An analytical calculation method for fission yield variation in strong neutron fields

Abstract

The present invention belongs to the field of calculation technology of fission product nuclear variation, and specifically relates to an analytical calculation method for fission yield variation in a strong neutron field, comprising the following steps: Step S1, determining initialization parameters, including product nuclear ID, burnup depth R, neutron energy E n In step S2, the spectral average cross section is read from the database; in step S3, the change in product nuclear density due to a nuclear reaction channel i is calculated relative to the change in the independent yield; in step S4, the contributions of each nuclear reaction channel calculated in step S3 are summed to obtain the change in product nuclear density. The analytical calculation method for strong neutron field fission yield variation provided by the present invention can rapidly calculate the change in strong neutron field fission yield and reveal the physical mechanism of yield variation, providing important technical support for strong neutron field research in nuclear testing.

Description

Technical Field

[0001] The present invention belongs to the technical field of calculation of fission product nuclear changes, and in particular relates to an analytical calculation method for strong neutron field fission yield changes. Background Art

[0002] During the fission process in a nuclear device, a large number of neutrons are produced. The maximum neutron flux can be orders of magnitude higher than that in a laboratory or reactor, creating a high-density neutron field (HDNS). This high-density neutron field reacts with the product nuclei in secondary reactions, changing their number density. The corresponding yield no longer matches the laboratory yield, necessitating burnup calculations to determine the yield change.

[0003] Currently, aside from Qian Jing's doctoral dissertation in China, which compiled the FIRENEQ calculation program ("A Theoretical Study of the Effect of Strong Neutron Fields on 235U Fission Yield"), no publicly available documentation describes methods for calculating burnup in strong neutron fields. Closer to the present invention are reactor burnup calculation programs. Reactor burnup calculation methods fall into two main categories: numerical methods based on matrix solutions to the burnup equations, and analytical methods based on single burnup chains. For example, the Origen2 program developed by Los Alamos National Laboratory in the 1980s is an analytical method based on Taylor expansion. Numerical calculations also include the burnup calculation module in the Serpent system developed by the Finnish VTT Center, the French burnup program MENDEL, and the European nuclide inventory calculation program FISPACT in the activation calculation system. For an introduction to these, see Wu Mingyu's doctoral dissertation, "Development and Research of a Transport-Burnup Coupling Calculation System Based on STEP 1.0 and MCMG-II." The following describes the analytically based CINDER90 program and the numerically based FIRENEQ calculation program, which are closest to the present invention.

[0004] The CINDER90 program decomposes the nuclear reaction network into individual nuclide chains and then analytically determines the change in nuclide density within each step. A key challenge is the decomposition of the reaction network, which is difficult when loops and nested loops are involved. A second key challenge is ensuring that the neutron flux remains approximately constant within the step length. Trial calculations have shown that the CINDER90 step length cannot be less than 0.1 ns. Within this step length, the neutron flux in strong neutron fields varies significantly. Therefore, CINDER90 is not suitable for burnup calculations in strong neutron fields, resulting in erroneous results.

[0005] The FIRENEQ program uses the numerical GEAR algorithm (see Xu Shiliang's "Common Algorithm Collection") to calculate the entire nuclear reaction network and local networks. There are over 1,300 fission product nuclei, participating in reactions such as (n,γ), (n,2n), (n,3n), (n,p), (n,d), (n,t), (n,3He), and (n,α). The numerical solution is a 1,300x1,300 matrix. Matrix rigidity must be addressed, and more importantly, computational time is a major issue, requiring several hours or even days for each calculation. This is impractical for calculations requiring time-varying model and parameter changes and tens of thousands of iterations. Summary of the Invention

[0006] The purpose of the present invention is to provide an analytical calculation method for the change of fission yield in a strong neutron field, which avoids the programming complexity and time-consuming shortcomings of numerical methods.

[0007] To achieve the above objectives, the technical solution adopted by the present invention is an analytical calculation method for the change of fission yield in a strong neutron field, comprising the following steps:

[0008] Step S1, determine the initialization parameters, including product nucleus ID, burnup depth R, neutron energy E n ,

[0009] Step S2, reading the spectrum average cross section from the database;

[0010] Step S3, calculating the change in product nuclear density for a nuclear reaction channel i relative to the change in independent yield;

[0011] Step S4, summing the contributions of the various nuclear reaction channels calculated in step S3 to obtain a certain product nuclear density change result.

[0012] Furthermore, in step S1, ID=1000A+10Z+Isomer, where A is the mass number of the product nucleus, Z is the charge number of the product nucleus, Isomer is the isomer state of the product nucleus, and E n It is the thermal energy point, fission spectrum energy region or 13.5–14.8MeV energy region.

[0013] Furthermore, in step S2, the spectrum average cross section is based on the microscopic cross section and is averaged by the fission neutron spectrum to obtain the average cross section of the nuclear reaction, as shown in the following formula:

[0014]

[0015] in, is the average, σ is the microscopic cross section, Φ n(E) is the neutron spectrum; the microscopic cross section is obtained through existing databases, including CENLD-3.2 and ENDF / B-VIII; the cross sections missing from the database are obtained through Talys theoretical calculations.

[0016] Furthermore, in step S2, the database is obtained by spectrally averaging the microscopic database.

[0017] Furthermore, in step S3, the change in product nuclear density of a nuclear reaction channel i is calculated according to the following formula:

[0018]

[0019] Among them, dY(i) is the absolute change of core i, Y i is the independent yield of the i-core;

[0020] is the disappearance or generation cross section of nuclear reaction channel i, is the average cross section of the fuel core disappearance; R is the burnup depth, which is an independent variable;

[0021] The cross sections of the product nuclei generation and disappearance are (n,g), (n,2n) and (n,3n) cross sections.

[0022] Furthermore, a CaborA.pl program was written in PERL language to implement the steps S1, S2, S3 and S4.

[0023] The beneficial effects of the present invention are as follows: the analytical calculation method for the change of fission yield in a strong neutron field provided by the present invention can quickly calculate the change of fission yield in a strong neutron field and reveal the physical mechanism of the yield change, providing important technical support for the research on strong neutron fields in nuclear testing. BRIEF DESCRIPTION OF THE DRAWINGS

[0024] Figure 1 This is a flow chart of an analytical calculation method for changes in strong neutron field fission yield in a specific embodiment of the present invention;

[0025] Figure 2 1 is a graph showing the relationship between the change in strong neutron field yield and burnup depth calculated using the CaborA.pl program in a specific embodiment of the present invention, where HE represents the proportion of high-energy neutrons, the lines are numerical calculation results, and the dots are analytical calculation results of the present invention. DETAILED DESCRIPTION

[0026] The present invention provides a method for analytically calculating the change in fission yield in a strong neutron field, comprising the following steps:

[0027] Step S1, determine the initialization parameters, including product nucleus ID, burnup depth R, neutron energy E n ,

[0028] Step S2, reading the spectrum average cross section from the database;

[0029] Step S3, calculating the change in product nuclear density for a nuclear reaction channel i relative to the change in independent yield;

[0030] In step S4, the contributions of the nuclear reaction channels calculated in step S3 are summed to obtain a result of a change in the nuclear density of a certain product.

[0031] In step S1, ID = 1000A + 10Z + Isomer, where A is the mass number of the product nucleus, Z is the charge number of the product nucleus, Isomer is the isomer state of the product nucleus (0, 1 represents the ground state and metastable state, respectively), E n It is the thermal energy point, fission spectrum energy region or 13.5–14.8MeV energy region.

[0032] In step S2, the spectrum average cross section is based on the microscopic cross section and is averaged by the fission neutron spectrum to obtain the average cross section of the nuclear reaction, as shown in the following formula:

[0033]

[0034] in, is the average, σ is the microscopic cross section, Φ n (E) is the neutron spectrum; microscopic cross sections can be obtained from existing databases, including CENLD-3.2 and ENDF / B-VIII (http: / / www-nds.iaea.org); cross sections missing from the databases are obtained through Talys theoretical calculations (http: / / www.talys.eu).

[0035] In step S2, the database is obtained by spectrally averaging the microscopic database.

[0036] In step S3, the change in product nuclear density for a nuclear reaction channel i is calculated according to the following formula:

[0037]

[0038] Among them, dY(i) is the absolute change of core i, Y i is the independent yield of the i-core;

[0039] is the disappearance or generation cross section of nuclear reaction channel i, is the average cross section of the fuel core disappearance; R is the burnup depth, which is an independent variable;

[0040] The cross sections for the generation and disappearance of product nuclei are mainly (n, g), (n, 2n) and (n, 3n) cross sections. Other cross sections are much smaller than these three cross sections and can be ignored.

[0041] The CaborA.pl program was written in PERL language to implement steps S1, S2, S3 and S4.

[0042] The present invention will be further described below with reference to the accompanying drawings and examples.

[0043] All cross sections below are average cross sections. For convenience, σ is used instead of represents the average cross section.

[0044] In a strong neutron field, the differential equation for the change of product nuclear density is:

[0045]

[0046] in, It is expressed as the density of the i-th product nuclide [unit: / b-cm] changing with time. The first term on the right is the number of nuclei i produced by fission per unit time, f(t) is the fission rate [1 / s], y i is the fission yield; the second term on the right is the consumption term of nucleus i, and n(t) is the neutron injection rate [1 / cm 2 -s],σ out is the spectrum average vanishing cross section, which mainly includes the (n,γ), (n,2n), (n,3n) reaction cross sections of the nucleus; the third term on the right is the production term of nucleus i, which is the contribution of other nuclei (j) to the production of nucleus i through reactions such as (n,γ), (n,2n), (n,3n), etc., and the corresponding N j is the nuclear density of other product nuclei, σ in is the corresponding average cross section.

[0047] The neutron flux at the end of the fission process reaches 10 n / cm 2 , the burnup time is x nanoseconds. Based on this information, the main fuel is constructed as X (X is the fuel core, such as uranium-plutonium fuel core), and the relationship between neutron flux and time is:

[0048] n(t)=n(0)exp(λT) (2)

[0049] The value of λ is around 1, and the initial neutron flux is very small, so the integrated flux of neutrons is:

[0050]

[0051] Assuming that the neutron flux increases exponentially, its expression is shown in formula (2). The main nuclear reaction processes of the fuel core X are fission (n, f) and capture (n, g) and other disappearance processes. Its burnup equation can be simplified as follows:

[0052]

[0053] N x represents the fuel core X density [1 / cm-b], σ x It represents the neutron disappearance cross section of the fuel core X, which is approximately equal to the sum of the fission cross section and the capture cross section, with the fission cross section accounting for the majority.

[0054] Transformed, the relationship between the density of the fuel core X and the burning time t can be obtained by integration:

[0055] N x (t) = N x (0)exp(-σ x N n (t)) (5)

[0056] where N n (t) is the integrated neutron flux.

[0057] Burnup depth R is the fraction (ratio) of fuel core consumed, that is,

[0058]

[0059] -σ x N n (t) = log(1-R) ​​(7)

[0060] The corresponding fission number of X is:

[0061] N f (t) = N x (0)Rσ f / σ x (8)

[0062] where σ f / σ x is the ratio of the fission cross section to the vanishing cross section. 147 Ce) as an example, derive 147 The relative change in Ce density. Represented by y7 147 The independent yield of Ce, σ7 represents the vanishing cross section, then 147 The density of Ce is equal to the number produced by fission minus the change in the neutron reaction (disappearance) cross section:

[0063] Ce7(t)≈N f (t)y7 (9)

[0064] Since ΔCe7 is a secondary effect and is small, 147 The density of Ce is approximately the number produced by fission, that is:

[0065]

[0066] in The number of neutrons flowing out due to neutron elimination reactions is:

[0067]

[0068]

[0069] The neutron flux N at the initial moment n (0) = 0. By deriving the above formula, we can get the relationship between the yield change and the cross section and burnup depth. Some processes are omitted. The final relative change in yield is:

[0070]

[0071] Where dY(i) is the yield change caused by nuclear reaction channel i, Y i is the independent output, σ i is the disappearance or generation cross section of the reaction channel of nuclear i, σ x is the fuel core disappearance cross section, and R is the burnup depth.

[0072] By summing up the yield changes related to a certain product core, we can get the yield change of the product core.

[0073] The physical meaning of this formula is concise and clear, and it has an intuitive physical meaning for understanding density changes. It shows that the change in yield has nothing to do with the time function of the neutron flux, but only with the integrated flux.

[0074] The specific implementation of the present invention is to use the PERL language to write the CaborA.pl program, the process is as follows Figure 1 As shown, the main steps are as follows:

[0075] A. Execute the main program CaborA.pl to perform the calculation. The code is shown in Table 1.

[0076] B. Input initialization parameters: product nucleus ID, burnup depth R, neutron energy E n ;

[0077] C. The program reads the reverse yield and average cross section from the database and calculates σ according to the formula i ;

[0078] D. Calculate the contribution of each nuclear reaction channel to the change in product nuclear density (yield) according to formula (13);

[0079] E. Sum the contributions of all nuclear reaction channels involving a product nucleus;

[0080] F. Output the results and end.

[0081] Table 1:

[0082]

[0083] The device described in the present invention is not limited to the embodiments described in the specific implementation manner. Those skilled in the art may derive other implementation manners based on the technical solution of the present invention, which also fall within the scope of the technical innovation of the present invention.

Claims

1. An analytical calculation method for the change of fission yield in a strong neutron field, comprising the following steps: Step S1, determine the initialization parameters, including product nucleus ID, burnup depth R, neutron energy E n , Step S2, reading the spectrum average cross section from the database; Step S3, calculating the change in product nuclear density for a nuclear reaction channel i relative to the change in independent yield; Step S4, summing the contributions of each nuclear reaction channel calculated in step S3 to obtain a result of a change in the nuclear density of a product; In step S3, the change in product nuclear density of a nuclear reaction channel i is calculated according to the following formula: in, dY(i) is the absolute change of core i, Y i is the independent yield of the i-core; is the disappearance or generation cross section of nuclear reaction channel i, is the average cross section of the fuel core disappearance; R is the burnup depth, which is an independent variable; The cross sections of the product nuclei generation and disappearance are (n,g), (n,2n) and (n,3n) cross sections.

2. The analytical calculation method for the change of strong neutron field fission yield as claimed in claim 1, characterized in that: In the step S1, ID=1000A+10Z+Isomer, where A is the mass number of the product nucleus, Z is the charge number of the product nucleus, Isomer is the isomer state of the product nucleus, and E n It is the thermal energy point, fission spectrum energy region or 13.5-14.8MeV energy region.

3. The analytical calculation method for the change of strong neutron field fission yield as claimed in claim 1, characterized in that: In step S2, the spectrum average cross section is based on the microscopic cross section and is averaged by the fission neutron spectrum to obtain the average cross section of the nuclear reaction, as shown in the following formula: in, is the average, σ is the microscopic cross section, Φ n (E) is the neutron spectrum; the microscopic cross section is obtained through existing databases, including CENLD-3.2 and ENDF / B-VIII; the cross sections missing from the database are obtained through Talys theoretical calculations.

4. The analytical calculation method for the change of strong neutron field fission yield according to claim 3, characterized in that: In step S2, the database is obtained by spectrally averaging the microscopic database.

5. The analytical calculation method for the change of fission yield in a strong neutron field according to claim 1, characterized in that: The CaborA.pl program is written in PERL language to implement the steps S1, S2, S3 and S4.

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