Improved neutron multiplex calculation model for uranium and plutonium analysis

Abstract

The invention belongs to the technical field of nuclear material balance analysis, and discloses an improved neutron multiplex calculation model for uranium and plutonium analysis, and the calculation model of a uranium increment factor M is a0 + a1M + a2M2 + a3M3 = 0; the calculation model of the plutonium multiplication factor M is a0 + a1M + a2M2 + a3M3 = 0; a novel relation calculation model of the plutonium multiplication factors M and alpha is a0 + a1N + a2N2 = 0; and the calculation model of the fission rate F is # imgabs0 # alpha, and the calculation model of the fission rate F is # imgabs1 #. A novel relational expression among related parameters is given, and an optimization processing algorithm is designed for the realization of the neutron multiplex calculation model, so that many problems of the existing model are eliminated, repeated calculation is avoided, and the calculation efficiency is greatly improved.

Description

Technical Field

[0001] The invention relates to the technical field of nuclear material balance analysis, in particular to an improved neutron multiplicity calculation model for uranium and plutonium analysis. Background Art

[0002] Nuclear material neutron measurement technology is to analyze samples by detecting neutrons emitted by spontaneous or induced fission of plutonium / uranium samples. There are three main methods: total neutron measurement technology, coincident neutron measurement technology and neutron multiplicity measurement technology. Compared with the first two technologies, neutron multiplicity technology has high measurement accuracy and fast measurement speed. In particular, fast neutron multiplicity experiments have transitioned from the original microsecond level to nanosecond level to collect and process data. The data processing volume is huge and has been applied to fields such as nuclear security and verification.

[0003] The neutron multiplicity measurement technology measures the neutron multiplicity counting rate (one count rate S, two count rate D, three count rate T), and then solves the unknown parameters (the ratio of the sample (α,n) reaction rate to the spontaneous fission neutron emission rate α, the sample's neutron multiplication factor M, the sample's induced fission rate F) through a calculation model between the sample's unknown parameters and the measurement parameters, and then calculates the equivalent mass of the nuclear material.

[0004] However, the current computational model has many problems and low computational efficiency. Summary of the invention

[0005] The present invention aims to provide an improved uranium and plutonium analysis neutron multiplicity calculation model, provides a new relationship between related parameters, and designs an optimization processing algorithm for the implementation of the neutron multiplicity calculation model, eliminating many problems of the existing model, avoiding repeated calculations, and greatly improving the calculation efficiency. Solve the problems in the background technology.

[0006] In order to achieve the above object, the present invention provides the following technical solutions:

[0007] An improved neutron multiplicity calculation model for uranium and plutonium analysis,

[0008] The calculation model of uranium multiplication factor M is: a0+a1M+a2M 2 +a3M 3 =0

[0009] in,

[0010]

[0011]

[0012] The calculation model of plutonium multiplication factor M is: a0+a1M+a2M 2 +a3M 3=0, where

[0013] a0=-T

[0014]

[0015] The calculation model of the new relationship between plutonium multiplication factor M and α is: a0+a1N+a2N 2 =0, where

[0016]

[0017] The calculation model of the fission rate F is:

[0018] The calculation model of α is:

[0019] Where ε is the detection efficiency; F is the sample induced fission rate; f D and f T are the coincidence shares of the second and third counting rates, respectively; M is the material multiplication factor; α is the ratio of the sample (α,n) reaction rate to the spontaneous fission neutron emission rate; V sk is the k-order distance of spontaneous fission neutron multiplicity, k = 1, 2, 3; S, D, T are the third-order distances of the neutron multiplicity distribution that finally escapes from the material, which are the first count rate, the second count rate, and the third count rate, respectively; G is the gate width, P d is the pre-delay, τ is the decay time, S0 is the background count rate of the Am-Li source, B is the ambient background count rate, S s It is the counting rate of the source background counting rate changed due to sample absorption and scattering after the sample is placed.

[0020] Furthermore, the calculation models of the secondary counting rate D and the tertiary counting rate T in the calculation model of the uranium multiplication factor M are as follows:

[0021]

[0022] Furthermore, when solving the calculation model of the uranium multiplication factor M, the calculation sequence is calculated in the following order:

[0023]

[0024] c0=b0b2

[0025] c1=b0v i2

[0026] a0=-b2(v s2 -b0)=b2v s2 -c0

[0027] a1=v s3 +c0-b1+c1

[0028] a2=b1-2c1

[0029] a3=c1.

[0030] Furthermore, the calculation model of the plutonium multiplication factor M, the calculation model of the first counting rate S, the second counting rate D and the third counting rate T in the calculation model of the new relationship between the multiplication factor M and α are as follows:

[0031] S=FMεv s1 (1+α)

[0032]

[0033] Furthermore, the calculation steps of M, F, and α of plutonium are calculated according to the following sequence:

[0034]

[0035] c4=v i2 c2

[0036] c5=3c1Dc4

[0037] a0=-T

[0038] a1=c1Dc3-c5

[0039] a3=c0c1s(c2v i3 -c4c3)

[0040] a2=-a3+c5;

[0041] Then call the cubic algebraic equation solver to calculate M, and then calculate F

[0042]

[0043] Finally, calculate α.

[0044] The beneficial effects of the technical solution are:

[0045] The invention discloses an improved uranium and plutonium analysis neutron multiplicity calculation model. Through research, the invention provides a detailed derivation process of the sample multiplication calculation equation in uranium and plutonium and a new relationship equation between the sample multiplication factor M and the reaction rate ratio α in the plutonium material research. The invention also provides a mathematical model of an optimization algorithm for calculating the sample multiplication factor M, the fission rate F and the reaction rate ratio α, thereby eliminating many problems of the existing model, avoiding repeated calculations and greatly improving the calculation efficiency. DETAILED DESCRIPTION

[0046] The present invention is further described in detail below in conjunction with the embodiments:

[0047] (I) The derivation process of the calculation model of uranium multiplication factor M is as follows:

[0048] S1. The S, D, and T calculation model for obtaining uranium material samples is as follows:

[0049] S=S0+B+S s +FMεV s1 (1)

[0050]

[0051] Among them, S0 is the background count rate of Am-Li source, B is the background count rate of environment, S s is the count rate of the source background count rate changed due to sample absorption and scattering after the sample is placed, ε is the detection efficiency; F is the sample induced fission rate; f D and f T are the coincidence shares of the second and third counting rates, respectively; M is the material multiplication factor; α is the ratio of the sample (α,n) reaction rate to the spontaneous fission neutron emission rate; V sk is the k-order distance of the spontaneous fission neutron multiplicity, k = 1, 2, 3; S, D, T are the third-order distances of the neutron multiplicity distribution that finally escapes from the material.

[0052] Note that the statistical value of D accounts for only a fraction of the second moment of the multiplicity distribution of neutrons escaping from the material, and its fraction is expressed by f D It means that under certain conversion conditions, f T =f D 2 , f D The calculation formula is

[0053]

[0054] Where G is the door width, P d is the pre-delay and τ is the decay time.

[0055] S2, obtained from (2) and (3)

[0056]

[0057] After reorganizing (5), the calculation model of uranium multiplication factor M can be obtained:

[0058] a0+a1M+a2M 2 +a3M 3 =0 (6)

[0059] in,

[0060]

[0061] Solve a0+a1M+a2M 2+a3M 3 =0, we need to calculate a0, a1, a2 a3 first, but it is troublesome to calculate directly and the amount of calculation is large. Observe the relationship between a0, a1, a2 a3, and calculate according to the following calculation sequence

[0062]

[0063] c0=b0b2 (14)

[0064] c1=b0v i2 (15)

[0065] a0=-b2(v s2 -b0)=b2v s2 -c0 (16)

[0066] a1=v s3 +c0-b1+c1 (17)

[0067] a2=b1-2c1 (18)

[0068] a3=c1 (19)

[0069] In this way, when simulating or automatically calculating, first calculate b0, b1, b2, c0, c1, then calculate a0, a1, a2 a3, and finally calculate a0+a1M+a2M according to the principle of solving the cubic equation. 2 +a3M 3 = 0, and obtain the sample proliferation factor M. After obtaining M, the sample induced fission rate F is calculated according to the calculation model (2).

[0070] Although theoretically, the sample induced fission rate F can be calculated using the T calculation model (3), the relevant technology emphasizes that the sample induced fission rate F should be calculated according to the D calculation model (2) because the measurement error of T is large. This is difficult to logically reason out, because the measurement result of T is used in the calculation of the sample proliferation factor M, and the measurement result of T is used in the calculation of the sample induced fission rate F. It is also possible to simulate or eliminate the influence of the measurement result of T. The correctness of this reasoning logic is difficult to eliminate. The best way is to start from the two situations, calculate them separately, and then perform a large number of simulation calculations and level tests, and finally provide a statistical analysis data processing table.

[0071] In summary, the present invention re-derives and obtains an optimized calculation model of the uranium multiplication factor M, and provides an optimized model for the equation solving method to avoid repeated calculations and greatly improve the calculation efficiency.

[0072] (II) The derivation process of the calculation model of the new relationship between the plutonium multiplication factor M and α is as follows:

[0073] S1. The calculation model for obtaining the first counting rate S, second counting rate D and third counting rate T of the plutonium material sample is as follows:

[0074] S=FMεv s1 (1+α) (20)

[0075]

[0076] The meanings of the symbols in the formula are as described in (I).

[0077] S2. First, the goal is to establish the relationship equation between M and α without using F, ε, f D ,f T Parameters such as and Divide them to get The calculation expression of F, ε, and f is eliminated immediately. D ,f T And other parameters. The specific process is as follows:

[0078]

[0079] make

[0080]

[0081] Then there is

[0082] a0+a1N+a2N 2 =0 (28)

[0083] Analytical equation a0+a1N+a2N 2 =0 It is not difficult to see that M and α are nonlinearly related.

[0084] (III) The derivation process of the calculation model of the plutonium multiplication factor M is as follows:

[0085] S1. Obtain the S, D, and T calculation formulas of the plutonium material sample as given in (20), (21), and (22). Eliminate F and α from S, D, and T to derive the calculation equation for M.

[0086] From the calculation formula of S,D, we can get

[0087]

[0088] From the calculation formula of D, T, we can get

[0089]

[0090] Divide the above two equations and eliminate (1+α)v s1 , after simplification, we can get the cubic equation of M

[0091] b0+b1M+b2M 2 +b3M 3 =0 (31)

[0092] in

[0093]

[0094] Then give b0+b1M+b2M 2 +b3M 3 =0 Multiply both sides by have to

[0095] a0+a1M+a2M 2 +a3M 3 =0 (36)

[0096] a0=-T (37)

[0097]

[0098] Observe the expressions of a0, a1, a2, and a3, and then compare them with those given in the existing calculation model. It is found that they are very similar, but not the same. To be the same, they need to satisfy

[0099]

[0100] Obviously also need

[0101]

[0102] Because f D and f T They are the coincidence proportions of the two-count rate and the three-count rate, respectively, so they are both less than 1, and this condition does not hold. Based on this, the coefficient calculation formula given by the existing calculation model is incorrect.

[0103] (IV) The derivation process of the fission rate F calculation model and the α calculation model is as follows:

[0104] According to the calculation formulas of D and S in (20) and (21), substituting the calculation formula of S into the calculation formula of D, we have

[0105]

[0106] then

[0107]

[0108] The calculation formula of F is different from that given by the existing calculation model in that it has an additional factor, but it cannot be eliminated. Based on this, the F calculation formula given by the existing calculation model is incorrect.

[0109] With M and F, we can get S = FMεv s1 (1+α) The calculation formula of α is derived as follows:

[0110]

[0111] The calculation formula of α differs from that given by the existing calculation model in that ε is included.

[0112] (V) Optimization steps for calculating M, F and α

[0113] 1. Calculate according to the following sequence

[0114]

[0115] c4=v i2 c2 (51)

[0116] c5=3c1Dc4 (52)

[0117] a0=-T (53)

[0118] a1=c1Dc3-c5 (54)

[0119] a3=c0c1s(c2v i3 -c4c3) (55)

[0120] a2=-a3+c5 (56)

[0121] 2. Call the cubic algebraic equation solver to calculate M, then calculate F

[0122]

[0123] Finally, calculate α.

[0124] In the S, D, and T calculation formulas given by the existing calculation model, the calculation formula coefficients of T are wrong, and the cubic equation coefficients of M are difficult to understand. Whether from the actual physical definition or from the pure equation solving theory, they are not correct. As for the calculation formulas of F and α, there are also obvious problems. The present invention provides a relatively detailed derivation process of the M calculation equation, the derivation process of the new relationship equation of M and α (given for the first time), the derivation process of the F, α calculation formulas, and their optimized calculation sequence algorithms, and briefly analyzes the S, D, and T calculation formulas given in the prior art.

[0125] In summary, neutron multiplicity measurement is a new method that has been gradually developed for many years at home and abroad. The experiment is complex, the conditions are high, the mathematical model is complicated, and the mathematical models given in many public reports and documents are not the same, and there are many problems. The present invention provides a detailed derivation process of the sample multiplication calculation equation in uranium and plutonium and a new relationship equation between the sample multiplication factor M and the reaction rate ratio α in the plutonium material research, and provides a mathematical model of the optimization algorithm for how to calculate the sample multiplication factor M, the fission rate F and the reaction rate ratio α.

[0126] The above is only an embodiment of the present invention, and the common knowledge such as the known specific technical solutions or characteristics in the solution is not described in detail here. It should be pointed out that for those skilled in the art, several modifications and improvements can be made without departing from the technical solution of the present invention, which should also be regarded as the protection scope of the present invention, and these will not affect the effect of the implementation of the present invention and the practicality of the patent. The scope of protection required by this application shall be based on the content of its claims, and the specific implementation methods and other records in the specification can be used to interpret the content of the claims.

Claims

1. An improved neutron multiplicity calculation model for uranium and plutonium analysis, characterized in that: The calculation model of uranium multiplication factor M is: a0+a1M+a2M 2 +a3M 3 =0, where The calculation model of plutonium multiplication factor M is: a0+a1M+a2M 2 +a3M 3 =0, where a0=-T The calculation model of the new relationship between plutonium multiplication factor M and α is: a0+a1N+a2N 2 =0, where The calculation model of the fission rate F is: The calculation model of α is: Where ε is the detection efficiency; F is the sample induced fission rate; f D and f T are the coincidence shares of the second and third counting rates, respectively; M is the material multiplication factor; α is the ratio of the sample (α,n) reaction rate to the spontaneous fission neutron emission rate; V sk is the k-order distance of spontaneous fission neutron multiplicity, k = 1, 2, 3; S, D, T are the third-order distances of the neutron multiplicity distribution that finally escapes from the material, which are the first count rate, the second count rate, and the third count rate, respectively; G is the gate width, P d is the pre-delay, τ is the decay time, S0 is the background count rate of the Am-Li source, B is the ambient background count rate, S s It is the counting rate of the source background counting rate changed due to sample absorption and scattering after the sample is placed.

2. An improved uranium and plutonium analysis neutron multiplicity calculation model according to claim 1, characterized in that: The calculation model of the second counting rate D and the third counting rate T in the calculation model of the uranium multiplication factor M is:

3. An improved neutron multiplicity calculation model for uranium and plutonium analysis according to claim 1, characterized in that: When solving the calculation model of uranium multiplication factor M, the calculation sequence is as follows: c0=b0b2 c1=b0v i2 <h2 style=";text-align:left;direction:ltr">a0=-b2(v<h2 style=";text-align:left;direction:ltr"> s2 <h2 style=";text-align:left;direction:ltr"> -b0)=b2v<h2 style=";text-align:left;direction:ltr"> s2 <h2 style=";text-align:left;direction:ltr"> -c0 a1=v s3 +c0-b1+c1 a2=b1-2c1 a3=c1.

4. An improved uranium and plutonium analysis neutron multiplicity calculation model according to claim 1, characterized in that: The calculation model of the plutonium multiplication factor M, the calculation model of the first counting rate S, the second counting rate D and the third counting rate T in the calculation model of the new relationship between the multiplication factor M and α are as follows: S=FMεv s1 (1+a) 5. An improved uranium and plutonium analysis neutron multiplicity calculation model according to claim 1, characterized in that: The calculation steps for M, F, and α of plutonium are calculated according to the following sequence: c4=v i2 c2 c5=3c1Dc4 a0=-T a1=c1Dc3-c5 <h2 style=";text-align:left;direction:ltr">a3 = c0c1s(c2v<h2 style=";text-align:left;direction:ltr"> i3 <h2 style=";text-align:left;direction:ltr"> -c4c3) a2=-a3+c5; Then call the cubic algebraic equation solver to calculate M, and then calculate F Finally, calculate α.

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