Method for Selecting Neutron Shielding Material

Abstract

A method of selecting one or more materials having a specific isotope composition for use in a neutron shield. A first list of materials is provided, each material having a different isotope composition. A value of an incident neutron beam that the neutron shield will encounter during use is provided. A set of criteria is provided that includes one or more of neutron beam, neutron dose, heating of a target protected by the neutron shield, damage to the target, gas generation within the target, tritium generation within the target, and nuclear conversion of the target. For each criterion, an overall weight is defined, and based on the incident neutron beam, a unique weighting factor is defined for each of a plurality of neutron energy groups. Using a computing system, an overall performance index is calculated for each material in a first set of materials, and the overall performance index for each material is based on determining a performance index for each neutron energy group based on the absorption coefficient and scattering coefficient of the material for each neutron energy group, determining a performance index for the criterion based on the performance index for each neutron energy group weighted by the unique weighting factor of the criterion for each criterion, and determining the overall performance index based on the performance index for each criterion weighted by the overall weight of the criterion. A second list of materials is selected based on the overall performance index of the materials and is a subset of the first list.

Description

Technical Field

[0001] The present invention relates to neutron shielding for use in a tokamak nuclear fusion reactor, although not particularly limited thereto.

Background Art

[0002] The problems in generating fusion power are very complex. Fusion neutrons are generated when a deuterium-tritium (D-T) or deuterium-deuterium (D-D) plasma is heated and has sufficient energy for the atomic nuclei to overcome the Coulomb electrostatic repulsive force and fuse together, releasing energetic neutrons and fusion products (e.g., 4 He for D-T). Currently, the most promising way to achieve this is to use a tokamak device. However, in conventional tokamak approaches to fusion (such as those implemented by ITER), the plasma needs to have a high confinement time, high temperature, and high density in order to optimize this process.

[0003] A tokamak provides a high-temperature stable plasma so that fusion can occur, characterized by a strong toroidal magnetic field B T , a high plasma current I p , and usually a combination of a large plasma volume and significant auxiliary heating. Auxiliary heating (e.g., via injection of tens of megawatts of neutral beams of high-energy H, D, or T) is necessary to raise the temperature to a sufficiently high value required for fusion to occur and / or to maintain the plasma current.

[0004] To ensure that the reactor is as compact as possible (which can increase efficiency, especially in the case of a "spherical tokamak" plasma configuration), the thickness of the neutron shielding should be reduced as much as possible while still maintaining adequate protection for other components. By minimizing the distance between the plasma and the magnetic field coils, a higher magnetic field in the plasma is made possible while reducing the current in the coils.

Summary of the Invention

Means for Solving the Problem

[0005] According to a first aspect, there is provided a method of selecting one or more materials having a specific isotope composition for use in a neutron shield. A first list of materials is provided, each material having a different isotope composition. The value φ of the incident neutron flux that the neutron shield will encounter during use g 0 is provided. A set of criteria is provided, the set of criteria including one or more of neutron flux, neutron dose, heating of the target protected by the neutron shield, damage to the target, gas generation in the target, tritium generation in the target, and nuclear transformation of the target. For each criterion, an overall weight β criteria is defined, and based on the incident neutron flux, a unique weighting factor α g is defined for each of a plurality of neutron energy groups. Using a computing system, an overall performance index Λ is calculated for each material in a first set of materials, and the overall performance index Λ for each material is based on the absorption coefficient and scattering coefficient of the material for each neutron energy group, determining the performance index Λ g for each neutron energy group, for each criterion, determining the performance index Λ of the criterion based on the performance index of each neutron energy group weighted by the unique weighting factor of the criterion, criteria and determining the overall performance index Λ based on the performance index of each criterion weighted by the overall weight of the criterion. is based on A second list of materials is selected based on the overall performance index Λ of the materials, and the second list is a subset of the first list.

[0006] According to a second aspect, a method is provided for selecting one or more materials of a specific isotope composition for use in a neutron shield. A first list of materials is provided, each material having a different isotope composition. A distribution of incident neutron beams that the neutron shield will encounter during use is provided. A set of criteria is provided, the set of criteria including one or more of neutron beam, neutron dose, heating of a target protected by neutron shielding, damage to the target, gas generation within the target, tritium generation within the target, and nuclear conversion of the target. For each criterion, an overall weight is defined, and based on the incident neutron beam, a specific weighting function that depends on neutron energy is defined. Using a computing system, an overall performance index for each material in a first set of materials is calculated, and the overall performance index for each material is determining a performance index function that depends on neutron energy based on the neutron energy-dependent absorption coefficient and scattering coefficient of the material; for each criterion, determining a criterion performance index based on the integral of the product of the specific weighting function and the performance index function; determining an overall performance index based on the criterion performance indices for each criterion, weighted by the overall weight of the criterion; is based on. A second list of materials is selected based on the overall performance index of the materials, and the second list is a subset of the first list.

[0007] According to a third aspect, the use of scandium borohydride, ScB3H 18 , or nickel hydride, NiH2 as a neutron shielding material is provided.

[0008] According to a fourth aspect, a neutron shield comprising scandium borohydride, ScB3H 18 , or nickel hydride, NiH2 is provided.

[0009] Further embodiments are presented in claims 2 and later.

Brief Description of the Drawings

[0010]

Fig. 1A

Fig. 1B

Fig. 1C

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Fig. 4

DETAILED DESCRIPTION OF THE INVENTION

[0011] To provide more efficient neutron shielding (i.e., greater neutron attenuation for a given thickness of shielding), a material that effectively blocks neutrons must be found. Neutrons can be blocked from further penetrating the material either through scattering or absorption. The neutron flux as a function of distance is attenuated by both mechanisms. However, considering the potentially large number of compounds of interest, discovery of such materials by experiment alone is unrealistic, and discovery of such materials by detailed simulation is computationally expensive.

[0012] Accordingly, the following disclosure provides a relatively simple way to calculate a “performance index” for neutron shielding materials, which quantifies the usefulness of a material as neutron shielding for a particular application. This performance index can then be used to identify suitable materials for use as neutron shielding or for further research to determine suitability for other engineering constraints, for example.

[0013] The performance index proposed in this specification is based on the diffusion model of neutron transport. The use of the drawings themselves does not rely on a complete derivation, but details of the derivation of the drawings are provided in this specification for context. The symbols used are defined at the end of the description.

[0014] The neutron transport equation is expressed as follows.

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[0015] 「Definition of the diffusion coefficient in scattering and absorbing media」, Elaloufi et al, j. Opt. Soc. Am. A / Vol. 20, No. 4 / April 2003 describes the definition of the diffusion coefficient for photons in scattering and absorbing media. The same derivation applies to neutrons. Within a slab of neutron-absorbing material, one term is dominant and the angular flux can be expressed as follows.

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[0016] For the model <g0>The appropriate value depends on neutron energy and the material and can be determined by numerically solving the neutron transport equation (Equation 1) using empirical formulas adapted to the solution of the neutron transport equation, or by fitting simulation or experimental data for neutron energy groups within a given material to the equation

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[0017] Returning to a simpler model, the attenuation of neutrons in the material in regions that do not contain material boundaries or neutron sources is governed by the function f.

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[0018] From the above discussion on diffusion, in a multigroup energy approximation, the subscript g can be seen to indicate applicability to a given energy group.

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[0019] Figures 1A, 1B, and 1C show the performance index Λ g It is a figure illustrating three potential graphical representations of those associated conjugate lines and the selection of candidate materials.

[0020] Figure 1A is a figure illustrating the performance index for a given energy group

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[0021] An alternative performance index for a given energy group M2 can be obtained by using the following relationship.

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[0022] A further alternative representation can be obtained by further decomposing Λ g

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[0023] In each of the above examples, the actual performance index of a given energy group to be maximized is Λ g (or, in the case of M2, the constant <g0>Based on the assumption of Λ g is proportional to), this expression is only a useful illustration or λ g etc., and only provides secondary performance indices such as

[0024] Since the value of each Σ (and σ) depends on neutron energy, in the above analysis, the average performance over a given neutron energy group is considered based on the value of Σ used. Depending on the selected energy group, the ranking of materials will vary due to different scattering and absorption characteristics at different energy levels. In practice, it is generally more useful to analyze the performance as a weighted average over multiple energy groups, for example, weighted by how much each group contributes to the heating or damage of the material to be protected.

[0025] Neutrons of different energies will have different effects on the material to be shielded. The performance index Λ for each energy group g To combine them, a weighting coefficient α based on the intrinsic cross-sectional characteristics of the material to be shielded g is used to obtain a metric for a given reference Λ criteria

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[0026] Reference and α g The choice of depends on the weighting required for a given design parameter. For example, if the shield is intended to protect from neutron heating, the appropriate choice of α g (or function A) will be the KERMA k of the material being protected g (Kinetic Energy Released in Material - a measure of the kinetic energy that a given neutron energy would deposit in a given material). In this way, neutron groups that generate more heat have a greater weight due to them and contribute more to the performance index against the neutron heating reference, i.e., the attenuation of the "more problematic" neutrons is preferred. This is shown in Figure 2A for the ReBCO superconducting material.

[0027] As a further example, when considering the potential for neutron damage to ReBCO HTS, a suitable set of constants is α g ∝(0.8T dam,g ) / (2E d ), which is a measure of the ballistic energy available for atomic displacements within ReBCO (ignoring properties that would be constant between energy groups and thus can be ignored as they are excluded when normalized). Figure 2B shows a graph of this measure.

[0028] Other examples include the use of an energy cutoff to account for fluxes within a given energy region that are independent of the material being protected, the absorption cross-section to account for activation / nuclear transformation of the material, the gas production cross-section to account for the amount of gaseous particles produced in the material, and the dose weighting factor to account for health effects.

[0029] KERMA, the ballistic energy available for atomic displacements, the absorption cross-section, the gas production cross-section, the dose weighting factor, and similar values can be obtained from standard reference tables and simulation techniques known in the art.

[0030] To account for the expected beam profile of the incoming neutrons, an additional set of scale factors may be applied to each energy group (or as an additional continuous function).

[0031] In practice, generally, a balance of multiple design considerations needs to be taken. For example, if there is a more effective shielding against neutron damage that is still appropriate for heating, a material that is an effective shield against neutron heating may not be appropriate. However, this can be accounted for by determining Λ for various sets of the constant α g corresponding to the required design goals and then taking the weighted average (or other linear function) of the resulting Λ. For the above heating example Λ h and the above damage example Λ d with respect to Λ h versus Λ d a plot of Λ h versus Λ d is shown in Figure 3, where each set of dashed lines represents conjugate lines for different weightings of Λ h + βΛ d = Λ tot in this case.

[0032] When considering materials as shields, it is necessary to consider multiple of these effects, and the relative importance of each of these criteria depends on the radiation environment being considered. A set of weighting factors β is used to combine all of these criteria into a single overall performance index Λ.

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[0033] Regarding the example of shielding for a fusion power reactor (FPP) and ReBCO HTS magnets, the shield should block low-speed (E < 0.1 MeV) and high-speed (E ≥ 0.1 MeV) neutrons, prevent atomic displacement (damage) within the HTS, and prevent nuclear conversion within the HTS. A numerical example showing the weighting factors relevant to β in this scenario and how they relate to the cross-sectional area specific to the material being shielded is provided in the following table.

Table 1

[0034] Regardless of which of the above relevant performance indices is used, Figure 4 is a flowchart of a method for selecting a neutron shielding material. In step 401, a plurality of initial candidate materials, i.e., a first set of materials, is selected. This may be a broad category such as "metal hydride" or "metal boride". In step 402, a value of the incident neutron flux representing the neutron flux that the shield is expected to encounter during use is provided. In step 403, a set of criteria for evaluating the performance index is provided, which may include any of the criteria in the above table. If these criteria refer to a target (e.g., heating or damage to the target), the characteristics of that target will be selected to represent the expected use of the neutron shielding. In step 404, an overall weight for each criterion is defined, and for each criterion, a set of specific weighting factors for each neutron energy group is defined based on the incident neutron flux. In step 405, in order to calculate the overall performance index for each material in the candidate list, determining the performance index for each neutron energy group based on the absorption coefficient and scattering coefficient of the material for the neutron energy group, determining the performance index for each criterion based on the performance index for each energy group weighted by the specific weighting factor of the criterion, determining the overall performance index based on the performance index for each criterion weighted by the overall weight for each criterion, based on which a computer system is used.

[0035] Next, based on the overall performance index of the materials, a final candidate list of materials, i.e., a second set, is selected.

[0036] In particular, the isotropy of scattering is likely to be the least reliable estimator used in the performance index. Thus, the threshold ratio of the performance index that "exhibits the best performance" is <g0>If erroneously estimated, any material that should be the material exhibiting the best performance may still be calculated to exceed the threshold. For example, Λ is <g0>depends on the inverse square root of, <g0>Since it can take a value between 1 and 1 / 3, in the worst case, the material that appears to exhibit the best performance is 1 / 3 of <g0>was calculated using, but in reality, 1 of <g0>It has. <g0>To ensure that any material that should exhibit best performance in the case of worst-case incorrect estimation is within the selected set of materials, the threshold is the

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[0037] The review of the performance index by the above method reveals two candidate materials that have not been previously suggested for use in neutron shielding, namely nickel hydride (NiH2) and scandium borohydride, ScB3H 18 is presented. NiH2 can be formed by reacting nickel with hydrogen at high pressure (about 60 GPa) and is stable at extremely low temperatures, making it particularly suitable for environments such as spherical tokamaks where extremely low temperature systems already exist. ScB3H 18 can be formed by ball milling scandium chloride hydrate and lithium borohydride, and even when it begins to decompose, it remains as scandium and boron compounds (i.e., only hydrogen is released), and it has particular further advantages in that it retains at least part of its shielding performance, for example, better shielding performance than metallic scandium.

[0038] The increased neutron attenuation for a given thickness of neutron shielding can be used to improve the attenuation for a shield of a set thickness compared to known shielding materials, or to provide a comparable neutron shielding with a reduced thickness compared to known shielding materials. The latter is particularly useful in applications such as the central column of a spherical tokamak fusion reactor where minimizing the thickness of the shield (as part of minimizing the overall diameter of the central column) is an important design goal.

[0039] List of terms in the formula Unless otherwise specified for a particular formula, each symbol used in this document has a consistent meaning as in the following list, regardless of where it appears.

[0040] In Equation (1) and the description of the Elaloufi paper, note that parentheses represent variables on which a quantity depends and are used elsewhere in the document for arithmetic grouping. Mathematical operators take their usual meaning.

[0041] In general, unless otherwise specified, the subscript 0 indicates a normalization or scale value for a particular quantity, i.e., for a quantity A, A = A0f(x), where A0 is a constant.

[0042] [Table 2] ​​

Claims

1. A method of selecting one or more materials of a specific isotope composition for use in a neutron shield, comprising: providing a first list of materials, each material having a different isotope composition; providing a value of the incident neutron flux that the neutron shield will encounter during use; 【Number 1】 providing a set of criteria, the set of criteria including: neutron flux; neutron dose; heating of the target protected by the neutron shield; damage to the target; gas generation within the target; tritium generation within the target; and nuclear transformation of the target; using a computing system to calculate an overall performance index Λ for each material in the first set of materials, the overall performance index Λ for each material being determined based on the performance index for each criterion weighted by the overall weight of the criterion; selecting a second list of materials based on the overall performance index Λ of the materials, the second list being a subset of the first list; For each reference, an overall weight β criteria is defined, and based on the incident neutron beam, a specific weighting factor α g is defined for each of a plurality of neutron energy groups, and including a method. Based on the absorption coefficient and scattering coefficient of the material for each neutron energy group, a performance index Λ for each neutron energy group g is determined, and Based on the performance index for each neutron energy group weighted by the unique weighting factor of the reference for each reference, the performance index Λ of the reference criteria is determined, and

2. The method according to claim 1, including selecting a single selected material from the second list of materials.

3. The method according to claim 2, including using the selected material as a neutron shield.

4. For each material in the second list, performing one or more further selection steps, the further selection steps including: including one or more of: the selected material being selected based on the further selection steps.

5. < g 0 > g using the fit derived towards the empirical formula for the solution of the neutron transport equation for each material of the candidate list for said selection of < g 0 > < g 0 > g performing a neutron attenuation experiment for each material in the candidate list for said selection of < g 0 > g performing a neutron transport simulation for each material in the candidate list for said selection of < g The method according to any one of claims 1 to 4, wherein selecting the second list includes selecting all materials in the first list for which the performance index exceeds a threshold value.

6. <g> 0 > g In the case of purely isotropic scattering, <g> 0 > g = 1 / 3, and in the case of purely forward scattering, <g> 0 > g = 1, and in the case of purely absorption, <g> 0 > g = 1, and in the case of intermediate conditions, 1 / 3 <<g> 0 > g < 1, which is a term indicating the isotropy of the absorption and the scattering in each energy group g, the method according to claim 2 or 3. The method according to claim 5, wherein the threshold value is a percentage of the highest performance index of the materials in the initial list of materials.

7. The method according to claim 6, wherein the percentage is at least 57%.

8. is proportional to, and is the average scattering cosine, the method according to any one of claims 1 to 7. The performance index Λ g is, for each energy group, 【Number 2】 is proportional to the diffusion coefficient D g is 【Number 3】 is, 【Number 4】 and 【Number 5】 and for each material in the list of said materials and for each energy group g, Σ R,g is the neutron removal cross section, and Σ s,g->g is the in-group neutron scattering cross section, and Σ s,g->g’ is the out-of-group neutron scattering cross section, and Σ’ s is the modified neutron scattering cross section, and Σ a,g is the neutron absorption cross section, 【Number 6】

10.

9. 【Fig. 7】 is proportional to the method according to claim 8. 【Number 8】

11. 【Number 9】 and <g 0 > g is 1 / 3 for purely isotropic scattering, <g 0 > g = 1 / 3, 1 for purely forward scattering, <g 0 > g = 1, 1 for purely absorption, <g 0 > g = 1, and 1 / 3 <<g 0 > g < 1 for intermediate conditions, which is a term indicating the isotropy of the absorption and the scattering in each energy group g, the method according to claim 8.

12. The performance index Λ for each of the energy groups g is 【Number 10】 is proportional to,

13. Performance index Λ for each energy group g The method according to any one of claims 1 to 7, wherein g is based on the neutron absorption and scattering cross sections for each energy group of each material and the atomic number density N of each material.

14. The performance index Λ for each energy group g is proportional to Nλ g where λ g is the secondary performance index for each energy group, and λ g is 【Number 11】 The intrinsic weighting factor is, Selecting a material based on the performance index involves selecting a material based on both the performance index Λ g and the secondary performance index λ g where σ R,g is the microscopic neutron removal cross-section, and σ’ s,g is the modified microscopic neutron scattering cross-section <g 0 > g is 1 / 3 in the case of purely isotropic scattering, <g 0 > g = 1 in the case of purely forward scattering, <g 0 > g = 1 in the case of purely absorption, <g 0 > g = 1, and is greater than 1 / 3 and less than 1, i.e., 1 / 3 <<g 0 > g <1, in the case of intermediate conditions, and is a term indicating the isotropy of the absorption and the scattering in each energy group g, the method according to claim 11. ​ ​ When the reference is a neutron beam, the incident neutron beam within a specific energy range, When the reference is a neutron dose, the incident neutron beam multiplied by a dose response function, When the reference is heating, the incident neutron beam multiplied by the kinetic energy KERMA released into the material for neutrons within an energy group, When the reference is damage, for the neutrons in the energy group, the incident neutron flux multiplied by the ballistic energy (0.8 T dam,g )(2E d ), where T dam,g is the available ballistic energy and E d is the threshold displacement energy of the material, is the incident neutron flux, When the reference is gas production, the incident neutron beam multiplied by the coefficient of the production rate of hydrogen and helium isotopes by the material for neutrons within the energy group, and When the reference is nuclear conversion, the incident neutron beam multiplied by the absorption coefficient of the material for neutrons within the energy group, The method according to any one of claims 1 to 12, comprising:

14. For each material, the neutron absorption cross-section and scattering cross-section are calculated based on the neutron absorption cross-section and scattering cross-section of each constituent isotope of the material, the method according to any one of claims 1 to 13.

15. A method of selecting one or more materials having a specific isotope composition for use in a neutron shield, Providing a first list of materials, each material having a different isotope composition, Providing the distribution of the incident neutron beam that the neutron shield will encounter during use, Providing a set of references, the set of references including Neutron beam, Neutron dose, Heating of the target protected by the neutron shield, Damage to the target, Gas production in the target, Tritium production in the target, and Nuclear conversion of the target Including one or more of them, For each reference, defining an overall weight and defining a specific weighting function that depends on neutron energy based on the incident neutron beam, Using a computing system to calculate an overall performance index for each material in the first set of materials, the overall performance index for each material being Determining a performance index that depends on neutron energy based on the neutron energy-dependent absorption coefficient and scattering coefficient of the material, For each reference, determining the performance index of the reference based on the integral of the product of the specific weighting function and the performance index function, Determining an overall performance index based on the performance index for each reference weighted by the overall weight of the reference. Selecting a second list of materials based on the overall performance index of the materials, the second list being a subset of the first list, A method comprising. Claim 16 Use of scandium borohydride, ScB 3 H 18 as a neutron shielding material, or nickel hydride, NiH 2 . 3 H 18 、 or nickel hydride, NiH 2 . Claim 17 Scandium borohydride, ScB 3 H 18 , or nickel hydride, NiH 2 A neutron shield containing

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