A method for multi-field coupling analysis of high-temperature superconducting cable under fusion conditions

Abstract

The application discloses a kind of high-temperature superconducting cable multi-field coupling analysis methods under fusion condition, systematically realize the whole process simulation of cable multi-field behavior, this method integrates electromagnetic field model, heat transfer model and mechanics model, and realizes multi-field synchronous transient solution through the mutual coupling relationship between physical field, effectively reflects the complex multi-field coupling behavior of high-temperature superconducting cable under fusion condition;Through model post-processing, this method can systematically calculate the key performance indicators of high-temperature superconducting cable, such as ac loss, temperature field distribution, stress and strain, during the process of applying external magnetic field, forming a complete link from input condition to performance response, providing a complete numerical analysis method for performance evaluation, failure prediction and structure optimization of high-temperature superconducting cable in extreme fusion environment.

Description

Technical Field

[0001] This invention belongs to the field of high-temperature superconducting technology, specifically a multi-field coupling analysis method for high-temperature superconducting cables under fusion conditions. Background Technology

[0002] Under fusion conditions, the electromagnetic and thermodynamic behavior of high-temperature superconducting cables is complex and variable. Strong currents and magnetic fields with high rates of change bring strong electromagnetic force loads, while the rise in temperature also causes large thermal strain in the material. These factors have a significant impact on the mechanical and thermal stability of the superconducting cable, thereby damaging its superconducting and mechanical properties. At the same time, temperature rise and strain further affect the critical current of the material, exacerbating irreversible damage to the superconducting material. However, existing superconducting simulations are mostly single-physics field solutions or use highly complex multi-field joint solution methods, which have high computational resource requirements and low simulation efficiency. Summary of the Invention

[0003] The purpose of this invention is to provide a multi-field coupling analysis method for high-temperature superconducting cables under fusion conditions, so as to solve the problems mentioned in the background art.

[0004] To achieve the above objectives, the present invention provides the following technical solution: a method for multi-field coupling analysis of high-temperature superconducting cables under fusion conditions, comprising the following steps:

[0005] S1: Constructing a three-dimensional multiphysics finite element model in finite element software; specifically including:

[0006] Electromagnetic model governing equations: In the formula, The resistivity of the material, The magnetic field strength, is the magnetic permeability, and t is time;

[0007] The governing equations for the heat transfer model are: In the formula, The density of a solid material The actual temperature of the solid material. This refers to the specific heat capacity of the material at temperature T. The thermal conductivity of the material at temperature T. This is the heat source term in the equation;

[0008] Governing equations of the mechanical model: In the formula, For stress tensor, It is a force vector;

[0009] S2: Constructing coupling relationships for multiphysics finite element models; specifically including:

[0010] S21: Establish the Maxwell's equations required for superconducting simulation calculations in the electromagnetic model and supplement the electromagnetic constitutive relations. The Maxwell's equations are as follows: In the formula, For electric field strength, It represents the magnetic flux density. Current density;

[0011] The electromagnetic constitutive relation is as follows: ;

[0012] S22: The electric field intensity of each element in the superconducting material domain of the electromagnetic model. and current density The instantaneous power of each unit is obtained by taking the dot product, and the instantaneous power is substituted into the control equation of the heat transfer model as a heat source term;

[0013] S23: Constructing the stress tensor in the mechanical model and strain tensor Constitutive relations: In the formula, For the elastic tensor; establish the body force vector generated by the strong electromagnetic field on the superconducting material in the electromagnetic model. The equation is as follows: ;

[0014] S3: Detect the resistivity of the material by consulting material parameter data or using existing methods. magnetic permeability Density of solid materials Specific heat capacity of materials at different temperatures T Thermal conductivity of materials at different temperatures T elastic tensor strain tensor magnetic induction intensity Current density By substituting the above parameters into the model established by the finite element software, the AC loss, temperature change, and stress-strain parameters used for superconductivity analysis can be calculated using the finite element software.

[0015] Furthermore, in step S3, in order to obtain a more accurate resistivity of the material that conforms to the fusion operating conditions... To ensure computational efficiency, a homogenization method is used. The layered structure of the material is simplified by calculating its engineering critical current density, based on a power-law model and the resistivity of the superconducting material. It is expressed as follows: ,in, The critical electric field has the following values: , The critical current density, The results were obtained using the experimental methods described in [Liu Wei. Development and Application Research of a Test Instrument for the Performance of High-Temperature Superconducting Materials under Extremely Low Temperature-Mechanical-Electromagnetic Multi-Field Environment [D]. Lanzhou: Lanzhou University, 2017.]. The value is an exponent, and the other solid materials and air domain are considered to be isotropic. The resistivity of the corresponding material is consulted and substituted into the control equation of the electromagnetic model for calculation.

[0016] To further improve the accuracy of the model calculations, a more precise critical current density is obtained through the following method. The steps are as follows: S31: In the electromagnetic model, the change of the critical current density of the superconductor with the magnetic field is considered, by adjusting the magnetic induction intensity... Decomposed into two components: one parallel to the material surface and one perpendicular to the material surface. The magnitudes of the two components are respectively... and To characterize the effect of material anisotropy, the specific expression is as follows: ,in, The critical current density varies with the magnetic field. It is the critical current density of the material in the absence of an external magnetic field. The critical magnetic field of the material, , Obtained using existing detection methods, These are the fitting coefficients. , The fitting index is... ;

[0017] S32: The electromagnetic model also considers the change in the critical current density of the superconducting material with temperature, defining the temperature dependence of the critical current density of the superconducting material as follows: ,and The effect of temperature on the critical current density is corrected by multiplication, as shown in the following formula:

[0018] ;in, The critical temperature of superconducting materials is obtained using existing detection methods. The initial temperature. This is the actual temperature;

[0019] S33: The electromagnetic model also considers the critical current density of superconducting materials as a function of axial strain. The change in the critical current density of superconducting materials is defined as follows: ,and The effect of axial strain on the critical current density is corrected by multiplication, as shown in the following formula:

[0020] ;

[0021] S34: Critical current density of superconducting materials The final result is as follows: ,

[0022] When the temperature has not reached the critical temperature of the superconducting material and the axial strain of the superconducting material is no greater than 0.67%, the critical current density of the superconducting material is expressed as:

[0023] .

[0024] To further improve the accuracy of the model calculations, when obtaining the density, specific heat capacity, and thermal conductivity of materials, solid materials are assumed to be isotropic. For superconducting materials, due to their layered structure, a homogenization method is used to average the density and specific heat capacity of each layer according to the geometric dimensions of the layered structure. The specific formula is as follows: ;in For the first Layer thickness, For the first The specific heat capacity and density of the layer material, These represent the specific heat capacity and density of the entire cross-section of the homogenized material, respectively. Considering the anisotropy of the material, the thermal conductivity calculation distinguishes between the thickness direction and the width and length directions. The thermal conductivity along the thickness direction and the width and length directions are then calculated using the following formulas: In the formula, For the first Thermal conductivity of the layer material To homogenize the thermal conductivity of the superconducting material along its thickness direction, The thermal conductivity of the superconducting material along its width and length after homogenization.

[0025] Furthermore, body force vector Calculated using the following formula:

[0026] In the formula, Current density along the global coordinate system The size of the projection in the direction, The magnetic induction intensity along the global coordinate system are respectively The size of the projection in the direction, global coordinate system The unit basis vectors for the direction.

[0027] Furthermore, temperature changes in the heat transfer model will cause corresponding temperature strain in the cable, thereby altering the stress-strain state at various points in the material. When a temperature change occurs... When thermal strain occurs along the length, width, and thickness directions of a superconducting material, it can be calculated using the following formula: ,in These represent the thermal strains occurring along the length, width, and thickness directions of the superconducting material, respectively. These are the coefficients of thermal expansion of the material along its length, width, and thickness, respectively.

[0028] Preferably, in step S3, the AC loss is calculated using the following method: In the formula, For AC loss, For the integration region, This is the integration time domain.

[0029] Compared with existing technologies, the beneficial effects of this invention are as follows: This invention proposes an electro-magnetic-thermal-mechanical coupling analysis method for high-temperature superconducting cables under fusion conditions. It systematically realizes the full-process simulation of the cable's multi-field behavior. This method integrates electromagnetic field models, Fourier heat transfer models, and linear elasticity models, and achieves synchronous transient solutions for multiple fields through the mutual coupling relationships between physical fields. This effectively reflects the complex multi-field coupling behavior of high-temperature superconducting cables under fusion conditions. Through model post-processing, this method can systematically calculate key performance indicators such as AC loss, temperature field distribution, stress, and strain of high-temperature superconducting cables during the application of an external magnetic field, forming a complete link from input conditions to performance response. This provides a complete numerical analysis method for performance evaluation, failure prediction, and structural optimization of high-temperature superconducting cables under extreme fusion environments. Attached Figure Description

[0030] Figure 1 This is a flowchart of the multi-field coupling analysis method for high-temperature superconducting cables under fusion conditions provided in the embodiments of the present invention;

[0031] Figure 2 This is a structural diagram of a superconducting cable provided in an embodiment of the present invention;

[0032] Figure 3 This is a line graph of the AC loss calculation structure provided in the embodiment of the present invention;

[0033] Figure 4 This is a line graph showing the average temperature change statistics provided in an embodiment of the present invention;

[0034] Figure 5 This is a graph showing the axial current density calculation results provided in an embodiment of the present invention;

[0035] Figure 6 This is a graph showing the calculated results of the von Mises stress in the superconducting material domain provided in an embodiment of the present invention. Detailed Implementation

[0036] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0037] Please see Figures 1-6 This invention provides a technical solution: a method for multi-field coupling analysis of high-temperature superconducting cables under fusion conditions. The flowchart of this method is shown below. Figure 1 As shown in the figure, the superconducting cable structure used for superconducting analysis in this method is illustrated in the following diagram. Figure 2 As shown, the specific plan is as follows:

[0038] 1. Constructing an electromagnetic model in finite element software

[0039] This invention uses the H-method to construct and solve the electromagnetic model of the cable. Its governing equations can be derived from Maxwell's equations. The Maxwell's equations required for superconducting simulation calculations are as follows:

[0040] (1)

[0041] in is the magnetic permeability, which is considered a constant, equal to the free permeability, and has a value of 1; Let E be the resistivity of the material, E be the electric field strength, and J be the current density. t represents the magnetic flux density and t represents time.

[0042] The electromagnetic constitutive relation is also supplemented as follows:

[0043] (2)

[0044] In the formula, denoted as , where is the magnetic field strength.

[0045] Combining equations (1) and (2), we obtain equation (3) as follows, which is the governing equation of the H method:

[0046] (3)

[0047] In the electromagnetic model, the macroscopic electromagnetic properties of high-temperature superconductors are described by a power-law model. A homogenization method is used, and the material's layered structure is simplified by calculating the engineering critical current density, thus improving computational efficiency. Based on the power-law model, the material's resistivity... It is expressed as follows:

[0048] (4)

[0049] in The critical electric field, The critical current density, The value is an exponent.

[0050] The electromagnetic model considers the variation of the critical current density of the superconductor with the magnetic field, and by incorporating the magnetic induction intensity Decomposed into two components: one parallel to the material surface and one perpendicular to the material surface (their magnitudes are respectively...). and The anisotropy of the material is used to characterize the effect of its anisotropy, and the specific expression is as follows:

[0051] (5)

[0052] in It is the critical current density of the material in the absence of an external magnetic field. The critical magnetic field of the material, These are the fitting coefficients. , The fitting index is... In this embodiment, with an initial temperature of 4.2K, , .

[0053] Meanwhile, the electromagnetic model considers the change in the critical current density of superconducting materials with temperature, defining the temperature dependence of the critical current density of superconducting materials as follows: It is a dimensionless quantity, and Multiplication is used to correct the effect of temperature on the critical current density.

[0054] (6)

[0055] in The critical temperature of superconducting materials. The initial temperature. In this embodiment, the actual temperature is used. .

[0056] Furthermore, the electromagnetic model further considers the critical current density of the superconducting material as a function of axial strain. The change; the strain dependence of the critical current density of superconducting materials is defined as It is a dimensionless quantity, and Multiplication is used to correct the effect of axial strain on the critical current density.

[0057] (7)

[0058] in This represents the axial strain of the superconducting material.

[0059] After considering the influence of temperature and mechanical fields on the electromagnetic field, the critical current density of superconducting materials The final result is as follows:

[0060] (8)

[0061] When the temperature has not reached the critical temperature of the superconducting material and the axial strain of the material is no greater than 0.67%, the critical current density of the superconducting material can be expressed as follows:

[0062] (9)

[0063] Except for the superconductor portion, the remaining solid materials and air domain of the cable are considered to be isotropic. The calculation is performed by giving the corresponding resistivity and substituting it into the governing equations. The boundary condition of the equations is the known external magnetic field.

[0064] 2. Establish a heat transfer model in finite element software.

[0065] The governing equations for the heat transfer model are as follows:

[0066] (10)

[0067] in To determine the density of solid materials, in this embodiment, the cable structure contains six materials: copper, silver, Hastelloy, superconducting material, stainless steel, and solder, each with a density of 8940 kg / m³. 3 10500kg / m 3 8910kg / m 3 5900kg / m 3 8000kg / m 3 8400kg / m 3 , The actual temperature of the solid material. This refers to the specific heat capacity of the material at temperature T. The thermal conductivity of the material at temperature T. The heat source term in the equation is specifically the heat generation power density of the superconducting material in this invention.

[0068] When setting the density, specific heat capacity, and thermal conductivity of each material, solid materials are assumed to be isotropic. However, due to the layered structure of superconducting materials, a homogenization method is required to average the density and specific heat capacity of each layer according to the geometric dimensions of its layered structure. The specific formula is as follows:

[0069] (11)

[0070] in For the first Layer thickness, For the first The specific heat capacity and density of the layer material, The specific heat capacity and density of the entire cross section of the homogenized superconducting material are given by, where, It varies with temperature. By taking points at different temperatures and fitting the data, we obtain the function of how each material changes with temperature. Then, we substitute this function into the equation for calculation. In this embodiment, .

[0071] Meanwhile, considering the anisotropy of superconducting materials, when calculating the thermal conductivity of superconducting materials, the thickness direction and the width and length directions of the superconducting materials are distinguished, and the thermal conductivity along the thickness direction and the width and length directions are calculated respectively according to the following formula.

[0072] (12)

[0073] in, For the first The thermal conductivity of layered superconducting materials is obtained by fitting the thermal conductivity of each material as a function of temperature using the difference method at different temperatures, and then substituting the results into the equation for calculation. To homogenize the thermal conductivity of the superconducting material along its thickness direction, After homogenization, the thermal conductivity of the superconducting material along its width and length directions is given by the tensor ( ) in the governing equations of the heat transfer model. Since the heat transfer model governing equations exist, they can be expanded in a Cartesian coordinate system. A local coordinate system can be established along the length (x-direction), width (y-direction), and thickness (z-direction) of the cable superconducting material. The governing equations of the heat transfer model can then be expanded in this coordinate system.

[0074] (13)

[0075] in For the material along the local coordinate system The thermal conductivity along the direction, for superconducting materials, is the thermal conductivity along its length (x direction), width (y direction), and thickness (z direction);

[0076] In the electromagnetic model, Joule heating generated by a changing external magnetic field affects the temperature field. By solving the governing equations of the electromagnetic model, the electric field strength of each element in the superconducting material domain of the model can be obtained. and current density Then, the instantaneous power of each unit is obtained by taking the dot product of the two. The heat source is then substituted into the governing equations of the heat transfer model for calculation, and the heat source is updated over time. Specific heat of heat transfer model and thermal conductivity .

[0077] 3. Establish a mechanical model in finite element software.

[0078] The governing equations of the mechanical model of this invention are as follows:

[0079] (14)

[0080] in For stress tensor, This is a force vector.

[0081] Stress tensor and strain tensor The following constitutive relation exists:

[0082] (15)

[0083] in It is an elastic tensor, which is related to the properties of the material.

[0084] The mechanical model further considers the application of loads, while the strong electromagnetic field in the electromagnetic model will generate a non-negligible electromagnetic body force vector on the superconducting material. The calculation method is as follows:

[0085] (16)

[0086] in, Current density Along the global coordinate system The size of the projection in the direction, They are magnetic induction intensity Along the global coordinate system The size of the projection in the direction, global coordinate system The unit basis vectors for the direction.

[0087] Meanwhile, temperature changes in the heat transfer model will cause corresponding temperature strain in the cable, thereby altering the stress-strain state at various points in the material. When a temperature change occurs... When the thermal strain of the superconducting material in the cable occurs along its length, width, and thickness, it can be calculated using the following formula:

[0088] (17)

[0089] in These represent the thermal strains occurring along the length, width, and thickness directions of the superconducting material, respectively. These are the coefficients of thermal expansion of the material along its length, width, and thickness directions, respectively. In this embodiment, .

[0090] All materials in the cable, except for the superconducting material, are isotropic. When temperature changes occur... The formulas for calculating the thermal strain of these materials are as follows:

[0091] (18)

[0092] in For thermal strain of isotropic materials, The coefficients of thermal expansion for isotropic materials are given. In the superconducting cable of this embodiment, stainless steel, copper, and solder are isotropic materials with coefficients of thermal expansion of 14.5e-6, 14e-6, and 11e-6, respectively.

[0093] It should be noted that in the mechanical model, the constitutive relations are tensor equations, and the solution approach in finite element software is as follows:

[0094] For the mechanical calculations of superconducting materials, the tensor formula can be expressed as follows:

[0095] A local coordinate system is established along the length (x-direction), width (y-direction), and thickness (z-direction) of the cable's superconducting material. Since the superconducting material of the cable is transversely isotropic, the stress-strain constitutive relation can be expressed in the local coordinate system of the model using Voigt notation as follows:

[0096] (19)

[0097] in For the material along the local coordinate system Young's modulus in the direction; For the unit volume in the local coordinate system In-plane shear modulus; Each element is located along the local coordinate system. Normal stress in the direction; These are the unit cells in the local coordinate system. The shear stress on the surface; Each element is located along the local coordinate system. Linear strain occurring in the direction of the strain; These are the unit cells in the local coordinate system. Shear strain occurring on the surface; Each element is located along the local coordinate system. Thermal strain occurring in the direction of the direction; There are six Poisson's ratios, representing materials in Under uniaxial stress loading in the direction, Direction line strain and The absolute value of the ratio of strain along the direction line. (These physical quantities can be obtained from the literature).

[0098] When the material changes temperature The thermal strain that occurs in a superconducting material can be described by the following equation:

[0099] (20)

[0100] in, For superconducting materials along the local coordinate system The coefficient of thermal expansion in the direction of temperature change can be obtained from literature review, while the coefficient of thermal expansion in the direction of temperature change is calculated from the heat transfer model.

[0101] Meanwhile, the geometric relationship between strain and displacement of superconducting materials can be described in the local coordinate system as follows:

[0102] (twenty one)

[0103] in, Each element is located along the local coordinate system. The magnitude of the displacement in the direction.

[0104] By combining the stress-strain constitutive relations, thermal strain calculation formulas, and geometric relations, the governing equations of the mechanical model can be simplified to concern only with respect to displacement. The partial differential equations can be used to solve the governing equations of the mechanical model by displacement. After obtaining the displacement, the results of mechanical quantities such as stress and strain can be obtained from the constitutive relation and geometric relation.

[0105] Furthermore, for the isotropic portions of a cable, the tensor equation can be more simply represented in a Cartesian coordinate system because their Young's modulus, shear modulus, Poisson's ratio, and coefficient of thermal expansion are the same in all directions.

[0106] Based on the construction of various electromagnetic, heat transfer, and mechanical models, this method uses the finite element method and an electromagnetic-thermal-mechanical coupling solution framework to realize the system simulation of multi-field coupling effects, ensuring the physical consistency of multi-field solutions.

[0107] 4. Multi-field coupling analysis and calculation of key physical quantities

[0108] After completing the construction of the three-dimensional multiphysics coupled finite element model and applying the load, the electro-magnetic-thermal-mechanical coupling response of the high-temperature superconducting cable under fusion conditions was systematically analyzed, and key physical quantities were calculated to quantify its performance evolution law.

[0109] (1) AC loss

[0110] The instantaneous power of each element in the superconducting material domain within the electromagnetic model can be calculated. Further integration over volume and time yields the AC loss of the cable during the magnetization process. AC loss is the heat loss generated by a superconductor when subjected to a strong magnetic field with a high rate of change in a low-temperature environment. Calculating AC loss can assess the energy loss of the superconductor during the application of the magnetic field. The calculation method is as follows: For the integration region, This is the integration time domain.

[0111] (twenty two)

[0112] Figure 3 This is the diagram showing the AC cable loss calculated using this method.

[0113] (2) Temperature change

[0114] The heat transfer model can be used to calculate the weighted average temperature of the solid material domain in the model at different times, and further obtain the temperature change of the cable. The temperature change directly affects the superconducting performance of the superconductor. By judging whether the temperature of the superconductor exceeds its critical temperature, it can be determined whether the superconductor has lost its superconductivity. The calculation of temperature change can be fed back to the temperature rise of the superconductor under fusion conditions, which is an important reference standard for judging whether the superconductor still has superconducting properties. Figure 4 This is the result of the weighted average temperature of the cable during the magnetization process calculated by this method, as a function of time.

[0115] (3) Axial current density distribution

[0116] Based on the electromagnetic model, the magnetic field strength in the solid material domain and air domain within the model can be calculated at different times. Furthermore, electromagnetic physical quantities such as magnetic induction, electric field strength, and current density can be derived. The calculation of these electromagnetic quantities reveals the electromagnetic field distribution within the superconducting cable at different times, further preparing for the analysis of the electromagnetic field variation patterns within the cable and the calculation of the electromagnetic forces acting on it. Simultaneously, the output results for physical quantities such as magnetic field and current density can further verify the correctness of the program's calculations (e.g., checking whether the external magnetic field boundary conditions are applied correctly through the magnetic field results). This method uses the axial current density of the cable as an example for result output. Figure 5 This is a two-dimensional distribution cloud map of the axial current density at 1 / 8 pitch cross section of the cable calculated by this method during the 1st, 2nd, 3.5th, and 5th seconds of the magnetization process.

[0117] (4) Stress and strain

[0118] Based on the mechanical model, the stress and strain of the solid material domain in the model at different times can be calculated. The calculation of stress-strain variables can assess the deformation and stress conditions of the material under mechanical loads. Excessive deformation (large strain) can lead to an irreversible decrease in the critical current of the superconducting tape, thus affecting the superconducting performance of the cable. Simultaneously, if the material is subjected to excessive mechanical loads (large stresses) in certain regions, it can cause mechanical damage to the cable, thereby destroying its mechanical structure. Therefore, it is necessary to calculate the stress-strain variables of the superconducting cable to assess whether the mechanical load will cause serious irreversible damage to the cable. This method uses the von Mises stress of the cable as an example for result output. Figure 6 This is the distribution cloud map of the von Mises stress in the cable calculated by this method during the 1st, 2nd, 3.5th, and 5th seconds of the magnetization process.

[0119] Although the present invention has been described in detail with reference to the foregoing embodiments, those skilled in the art can still modify the technical solutions described in the foregoing embodiments or make equivalent substitutions for some of the technical features. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of the present invention should be included within the protection scope of the present invention.

Claims

1. A method for multi-field coupling analysis of high-temperature superconducting cables under fusion conditions, characterized in that, Includes the following steps: S1: Constructing a three-dimensional multiphysics finite element model in finite element software; specifically including: Electromagnetic model governing equations: In the formula, The resistivity of the material, The magnetic field strength, is the magnetic permeability, and t is time; The governing equations for the heat transfer model are: In the formula, The density of a solid material The actual temperature of the solid material. This refers to the specific heat capacity of the material at temperature T. The thermal conductivity of the material at temperature T. This is the heat source term in the equation; Governing equations of the mechanical model: In the formula, For stress tensor, It is a force vector; S2: Constructing coupling relationships for multiphysics finite element models; specifically including: S21: Establish the Maxwell's equations required for superconducting simulation calculations in the electromagnetic model and supplement the electromagnetic constitutive relations. The Maxwell's equations are as follows: In the formula, For electric field strength, Magnetic flux density Let the current density be denoted as ; the electromagnetic constitutive relation is as follows: ; S22: The electric field intensity of each element in the superconducting material domain of the electromagnetic model. and current density The instantaneous power of each unit is obtained by multiplying the dot product, and the instantaneous power is substituted into the control equation of the heat transfer model as a heat source term; S23: Constructing the stress tensor in the mechanical model and strain tensor Constitutive relations: , In the formula, For the elastic tensor; establish the body force vector generated by the strong electromagnetic field on the superconducting material in the electromagnetic model. The equation is as follows: ; S3: Detect the resistivity of the material by consulting material parameter data or using existing methods. magnetic permeability Density of solid materials Specific heat capacity of materials at different temperatures T Thermal conductivity of materials at different temperatures T elastic tensor strain tensor magnetic induction intensity Current density By substituting the above parameters into the model established by the finite element software, the AC loss, temperature change, and stress-strain parameters used for superconductivity analysis can be calculated using the finite element software.

2. The multi-field coupling analysis method for high-temperature superconducting cables under fusion conditions according to claim 1, characterized in that, In step S3, in order to obtain a more accurate material resistivity that conforms to the fusion operating conditions... To ensure computational efficiency, a homogenization method is used. The layered structure of the material is simplified by calculating its engineering critical current density, based on a power-law model and the resistivity of the superconducting material. It is expressed as follows: ,in, The critical electric field has the following values: , The critical current density, Detected using existing experimental methods, The value is an exponent, and the other solid materials and air domain are considered to be isotropic. The resistivity of the corresponding material is consulted and substituted into the control equation of the electromagnetic model for calculation.

3. The multi-field coupling analysis method for high-temperature superconducting cables under fusion conditions according to claim 2, characterized in that, To further improve the accuracy of the model calculations, a more precise critical current density is obtained through the following method. The steps are as follows: S31: The electromagnetic model considers the variation of the critical current density of the superconductor with the magnetic field by adjusting the magnetic induction intensity. Decomposed into two components: one parallel to the material surface and one perpendicular to the material surface. The magnitudes of the two components are respectively... and To characterize the effect of material anisotropy, the specific expression is as follows: ,in, The critical current density varies with the magnetic field. It is the critical current density of the material in the absence of an external magnetic field. The critical magnetic field of the material, , Obtained using existing detection methods, These are the fitting coefficients. , The fitting index is... ; S32: The electromagnetic model also considers the change in the critical current density of the superconducting material with temperature, defining the temperature dependence of the critical current density of the superconducting material as follows: ,and The effect of temperature on the critical current density is corrected by multiplication, as shown in the following formula: ;in, The critical temperature of superconducting materials is obtained using existing detection methods. The initial temperature. This is the actual temperature; S33: The electromagnetic model also considers the critical current density of superconducting materials as a function of axial strain. The change in the critical current density of superconducting materials is defined as follows: ,and The effect of axial strain on the critical current density is corrected by multiplication, as shown in the following formula: ; S34: Critical current density of superconducting materials The final result is as follows: , When the temperature has not reached the critical temperature of the superconducting material and the axial strain of the superconducting material is no greater than 0.67%, the critical current density of the superconducting material is expressed as: 。 4. The multi-field coupling analysis method for high-temperature superconducting cables under fusion conditions according to claim 3, characterized in that, When obtaining the density, specific heat capacity, and thermal conductivity of a material, solid materials are assumed to be isotropic. However, due to the layered structure of superconducting materials, a homogenization method is used to average the density and specific heat capacity of each layer according to the geometric dimensions of the layered structure. The specific formula is as follows: ;in For the first Layer thickness, For the first The specific heat capacity and density of the layer material, These represent the specific heat capacity and density of the entire cross-section of the homogenized material, respectively. Considering the anisotropy of the material, the thermal conductivity calculation distinguishes between the thickness direction and the width and length directions. The thermal conductivity along the thickness direction and the width and length directions are then calculated using the following formulas: In the formula, For the first Thermal conductivity of the layer material To homogenize the thermal conductivity of the superconducting material along its thickness direction, The thermal conductivity of the superconducting material along its width and length after homogenization.

5. The multi-field coupling analysis method for high-temperature superconducting cables under fusion conditions according to claim 4, characterized in that, Body force vector Calculated using the following formula: In the formula, Current density along the global coordinate system The size of the projection in the direction, The magnetic induction intensity along the global coordinate system are respectively The size of the projection in the direction, global coordinate system The unit basis vectors for the direction.

6. The multi-field coupling analysis method for high-temperature superconducting cables under fusion conditions according to claim 5, characterized in that, In the heat transfer model, temperature changes cause corresponding temperature strain in the cable, thereby altering the stress-strain state at various points in the material. When a temperature change occurs... When thermal strain occurs along the length, width, and thickness directions of a superconducting material, it can be calculated using the following formula: ,in These represent the thermal strains occurring along the length, width, and thickness directions of the superconducting material, respectively. These are the coefficients of thermal expansion of the material along its length, width, and thickness, respectively.

7. The method for multi-field coupling analysis of high-temperature superconducting cables under fusion conditions according to claim 1, characterized in that, In step S3, the AC loss is calculated as follows: In the formula, For AC loss, For the integration region, This is the integration time domain.

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