A method for calculating equivalent winding material parameters of a fusion reactor CICC superconducting magnet

Abstract

This application provides a method for calculating the material parameters of the equivalent winding of a CICC superconducting magnet. The method includes: determining the smallest unit cell corresponding to the superconducting magnet winding; constructing a finite element model of the smallest unit cell; applying specific loads and constraints to the finite element model and outputting the calculation parameters corresponding to the initial material parameters; calculating the initial material parameters using the generalized Hooke's law based on the calculation parameters; establishing an equivalent model of the superconducting magnet winding based on the initial material parameters; and comparing and verifying the equivalent model with a pre-established detailed model of the superconducting magnet winding. If the comparison and verification pass, the initial material parameters are used as the material parameters of the equivalent winding corresponding to the superconducting magnet winding; if the comparison and verification fail, a new smallest unit cell is determined. This application replaces the entire winding with a smallest unit cell and simplifies the winding into a set of smallest unit cells, which can improve computational efficiency while ensuring the accuracy of the equivalent parameters.

Description

Technical Field

[0001] This invention relates to the field of superconducting magnet simulation technology, and in particular to a method for calculating the equivalent winding material parameters of a CICC superconducting magnet in a fusion reactor. Background Technology

[0002] Superconducting magnets are core components of fusion reactors, operating in environments characterized by high current carrying capacity and high magnetic fields, posing a significant challenge to the structural stability of these magnets. Currently, most fusion reactor superconducting magnets utilize CICC (Cable-In-Conduit Conductors). A superconducting magnet winding typically comprises several components from the outside in, including ground insulation, inter-turn insulation, turn-to-turn insulation, armor, and superconducting cables.

[0003] In the structural mechanics simulation analysis of superconducting magnets in fusion reactors, the material parameters of the windings are fundamental to accurately evaluating the mechanical properties of external components such as the coil housing and support structure. However, the calculation and modeling of material parameters for superconducting magnet windings (especially CICC superconducting magnets) in existing technologies suffer from the following problems:

[0004] First, the structure of superconducting magnet windings is extremely complex, with components arranged periodically in space and significant differences in material properties between different components. This is especially true for CICC superconducting magnets, which not only have complex structures but also include anisotropic materials such as G10. This multi-component, anisotropic structural characteristic makes it difficult to directly derive the overall equivalent material properties of the windings through theoretical derivation, easily leading to a lack of fundamental data in structural mechanics analysis.

[0005] Secondly, the dimensions of the various components in a superconducting magnet winding vary greatly, making modeling difficult and computationally expensive. This is especially true for CICC superconducting magnets, where critical components such as the insulation layer and superconducting strands inside the winding are only a few millimeters thick, while the overall size of the winding can reach the 10-meter scale, resulting in a scale ratio as high as 10-10. 4 If a full-scale detailed finite element model of the winding is performed, the geometry and material properties of each component need to be accurately characterized. This not only generates a massive number of mesh elements and consumes a huge amount of computing resources, but also leads to difficulties in simulation convergence and seriously affects analysis efficiency.

[0006] Furthermore, in the mechanical property analysis of external components of the winding, such as the coil box and support structure, the core requirement is to obtain the stress and displacement responses of the external components, rather than the local mechanical behavior inside the winding. However, simplifying the winding model will lead to excessive errors in electromagnetic force transmission, affecting the accuracy of the analysis results for the external components; while using detailed modeling will result in extremely low computational efficiency.

[0007] Therefore, existing methods for calculating the equivalent winding material parameters of superconducting magnets are difficult to balance computational accuracy and efficiency. Summary of the Invention

[0008] The purpose of this invention is to solve the problem that existing methods for calculating the equivalent winding material parameters of superconducting magnets are difficult to balance in terms of both calculation accuracy and efficiency.

[0009] To address the aforementioned problems, this invention discloses a method for calculating the equivalent winding material parameters of a CICC superconducting magnet, comprising the following steps: determining the minimum unit cell corresponding to the superconducting magnet winding based on its structural parameters; constructing a finite element model of the minimum unit cell; obtaining specific loads and constraints corresponding to the initial material parameters of the minimum unit cell, applying the specific loads and constraints to the finite element model, and outputting the calculation parameters corresponding to the initial material parameters through the finite element model; calculating the initial material parameters using the generalized Hooke's law based on the calculation parameters; establishing an equivalent model of the superconducting magnet winding based on the initial material parameters, and comparing and verifying the equivalent model with a pre-established detailed model of the superconducting magnet winding; wherein, if the comparison and verification pass, the initial material parameters are used as the material parameters of the equivalent winding corresponding to the superconducting magnet winding; if the comparison and verification fail, a new minimum unit cell is determined, and the steps after determining the minimum unit cell are repeated until the comparison and verification between the corrected equivalent model and the detailed model pass; wherein, the new minimum unit cell is obtained by expanding the size of the minimum unit cell.

[0010] According to another specific embodiment of the present invention, the method for calculating the equivalent winding material parameters of the superconducting magnet in a CICC fusion reactor disclosed in this embodiment includes structural parameters such as the stacked structure of the superconducting magnet winding in its radial direction and the arrangement of the superconducting magnet winding in its axial direction. Furthermore, determining the smallest unit cell corresponding to the superconducting magnet winding based on the structural parameters of the superconducting magnet winding includes: taking a cable unit in the superconducting magnet winding whose stacked structure in its radial direction is a first structure and whose arrangement in its axial direction is a first arrangement as the smallest unit cell; wherein, the first structure is: the superconducting magnet winding is coaxially arranged from the inner layer to the outer layer with a superconducting cable, an armor layer, an inter-turn insulation layer, an inter-layer insulation layer, and a ground insulation layer, and a filling material is also provided on the outer periphery of the ground insulation layer, the filling material at least partially covering the outer peripheral wall of the ground insulation layer; the first arrangement is: the cable unit is arranged periodically along the axial direction as the smallest repeating unit.

[0011] Furthermore, the finite element model of the smallest unit cell is constructed, including: geometrically modeling the smallest unit cell to generate a unit cell geometric assembly; assigning material properties to the unit cell geometric assembly to generate a unit cell material assembly; wherein, for anisotropic materials, the material parameters of the anisotropic material in different directions are input; for isotropic materials, the standard material parameters of the isotropic material are input; for superconducting cables, the superconducting cable is assigned a preset elastic modulus; and meshing is performed on the unit cell material assembly to generate a finite element model.

[0012] Furthermore, the smallest unit cell is a hexahedral structure, and includes a length constraint surface and a length coupling surface perpendicular to the length direction, a width constraint surface and a width coupling surface perpendicular to the width direction, and a height constraint surface and a height coupling surface perpendicular to the height direction.

[0013] According to another specific embodiment of the present invention, the method for calculating the equivalent winding material parameters of the CICC superconducting magnet disclosed in this embodiment of the present invention includes initial material parameters including the elastic modulus of the smallest unit cell in its length direction, width direction, and height direction; wherein, the specific load corresponding to the elastic modulus of the smallest unit cell in its length direction includes: applying a first pressure on the length coupling surface; the specific load corresponding to the elastic modulus of the smallest unit cell in its width direction includes: applying a second pressure on the width coupling surface; the specific load corresponding to the elastic modulus of the smallest unit cell in its height direction includes: applying a third pressure on the height coupling surface; the constraint conditions corresponding to the elastic modulus of the smallest unit cell in its length direction, width direction, and height direction all include: constraining the length constraint surface in the length direction, coupling the length coupling surface in the length direction; constraining the width constraint surface in the width direction, coupling the width coupling surface in the width direction; constraining the height constraint surface in the height direction, coupling the height coupling surface in the height direction.

[0014] According to another specific embodiment of the present invention, the method for calculating the equivalent winding material parameters of the CICC superconducting magnet in a fusion reactor disclosed in this embodiment includes the calculation parameters as follows: the displacement of the smallest unit cell in its length, width, and height directions under specific loads and constraints, as well as the length, width, and height values ​​of the smallest unit cell; wherein, the elastic modulus is calculated according to the following formula:

[0015]

[0016] in, It is the elastic modulus of the smallest unit cell along its length. As the primary pressure, ; The strain of the smallest unit cell along its length. ,in, The displacement of the smallest unit cell along its length direction. This is the length value of the smallest unit cell; The elastic modulus of the smallest unit cell in its width direction; As the second pressure, ; The strain of the smallest unit cell in its width direction. ,in, The displacement of the smallest unit cell in its width direction. This is the width value of the smallest unit cell; The elastic modulus of the smallest unit cell in its height direction; As the third pressure, ; The strain of the smallest unit cell in its height direction. ,in, This represents the displacement of the smallest unit cell in its height direction. This represents the height value of the smallest unit cell.

[0017] According to another specific embodiment of the present invention, the method for calculating the equivalent winding material parameters of the CICC superconducting magnet disclosed in this embodiment of the present invention includes initial material parameters including a first Poisson's ratio when the smallest unit cell is subjected to a load in its length direction and strain in its width direction, a second Poisson's ratio when the smallest unit cell is subjected to a load in its length direction and strain in its height direction, and a third Poisson's ratio when the smallest unit cell is subjected to a load in its width direction and strain in its height direction; wherein, the specific loads corresponding to the first and second Poisson's ratios both include: applying a fourth pressure on the length coupling surface; the specific loads corresponding to the third Poisson's ratio include: applying a fifth pressure on the width coupling surface; the constraint conditions corresponding to the first, second, and third Poisson's ratios all include: constraining the length constraint surface's degrees of freedom in the length direction, coupling the length coupling surface's degrees of freedom in the length direction; constraining the width constraint surface's degrees of freedom in the width direction, coupling the width coupling surface's degrees of freedom in the width direction; constraining the height constraint surface's degrees of freedom in the height direction, coupling the height coupling surface's degrees of freedom in the height direction.

[0018] According to another specific embodiment of the present invention, the method for calculating the equivalent winding material parameters of the CICC superconducting magnet of the present invention includes the displacement of the smallest unit cell in its length, width and height directions under specific loads and constraints, as well as the length, width and height values ​​of the smallest unit cell.

[0019] Initial material parameters include the Poisson's ratio of the smallest unit cell. The Poisson's ratio is calculated using the following formula:

[0020]

[0021] in, The first Poisson's ratio; The second Poisson's ratio; The third Poisson's ratio; ,in, The displacement of the smallest unit cell along its length direction. This is the length value of the smallest unit cell; ,in, The displacement of the smallest unit cell in its width direction. This is the width value of the smallest unit cell; ,in, This represents the displacement of the smallest unit cell in its height direction. The height value is the smallest unit cell, and the fourth and fifth pressures are both 1 MPa.

[0022] According to another specific embodiment of the present invention, the method for calculating the equivalent winding material parameters of the CICC superconducting magnet disclosed in this embodiment of the present invention includes initial material parameters including the first shear modulus of the smallest unit cell when a shear force is applied to the width direction along the length direction, the second shear modulus of the smallest unit cell when a shear force is applied to the height direction along the length direction, and the third shear modulus of the smallest unit cell when a shear force is applied to the height direction along the width direction; wherein, the specific load corresponding to the first shear modulus includes: applying a sixth pressure along the length direction to the width coupling surface; the specific load corresponding to the second shear modulus includes: applying a seventh pressure along the height direction to the length coupling surface; the specific load corresponding to the third shear modulus includes: applying an eighth pressure along the height direction to the width coupling surface; the constraint condition corresponding to the first shear modulus includes: constraining all degrees of freedom of the width constraint surface and the degrees of freedom in the length direction of the coupling width surface; and the length constraint surface and the length coupling surface satisfy the following equation:

[0023]

[0024] in, Let c be the y-coordinate. Let b be the displacement along the length direction; points a and b are points on the bottom and top edges of a surface, respectively; point c is any point on the surface. That is, for any surface, any point c should satisfy the above equation with respect to points a and b.

[0025] The constraints corresponding to the second shear modulus include: all degrees of freedom of the constraint length constraint surface, and the degrees of freedom in the height direction of the coupling length coupling surface; furthermore, the height constraint surface and the height coupling surface satisfy the following equation:

[0026]

[0027] in, Let c be the x-coordinate of point c. Let b be the vertical displacement of point b; points a and b are points on the bottom and top edges of a surface, respectively; point c is any point on the surface. That is, for any surface, any point c should satisfy the above equation with respect to points a and b.

[0028] The constraints corresponding to the third shear modulus include:

[0029] All degrees of freedom of the constraint width surface, and the degrees of freedom in the height direction of the coupling width surface; and the height constraint surface and the height coupling surface satisfy the following equation:

[0030]

[0031] in, Let c be the y-coordinate. Let b be the vertical displacement of point b; points a and b are points on the bottom and top edges of a surface, respectively; point c is any point on the surface. That is, for any surface, any point c should satisfy the above equation with respect to points a and b.

[0032] According to another specific embodiment of the present invention, the method for calculating the equivalent winding material parameters of the CICC superconducting magnet of the present invention includes the length, width and height values ​​of the smallest unit cell, as well as the displacement of the width coupling surface and the displacement of the height coupling surface in the length direction of the smallest unit cell under specific loads and constraints; wherein, the sixth pressure, the seventh pressure and the eighth pressure are all 1N.

[0033] Calculate the shear modulus using the following formula:

[0034]

[0035] in, The first shear modulus; The shear stress of the length constraint surface and the length coupling surface relative to the width constraint surface and the width coupling surface; This is the length value of the smallest unit cell; This is the width value of the smallest unit cell; The shear strain of the length-constrained surface and the length-coupled surface relative to the width-constrained surface and the width-coupled surface; This represents the displacement of the width coupling surface along its length.

[0036]

[0037] in, The second shear modulus; The shear stress of the length constraint surface and the length coupling surface relative to the height constraint surface and the height coupling surface; This is the length value of the smallest unit cell; This represents the height of the smallest unit cell. The shear strain of the length-constrained surface and the length-coupled surface with respect to the height-constrained surface and the height-coupled surface; This represents the displacement of the highly coupled surface along its length.

[0038]

[0039] in, It is the third shear modulus; The shear stress of the width-constrained surface and the width-coupled surface relative to the height-constrained surface and the height-coupled surface; This is the width value of the smallest unit cell; This represents the height of the smallest unit cell. The shear strain of the width-constrained surface and the width-coupled surface with respect to the height-constrained surface and the height-coupled surface; This represents the displacement of the highly coupled surface along its length.

[0040] According to another specific embodiment of the present invention, the method for calculating the equivalent winding material parameters of the CICC superconducting magnet disclosed in this embodiment of the present invention includes initial material parameters including the thermal expansion rates of the smallest unit cell in its length, width, and height directions; wherein, the specific loads corresponding to the thermal expansion rates of the smallest unit cell in its length, width, and height directions all include: the operating temperature at which superconductivity is applied; the constraint conditions corresponding to the thermal expansion rates of the smallest unit cell in its length, width, and height directions all include: the degree of freedom of the constraint length constraint surface in the length direction, the degree of freedom of the coupling length coupling surface in the length direction; the degree of freedom of the constraint width constraint surface in the width direction, the degree of freedom of the coupling width coupling surface in the width direction; the degree of freedom of the constraint height constraint surface in the height direction, and the degree of freedom of the coupling height coupling surface in the height direction.

[0041] According to another specific embodiment of the present invention, the method for calculating the equivalent winding material parameters of the CICC superconducting magnet disclosed in this embodiment includes the displacement of the smallest unit cell along a predetermined direction under specific loads and constraints, as well as the length, width, and height values ​​of the smallest unit cell; wherein the thermal expansion coefficient is calculated according to the following formula:

[0042]

[0043] in, The thermal expansion coefficient of the smallest unit cell along its length; This represents the displacement of the length coupling surface along its length direction. This is the length value of the smallest unit cell; The thermal expansion coefficient of the smallest unit cell in its width direction; This represents the displacement of the width coupling surface along the width direction. This is the width value of the smallest unit cell; The thermal expansion coefficient of the smallest unit cell in its height direction; This represents the displacement of the highly coupled surface along the height direction. This represents the height value of the smallest unit cell.

[0044] According to another specific embodiment of the present invention, the method for calculating the equivalent winding material parameters of the CICC superconducting magnet disclosed in this embodiment of the present invention compares and verifies the equivalent model with a pre-established detailed model of the superconducting magnet winding, including: applying the same simulation conditions to the equivalent model and the detailed model, and extracting the structural data of the external components corresponding to the equivalent model and the detailed model respectively; calculating the deviation between the structural data of the equivalent model and the structural data of the detailed model; and determining that the comparison verification is passed if the deviation is less than a preset deviation threshold; and determining that the comparison verification is failed if the deviation is greater than or equal to the preset deviation threshold; wherein, the deviation threshold ranges from 3% to 5%.

[0045] The beneficial effects of this invention are:

[0046] The method for calculating the equivalent winding material parameters of the CICC superconducting magnet in this application reduces the number of meshes in the model by replacing the entire winding with the smallest unit cell, effectively improving the modeling efficiency of the equivalent model. Furthermore, the equivalent model simplifies the winding into a uniform block composed of the smallest unit cells, reducing computational requirements and improving convergence speed and stability during calculation. In addition, when performing stress analysis on the external structure of the winding, it is not necessary to focus on the internal details of the winding, avoiding the problems of large computational load and long computation time caused by the accuracy redundancy of traditional overall modeling.

[0047] Furthermore, this calculation method designs different loads and constraints for different material parameters, which can not only adapt to the anisotropy and structural characteristics of superconducting magnet windings, but also ensure the rigor of the mechanical logic of the material parameter solution, providing a reliable initial parameter basis for the equivalent modeling of the entire winding, while ensuring the mechanical simulation accuracy of the subsequent equivalent model. Attached Figure Description

[0048] Figure 1 This is a flowchart illustrating the method for calculating the equivalent winding material parameters of the CICC superconducting magnet in a fusion reactor, as provided in this embodiment of the invention.

[0049] Figure 2This is a schematic diagram of the smallest unit cell in the method for calculating the equivalent winding material parameters of the CICC superconducting magnet in the fusion reactor provided in this embodiment of the invention.

[0050] Figure 3 This is a schematic diagram illustrating the constraint conditions applied when obtaining the shear modulus in the calculation method of equivalent winding material parameters of CICC superconducting magnet provided in the embodiment of the present invention.

[0051] Figure 4 This is a schematic diagram of the equivalent model and detailed model in the calculation method of equivalent winding material parameters of CICC superconducting magnet in fusion reactors provided in the embodiments of the present invention;

[0052] Figure 5 This is a schematic diagram comparing the stress of the equivalent model and the detailed model in the calculation method of equivalent winding material parameters of CICC superconducting magnet in the fusion reactor provided in the embodiments of the present invention.

[0053] Figure 6 This is a schematic diagram comparing the displacement of the equivalent model and the detailed model in the calculation method of equivalent winding material parameters of CICC superconducting magnet provided in the embodiment of the present invention.

[0054] Explanation of reference numerals in the attached figures:

[0055] 1. Superconducting cable; 2. Armor layer; 3. Insulation layer; 4. Filler material. Detailed Implementation

[0056] As described in the background section, existing methods for calculating the equivalent winding material parameters of superconducting magnets struggle to balance computational accuracy and efficiency. To address these issues, this embodiment provides a method for calculating the equivalent winding material parameters of a CICC superconducting magnet. This method improves modeling efficiency by replacing the entire winding with the smallest unit cell; furthermore, simplifying the winding into a set of smallest unit cells reduces the degrees of freedom of the equivalent model and decreases the computational load. Since high equivalent model accuracy is not required when analyzing external structures such as coil boxes, this method improves computational efficiency while maintaining accuracy.

[0057] Next, the method for calculating the equivalent winding material parameters of the CICC superconducting magnet in this embodiment will be described in detail with reference to the accompanying drawings. Before the description, the relevant terms will be explained:

[0058] CICC is an abbreviation for Cable-In-Conduit Conductor, a superconducting conductor technology specifically designed for strong magnetic fields and high current environments, such as fusion reactors. It involves twisting multiple superconducting wires into a cable, then encapsulating it within a metal conduit filled with helium as a cooling medium and providing mechanical support.

[0059] CICC superconducting magnet winding in fusion reactors: refers to the superconducting magnet winding component with CICC (Cable-in-Conduit Conductor) structure used in fusion reactors (such as tokamak devices and stellarator devices). Its core function is to generate the strong magnetic field required to confine plasma. It is composed of a variety of materials such as superconducting wire, copper matrix, stainless steel conduit, and insulating layer, and its structure has the characteristics of multi-scale and anisotropy.

[0060] The smallest unit cell is the smallest repeating structural unit that can completely reflect the periodic structural characteristics of a superconducting magnet winding. Analyzing this unit allows for the derivation of the equivalent characteristics of the entire winding, avoiding redundant modeling of the overall structure. Its size is much smaller than the entire winding, but its material properties can be characterized through periodic expansion. For example, in the CICC superconducting magnet winding of a fusion reactor, the smallest unit cell could be the smallest repeating module containing a superconducting cable, its corresponding armor, and surrounding insulation.

[0061] Finite element model: refers to a numerical model based on the finite element method, which discretizes the smallest unit cell into several nodes and elements, and assigns actual material properties, geometric features and boundary conditions to each component (superconducting wire, copper matrix, insulating layer, etc.) to simulate the mechanical and physical properties of the unit cell.

[0062] Calculation parameters: These are data obtained through finite element model simulation calculations that can characterize the overall mechanical and physical properties of the smallest unit cell.

[0063] Generalized Hooke's Law: A physical law describing the linear relationship between stress and strain in isotropic linear elastic materials under complex stress states.

[0064] Initial material parameters: These are the set of parameters calculated based on computational parameters and the generalized Hooke's law, used to describe the macroscopic mechanical properties of the smallest unit cell, and can be directly used to establish subsequent equivalent models.

[0065] Equivalent model: refers to a macroscopic model that simplifies the entire superconducting magnet winding into a continuous dielectric structure based on initial material parameters, without considering the microstructure inside the unit cell, and only retains the overall mechanical and physical response characteristics.

[0066] Detailed model: refers to a numerical model based on the actual winding structure that fully restores the geometry and material properties of each component such as superconducting cable, copper matrix, insulation layer, and conduit, and can accurately reflect the influence of the winding microstructure on the overall performance, serving as a benchmark for comparison and verification.

[0067] Example 1:

[0068] This embodiment provides a method for calculating the equivalent winding material parameters of a CICC superconducting magnet in a fusion reactor, referencing... Figure 1 This includes the following steps:

[0069] The minimum unit cell corresponding to the superconducting magnet winding is determined based on its structural parameters. A finite element model of the minimum unit cell is constructed. The calculation parameters of the superconducting magnet winding are output from the finite element model. Specific loads and constraints corresponding to the initial material parameters of the minimum unit cell are obtained. Specific loads and constraints are applied to the finite element model, and the calculation parameters corresponding to the initial material parameters are output from the finite element model. The initial material parameters are calculated using the generalized Hooke's law based on the calculation parameters. An equivalent model of the superconducting magnet winding is established based on the initial material parameters. The equivalent model is compared and verified with a pre-established detailed model of the superconducting magnet winding. If the comparison verification passes, the initial material parameters are used as the material parameters of the equivalent winding corresponding to the superconducting magnet winding. If the comparison verification fails, a new minimum unit cell is determined, and the steps after determining the minimum unit cell are repeated until the comparison verification between the corrected equivalent model and the detailed model passes. The new minimum unit cell is obtained by increasing the size of the minimum unit cell.

[0070] Specifically, the structural parameters of a superconducting magnet include, but are not limited to, the number of winding layers, the number of turns per layer, the size and arrangement of each component, etc. The smallest unit cell can be a single-strand cable unit cell containing one superconducting wire, a copper matrix surrounding it, and a local insulating layer; it can also be a multi-strand interwoven unit cell containing 3-7 interwoven superconducting wires, a shared copper matrix, and an insulating layer; it can also be a conduit-cable composite unit cell containing a multi-strand interwoven cable, a stainless steel conduit inner wall, and a filling medium; or it can be a layered composite unit cell containing a conductor (superconducting wire + copper matrix), an insulating layer, and a local structure of adjacent conductors.

[0071] Finite element models include, but are not limited to, solid element finite element models, shell-body hybrid finite element models, or anisotropic element finite element models.

[0072] The calculation parameters include, but are not limited to, displacement data representing the deformation of the unit cell in the X, Y, and Z directions, stress data representing the stress components of the unit cell in each direction, and thermal data representing the thermal deformation of the unit cell in a low-temperature environment (such as 4K).

[0073] More specifically, this calculation method first performs step S1: determining the smallest unit cell. That is, based on the structural parameters and periodic arrangement characteristics of the superconducting magnet winding, the smallest unit cell with a repeating pattern in the winding is extracted as the smallest unit cell. For example, a certain smallest unit cell consists of a superconducting cable, a square armor, turn insulation, layer insulation, and resin filler, with lengths of Lx=50mm, Ly=30mm, and Lz=40mm in the X, Y, and Z directions, respectively. This unit cell is periodically arranged in the winding along the X, Y, and Z directions, forming a complete superconducting magnet winding structure.

[0074] Next, proceed to step S2: construct the finite element model of the smallest unit cell. That is, based on the geometric dimensions of the smallest unit cell determined in step S1, a three-dimensional finite element model is built using finite element simulation software.

[0075] Next, step S3 is executed: The specific loads and constraints corresponding to the initial material parameters of the smallest unit cell are obtained; these specific loads and constraints are applied to the finite element model; and the calculated parameters corresponding to the initial material parameters are output through the finite element model. The initial material parameters are then calculated based on these calculated parameters using the generalized Hooke's law. In other words, based on the established finite element model, the initial material parameters of the smallest unit cell are calculated by applying specific constraints, loads, and temperature boundaries, combined with the generalized Hooke's law.

[0076] Next, step S4 is performed: comparison and verification of the equivalent model and the detailed model. Specifically, an equivalent model is first established. This means the entire superconducting magnet winding is equivalent to a uniform dielectric block, and the initial material parameters calculated in step S3 are assigned to this dielectric block. A stainless steel coil box is then wrapped around the winding. Next, a detailed model is established, that is, according to the actual structure of the superconducting magnet winding, each part is modeled in detail, and the corresponding intrinsic material parameters are assigned to each component. The same stainless steel coil box is then wrapped around the winding. Next, the same loads and boundary conditions are applied to both the equivalent and detailed models. For example, a uniformly distributed pressure load of 1 MPa is applied to the outer surface of the coil box, while a low-temperature environment of 4 K is applied, constraining all degrees of freedom at the bottom of the coil box. Then, the maximum stress and maximum displacement values ​​of the coil box in both models are extracted, and the stress and displacement errors of the two models are calculated. When any error exceeds a preset threshold (e.g., 5%), the size of the original smallest unit cell is enlarged (e.g., doubled, and the lengths of the new unit cell in the X, Y, and Z directions are adjusted to 100mm, 60mm, and 80mm respectively). Steps 2 to 4 are then repeated until the stress and displacement errors of the equivalent model and the detailed model are both less than the preset threshold. In other possible implementations, the same load and boundary conditions can be applied to the support structure of the coil box, and multiple samples can be taken to extract the average stress or average displacement values ​​of the support structure in both models. If the stress difference between the two average stress values ​​exceeds the threshold, or the displacement difference between the two average displacement values ​​exceeds the threshold, the comparison verification is deemed unsuccessful.

[0077] Next, step S5 is executed: determine the final equivalent material parameters. The initial material parameters calculated in step S3 when the comparison and verification pass are used as the equivalent winding material parameters corresponding to the CICC superconducting magnet winding of the fusion reactor.

[0078] This approach, by replacing the entire winding with the smallest unit cell with a size on the centimeter scale, reduces the number of meshes in the model and effectively improves the modeling efficiency of the equivalent model. Furthermore, the equivalent model simplifies the winding into a uniform block composed of the smallest unit cells, reducing computational requirements and improving convergence speed and stability during computation. In addition, when performing stress analysis on the external structure of the winding (such as the coil box), there is no need to focus on the internal details of the winding. This avoids unnecessary high-precision calculations while ensuring the required engineering accuracy, improving the efficiency of engineering design and avoiding the problems of large computational load and long computation time caused by the precision redundancy of traditional overall modeling.

[0079] Furthermore, for CICC superconducting magnets, unit cell modeling can directly integrate anisotropic material parameters, and the equivalent anisotropic parameters can be automatically calculated through finite element simulation. Therefore, only the anisotropic material parameters need to be set in the smallest unit cell to obtain the equivalent anisotropic parameters of the entire winding through simulation, greatly simplifying the operation process and improving work efficiency. This avoids the cumbersome and error-prone problems caused by individually defining the material orientation of each component in overall modeling.

[0080] Furthermore, this method can adapt to the structural characteristics of CICC superconducting magnets by setting different loads and constraints for different material parameters. Specifically, it can adapt to the anisotropy of insulating materials (such as G10), for example, by applying loads in separate directions and constraining degrees of freedom to avoid mutual interference between parameters in different directions. Moreover, the simulation results under load constraints can reflect the influence of this characteristic on the mechanical properties of the material in the parameter calculations, thus adapting to the structural characteristics of the porosity of superconducting cables. In addition, by accurately solving the parameters of unit cells, the complex modeling of the entire winding is replaced, laying a precise parameter foundation for subsequent equivalent modeling, thus adapting to the large scale ratio of the winding. Furthermore, applying different loads and constraints to different parameters can follow different mechanical foundations, ensuring that the calculated parameters output by the finite element method conform to the real mechanical deformation laws, avoiding parameter distortion caused by unreasonable load or constraint design, and improving the accuracy of material parameter calculations.

[0081] Furthermore, in the calculation method of the equivalent winding material parameters of the CICC superconducting magnet in this fusion reactor, the structural parameters include the stacked structure of the superconducting magnet winding in its radial direction and the arrangement of the superconducting magnet winding in its axial direction.

[0082] Furthermore, the smallest unit cell corresponding to the superconducting magnet winding is determined based on the structural parameters of the superconducting magnet winding, including: taking the cable unit in the superconducting magnet winding whose radial stacking structure is the first structure and whose axial arrangement is the first arrangement as the smallest unit cell. Wherein, reference... Figure 2 The first structure is as follows: a superconducting magnet winding is coaxially arranged from the inner layer to the outer layer with a superconducting cable 1, an armor layer 2, and an insulation layer 3. The insulation layer 3 includes an inter-turn insulation layer, an inter-layer insulation layer, and a ground insulation layer, coaxially arranged from the inner layer to the outer layer. Furthermore, a filling material 4 is provided on the outer periphery of the ground insulation layer, at least partially covering the outer periphery of the ground insulation layer. The first arrangement is as follows: the cable unit is arranged periodically along the axial direction as the smallest repeating unit.

[0083] Specifically, the superconducting cable 1 is generally formed by twisting multiple superconducting strands. The armor layer 2 has a square cross-section, and its inner wall is tightly fitted to the outer periphery of the superconducting cable 1 to improve the mechanical strength and structural stability of the superconducting cable 1. The inter-turn insulation layer uses G10 epoxy glass cloth material and is wrapped around the outer periphery of the armor layer 2 to provide insulation between adjacent turns. The interlayer insulation layer uses polyimide film and is laid on the outside of the inter-turn insulation layer to achieve electrical isolation between different winding layers. The ground insulation layer uses epoxy resin impregnated glass fiber tape and is wrapped around the outer periphery of the interlayer insulation layer to ensure the reliability of insulation between the winding and the external structure. The filler material 4 is an epoxy resin-based composite material and is filled around the outer periphery of the ground insulation layer to fill the gap between the winding and the coil box, making the overall winding structure more compact.

[0084] The axial length of the cable unit is the same as the length of the smallest unit cell in the longitudinal direction. The arrangement period for the first layout can be such that the axial spacing between two adjacent cable units is 0 mm, meaning adjacent units are closely arranged. Furthermore, adjacent cable units are aligned radially, and the axial end faces of the armor layer, insulation layers, and filler material are flush, ensuring the structural uniformity and periodicity of the entire winding in the axial direction. The arrangement range is periodically arranged along the entire axial length of the superconducting magnet winding.

[0085] More specifically, in one implementation, the process of determining the smallest cell unit is as follows: First, the radial stacked structure of the superconducting magnet winding is analyzed to screen out complete cable units that simultaneously include superconducting cables, armor layers, inter-turn insulation layers, inter-layer insulation layers, ground insulation layers, and filling material. Next, the structure in the axial direction of the winding is observed and its dimensions measured, with the selected cable units arranged axially with the length of the smallest cell unit repeating periodically in the longitudinal direction. Finally, the cable unit is verified as the smallest unit in the winding with the aforementioned structural characteristics by narrowing the scope (e.g., including only superconducting cables and armor layers) and expanding the scope (e.g., including two adjacent cable units), thus determining the smallest cell unit.

[0086] This approach requires modeling only a single minimum unit cell and setting anisotropic material parameters for that unit cell. It eliminates the need to handle the repetitive structures and assembly relationships of hundreds of units in the overall model, and avoids assigning anisotropic material parameters to each layer of every unit, effectively reducing modeling difficulty and computational requirements. Furthermore, the minimum unit cell contains all the layered structures and material composition in the radial direction of the winding, and its periodic arrangement along the axial direction not only fully reflects the material distribution and structural characteristics of the winding but also accurately represents the average characteristics of the entire winding, avoiding accuracy losses caused by structural simplification in the overall model (such as ignoring filler materials or simplifying the insulation layer structure). In addition, if the model needs modification or material change, only the relevant parameters of the minimum unit cell need to be modified, without modifying all cable units individually, improving the efficiency of model modification and optimization.

[0087] Furthermore, in the method for calculating the equivalent winding material parameters of the CICC superconducting magnet in this fusion reactor, a finite element model of the smallest unit cell is constructed, including: First, geometric modeling of the smallest unit cell is performed to generate a unit cell geometric assembly. Then, material properties are assigned to the unit cell geometric assembly to generate a unit cell material assembly. Specifically, for anisotropic materials, material parameters in different directions are input; for isotropic materials, standard material parameters are input; and for superconducting cables, due to their porosity, a preset low elastic modulus is assigned. The preset elastic modulus ranges from 1 GPa to 10 GPa. Next, the unit cell material assembly is meshed to generate a finite element model.

[0088] Specifically, the operations for constructing the finite element model are all performed in finite element simulation software (such as ANSYS and ABAQUS).

[0089] More specifically, in the geometric modeling stage, it is necessary to create basic geometric entities using the modeling module of finite element software based on the minimum unit cell structural parameters, and generate the three-dimensional models of each layer in sequence according to the actual assembly relationship, ensuring that the boundaries of each layer fit accurately without interference or gap deviation; then Boolean operations are performed on the model to form a complete unit cell geometric assembly.

[0090] During the material property assignment stage, custom materials need to be created in the software material library for anisotropic insulating materials (such as G10); it is also necessary to consider that the superconducting cable has a porosity of 25% to 40%, and assign it a low elastic modulus (e.g., 10 GPa). As for isotropic materials such as armor layers and filler materials, the standard mechanical parameters of the corresponding materials (such as the elastic modulus and Poisson's ratio of stainless steel) are directly input.

[0091] During the mesh generation stage, it is necessary to first determine the mesh type and set a mesh size control strategy. For example, critical components (such as insulation layers and superconducting cables) should use a denser mesh, while minor components should have a larger mesh to balance accuracy and computational load. Afterward, the generated mesh should be quality checked, and substandard meshes should be removed and regenerated to ensure that the mesh quality meets the simulation convergence requirements.

[0092] Continue to refer to Figure 2 The smallest unit cell is hexahedral in shape and includes a component perpendicular to the height direction Z, located at... Figure 2 The height constraint face Z1 of the hexahedron shown is located at the front of the hexahedron. Figure 2 The highly coupled face Z2 of the hexahedron shown is perpendicular to the length direction X and located at the rear. Figure 2 The length constraint surface X1 of the right side face of the hexahedron shown is located at... Figure 2 The length coupling surface X2 of the left side face of the hexahedron shown is perpendicular to the width direction Y and located at... Figure 2 The width constraint surface Y1 of the bottom face of the hexahedron shown is located at... Figure 2 The width of the coupling surface Y2 of the top face of the hexahedron shown.

[0093] Furthermore, in the calculation method for the equivalent winding material parameters of the CICC superconducting magnet in this fusion reactor, the initial material parameters include the elastic modulus of the smallest unit cell in its length, width, and height directions. Specifically, the specific loads corresponding to the elastic modulus of the smallest unit cell in its length direction include: applying a first pressure on the length coupling surface; the specific loads corresponding to the elastic modulus of the smallest unit cell in its width direction include: applying a second pressure on the width coupling surface; the specific loads corresponding to the elastic modulus of the smallest unit cell in its height direction include: applying a third pressure on the height coupling surface; the constraint conditions corresponding to the elastic modulus of the smallest unit cell in its length, width, and height directions all include: constraining the length constraint surface's degrees of freedom in the length direction, coupling the length coupling surface's degrees of freedom in the length direction; constraining the width constraint surface's degrees of freedom in the width direction, coupling the width coupling surface's degrees of freedom in the width direction; constraining the height constraint surface's degrees of freedom in the height direction, coupling the height coupling surface's degrees of freedom in the height direction.

[0094] The calculation parameters include the displacements of the smallest unit cell in its length, width, and height directions under specific loads and constraints, as well as... Figure 2 The length, width, and height values ​​of the smallest unit cell are shown.

[0095] Specifically, the displacements of the smallest unit cell in its length, width, and height directions are obtained as follows: First, constraints are set for the finite element model. The X-direction degree of freedom of the unit cell's X1 surface (the end face perpendicular to the X-axis) is constrained to prevent displacement in the X-direction. The X-direction degree of freedom of the X2 surface (the other end face perpendicular to the X-axis) is coupled to ensure that the displacements of each node on the X2 surface in the X-direction are consistent. Similarly, the Y-direction degree of freedom of the Y1 surface is constrained, and the Y-direction degree of freedom of the Y2 surface is coupled; the Z-direction degree of freedom of the Z1 surface is constrained, and the Z-direction degree of freedom of the Z2 surface is coupled. This constraint method simulates the interaction between the unit cell and adjacent units in the winding, ensuring that the stress and deformation conform to the actual working conditions. Then, a uniform compressive load of 1 MPa is applied to the X2, Y2, and Z2 surfaces to obtain displacement data in the length (X), width (Y), and height (Z) directions. Finally, the calculation parameter data is extracted, and the displacement data of the unit cell in the X, Y, and Z directions are extracted using the post-processing module of the finite element simulation software.

[0096] The elastic modulus is calculated using the following formula:

[0097]

[0098] in, It is the elastic modulus of the smallest unit cell along its length. As the primary pressure, ; The strain of the smallest unit cell along its length. ,in, The displacement of the smallest unit cell along its length direction. This is the length value of the smallest unit cell. The elastic modulus of the smallest unit cell in its width direction; As the second pressure, ; The strain of the smallest unit cell in its width direction. ,in, The displacement of the smallest unit cell in its width direction. This is the width value of the smallest unit cell. The elastic modulus of the smallest unit cell in its height direction; As the third pressure, ; The strain of the smallest unit cell in its height direction. ,in, This represents the displacement of the smallest unit cell in its height direction. This represents the height value of the smallest unit cell.

[0099] This method allows for the calculation of the elastic modulus by applying a single 1MPa load and extracting a set of displacement data, eliminating the need for complex data fitting processes and improving computational efficiency. Furthermore, by directly obtaining the overall displacement of the unit cell through finite element simulation, the influence of anisotropic materials and porous structures on the elastic modulus can be automatically accounted for, without needing to consider the material properties and structural details of individual components, thus improving calculation accuracy. In addition, the elastic modulus can be calculated using a unified formula based solely on the actual geometric dimensions and displacement data of the unit cell, demonstrating high versatility.

[0100] Furthermore, in the calculation method for the equivalent winding material parameters of the CICC superconducting magnet in this fusion reactor, the initial material parameters include a first Poisson's ratio when the smallest unit cell is subjected to a load in its length direction and strain in its width direction, a second Poisson's ratio when the smallest unit cell is subjected to a load in its length direction and strain in its height direction, and a third Poisson's ratio when the smallest unit cell is subjected to a load in its width direction and strain in its height direction. The specific loads corresponding to the first and second Poisson's ratios both include: applying a fourth pressure on the length coupling surface; the specific loads corresponding to the third Poisson's ratio include: applying a fifth pressure on the width coupling surface; the constraint conditions corresponding to the first, second, and third Poisson's ratios all include: constraining the length constraint surface's degrees of freedom in the length direction, and the coupling length coupling surface's degrees of freedom in the length direction; constraining the width constraint surface's degrees of freedom in the width direction, and the coupling width coupling surface's degrees of freedom in the width direction; constraining the height constraint surface's degrees of freedom in the height direction, and the coupling height coupling surface's degrees of freedom in the height direction.

[0101] The calculation parameters include the displacements of the smallest unit cell in its length, width, and height directions under specific loads and constraints, as well as the length, width, and height values ​​of the smallest unit cell. Poisson's ratio is calculated using the following formula:

[0102]

[0103] in, The first Poisson's ratio; The second Poisson's ratio; The third Poisson's ratio; ,in, The displacement of the smallest unit cell along its length direction. This is the length value of the smallest unit cell; ,in, The displacement of the smallest unit cell in its width direction. This is the width value of the smallest unit cell; ,in, This represents the displacement of the smallest unit cell in its height direction. This represents the height of the smallest unit cell. Both the fourth and fifth pressures are 1 MPa.

[0104] This approach eliminates the need for additional loads or separate simulations, as the strain data required for Poisson's ratio calculation is identical to the displacement and geometric data already obtained during the elastic modulus calculation. This reduces computational load and improves overall efficiency. Furthermore, directly calculating Poisson's ratio based on strain significantly reduces computational load compared to the complex process of fitting Poisson's ratio through multiple load tests, and avoids errors that might be introduced during the fitting process. Moreover, for the smallest unit cell containing anisotropic materials and porous structures, directly obtaining the overall displacement through finite element simulation automatically accounts for the combined effects of each component, resulting in higher accuracy.

[0105] Furthermore, in the calculation method of the equivalent winding material parameters of the CICC superconducting magnet in this fusion reactor, the initial material parameters include the first shear modulus of the smallest unit cell when shear force is applied to the width direction along the length direction, the second shear modulus of the smallest unit cell when shear force is applied to the height direction along the length direction, and the third shear modulus of the smallest unit cell when shear force is applied to the height direction along the width direction.

[0106] The specific load corresponding to the first shear modulus includes: applying a sixth pressure along the length direction on the width coupling surface; the specific load corresponding to the second shear modulus includes: applying a seventh pressure along the height direction on the length coupling surface; and the specific load corresponding to the third shear modulus includes: applying an eighth pressure along the height direction on the width coupling surface.

[0107] refer to Figure 3 The constraints corresponding to the first shear modulus include: all degrees of freedom of the constraint width surface and the degrees of freedom in the length direction of the coupling width surface; and the length constraint surface and the length coupling surface satisfy the following equation:

[0108]

[0109] in, Let c be the y-coordinate. Let b be the displacement along the length direction; points a and b are points on the bottom and top edges of a surface, respectively; point c is any point on the surface. That is, for any surface, any point c should satisfy the above equation with respect to points a and b.

[0110] The constraints corresponding to the second shear modulus include: all degrees of freedom of the constraint length constraint surface, and the degrees of freedom in the height direction of the coupling length coupling surface; furthermore, the height constraint surface and the height coupling surface satisfy the following equation:

[0111]

[0112] in, Let c be the x-coordinate of point c. Let b be the vertical displacement of point b; points a and b are points on the bottom and top edges of a surface, respectively; point c is any point on the surface. That is, for any surface, any point c should satisfy the above equation with respect to points a and b.

[0113] The constraints corresponding to the third shear modulus include:

[0114] All degrees of freedom of the constraint width surface, and the degrees of freedom in the height direction of the coupling width surface; and the height constraint surface and the height coupling surface satisfy the following equation:

[0115]

[0116] in, Let c be the y-coordinate. Let b be the vertical displacement of point b; points a and b are points on the bottom and top edges of a surface, respectively; point c is any point on the surface. That is, for any surface, any point c should satisfy the above equation with respect to points a and b.

[0117] The calculation parameters include the length, width, and height values ​​of the minimum unit cell, as well as the displacements of the width coupling surface and the height coupling surface in the length direction under specific loads and constraints.

[0118] The sixth, seventh, and eighth pressures are all 1N.

[0119] The shear modulus is calculated using the following formula:

[0120]

[0121] in, The first shear modulus; The shear stress of the length constraint surface and the length coupling surface relative to the width constraint surface and the width coupling surface; This is the length value of the smallest unit cell; This is the width value of the smallest unit cell; The shear strain of the length-constrained surface and the length-coupled surface relative to the width-constrained surface and the width-coupled surface; This represents the displacement of the width coupling surface along its length.

[0122]

[0123] in, The second shear modulus; The shear stress of the length constraint surface and the length coupling surface relative to the height constraint surface and the height coupling surface; This is the length value of the smallest unit cell; This represents the height of the smallest unit cell. The shear strain of the length-constrained surface and the length-coupled surface with respect to the height-constrained surface and the height-coupled surface; This represents the displacement of the highly coupled surface along its length.

[0124]

[0125] in, It is the third shear modulus; The shear stress of the width-constrained surface and the width-coupled surface relative to the height-constrained surface and the height-coupled surface; This is the width value of the smallest unit cell; This represents the height of the smallest unit cell. The shear strain of the width-constrained surface and the width-coupled surface with respect to the height-constrained surface and the height-coupled surface; This represents the displacement of the highly coupled surface along its length.

[0126] Furthermore, in the calculation method for the equivalent winding material parameters of the CICC superconducting magnet in this fusion reactor, the initial material parameters include the thermal expansion rates of the smallest unit cell in its length, width, and height directions. The specific loads corresponding to the thermal expansion rates of the smallest unit cell in its length, width, and height directions all include the applied superconducting operating temperature. The constraint conditions corresponding to the thermal expansion rates of the smallest unit cell in its length, width, and height directions all include: the constraint length constraint surface's degrees of freedom in the length direction, the coupling length coupling surface's degrees of freedom in the length direction; the constraint width constraint surface's degrees of freedom in the width direction, the coupling width coupling surface's degrees of freedom in the width direction; the constraint height constraint surface's degrees of freedom in the height direction, and the coupling height coupling surface's degrees of freedom in the height direction.

[0127] Specifically, the superconducting operating temperature is 4K.

[0128] The calculation parameters include the displacement of the smallest unit cell along a predetermined direction under specific loads and constraints, as well as the length, width, and height of the smallest unit cell.

[0129] The coefficient of thermal expansion is calculated using the following formula:

[0130]

[0131] in, The thermal expansion coefficient of the smallest unit cell along its length; This represents the displacement of the length coupling surface along its length direction. This is the length value of the smallest unit cell; The thermal expansion coefficient of the smallest unit cell in its width direction; This represents the displacement of the width coupling surface along the width direction. This is the width value of the smallest unit cell; The thermal expansion coefficient of the smallest unit cell in its height direction; This represents the displacement of the highly coupled surface along the height direction. This represents the height value of the smallest unit cell.

[0132] This approach, by applying temperature loads, can realistically simulate the thermal deformation characteristics of unit cells in actual working environments, improving the practicality of the calculation results. Furthermore, the equivalent thermal expansion rate can be calculated directly from the overall thermal displacement of the unit cell, eliminating the need to separately test the thermal expansion rates of each component material and then perform weighted calculations, simplifying the calculation process and improving computational efficiency. In addition, finite element simulation can automatically account for the synergistic effects of thermal expansion of each material, as well as the influence of void structures and anisotropic materials on the overall thermal expansion characteristics, avoiding errors caused by neglecting these factors in traditional weighted calculations, resulting in higher accuracy of the calculation results.

[0133] Furthermore, in the calculation method for the equivalent winding material parameters of the CICC superconducting magnet in this fusion reactor, the equivalent model is compared and verified with a pre-established detailed model of the superconducting magnet winding. This includes: applying the same simulation conditions to both the equivalent and detailed models, and extracting the structural data of the corresponding external components for both models; calculating the deviation between the structural data of the equivalent model and the detailed model. A deviation less than a preset deviation threshold is considered a successful verification; a deviation greater than or equal to the preset deviation threshold is considered a failed verification; the deviation threshold ranges from 3% to 5%.

[0134] The schematic diagrams of the equivalent model and the detailed model are shown in the reference diagram. Figure 4 , Figure 4 The left image shows the equivalent model, and the right image shows the detailed model. The detailed model models the armor, cable, and turn insulation, while the equivalent model represents the winding section as a uniform block.

[0135] Specifically, during the comparison and verification, the simulation conditions were set as follows: a uniformly distributed pressure load of 1 MPa was applied to the outer surface of the coil box, simulating the external constraint pressure experienced by the superconducting magnet during operation. Simultaneously, a cryogenic environment of 4 K was applied to the entire model, with an initial temperature of room temperature (293 K), simulating the cryogenic operation of the superconducting magnet. Furthermore, all degrees of freedom at the bottom of the coil box were constrained, limiting its displacement and rotation in the X, Y, and Z directions. When extracting structural data from external components, the extracted data specifically included the maximum principal stress of the coil box under the simulation conditions and the maximum total displacement of the coil box under the simulation conditions.

[0136] In other words, during the comparison and verification process, the specific comparison object in this scheme is the coil box, i.e., the supporting structure that encloses the winding. The comparison parameters specifically include stress parameters and displacement parameters, namely, the maximum principal stress (stress intensity) of the coil box under the same simulation conditions, in MPa, and the maximum total deformation displacement of the coil box under the same simulation conditions, in mm. The premise for parameter extraction is to apply identical simulation conditions to the equivalent model and the detailed model, including the same loads (such as uniformly distributed pressure on the outer surface of the coil box), the same environmental conditions (such as 4K superconducting operation at low temperatures), and the same boundary constraints (such as constraining all degrees of freedom at the bottom of the coil box), ensuring the objectivity and comparability of the comparison results.

[0137] More specifically, the deviation = |equivalent model structure data - detailed model structure data| / detailed model structure data × 100%. Furthermore, if the deviation threshold is set too low (e.g., <3%), it may result in repeated attempts to increase the unit cell size without passing verification; if the deviation threshold is set too high (e.g., >5%), insufficient accuracy may lead to structural design risks. In this embodiment, the deviation is set to 3% to 5%, which ensures the accuracy of the equivalent model while fully leveraging the advantages of equivalent modeling.

[0138] This method selects the maximum stress and maximum displacement of the coil box as comparison indicators, which are directly related to the strength and deformation of the structural design. Compared with selecting indicators such as the internal stress of the winding, this method is more realistic and improves the accuracy of the parameters.

[0139] Furthermore, the mechanical response (stress, displacement) of the equivalent model is determined by the initial material parameters (elastic modulus, Poisson's ratio, shear modulus, thermal expansion coefficient). The stress or displacement deviation of the external components is essentially the deviation between the initial material parameters and the true equivalent characteristics of the winding. If the deviation is less than or equal to the threshold, it indicates that the initial material parameters calculated based on the smallest unit cell can accurately characterize the overall equivalent mechanical and thermal properties of the winding and can be directly used as the final equivalent winding material parameters. If the deviation is greater than the threshold, it indicates that the unit cell size is too small and cannot reflect the true characteristics of the winding. The unit cell size needs to be increased and recalculated. This comparison achieves closed-loop verification and optimization of the equivalent material parameters.

[0140] Furthermore, by selecting the stress and displacement of external components as comparison parameters, redundant verification of the accuracy of the complex internal structure of the winding is avoided. Specifically, there is no need to compare local stress or displacement within the winding, avoiding the problem of high computational load and retaining the advantages of the equivalent model, such as low computational load, fast convergence, and low computational power requirements. Moreover, only external component parameters directly related to engineering design are verified, ensuring the effectiveness of the equivalent model in practical application scenarios (strength and deformation analysis of the coil box and support structure), achieving the design goal of maximizing efficiency while ensuring accuracy. As the core support component of the superconducting magnet, the maximum stress of the coil box directly relates to the structural strength safety (whether it exceeds the allowable stress of the material), and the maximum displacement directly relates to the deformation control of the structure (whether it affects the magnetic field accuracy and operational stability of the magnet). Using these two parameters as the basis for comparison ensures that the verified equivalent model can be directly used for actual engineering design and simulation analysis. The calculation results can directly guide the size optimization and material selection of the coil box and support structure, avoiding the problem of the comparison parameters being out of touch with engineering applications.

[0141] refer to Figure 5 The stress comparison between the equivalent model and the detailed model is shown (left figure is the detailed model, right figure is the equivalent model), and Figure 6 The displacement comparison between the equivalent model and the detailed model is shown (left figure is the detailed model, right figure is the equivalent model). The stresses are 216.3 MPa and 219.5 MPa, respectively, with an error of 1.5%; the displacements are 0.304 mm and 0.293 mm, respectively, with an error of 3.6%. That is, the equivalent winding parameters obtained by this method have sufficient accuracy.

[0142] This calculation method applies different specific loads (such as 1MPa pressure, 1N tangential force, and 4K operating temperature) and constraints (such as degree-of-freedom constraints, surface coupling, and planar parallel constraints) to different material parameters. It strictly follows the fundamental principles of mechanics, such as the generalized Hooke's law, shear deformation law, and thermal expansion deformation law, to ensure that the calculation parameters (displacement, strain, etc.) output by the finite element method conform to the real mechanical deformation law. This avoids parameter distortion caused by unreasonable load or constraint design, and allows the calculated initial equivalent material parameters to truly reflect the actual mechanical and thermal characteristics of the winding unit cell.

[0143] It should be noted that this embodiment only uses CICC magnets as an example. In fact, this calculation method can be applied to different types of superconducting magnets (such as ITER and CFETR), only requiring adjustment of the unit cell parameters (such as the number of superconducting cables and the thickness of the insulation layer) according to the structure of different types of superconducting magnets.

[0144] Example 2:

[0145] Based on the calculation method for equivalent winding material parameters of CICC superconducting magnets in fusion reactors provided in Example 1, this embodiment also provides an electronic device and a computer-readable storage medium.

[0146] The electronic device includes a processor and a memory that is communicatively connected to the processor; the memory stores computer-executed instructions; the processor executes the computer-executed instructions stored in the memory to implement the method for calculating the equivalent winding material parameters of the CICC superconducting magnet in the fusion reactor as described in Example 1.

[0147] The computer-readable storage medium stores computer-executable instructions, which, when executed by a processor, are used to implement the method for calculating the equivalent winding material parameters of the CICC superconducting magnet in a fusion reactor as described in Example 1.

[0148] While the present invention has been illustrated and described with reference to certain preferred embodiments, those skilled in the art should understand that the above description is a further detailed explanation of the invention in conjunction with specific embodiments, and should not be construed as limiting the specific implementation of the invention to these descriptions. Various changes in form and detail can be made by those skilled in the art, including several simple deductions or substitutions, without departing from the spirit and scope of the invention.

Claims

1. A method for calculating the equivalent winding material parameters of a CICC superconducting magnet in a fusion reactor, characterized in that, Includes the following steps: The smallest unit cell corresponding to the superconducting magnet winding is determined based on the structural parameters of the superconducting magnet winding. Construct the finite element model of the smallest unit cell; Obtain the specific loads and constraints corresponding to the initial material parameters of the smallest unit cell, apply the specific loads and constraints to the finite element model, and output the calculation parameters corresponding to the initial material parameters through the finite element model; The initial material parameters are calculated using the generalized Hooke's law based on the calculated parameters. An equivalent model of the superconducting magnet winding is established based on the initial material parameters, and the equivalent model is compared and verified with a pre-established detailed model of the superconducting magnet winding; wherein If the comparison and verification pass, the initial material parameters will be used as the material parameters of the equivalent winding corresponding to the superconducting magnet winding. If the comparison verification fails, a new minimum unit cell is determined, and the steps after determining the minimum unit cell are repeated until the comparison verification between the corrected equivalent model and the detailed model passes; wherein, the new minimum unit cell is obtained by increasing the size of the minimum unit cell.

2. The method for calculating the equivalent winding material parameters of the CICC superconducting magnet in a fusion reactor as described in claim 1, characterized in that, The structural parameters include the stacked structure of the superconducting magnet windings in its radial direction and the arrangement of the superconducting magnet windings in its axial direction. and Determining the smallest unit cell corresponding to the superconducting magnet winding based on the structural parameters of the superconducting magnet winding includes: The cable unit in the superconducting magnet winding, whose radial stacking structure is the first structure and whose axial arrangement is the first arrangement, is taken as the smallest unit cell; wherein The first structure is as follows: the superconducting magnet winding is coaxially provided with a superconducting cable, an armor layer and an insulating layer from the inner layer to the outer layer, and the outer periphery of the insulating layer is also provided with a filling material, the filling material at least partially covering the outer periphery of the insulating layer; The first arrangement is as follows: the cable unit is arranged periodically along the axial direction, with the cable unit as the smallest repeating unit; and Constructing the finite element model of the smallest unit cell includes: Geometric modeling is performed on the smallest unit cell to generate a unit cell geometric assembly; Material properties are assigned to the unit cell geometric assembly to generate a unit cell material assembly; wherein, for anisotropic materials, material parameters of the anisotropic materials in different directions are input; for isotropic materials, standard material parameters of the isotropic materials are input; for the superconducting cable, a preset elastic modulus is assigned to the superconducting cable. The unit cell material assembly is meshed to generate the finite element model; wherein The smallest unit cell is a hexahedral structure, and includes a length constraint surface and a length coupling surface perpendicular to the length direction, a width constraint surface and a width coupling surface perpendicular to the width direction, and a height constraint surface and a height coupling surface perpendicular to the height direction.

3. The method for calculating the equivalent winding material parameters of the CICC superconducting magnet in a fusion reactor as described in claim 2, characterized in that, The initial material parameters include the elastic modulus of the smallest unit cell in its length, width, and height directions; in The specific load corresponding to the elastic modulus of the smallest unit cell in its length direction includes: applying a first pressure on the length coupling surface; The specific load corresponding to the elastic modulus of the smallest unit cell in its width direction includes: applying a second pressure on the width coupling surface; The specific load corresponding to the elastic modulus of the smallest unit cell in its height direction includes: applying a third pressure on the height coupling surface; The constraints corresponding to the elastic moduli of the smallest unit cell in its length, width, and height directions all include: constraining the degree of freedom of the length constraint surface in the length direction and coupling the degree of freedom of the length coupling surface in the length direction; constraining the degree of freedom of the width constraint surface in the width direction and coupling the degree of freedom of the width coupling surface in the width direction; constraining the degree of freedom of the height constraint surface in the height direction and coupling the degree of freedom of the height coupling surface in the height direction.

4. The method for calculating the equivalent winding material parameters of the CICC superconducting magnet in a fusion reactor as described in claim 3, characterized in that, The calculation parameters include the displacement of the smallest unit cell in its length, width, and height directions under the action of the specific load and the constraint conditions, as well as the length, width, and height values ​​of the smallest unit cell. in The elastic modulus is calculated using the following formula: in, Let be the elastic modulus of the smallest unit cell along its length. For the first pressure, ; The strain of the smallest unit cell in its length direction. ,in, The displacement of the smallest unit cell along its length direction. The length value of the smallest unit cell; Let be the elastic modulus of the smallest unit cell in its width direction; For the second pressure, ; The strain of the smallest unit cell in its width direction. ,in, The displacement of the smallest unit cell in its width direction. The width value of the smallest unit cell; is the elastic modulus of the minimum unit cell in its height direction; is the third pressure, ; is the strain of the minimum unit cell in its height direction, wherein, is the displacement of the minimum unit cell in its height direction, is the height value of the minimum unit cell.

5. The method for calculating the equivalent winding material parameters of the CICC superconducting magnet in a fusion reactor as described in claim 2, characterized in that, The initial material parameters include a first Poisson's ratio when the smallest unit cell is loaded in its length direction and strained in its width direction, a second Poisson's ratio when the smallest unit cell is loaded in its length direction and strained in its height direction, and a third Poisson's ratio when the smallest unit cell is loaded in its width direction and strained in its height direction. in The specific loads corresponding to the first Poisson's ratio and the second Poisson's ratio both include: applying a fourth pressure on the length coupling surface; The specific load corresponding to the third Poisson's ratio includes: applying a fifth pressure on the width coupling surface; The constraint conditions corresponding to the first Poisson's ratio, the second Poisson's ratio, and the third Poisson's ratio all include: constraining the degree of freedom of the length constraint surface in the length direction and coupling the degree of freedom of the length coupling surface in the length direction; constraining the degree of freedom of the width constraint surface in the width direction and coupling the degree of freedom of the width coupling surface in the width direction; constraining the degree of freedom of the height constraint surface in the height direction and coupling the degree of freedom of the height coupling surface in the height direction.

6. The method for calculating the equivalent winding material parameters of the CICC superconducting magnet in a fusion reactor as described in claim 5, characterized in that, The calculation parameters include the displacement of the smallest unit cell in its length, width, and height directions under the action of the specific load and the constraint conditions, as well as the length, width, and height values ​​of the smallest unit cell. in The Poisson's ratio is calculated using the following formula: wherein, is the first Poisson's ratio; is the second Poisson's ratio; is the third Poisson's ratio; wherein, is the displacement of the smallest unit cell in its length direction, is the length value of the smallest unit cell; wherein, is the displacement of the smallest unit cell in the width direction, is the width value of the smallest unit cell; wherein, is the displacement of the smallest unit cell in its height direction, is the height value of the smallest unit cell; and Both the fourth and fifth pressures are 1 MPa.

7. The method for calculating the equivalent winding material parameters of the CICC superconducting magnet in a fusion reactor as described in claim 2, characterized in that, The initial material parameters include the first shear modulus of the smallest unit cell when shear force is applied to the width direction along the length direction, the second shear modulus of the smallest unit cell when shear force is applied to the height direction along the length direction, and the third shear modulus of the smallest unit cell when shear force is applied to the height direction along the width direction. in The specific load corresponding to the first shear modulus includes: applying a sixth pressure along the length direction on the width coupling surface; The specific load corresponding to the second shear modulus includes: applying a seventh pressure along the height direction on the length coupling surface; The specific load corresponding to the third shear modulus includes: applying an eighth pressure along the height direction on the width coupling surface; The constraint conditions corresponding to the first shear modulus include: constraining all degrees of freedom of the width constraint surface and coupling the degrees of freedom in the length direction of the width coupling surface; and the length constraint surface and the length coupling surface satisfy the following equation: in, Let c be the y-coordinate. Let b be the displacement along the length direction; points a and b are points on the bottom and top edges of a surface, respectively; point c is any point on the surface. That is, for any surface, any point c should satisfy the above equation with respect to points a and b. The constraint conditions corresponding to the second shear modulus include: constraining all degrees of freedom of the length constraint surface and coupling the degrees of freedom in the height direction of the length coupling surface; and the height constraint surface and the height coupling surface satisfy the following equation: in, Let c be the x-coordinate of point c. Let b be the vertical displacement of point b; points a and b are points on the bottom and top edges of a surface, respectively; point c is any point on the surface. That is, for any surface, any point c should satisfy the above equation with respect to points a and b. The constraint conditions corresponding to the third shear modulus include: Constrain all degrees of freedom of the width-constrained surface and couple the degrees of freedom in the height direction of the width-coupled surface; and the height-constrained surface and the height-coupled surface satisfy the following equation: in, Let c be the y-coordinate. Let b be the vertical displacement of point b; points a and b are points on the bottom and top edges of a surface, respectively; point c is any point on the surface. That is, for any surface, any point c should satisfy the above equation with respect to points a and b.

8. The method for calculating the equivalent winding material parameters of the CICC superconducting magnet in a fusion reactor as described in claim 7, characterized in that, The calculation parameters include the length, width, and height values ​​of the minimum unit cell, as well as the displacements of the width coupling surface and the height coupling surface in the length direction of the minimum unit cell under the specific load and constraints; wherein The sixth pressure, the seventh pressure, and the eighth pressure are all 1N; The shear modulus is calculated using the following formula: in, This is the first shear modulus; The shear stress of the length constraint surface and the length coupling surface relative to the width constraint surface and the width coupling surface; The length value of the smallest unit cell; The width value of the smallest unit cell; The shear strain of the length constraint surface and the length coupling surface with respect to the width constraint surface and the width coupling surface; The displacement of the width coupling surface in the length direction; in, This is the second shear modulus; The shear stress of the length constraint surface and the length coupling surface with respect to the height constraint surface and the height coupling surface; The length value of the smallest unit cell; The height value of the smallest unit cell; The shear strain of the length constraint surface and the length coupling surface with respect to the height constraint surface and the height coupling surface; The displacement of the highly coupled surface in the length direction; in, The third shear modulus; The shear stress of the width constraint surface and the width coupling surface with respect to the height constraint surface and the height coupling surface; The width value of the smallest unit cell; The height value of the smallest unit cell; The shear strain of the width constraint surface and the width coupling surface with respect to the height constraint surface and the height coupling surface; The displacement of the highly coupled surface in the length direction.

9. The method for calculating the equivalent winding material parameters of the CICC superconducting magnet in a fusion reactor as described in claim 2, characterized in that, The initial material parameters include the thermal expansion rates of the smallest unit cell in its length, width, and height directions; wherein The specific loads corresponding to the thermal expansion rates of the smallest unit cell in its length, width, and height directions all include: the operating temperature at which the superconductor is applied; The constraint conditions corresponding to the thermal expansion rates of the smallest unit cell in its length, width, and height directions all include: constraining the degree of freedom of the length constraint surface in the length direction and coupling the degree of freedom of the length coupling surface in the length direction; constraining the degree of freedom of the width constraint surface in the width direction and coupling the degree of freedom of the width coupling surface in the width direction; constraining the degree of freedom of the height constraint surface in the height direction and coupling the degree of freedom of the height coupling surface in the height direction.

10. The method for calculating the equivalent winding material parameters of the CICC superconducting magnet in a fusion reactor as described in claim 9, characterized in that, The calculation parameters include the displacement of the smallest unit cell along a predetermined direction under the action of the specific load and the constraint conditions, as well as the length, width and height values ​​of the smallest unit cell. in The coefficient of thermal expansion is calculated using the following formula: wherein, is the thermal expansion rate of the minimum unit cell in its length direction; is the displacement of the length coupling surface in the length direction; is the length value of the minimum unit cell; a thermal expansion rate of the minimum unit cell in a width direction thereof; a displacement of the width coupling surface in a width direction; a width value of the minimum unit cell; a thermal expansion rate of the minimum unit cell in a height direction thereof; a displacement of the height coupling surface in the height direction; a height value of the minimum unit cell.

11. The method for calculating the equivalent winding material parameters of the CICC superconducting magnet in a fusion reactor as described in claim 1, characterized in that, The equivalent model is compared and verified with a pre-established detailed model of the superconducting magnet winding, including: The same simulation conditions are applied to the equivalent model and the detailed model, and the structural data of the external components corresponding to the equivalent model and the detailed model are extracted respectively. Calculate the deviation between the structural data of the equivalent model and the structural data of the detailed model; and If the deviation is less than the preset deviation threshold, the comparison and verification are considered successful. The deviation greater than or equal to a preset deviation threshold is determined as a comparison verification failure; wherein The deviation threshold ranges from 3% to 5%.

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