Neutron shielding material selection method

Abstract

A method of selecting one or more materials having a specific isotope composition for neutron shielding. A first list of materials is provided, each material having a different isotope composition. A value of incident neutron flux # imgabs0 # that the neutron shield will encounter in use is provided. A set of criteria is provided that includes one or more of neutron flux, neutron dose, heating of a target protected by a neutron shield, damage to the target, gas production within the target, tritium production within the target, and transmutation of the target. For each criterion, a total weight # imgabs1 # is defined, and for each of the plurality of neutron energy groups, an intrinsic weighting factor # imgabs2 # is defined based on the incident neutron flux. Calculating a total figure of merit # imgabs3 # for each material in the first set of materials using the computing system, where the total figure of merit # imgabs4 # for each material is based on: determining a figure of merit # imgabs5 # for each neutron energy pack based on the absorption and scattering coefficients of the material for each energy pack; for each criterion, determining a figure of merit # imgabs6 # of the criterion based on the figure of merit of each neutron energy pack weighted by the intrinsic weighting factor of the criterion; a total figure of merit # imgabs7 # is determined based on each standard figure of merit weighted by the total weight of the standards. A second list of materials is selected based on the total figure of merit # imgabs8 # of the materials, wherein the second list is a subset of the first list.

Description

Technical Field

[0001] The present invention relates to neutron shielding, particularly but not exclusively, for use in tokamak fusion reactors. Background Art

[0002] The challenges of producing fusion energy are complex. When deuterium-tritium (DT) or deuterium-deuterium (DD) plasma is heated, fusion neutrons are produced, giving atomic nuclei enough energy to overcome Coulomb electrostatic repulsion and fuse together, releasing high-energy neutrons and fusion products (e.g., 4 The most promising way to achieve this so far is to use a tokamak device; in the traditional tokamak approach to fusion (as embodied in ITER), the plasma needs to have high confinement times, high temperatures, and high densities to optimize the process.

[0003] The characteristic of Tokamak is that a strong circular magnetic field B T , high plasma current I p This is combined with typically large plasma volumes and significant auxiliary heating to provide a thermally stable plasma from which fusion can occur. Auxiliary heating (e.g., by injection of tens of megawatts of high-energy neutral beams of H, D, or T) is necessary to raise the temperature to sufficiently high values ​​for nuclear fusion to occur and / or to maintain plasma flux.

[0004] To ensure that the reactor is as compact as possible (which allows for higher efficiency, especially for a "spherical tokamak" plasma configuration), the thickness of the neutron shielding should be reduced as much as possible, while still maintaining adequate protection for the other components. Minimizing the distance between the plasma and the field coils allows for higher magnetic fields in the plasma, and lower currents in the coils. Summary of the invention

[0005] According to a first aspect, a method of selecting one or more materials having a specific isotopic composition for use in a neutron shield is provided. A first list of materials is provided, each material having a different isotopic composition. An incident neutron flux that the neutron shield will encounter in use is provided. A set of criteria is provided, the set of criteria including one or more of: neutron flux, neutron dose, heating of a target protected by the neutron shield, damage to the target, gas production within the target, tritium production within the target, and transmutation of the target. For each criterion, a total weight is defined , and defining, for each of a plurality of neutron energy groups, an intrinsic weighting factor based on the incident neutron flux . Calculate, using a computing system, an overall quality factor for each material in the first set of materials , where the total quality factor of each material is based on:

[0006] Determine the quality factor for each neutron energy group based on the absorption and scattering coefficients of the material for each energy group ;

[0007] For each standard, determining a quality factor of the standard based on the quality factor of each neutron energy group weighted by the intrinsic weighting factor of the standard ;

[0008] Determining an overall quality factor based on the quality factor of each criterion weighted by the overall weight of the criterion .

[0009] Based on the overall quality factor of the material A second list of materials is selected, wherein the second list is a subset of the first list.

[0010] According to a second aspect, a method for selecting one or more materials having a specific isotopic composition for neutron shielding is provided. A first list of materials is provided, each material having a different isotopic composition. A distribution of incident neutron fluxes that the neutron shielding will encounter in use is provided. A set of criteria is provided, the set of criteria including one or more of the following: neutron flux, neutron dose, heating of a target protected by the neutron shielding, damage to the target, gas production within the target, tritium production within the target, and transmutation of the target. For each criterion, a total weight is defined, and an inherent weighting factor that depends on the neutron energy is defined based on the incident neutron flux. A total quality factor for each material in the first set of materials is calculated using a computing system, wherein the total quality factor for each material is based on:

[0011] determining a quality factor function that depends on neutron energy based on the absorption and scattering coefficients of the material in dependence on the neutron energy;

[0012] for each criterion, determining a quality factor for the criterion based on an integral of a product of the intrinsic weighting function and the quality factor function;

[0013] An overall quality factor is determined based on the quality factor of each criterion weighted by the overall weight of the criteria.

[0014] A second list of materials is selected based on an overall quality factor of the materials, wherein the second list is a subset of the first list.

[0015] According to a third aspect, scandium borohydride ScB3H is provided 18 Or the use of nickel hydride NiH2 as neutron shielding material.

[0016] According to a fourth aspect, there is provided a neutron shield comprising scandium borohydride ScB3H 18 Or nickel hydride NiH2.

[0017] Further embodiments are presented in claim 2 et seq. BRIEF DESCRIPTION OF THE DRAWINGS

[0018] Figure 1A , 1B and 1C is a chart showing candidate neutron shielding materials according to respective exemplary figures of merit;

[0019] Figure 2A and 2B is a chart illustrating candidate neutron shielding materials according to another exemplary figure of merit;

[0020] Figure 3 is a chart showing candidate neutron shielding materials for three different weights according to yet another exemplary quality factor; and

[0021] Figure 4 is a flow chart of a method for selecting neutron shielding materials. DETAILED DESCRIPTION

[0022] In order to provide more effective neutron shielding (i.e., greater neutron attenuation for a specific shield thickness), materials that effectively block neutrons must be found. Neutrons can be blocked from further penetration into a material either by scattering or by being absorbed. Due to both mechanisms, the neutron flux decays as a function of distance. However, given the number of potential compounds of interest, it is impractical to find such materials experimentally alone, and it is computationally expensive to find such materials through detailed simulations.

[0023] Thus, the following disclosure provides a relatively simple method to calculate a "quality factor" for a neutron shielding material, which quantifies the usefulness of a material as a neutron shield for a particular application. This quality factor can then be used to determine suitable materials for use as neutron shielding, or for further study, for example, to determine suitability relative to other engineering constraints.

[0024] The quality factors presented in this paper are based on a diffusion model of neutron migration. Although the use of the factors themselves does not rely on a complete derivation, details of the derivation of the factors are provided in this paper for reference. The symbols used are defined at the end of the specification.

[0025] The neutron transport equation is expressed as follows:

[0026] 1)

[0027] However, in low-absorbing, strongly scattering media, diffusion can be described by a simplified conservation statement (Eq. 2) in the absence of fission.

[0028] 2)

[0029] Assuming that neutron scattering in bulk materials is linearly isotropic (i.e., has only a weak dependence on the position within the material or the angle of travel of the neutrons), this can be expressed in another form via Fick's law:

[0030]

[0031] 3)

[0032] "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 of photons in scattering and absorbing media. The same derivation applies to neutrons. Within a block of neutron absorbing material, one term will dominate and the angular flux can be expressed as follows.

[0033]

[0034]

[0035] This gives the coefficient D:

[0036] 4) ,

[0037] is a measure of the anisotropy of the scattering. For purely isotropic scattering, =1 / 3, for pure forward scattering, =1 (where ). Pure absorption is mathematically identical to pure forward scattering, i.e. =1 and ,in addition (Because there is no scattering).

[0038] The model The appropriate value of will depend on the neutron energy and the material, and can be found by numerically solving the neutron transport equation (Equation 1), using empirical equations fitted to the solution of the neutron transport equation, or by fitting simulated or experimental data for a set of neutron energies within a given material to the equation.

[0039]

[0040] That is, find the best fit to the data by methods known in the art (e.g., least squares error) The value of .

[0041] Falling back to a simpler model, in a region that does not contain material boundaries or neutron sources, the attenuation of neutrons within the material is given by the function control.

[0042]

[0043] function will vary depending on the geometry of the material, but it is always a monotonically decreasing function, i.e. neutrons will be absorbed in all materials where the neutron multiplication cross section is smaller than the absorption cross section as they travel through the material, so the number of neutrons must decrease with increasing distance (thickness) t. Λ is the macroscopic attenuation coefficient, with larger Λ indicating improved behavior of the material as a neutron attenuator - i.e. Λ is the desired figure of merit. Function No further specification is required to determine the quality factor - for all monotonically decreasing functions, increasing Λ will result in increased neutron attenuation. As some examples, for a simple one-dimensional slab of material, the function is a decreasing exponential function, and for a toroidal geometry, the function is one of the family of modified Bessel functions (or spherical Bessel functions modified for spherical geometry). Function The choice of can scale Λ by some factor (e.g., for the first geometry, the function can be some function of aΛt, and for the second geometry, the function can be some function of bΛt (where both a and b are constants), but this does not change the order of the material using Λ or the quality factors derived from Λ.

[0044] From the above discussion on diffusion, we can find that in the multi-group energy approximation, the subscript Indicates suitability for a given energy group:

[0045]

[0046]

[0047]

[0048]

[0049]

[0050] Figure 1A , 1Band 1C shows the quality factor Three potential graphical representations, their associated connecting lines and candidate material choices.

[0051] Figure 1A shows the quality factor for a given energy group , by plotting on a logarithmic scale and The relationship diagram is used to display. Figure 1A The upper left corner of the graph in the figure represents a larger M1, and the connecting line (the line of equal M1) is shown as a dashed line in the graph and forms an equally spaced diagonal line on the logarithmic graph. Although M1 is a suitable figure of merit because better performing materials will have a larger M1, it does not provide good separation between materials, as can be seen from the clustering of the results. In part, this is because yes , so the materials are clustered around a line in the graph.

[0052] The alternative quality factor M2 for a given energy group can be obtained by using the following relationship:

[0053]

[0054] Using the additional assumption that is constant for all materials within a given energy group, which leads to the quality factor ,like Figure 1B As shown, Figure 1B yes and In this figure, M2 increases towards the right side of the graph and the connecting line has the following equation:

[0055]

[0056] This improves the separation of materials, making candidate materials easier to distinguish, but the representation is less intuitive due to the curved connecting lines, and The assumption that is constant does not hold for all materials.

[0057] By further decomposing , another alternative representation can be obtained.

[0058]

[0059]

[0060] This is shown in Figure 1C middle, Figure 1C is N and where M3 increases towards the upper right corner of the graph. This representation provides good separation of the materials, a linear connecting line (when plotted on a logarithmic scale), and in addition, N provides a useful representation of the physical properties of the material, and Provides a useful indication of the nuclear properties of a material.

[0061] In each of the above examples, the actual figure of merit for a given energy set (which should be maximized) is (Or, in the case of M2, assuming the constant In the case of proportional to the value of the product), these representations only provide a useful illustration, or secondary figures of merit (such as ).

[0062] The value of each ∑ (and σ) depends on the neutron energy, so the above analysis considers the average performance for a given neutron energy group, depending on the value of ∑ used. Depending on the energy group chosen, the ranking of the materials will change because their scattering and absorption properties differ at different energy levels. In practice, it is often more useful to analyze the performance as a weighted average of multiple energy groups, weighted, for example, by how much each group contributes to heating or damage of the protected material.

[0063] Neutrons of different energies have different effects on the materials that need to be shielded. In order to combine the quality factors of each energy group , using weighting factors based on the inherent cross-sectional properties of the material to be shielded To obtain a given standard The measurement of.

[0064]

[0065] Although a "binning" approach is shown above, where a constant is calculated for each of the multiple energy groups , but a continuous method can also be used, in which a function A is defined, where A depends on the neutron energy, and the total penalty function can then be calculated as the integral of AΛ over all neutron energies (although A may be 0 outside the range of interest, which is equivalent to integrating only over that range of interest). can be normalized to , or equivalently, the function A can be normalized so that .

[0066] Standards and The choice of depends on the weight required for a given design parameter. For example, when shielding is intended to prevent neutron heating, An appropriate choice of (or function A) would be the KERMA k of the material being protected. g(Kinetic energy released in a material—a measure of the kinetic energy deposited in a given material by a given neutron energy.) In this way, groups of neutrons that produce more heat have a greater weight attributed to them and contribute more to the quality factor of the neutron heating criterion—i.e., favoring the attenuation of the "more problematic" neutrons. Figure 2A The case of the ReBCO superconductor material is shown.

[0067] As another example, when considering the potential damage of neutrons to ReBCO HTS, a suitable set of constants is , which is a measure of the ballistic energy available for atomic displacements within ReBCO (ignoring the constant properties between energy groups, and thus negligible since they are omitted in the normalization). Figure 2B A graph showing this measure is shown.

[0068] Other examples include: using energy cutoffs to account for fluxes in a given energy region that are independent of the material being protected; using absorption cross sections to account for activation / transmutation of materials; using gas generation cross sections to account for the amount of gaseous particles generated in a material; and using dose weighting factors to account for health effects.

[0069] KERMA, ballistic energies available for atomic displacements, absorption cross sections, gas generation cross sections, dose weighting factors, and similar values ​​can be obtained from standard reference tables and simulation techniques known in the art.

[0070] An additional set of scaling factors may be applied to each energy group (or as an additional continuous function) to account for the expected flux distribution of incident neutrons.

[0071] In practice, it is often necessary to balance multiple design considerations—for example, a material that is an effective shield against neutron heating may not be suitable if there is a more effective shield against neutron damage that is also adequate to resist heating. However, this can be achieved by determining the constants that correspond to the desired design goals. of each collection , and then obtain Take a weighted average (or other linear function) into account. The heating examples above and The above damage example, Figure 3 It is shown in and Each dotted line represents a relationship between and The connecting line, .

[0072] When considering a material as a shield, several of these effects need to be taken into account, with the relative importance of each of these criteria depending on the radiation environment being considered. A collection of all these criteria combined into a single overall quality factor .

[0073]

[0074] Among them, each standard The quality factor is the maximum value of this metric for all shielding materials considered. Normalize so that different standards can be more easily compared and combined.

[0075] Taking the shielding of fusion power reactors (FPP) and ReBCO HTS magnets as an example, the shielding needs to block slow neutrons ( ) and fast neutrons ( , preventing atomic displacement (damage) in the HTS and preventing transmutation inside the HTS. The following table provides the Numerical examples of relevant weighting factors and their relationship to the inherent cross-section of the material being shielded.

[0076]

[0077] Regardless of which of the above related quality factors is used, Figure 4 All are flow charts of a method for selecting neutron shielding materials. In step 401, a plurality of initial candidate materials, i.e., a first material combination, are selected. This may be a broad group, such as "metal hydride" or "metal boride". In step 402, a value for incident neutron flux is provided, representing the expected neutron flux that the shield will encounter in use. In step 403, a set of criteria for evaluating the quality factor is provided, which may include any of the criteria in the above table. If these criteria involve a target (e.g., the heat or damage of the target), the properties of the target that represent the intended use of the neutron shielding will be selected. In step 404, a total weight is defined for each criterion, and for each criterion, a set of inherent weight factors is defined for each neutron energy group based on the incident neutron flux. In step 405, a total quality factor for each material in the candidate list is calculated using a computer system based on the following:

[0078] Determine the quality factor for each neutron energy group based on the absorption and scattering coefficients of the material for that energy group,

[0079] determining a figure of merit for each standard based on the figure of merit of each energy group weighted by an intrinsic weighting factor of the standard,

[0080] The total quality factor is determined from the quality factor of each criterion weighted by the total weight of the criterion.

[0081] A candidate list of materials, ie, a second set of materials, is then selected based on their overall quality factors.

[0082] In particular, the isotropy of the scattering is probably the least reliable estimator used in the quality factor. Therefore, a threshold ratio for the “best performing” quality factor can be calculated such that if is estimated incorrectly, then any material that should be the best performing material will still be above the threshold—for example, since Λ depends on The reciprocal of the square root of It may take a value between 1 and 1 / 3, so the worst case is that the best performing material uses 1 / 3 of the Calculated, but actually 1. Make sure that the error estimate The worst case threshold for any material that should perform best to be within the selected set is In practice, a larger threshold can be used because = 1 / 3 of the materials will have purely isotropic scattering, which is unlikely to be relevant for neutron shielding applications. This approach allows for a constant for all materials to be used. An initial approximation is made, and then the candidate list with quality factors above a threshold can be refined, for example by numerical evaluation, experimentation, or Monte-Carlo simulation to determine the Once the exact value is determined, the quality factor for each material can be recalculated and additional thresholds applied to narrow the candidate list. This approach greatly simplifies the selection of the candidate list because The calculations can be complex, and this approach reduces the need to determine The number of materials.

[0083] A review of the quality factors based on the above approach suggested two candidate materials that had not been previously suggested for neutron shielding—nickel hydride (NiH2) and scandium borohydride (ScB3H). 18 NiH2 can be formed by reacting nickel with hydrogen at high pressure (~60 GPa) and is stable at low temperatures, making it particularly suitable for environments where cryogenic systems already exist (such as spherical tokamaks). ScB3H 18 It can be formed by ball milling scandium chloride hydrate and lithium borohydride, and has inter alia the additional advantage that even when it begins to decompose, it remains a scandium and boron compound (i.e., only hydrogen is released), and retains at least some of its barrier properties, e.g., better barrier properties than metallic scandium.

[0084] The increased neutron attenuation of a given thickness of neutron shielding can be used to provide improved attenuation for a given thickness of shielding compared to known shielding materials, or it can provide a similar degree of neutron shielding at 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 shield thickness (as part of minimizing the overall diameter of the central column) is an important design goal.

[0085] List of terms in equation

[0086] Unless otherwise noted for a specific equation, each symbol used in this document has the meaning consistent with the following list when it appears.

[0087] Note that in equation 1) and in the description of Elaloufi's paper, the brackets indicate the variables on which the quantity depends, while elsewhere in the document, the brackets are used for arithmetic grouping. Mathematical operators have their conventional meanings.

[0088] In general, unless otherwise stated, the subscript 0 denotes a normalized or scaled value of a particular quantity, i.e., such that for some quantity A, A=A0f(x), where A0 is a constant.

[0089]

[0090]

[0091]

[0092]

Claims

1. A method for selecting one or more materials of a specific isotopic composition for neutron shielding, the method comprising: providing a first list of materials, each material having a different isotopic composition; Provide the incident neutron flux that the neutron shield will encounter in use The value of A set of criteria is provided, the set of criteria including one or more of the following: Neutron flux, Neutron dose, heating of the target protected by the neutron shield, damage to said target, Gas production within the stated target, the tritium yield within the target, and Transmutation of said objectives; For each criterion, define the total weight , and defining, for each of a plurality of neutron energy groups, an intrinsic weighting factor based on the incident neutron flux ; Calculating, using a computing system, an overall quality factor for each material in the first set of materials , where the total quality factor of each material is based on: Determine the quality factor for each neutron energy group based on the absorption coefficient and scattering coefficient of the material for each energy group ; For each standard, determining a quality factor of the standard based on the quality factor of each neutron energy group weighted by the intrinsic weighting factor of the standard ; Determining an overall quality factor based on the quality factor of each criterion weighted by the overall weight of the criterion ; Based on the overall quality factor of the material A second list of materials is selected, wherein the second list is a subset of the first list.

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

3. The method of claim 2, comprising using the selected material as a neutron shield.

4. The method according to claim 2 or 3, comprising performing one or more further selection steps for each material in the second list, wherein the further selection steps comprise one or more of the following: The neutron transport equation is solved using a derived fit to the empirical equation to select for each material in the candidate list ; Neutron decay experiments are performed on each material in the candidate list to select ; A neutron migration simulation is performed for each material in the candidate list to select ; wherein said selected material is selected based on said other selecting step; and in It means that each energy group The absorption and scattering terms in are isotropic, so that for pure isotropic scattering, =1 / 3, for pure forward scattering, = 1, for pure absorption, =1, and for the intermediate condition, 1 / 3< <1. 5 . The method of claim 1 , wherein selecting the second list comprises selecting all materials in the first list whose quality factor is above a threshold value. The method of claim 5 , wherein the threshold is a proportion of the highest quality factors of materials in the initial list of materials.

7. The method of claim 6, wherein the ratio is at least 57%.

8. A method according to any one of the preceding claims, wherein for each energy group, the quality factor and Proportional to where the diffusion coefficient and Proportional, where and , where for each material in the list of materials and for each energy group , is the neutron removal cross section, is the intra-group neutron scattering cross section, is the out-of-group neutron scattering cross section, Σ' s is the corrected neutron scattering cross section; is the neutron absorption cross section; and is the mean scattered cosine.

9. The method according to claim 8, wherein ,in and ,in It means that each energy group The absorption and scattering terms in are isotropic, so that for pure isotropic scattering, =1 / 3, for pure forward scattering, = 1, for pure absorption, =1, and for intermediate conditions, 1 / 3< <1.

10. The method of claim 8, wherein the quality factor of each energy group and Proportional.

11. The method according to any one of claims 1 to 7, wherein the quality factor of each energy group is Based on the neutron absorption and scattering cross sections for each energy group for each material and the atomic number density N of each material.

12. The method according to claim 11, wherein Quality factor for each energy group and Proportional, where is the secondary quality factor for each energy group, and and proportional; and Selecting materials based on quality factors includes selecting materials based on quality factors. and secondary quality factor Select the material, where is the microscopic neutron removal cross section, is the corrected microscopic neutron scattering cross section, and in It means that each energy group The absorption and scattering terms in are isotropic, so that for pure isotropic scattering, =1 / 3, for pure forward scattering, = 1, for pure absorption, =1, and for intermediate conditions, 1 / 3< <1.

13. A method according to any one of the preceding claims, wherein the intrinsic weighting factors comprise: where said criterion is neutron flux, said incident neutron flux within a specified energy range; In the case where the criterion is neutron dose, the incident neutron flux is multiplied by the dose response function, Where the criterion is heat, the incident neutron flux multiplied by the kinetic energy released in the material for the target for the neutrons in the energy group, KERMA; In the case where the criterion is damage, the incident neutron flux is multiplied by the ballistic energy for the target, for neutrons in the energy group, which can be used for atomic displacement, ,in is the available ballistic energy, and E d is the threshold displacement energy of the material; where the criterion is gas production, the incident neutron flux multiplied by the material production rate coefficients for hydrogen and helium isotopes for neutrons in the energy group; In the case where the standard is transmutation, the incident neutron flux is multiplied by the absorption coefficient of the material for neutrons in the energy group.

14. A method according to any one of the preceding claims, wherein for each material the neutron absorption and scattering cross sections are calculated based on the neutron absorption and scattering cross sections of each constituent isotope of the material.

15. A method of selecting one or more materials of a particular isotopic composition for neutron shielding, the method comprising: providing a first list of materials, each material having a different isotopic composition; providing a distribution of incident neutron flux that the neutron shield will encounter in use; A set of criteria is provided, the set of criteria including one or more of the following: Neutron flux, Neutron dose, heating of the target protected by the neutron shield, damage to said target, Gas production within the stated target, the tritium yield within the target, and Transmutation of said objectives; For each criterion, defining a total weight and, based on said incident neutron flux, defining an intrinsic weighting factor depending on the neutron energy; Calculating, using a computing system, an overall quality factor for each material in the first set of materials, wherein the overall quality factor for each material is based on: determining a quality factor function that depends on neutron energy based on the absorption and scattering coefficients of the material in dependence on the neutron energy; for each criterion, determining a quality factor for the criterion based on an integral of a product of the intrinsic weighting function and the quality factor function; determining an overall quality factor based on the quality factor of each criterion weighted by the overall weight of the criterion; A second list of materials is selected based on an overall quality factor of the materials, wherein the second list is a subset of the first list.

16. Scandium borohydride ScB3H 18 Or the use of nickel hydride NiH2 as neutron shielding material.

17. A neutron shield comprising scandium borohydride ScB3H 18 Or nickel hydride NiH2.

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