray characteristic peaks at different characteristic energies;

[0013] S4. Based on the net count data of the prompt gamma-ray characteristic peaks obtained in step S3, combined with the response matrix established in step S2, use a mathematical algorithm for inversion calculation to obtain the neutron flux values in different intervals, thereby obtaining the neutron flux distribution within the neutron field.

[0014] Preferably, in step S1, the Monte Carlo simulation software is selected from any one of MCNP, Geant4, and FLUKA.

[0015] Preferably, in step S1, the gamma-ray detector is selected from any one of a sodium iodide (NaI) detector, a bismuth germanate (BGO) detector, a lanthanum bromide (LaBr3) detector, and a high-purity germanium (HPGe) detector.

[0016] Preferably, in step S1, the neutron source is selected from any one of a deuterium-tritium neutron generator (DT), a deuterium-deuterium neutron generator (DD), an americium-beryllium neutron source (AmBe), and a californium neutron source (Cf);

[0017] The structural material in the neutron field is selected from at least one of water (H2O), graphite (C), and boric acid (H3BO3).

[0018] Preferably, in step S2, the response matrix is:

[0019]

[0020] where f ij is the net count of the gamma-ray characteristic peak emitted by the gamma-ray source in the j th interval in the neutron field obtained by the i th gamma-ray detector, that is, the gamma-ray response factor.

[0021] Preferably, in step S3, the specific method for obtaining the corresponding gamma energy spectrum by using the gamma-ray detector array and then calculating the net count of the prompt gamma-ray characteristic peak at different characteristic energies is as follows: Use the gamma-ray detector array to obtain the corresponding gamma energy spectrum, calculate the count of the prompt gamma-ray characteristic peak at different characteristic energies, use the difference calculation method to subtract the background under the characteristic peak, and obtain the net count of the prompt gamma-ray characteristic peak at different characteristic energies.

[0022] Preferably, in step S4, according to the mathematical mapping relationship between the net count of the prompt gamma-ray characteristic peak and the neutron flux in the PGNAA technology, the neutron flux is expressed as:

[0023]

[0024] where N is the neutron flux, A is the net count of a certain prompt gamma-ray characteristic peak, f is the gamma-ray response factor, and σ is the neutron reaction cross-section corresponding to the characteristic energy;

[0025] The mathematical mapping relationship expression between the net count of the prompt gamma-ray characteristic peak generated by the reaction of neutrons collected by the gamma-ray detector with the material and the neutron flux in each interval, that is, the neutron flux distribution in the neutron field is:

[0026]

[0027] where N i is the neutron flux in the i-th interval, and A j is the net count of the prompt gamma-ray characteristic peak with a certain characteristic energy collected by the j-th gamma-ray detector in the gamma-ray detector array, and f is the gamma-ray response factor.

[0028] Preferably, in step S4, the mathematical algorithm is selected from one of the algebraic reconstruction algorithm (ART), total variation minimization of the image (TVM), maximum likelihood expectation maximization algorithm (MLEM), and iteratively reweighted least squares method (IRLS).

[0029] The present invention overcomes the deficiencies of the prior art and provides a method for inverting neutron flux distribution based on the PGNAA technology. This method mainly utilizes the characteristics of the in-situ emission and high penetrability of neutron-induced gamma rays of the PGNAA technology. The interval is divided according to the neutron field distribution to be analyzed, and a gamma-ray detector array is set around the neutron field. Based on Monte Carlo simulation, gamma-ray volume sources are set in each interval, and the response factor between each gamma-ray volume source and the detector array, that is, the response function of the detector to the gamma-ray volume source in each interval, is obtained through simulation calculation to establish a response matrix. The neutron-induced gamma rays in the material in the neutron field are collected by the gamma-ray detector array, and the inversion calculation is carried out in combination with the response matrix obtained by simulation calculation to obtain the neutron flux in each interval of the neutron field, and then the neutron flux distribution of the neutron field can be obtained.

[0030] Compared with the disadvantages and deficiencies of the prior art, the present invention has the following beneficial effects:

[0031] (1) Compared with the traditional neutron flux measurement method, the present invention faces the complex radiation field environment of the reactor core. Through "off-site" measurement, effective nuclear information extraction is carried out on the gamma-ray background induced by neutrons, and the neutron information is converted into prompt characteristic gamma-ray information, and the spatial distribution information of the neutron fluence in the radiation field is inversely obtained, effectively reducing the interference effects of the gamma-ray background and the strong radiation field on neutron measurement in the traditional method. At the same time, it provides a new measurement method for neutron diagnostic analysis;

[0032] (2) The present invention uses the signal-to-interference ratio (VIR) as an evaluation parameter, and optimizes the physical structure of the PGNAA experimental platform based on a new signal-to-interference ratio optimization design method, improves the utilization rate of effective signals, reduces the influence of system interference noise on the statistical nature of effective nuclear information, and improves the measurement level of the PGNAA experimental platform from a hardware perspective;

[0033] (3) The method of the present invention utilizes the neutron information implicit in gamma rays to realize the inversion of neutron flux distribution. The measurement is simple and highly accurate, greatly improving the feasibility of the indirect measurement method for neutron flux distribution. BRIEF DESCRIPTION OF THE DRAWINGS

[0034] Figure 1 is a flowchart of the method steps in an embodiment of the present invention;

[0035] Figure 2 is a top view of the neutron field model in an embodiment of the present invention;

[0036] Figure 3 is a gamma energy spectrum diagram of the interaction between neutrons and materials in an embodiment of the present invention;

[0037] Figure 4 is a schematic distribution diagram of neutron sources ① and ② at two different positions in an embodiment of the present invention;

[0038] Figure 5 is a thermal neutron flux distribution diagram under neutron source ① in an embodiment of the present invention; wherein, Figure A is the inversion distribution diagram, and Figure B is the actual distribution diagram;

[0039] Figure 6 is a fast neutron flux distribution diagram under neutron source ① in an embodiment of the present invention; wherein, Figure A is the inversion distribution diagram, and Figure B is the actual distribution diagram;

[0040] Figure 7 is a thermal neutron flux distribution diagram under neutron source ② in an embodiment of the present invention; wherein, Figure A is the inversion distribution diagram, and Figure B is the actual distribution diagram;

[0041] Figure 8 is a fast neutron flux distribution diagram under neutron source ② in an embodiment of the present invention; wherein, Figure A is the inversion distribution diagram, and Figure B is the actual distribution diagram. DETAILED DESCRIPTION OF THE EMBODIMENTS

[0042] In order to make the objectives, technical solutions and advantages of the present invention clearer and more understandable, the present invention will be further described in detail below with reference to the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are only used to explain the present invention and are not used to limit the present invention.

[0043] An embodiment of the present invention discloses a method for inverting neutron flux distribution based on PGNAA technology, in combination with Figure 1It is understood that the method includes the following steps:

[0044] S1. Based on Monte Carlo simulation software, construct a neutron field model, and construct a corresponding PGNAA experimental platform, including a neutron source, a gamma-ray detector array, and structural materials in the neutron field, and divide the neutron field into intervals.

[0045] Specifically, based on Monte Carlo simulation software, construct a neutron field model, a neutron source, a gamma-ray detector array, and structural materials. The Monte Carlo simulation software includes several or all of MCNP, Geant4, and FLUKA. The gamma-ray detector is one of a sodium iodide (NaI) detector, a bismuth germanate (BGO) detector, a lanthanum bromide (LaBr3) detector, or a high-purity germanium (HPGe) detector. The neutron source is one of a deuterium-tritium neutron generator (DT), a deuterium-deuterium neutron generator (DD), an americium-beryllium neutron source (AmBe), or a californium neutron source (Cf). The structural materials in the neutron field are one or several of water (H2O), graphite (C), and boric acid (H3BO3).

[0046] S2. Set gamma-ray body sources in each interval, and obtain the response factors between each gamma-ray body source and the detector array through simulation calculation or experimental testing, that is, the response function of the detector to the gamma-ray body source in each interval, and establish a response matrix.

[0047] Specifically, set gamma-ray body sources in the intervals in sequence, use the set gamma-ray detectors to obtain the gamma-ray energy spectra of the gamma-ray body sources in each interval respectively, and obtain the net counts of the characteristic peaks in the corresponding energy spectra to form response factors, and establish a response matrix. The response matrix F is:

[0048] (1)

[0049] In formula (1), f ij is the j th gamma-ray detector to obtain the net count of the characteristic peak of the gamma-ray emitted by the gamma-ray body source in the i th interval in the neutron field, that is, the gamma-ray response factor.

[0050] S3. Set the neutron source to perform Monte Carlo simulation calculation or experimental testing. The neutrons react with the structural materials in the neutron field to undergo radiative capture or inelastic scattering reactions, generating prompt gamma rays with characteristic energies. Use the gamma-ray detector array to obtain the corresponding gamma energy spectra, and thus calculate the net counts of the characteristic peaks of the prompt gamma rays at different characteristic energies.

[0051] Specifically, a neutron source is set in the Monte Carlo simulation calculation or the PGNAA experimental platform. Neutrons react with the structural materials in the neutron field, and the generated gamma rays are collected by gamma ray detectors to form an energy spectrum. The prompt gamma ray characteristic peak counts at different characteristic energies are calculated, and the background under the characteristic peaks is subtracted using the difference calculation method to obtain the net counts of different prompt gamma ray characteristic peaks.

[0052] S4. Based on the net count data of the prompt gamma ray characteristic peaks obtained in step S3, combined with the response matrix established in step S2, an inversion calculation is performed using a mathematical algorithm to obtain the neutron flux values in different intervals, thereby obtaining the neutron flux distribution in the neutron field.

[0053] Specifically, according to the mathematical mapping relationship between the net count of the prompt gamma ray characteristic peaks and the neutron flux in the PGNAA technology, it can be expressed as:

[0054] (2)

[0055] In formula (2), N is the neutron flux, A is the net count of the prompt gamma ray characteristic peak at a certain characteristic energy, f is the gamma ray response factor, and σ is the neutron reaction cross section corresponding to the characteristic energy.

[0056] Therefore, the mathematical mapping relationship expression (i.e., the neutron flux distribution in the neutron field) between the net count of the prompt gamma ray characteristic peaks generated by the reaction of neutrons collected by the gamma ray detector with the material and the neutron flux in each interval is: (3)

[0057] In formula (3), N i is the neutron flux in the i-th interval, A j is the net count of the prompt gamma ray characteristic peak at a certain characteristic energy collected by the j-th gamma ray detector in the gamma ray detector array, and f is the gamma ray response factor.

[0058] In step S4, an inversion calculation is performed using a mathematical algorithm, and the mathematical algorithm is one or several of the algebraic reconstruction algorithm (ART), total variation minimization of images (TVM), maximum likelihood expectation maximization algorithm (MLEM), and iterative reweighted least squares method (IRLS).

[0059] The present invention and its beneficial effects will be further described below through specific examples:

[0060] Based on Monte Carlo simulation, the simulation container is a cylindrical barrel with a diameter of 150 cm and a height of 50 cm. The barrel is divided into 5×5 = 25 grid voxels, as Figure 2As shown in the figure; the material inside the container is water (H2O); the photon detector selects a BGO scintillation detector, numbered 1 to 30 and evenly distributed around the barrel, and the center height of the detector is at the same horizontal height as the position where the neutrons are emitted by the neutron generator. Based on the in-situ emission characteristics of prompt gamma rays, neutrons generated by the neutron source bombard the surrounding water, and reactions such as radiative capture and inelastic scattering occur, emitting characteristic gamma rays with energies of 2.23 and 6.13 MeV in a very short time. The gamma-ray energy spectrum is obtained through the detector.

[0061] As Figure 3 shown is the gamma-ray energy spectrum generated by the interaction between neutrons and the material inside the barrel in this embodiment. The characteristic energy peaks corresponding to different elements can be easily found. Considering the expression for the net count of the characteristic energy prompt gamma-ray characteristic peak generated by the neutron reaction in a certain voxel received by a single photon detector is: (4)

[0062] In Equation (4), N1 represents the neutron flux magnitude at position 1, A 11 represents the net count of the characteristic peak of the prompt gamma rays generated by N1 received by the No. 1 detector, and f 11 represents the response factor between the No. 1 detector and the gamma-ray voxel at position 1, that is, the photon detection efficiency.

[0063] Furthermore, according to the response equations of each detector separately for the net count of the characteristic energy prompt gamma-ray characteristic peak generated by neutrons in each voxel, the following system of equations is established

[0064] (5)

[0065] where A1 = A 11 + A 21 + A 31 + … + A 251 represents the sum of the net counts of the characteristic energy prompt gamma-ray characteristic peaks generated by neutrons in all 25 voxels received by the No. 1 detector. For the convenience of later data processing, the system of equations established above can be expressed in the form of a matrix equation: (6)

[0066] In Equation (6), N 1~25 represents the neutron flux magnitude, and the response matrix F is the response relationship between the net count of the characteristic peak of the prompt gamma rays generated by the interaction between neutrons and matter and the detector.

[0067] Design two groups of neutron source distributions. As Figure 4 shown, ① and ② are two neutron sources at different positions. A deuterium-tritium neutron generator (DT) is used. They only differ in position, and their energies and other parameters are the same.

[0068] Using Monte Carlo simulation, the response matrix F in Equation (6) is obtained according to the steps described in S2. The prompt gamma-ray characteristic peak net counts A1 to A in Equation (6) are respectively detected using a gamma-ray detector 30 , and an A matrix on the left side of Equation (6) is formed. The maximum likelihood expectation maximization algorithm (MLEM) is used for back-solving to obtain the neutron flux magnitudes N1 to N of each voxel 30 . The back-solving results are quantitatively compared with the measured results and visualized.

[0069] Specifically, Figure 5 、 Figure 6 are the thermal neutron and fast neutron distributions obtained by inverse inversion of the radiation capture and inelastic scattering of neutrons with H and O in water under neutron source ① Figure 7 、 Figure 8 are the thermal neutron and fast neutron distributions obtained by inverse inversion of the radiation capture and inelastic scattering of neutrons with H and O in water under neutron source ②. The quantitative evaluation criterion structural similarity (SSIM) is introduced, and the inversion results are compared with the corresponding actual results:

[0070] (7)

[0071] In Equation (7), 、 are the means of images x and y; 、 are the standard deviations of images x and y; is the covariance; c 1、 c 2 are constant terms to avoid a denominator of 0. The range of SSIM is -1 to 1. The more similar images x and y are, the closer the value is to 1.

[0072] Analysis of the comparison results: The similarity between the fast neutron inversion distribution of neutron source ② and the actual distribution is equal to 0.74. The SSIM values of the remaining inversion distributions and the simulated and measured distributions are all greater than 0.8, that is, the neutron flux distribution obtained by inversion has a high similarity with the simulated and measured distributions.

[0073] Based on prompt gamma rays, the present invention utilizes its in-situ emission characteristics and high penetrability, and combines the deconvolution iterative algorithm MLEM to inversely obtain the neutron flux distribution, optimizing the method for solving the neutron flux distribution based on the traditional neutron transport theory, with good results.

[0074] The above are only the preferred embodiments of the present invention and are not intended to limit the present invention. Any modifications, equivalent replacements, and improvements made within the spirit and principles of the present invention shall be included within the protection scope of the present invention.

Claims

1. A method for inverting neutron flux distribution based on PGNAA technology, characterized in that, The method includes the following steps: S1. Construct a neutron field model based on Monte Carlo simulation software, and construct a corresponding PGNAA experimental platform, including a neutron source, a gamma-ray detector array, and structural materials in the neutron field, and divide the neutron field into intervals; S2. Set gamma body sources in each interval, and obtain the response factors between each gamma body source and the detector array through simulation calculation or experimental testing, that is, the response function of the detector to the gamma body sources in each interval, and establish a response matrix; S3. Set the neutron source to conduct Monte Carlo simulation calculation or experimental testing. The neutrons react with the structural materials in the neutron field to generate prompt gamma rays with characteristic energies through radiative capture or inelastic scattering reactions. Use the gamma-ray detector array to obtain the corresponding gamma energy spectra, and thus calculate the net counts of the prompt gamma-ray characteristic peaks at different characteristic energies; S4. Based on the net count data of the prompt gamma-ray characteristic peaks obtained in step S3, combined with the response matrix established in step S2, use a mathematical algorithm for inversion calculation to obtain the neutron flux values in different intervals, and thus obtain the neutron flux distribution in the neutron field; In step S3, the specific process of using the gamma-ray detector array to obtain the corresponding gamma energy spectra and thus calculate the net counts of the prompt gamma-ray characteristic peaks at different characteristic energies is as follows: Use the gamma-ray detector array to obtain the corresponding gamma energy spectra, and thus calculate the counts of the prompt gamma-ray characteristic peaks at different characteristic energies. Use the difference calculation method to subtract the background under the characteristic peaks to obtain the net counts of the prompt gamma-ray characteristic peaks at different characteristic energies.

2. The method according to claim 1, wherein In step S1, the Monte Carlo simulation software is selected from any one of MCNP, Geant4, and FLUKA.

3. The method according to claim 1, wherein In step S1, the gamma-ray detector is selected from any one of sodium iodide detectors, bismuth germanate detectors, lanthanum bromide detectors, and high-purity germanium detectors.

4. The method according to claim 1, wherein In step S1, the neutron source is selected from any one of deuterium-tritium neutron generators, deuterium-deuterium neutron generators, americium-beryllium neutron sources, and californium neutron sources; The structural materials in the neutron field are selected from at least one of water, graphite, and boric acid.

5. The method according to claim 1, characterized in that, In step S2, the response matrix is: ； Among them, f ij is the j net count of the gamma-ray characteristic peak emitted by the gamma body source in the i th interval within the neutron field obtained by the th gamma-ray detector, that is, the gamma-ray response factor.

6. The method according to claim 1, characterized in that In step S4, according to the mathematical mapping relationship between the net count of the prompt gamma-ray characteristic peak and the neutron flux in PGNAA technology, the neutron flux is expressed as: ； where N is the neutron flux, A is the net count of a certain prompt gamma-ray characteristic peak, f is the gamma-ray response factor, and σ is the neutron reaction cross-section corresponding to the characteristic energy; The mathematical mapping relationship expression between the net count of the prompt gamma-ray characteristic peak generated by the reaction of the neutrons collected by the gamma-ray detector with the material and the neutron flux in each interval, that is, the neutron flux distribution in the neutron field is: ； Among them, N i is the neutron flux in the i-th interval, A j is the net count of a characteristic peak of prompt gamma rays with a certain characteristic energy collected by the j-th gamma ray detector in the gamma ray detector array, f ij is the gamma ray response factor.

7. The method according to claim 1, wherein In step S4, the mathematical algorithm is selected from one of the algebraic reconstruction algorithm, total variation minimization of the image, maximum likelihood expectation maximization algorithm, and iterative reweighted least squares method.

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