CN113609099A - Method for manufacturing fusion reactor multi-group shielding database based on Monte Carlo method - Google Patents

Method for manufacturing fusion reactor multi-group shielding database based on Monte Carlo method Download PDF

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CN113609099A
CN113609099A CN202110882704.6A CN202110882704A CN113609099A CN 113609099 A CN113609099 A CN 113609099A CN 202110882704 A CN202110882704 A CN 202110882704A CN 113609099 A CN113609099 A CN 113609099A
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贺清明
李捷
黄金龙
曹良志
吴宏春
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Abstract

A method for manufacturing a fusion reactor multi-group shielding database based on a Monte Carlo method comprises the following steps: 1. processing the evaluation nuclear database into a continuous energy ACE format nuclear database; 2. adding information in all scattering reaction channels of each nuclide in an ACE format database to obtain a continuous energy scattering response coefficient database; 3. designing a simplified one-dimensional model according to a real three-dimensional structure of a fusion reactor; 4. calculating a simplified model by adopting a Monte Carlo method based on an ACE format database and a continuous energy scattering response coefficient database; 5. obtaining a plurality of groups of high-order scattering cross sections according to the obtained low-order flux, high-order flux and high-order scattering reaction rate; 6. and combining the multiple groups of high-order scattering cross sections with a total cross section, a neutron generation cross section, an absorption cross section, a low-order scattering cross section and a response function library in the multiple groups of shielding databases to generate a new fusion reactor multiple groups of shielding databases. The data base enables the calculation of the radiation shielding of the fusion reactor to be more accurate and reduces the safety margin of the fusion reactor.

Description

Method for manufacturing fusion reactor multi-group shielding database based on Monte Carlo method
Technical Field
The invention relates to the field of particle transport calculation and radiation shielding calculation, in particular to a method for manufacturing a fusion reactor multi-group shielding database based on a Monte Carlo method.
Background
In the design process of the fusion reactor, the calculation of radiation shielding of a reactor core and a factory building is a critical task. The current radiation shielding calculation adopts two main methods: a monte carlo method based on a continuous energy database; a determinism method based on a multi-cluster mask database. The basic idea of the deterministic method is to disperse space, angle and energy, solve the dispersed particle transport equation and approximate the continuous distribution by the discrete grid distribution.
When the particle transport equation is solved by using a determinism method, the emergent angle of the particles after each scattering can be processed according to a function expansion method. It has been proved that the zero-order expansion coefficient of the angular flux density in the particle transport equation is the particle flux density of the full-angle spatial integral, or called low-order flux; the higher order flux is when the expansion coefficient is greater than or equal to the first order. And performing function expansion on the scattering cross section, wherein the expansion coefficient is zero order, namely the low order scattering cross section, and the expansion coefficient is more than or equal to first order, namely the high order scattering cross section.
And a plurality of groups of shielding databases are databases which adopt weighted average of weight functions and are distributed discretely along with energy segments. The selection of the weight function directly influences the precision of the multi-group shielding database. When a multi-cluster shielding database is manufactured, a calculation model needs to be simplified to obtain a simplified model, then the simplified model is calculated, and flux density in the simplified model is used as a weight function to carry out weighted average. The methods for creating multi-cluster databases can be divided into two broad categories, depending on the method used in computing the simplified model. The first is a method for making a multi-group shielding database based on deterministic theory, and the second is a method for making a multi-group shielding database based on statistics. A method for manufacturing a multi-group shielding database based on statistics is characterized in that a Monte Carlo method is adopted to calculate a simplified model, and flux density and reaction rates of various reactions, such as total reaction rate, absorption reaction rate, scattering reaction rate, high-order scattering reaction rate and the like, in the simplified model are obtained through statistics. The method is based on a continuous energy database, directly simulates the transportation process of particles, does not carry out equation dispersion, and avoids errors caused by dispersion.
However, the conventional statistical-based method for creating a multi-cluster mask database, which is referred to as the conventional statistical method, has some problems. First, the dimension of the higher order scattering reactivity is larger than the dimensions of other reactivity, and under the same calculation condition, the statistical fluctuation of the higher order scattering reactivity is larger and the convergence is more difficult. Secondly, theoretically, a high-order scattering cross section should be obtained based on high-order flux, but the high-order scattering cross section is still obtained based on low-order flux by the conventional statistical method at present, so that systematic deviation exists in the high-order scattering cross section obtained by the conventional statistical method, the manufactured fusion reactor multi-group shielding database is not accurate enough, more safety margins need to be considered during design of a fusion reactor radiation shielding, and the economy of the design of the fusion reactor radiation shielding is reduced.
Disclosure of Invention
In order to overcome the problems in the prior art, the invention aims to provide a method for manufacturing a fusion reactor multi-group shielding database based on a monte carlo method. And when Monte Carlo simulation of the fusion reactor simplified model is carried out, counting to obtain the high-order scattering reaction rate. The continuous energy scattering response coefficient database avoids the reaction channel sampling which is necessary for obtaining the high-order scattering reaction rate in the traditional statistical method, thereby reducing the statistical dimension of the high-order scattering reaction rate and reducing the statistical fluctuation of the high-order scattering reaction rate. Meanwhile, the method obtains a statistical formula of high-order flux based on infinite homogeneous medium approximation and zero-order curvature approximation, can directly obtain the high-order flux while obtaining the low-order flux, and can obtain a plurality of groups of high-order scattering cross sections by substituting the obtained high-order flux into a solving formula of the high-order scattering cross sections, thereby ensuring the consistency of program development and theoretical derivation.
In order to achieve the purpose, the invention adopts the following technical scheme to implement:
a method for manufacturing a fusion reactor multi-group shielding database based on a Monte Carlo method comprises the following steps:
step 1: processing the evaluation nuclear database into an ACE (adaptive communication interface) format nuclear database, which is an ACE format database for short, by using nuclear database processing software;
step 2: adding the information in all scattering reaction channels of each nuclide in an ACE format database to obtain a continuous energy scattering response coefficient database, and recording the scattering response coefficient of each nuclide with the expansion coefficient order of k, the serial number of i and the emergent energy group serial number of g of each energy point E' as hi,k,g(E′)；
And step 3: according to the real three-dimensional structure of the fusion reactor, a simplified one-dimensional model is designed, namely the simplified model, and material regions of the simplified model are sequentially from left to right: stainless steel, vacuum, stainless steel, water, a multiplication plate, a neutron multiplication plate, vacuum, the neutron multiplication plate, the multiplication plate, water, stainless steel, vacuum, stainless steel and a coil, wherein the size of a material area in the simplified model is consistent with that of a material area corresponding to the real three-dimensional structure of the fusion reactor, and the material components of the material area are obtained by mixing materials in the material area corresponding to the real three-dimensional structure of the fusion reactor according to the principle of mass conservation and substance conservation;
and 4, step 4: calculating a simplified model by adopting a Monte Carlo method based on an ACE format database and a continuous energy scattering response coefficient database to obtain energy cluster-related low-order flux, high-order flux and high-order scattering reaction rate information; for the mth wandering, the track length delta l of the neutron in the material area is randomly extracted firstlymCounting the high-order flux and the high-order scattering reaction rate according to the track length; the statistical formula for the flux of the higher order is shown as formula (1), and the statistical formula for the reaction rate of the higher order scattering is shown as formula (2);
Figure BDA0003192649650000031
in the formula:
k-the order of the expansion coefficient;
g' - -incident energy group number;
φk,g′-a high order flux of the g' th energy group with an order of expansion coefficient k;
w- -the total weight of the initial neutrons;
n- - -the total number of initial neutrons;
n- - -the number of neutrons currently simulated;
Mn-the total number of traces of the nth neutron;
m- - -the mth walk of the nth neutron;
wgtn,m-weight of mth walk of nth neutron;
Δln,m-the trace length resulting from the mth walk of the nth neutron;
i-total number of species of nuclear in the fusion reactor material region;
i-numbering of nuclides in the fusion reactor material region;
Di-density of species i in the fusion reactor material region;
Em-the energy at the m-th walk of the nth neutron;
σt,i(Em) -the i-th nuclear species having an energy point EmA microscopic total cross-section of;
Eg′-1-the g' th lower energy group boundary;
Eg′-the upper energy limit of the g' th energy cluster;
Figure BDA0003192649650000041
-counting the traces of neutrons in all wandering processes that satisfy the condition that the nth neutron has the mth wandering energy EmIn (E)g′-1,Eg′]To (c) to (d); the number of counts per count is
Figure BDA0003192649650000042
Figure BDA0003192649650000051
In the formula:
s- - -scattering cross section;
g- - -exit energy group numbering;
Rs,g′→g,k,i-a higher order scattering reactivity of the i-th nuclide scattered from the g 'th energy cluster to the g' th energy cluster with an expansion coefficient order of k;
hi,k,g(Em) Incident energy of the ith nuclear species EmThe number of the emergent energy group is g, and the order of the expansion coefficient is k;
Figure BDA0003192649650000052
-counting the traces of neutrons in all wandering processes that satisfy the condition that the nth neutron has the mth wandering energy EmIn (E)g′-1,Eg′]In the meantime. The count amount per count is wgtn,mΔln,mhi,k,g(Em)；
And 5: obtaining a plurality of groups of high-order scattering cross sections according to the low-order flux, the high-order flux and the high-order scattering reaction rate obtained in the step (4), wherein a calculation formula is shown as a formula (3);
Figure BDA0003192649650000053
in the formula:
σs,g′→g,k,i-a scattering cross section of the ith nuclear species scattering from the g 'th energy cluster to the g' th energy cluster with an expansion coefficient order of k;
step 6: and (4) combining the multiple groups of high-order scattering cross sections obtained in the step (5) with a total cross section, a neutron generation cross section, an absorption cross section, a low-order scattering cross section and a response function library in a multiple group shielding database to generate a new fusion reactor multiple group shielding database.
Compared with the prior art, the invention has the following advantages:
1. compared with a method for obtaining a plurality of groups of high-order scattering cross sections through low-order flux and high-order scattering reaction rate in the traditional statistical method, the method adopts the high-order flux and the high-order scattering reaction rate to obtain the plurality of groups of high-order scattering cross sections, and therefore consistency of program development and theoretical derivation is guaranteed.
2. The fusion reactor multi-group shielding database manufactured based on the method has higher calculation precision, so that the calculation result of the fusion reactor radiation shielding is more accurate, the safety margin of the fusion reactor radiation shielding is reduced, and the economy of the design of the fusion reactor radiation shielding is improved.
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FIG. 1 is a method for manufacturing a fusion reactor multi-group shielding database based on a Monte Carlo method.
FIG. 2 is a schematic diagram of a one-dimensional simplified model of a fusion reactor.
Detailed Description
The invention is described in further detail below with reference to the following figures and specific examples:
as shown in FIG. 1, the method for manufacturing the fusion reactor multi-group shielding database based on the Monte Carlo method comprises the following steps:
step 1: an evaluation nuclear database, such as the ENDF database, is processed into a continuous energy database, i.e., an ACE format database, using nuclear database processing software. The main work of the general process is divided into three parts. Firstly, compressing information in an evaluation kernel database on the premise of meeting linear interpolation; secondly, processing the data of the indistinguishable resonance area into a probability table; and finally, copying other data from the evaluation core database and storing the data into the ACE format database. In ACE format databases, the number of energy grids can reach tens or even hundreds of thousands. The ACE format database includes the following information: the total cross section, the elastic scattering cross section and the absorption cross section under each energy point of different nuclides; the section of each neutron reaction channel changing along with energy, the type of the emergent particles, the energy distribution rule of the emergent particles and the angle distribution rule of the emergent particles; information blocks such as the energy distribution rule of delayed fission neutrons and the angle distribution rule of delayed fission neutrons.
Step 2: and processing all scattering reaction channels of each nuclide according to data in the ACE format database, wherein the data comprises the section of the neutron reaction channel changing along with energy, the type of the emergent particle, the energy distribution rule of the emergent particle and the angle distribution rule of the emergent particle, so as to obtain a continuous energy scattering response coefficient database. The processing formula is as formula (4).
Figure BDA0003192649650000071
In the formula:
e' - -energy of incident neutrons;
e- -energy of the outgoing neutron;
Eg-1-the lower energy group;
Eg-the upper energy limit of the g-th energy cluster;
hi,k,g(E ') - - -the scattering response coefficient value for the ith nuclide, for an incident energy E', an emergent energy cluster number g, and an expansion coefficient order k;
MT- - -number of scattering reaction channel;
Yi,MT-the neutron yield of the scattering reaction channel of the i-th nuclide, numbered MT;
σi,MT(E ') - - -the reaction cross-section of the i-th species with channel number MT and incident energy E';
mu- - -scattering angle, i.e. cosine value of the angle between the emergent direction and the incident direction;
fi,MTreaction cross section of (E '→ E, mu) - - -i-th nuclide, with reaction channel number MT, incident energy E' and emergent energy E, and scattering included angle mu;
Pka spherical harmonic value with the (mu) - - -expansion coefficient order of k and the scattering included angle of mu;
the scattering reaction channels can be divided into inelastic scattering reaction channels, elastic scattering reaction channels, and thermal scattering of molecules and crystals. For the different inelastic scattering reaction channels,the ACE format database describes the energy distribution rule and the angle distribution rule of the emergent particles by different rules. F of different scattering reaction channelsi,MT(E' → E, μ) are different, but equation (4) ensures that the scattering information for each species, including the higher order scattering information, is not lost. Thus, the continuous energy scattering response coefficient database can be used to obtain higher order scattering responsivity.
And step 3: according to the real three-dimensional structure of the fusion reactor, a simplified one-dimensional model is designed, namely a simplified model, and as shown in FIG. 2, the material regions of the simplified model are as follows from left to right: the size of a material area in the simplified model is consistent with that of a material area corresponding to the real three-dimensional structure of the fusion reactor, and the material components of the material area are obtained by mixing materials of the material area corresponding to the real three-dimensional structure of the fusion reactor according to the principle of mass conservation and substance conservation. The blending formula is shown in formula (5).
Figure BDA0003192649650000081
In the formula:
z- - -feature region number of the simplified model;
k is the material area number in the real three-dimensional structure of the fusion reactor;
Di,z-the nuclear density of the ith species in the z-th characteristic region of the simplified model;
Di,k,z-nuclear density of the ith species in the kth material region in the true three-dimensional structure of the corresponding fusion reactor within the z-th characteristic region of the simplified model;
Kz-the number of material regions in the true three-dimensional structure of the fusion reactor contained in the z-th characteristic region of the simplified model;
Figure BDA0003192649650000082
- - -the z-th feature of the simplified modelIn the region, the total number of the atomic nuclei of the ith nuclide in the corresponding fusion reactor real three-dimensional structure;
Vk,z-simplifying the volume of the kth material region within the z-th feature region of the model;
Sz-the area of the z-th feature region of the simplified model;
and 4, step 4: and calculating a simplified model by adopting a Monte Carlo method based on an ACE format database and a continuous energy scattering response coefficient database to obtain energy cluster-related low-order flux, high-order flux and high-order scattering reaction rate. By adopting the random walk idea, for the mth walk, the track length of the neutron in the material area is firstly randomly extracted, and the sampling formula is shown as formula (6). After extracting the track length of the neutron in the material area, moving the neutron along the motion direction of the neutron, and calculating the new position of the neutron according to the formula (7). And at the new position, extracting the reaction channels with the reaction according to the section information of each reaction channel stored in the ACE format database. And sampling the energy and the angle of the emergent neutrons according to the physical law of the extracted reaction channel. And carrying out the next wandering according to the energy and the angle of the emergent neutrons.
Δln,m＝-lnξ/∑t(Em) Formula (6)
In the formula:
ξ - -a pseudo-random number generated by a pseudo-random number generator;
∑t(Em) - -neutron energy EmThe total cross section of the material;
Figure BDA0003192649650000091
in the formula:
Figure BDA0003192649650000092
-new spatial position of nth neutron after mth walk;
Figure BDA0003192649650000093
-the spatial position of the nth neutron before the mth walk;
Figure BDA0003192649650000094
-the angle of motion of the neutron at the mth wandering;
in the process of simulating the migration of neutrons, different methods can be adopted to count the neutron flux and the reaction rate of various reactions. Taking the track length counting method as an example, the method is used for counting neutron flux, namely a formula for counting low-order flux is shown as a formula (8), a formula for counting high-order flux is shown as a formula (1), and a formula for counting high-order scattering reaction rate is shown as a formula (2).
Figure BDA0003192649650000101
In the formula:
φ0,g′- -clusters of low order fluxes with cluster number g';
Figure BDA0003192649650000102
-counting the traces of neutrons in all wandering processes that satisfy the condition that the nth neutron has the mth wandering energy EmIn (E)g′-1,Eg′]In between, the number of counts per count is wgtn,mΔln,m；
And 5: and (4) obtaining a plurality of groups of high-order scattering cross sections according to the low-order flux, the high-order flux and the high-order scattering reaction rate obtained in the step (4), wherein the calculation formula is shown as a formula (3).
Figure BDA0003192649650000103
In the formula:
σs,g′→g,k,i-a scattering cross section of the ith nuclear species scattering from the g 'th energy cluster to the g' th energy cluster with an expansion coefficient order of k;
step 6: and (4) combining the multiple groups of high-order scattering cross sections obtained in the step (5) with a total cross section, a neutron generation cross section, an absorption cross section, a low-order scattering cross section and a response function library in a multiple group shielding database to generate a new fusion reactor multiple group shielding database. The multi-group shielding database can be used for subsequent fusion reactor shielding calculation based on a determinism method, and the shielding calculation precision of the multi-group shielding database is improved.

Claims (1)

1. A method for manufacturing a fusion reactor multi-group shielding database based on a Monte Carlo method is characterized by comprising the following steps: the method comprises the following steps:
step 1: processing the evaluation nuclear database into an ACE (adaptive communication interface) format nuclear database, which is an ACE format database for short, by using nuclear database processing software;
step 2: adding the information in all scattering reaction channels of each nuclide in an ACE format database to obtain a continuous energy scattering response coefficient database, and recording the scattering response coefficient of each nuclide with the expansion coefficient order of k, the serial number of i and the emergent energy group serial number of g of each energy point E' as hi,k,g(E′)；
And step 3: according to the real three-dimensional structure of the fusion reactor, a simplified one-dimensional model is designed, namely the simplified model, and material regions of the simplified model are sequentially from left to right: stainless steel, vacuum, stainless steel, water, a multiplication plate, a neutron multiplication plate, vacuum, the neutron multiplication plate, the multiplication plate, water, stainless steel, vacuum, stainless steel and a coil, wherein the size of a material area in the simplified model is consistent with that of a material area corresponding to the real three-dimensional structure of the fusion reactor, and the material components of the material area are obtained by mixing materials in the material area corresponding to the real three-dimensional structure of the fusion reactor according to the principle of mass conservation and substance conservation;
and 4, step 4: calculating a simplified model by adopting a Monte Carlo method based on an ACE format database and a continuous energy scattering response coefficient database to obtain energy cluster-related low-order flux, high-order flux and high-order scattering reaction rate information; for the mth wandering, the track length delta l of the neutron in the material area is randomly extracted firstlymAccording to the trace length, the response rate to higher order flux and higher order scatteringCarrying out statistics; the statistical formula for the flux of the higher order is shown as formula (1), and the statistical formula for the reaction rate of the higher order scattering is shown as formula (2);
Figure FDA0003192649640000011
in the formula:
k-the order of the expansion coefficient;
g' - -incident energy group number;
φk,g′-a high order flux of the g' th energy group with an order of expansion coefficient k;
w- -the total weight of the initial neutrons;
n- - -the total number of initial neutrons;
n- - -the number of neutrons currently simulated;
Mn-the total number of traces of the nth neutron;
m- - -the mth walk of the nth neutron;
wgtn,m-weight of mth walk of nth neutron;
Δln,m-the trace length resulting from the mth walk of the nth neutron;
i-total number of species of nuclear in the fusion reactor material region;
i-numbering of nuclides in the fusion reactor material region;
Di-density of species i in the fusion reactor material region;
Em-the energy at the m-th walk of the nth neutron;
σt,i(Em) -the i-th nuclear species having an energy point EmA microscopic total cross-section of;
Eg′-1-the g' th lower energy group boundary;
Eg′-the upper energy limit of the g' th energy cluster;
Figure FDA0003192649640000021
- - -for all wandering processes satisfying the conditionsThe trace of the neutron is counted, and the condition is that the mth migration time energy E of the nth neutronmIn (E)g′-1,Eg′]To (c) to (d); the number of counts per count is
Figure FDA0003192649640000031
Figure FDA0003192649640000032
In the formula:
s- - -scattering cross section;
g- - -exit energy group numbering;
Rs,g′→g,k,i-a higher order scattering reactivity of the i-th nuclide scattered from the g 'th energy cluster to the g' th energy cluster with an expansion coefficient order of k;
hi,k,g(Em) Incident energy of the ith nuclear species EmThe number of the emergent energy group is g, and the order of the expansion coefficient is k;
Figure FDA0003192649640000033
-counting the traces of neutrons in all wandering processes that satisfy the condition that the nth neutron has the mth wandering energy EmIn (E)g′-1,Eg′]In the meantime. The count amount per count is wgtn,mΔln,mhi,k,g(Em)；
And 5: obtaining a plurality of groups of high-order scattering cross sections according to the low-order flux, the high-order flux and the high-order scattering reaction rate obtained in the step (4), wherein a calculation formula is shown as a formula (3);
Figure FDA0003192649640000034
in the formula:
σs,g′→g,k,idispersion of the ith nuclear species from the g' th energy clusterA scattering cross section with an expansion coefficient order of k and which strikes the g-th energy group;
step 6: and (4) combining the multiple groups of high-order scattering cross sections obtained in the step (5) with a total cross section, a neutron generation cross section, an absorption cross section, a low-order scattering cross section and a response function library in a multiple group shielding database to generate a new fusion reactor multiple group shielding database.
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