Superconducting magnet rapid modeling method based on two-dimensional section equation and three-dimensional track

Abstract

The invention provides a superconducting magnet rapid modeling method based on a two-dimensional section equation and a three-dimensional track, and belongs to the technical field of superconducting magnets. The method comprises the following steps: determining two-dimensional section point set data of a coil based on a Biot-Savart law, critical magnetic field characteristics of a superconducting material and target magnetic field distribution requirements; processing each point in the two-dimensional section point set data of the coil to generate three-dimensional space trajectory data; and based on the three-dimensional space trajectory data, creating a sweeping path and a cross section contour of the superconducting conductor, executing sweeping operation, and generating a coil entity model.

Description

Technical Field

[0001] This disclosure relates to the field of superconducting magnet technology, and more specifically, to a method for rapid modeling of superconducting magnets based on two-dimensional section equations and three-dimensional trajectories. Background Technology

[0002] In existing technologies, the modeling of superconducting magnets usually relies on general-purpose finite element analysis software. Designers need to manually construct three-dimensional geometric models one by one, and then carry out multi-physics field coupling simulation of electromagnetic field, thermal field and structural stress field on this basis.

[0003] However, this method has significant drawbacks: First, the modeling process is highly dependent on manual operation. For superconducting coils with complex winding structures, a single modeling session can take hours or even days. When the target magnetic field distribution changes, geometric parameters need to be repeatedly adjusted and the model rebuilt, resulting in a lengthy and inefficient design cycle. Second, existing modeling tools lack a direct linkage mechanism with the magnetic field theory equations, making it impossible to automatically drive geometric generation based on the target magnetic field distribution. Parameter modifications must be done manually, resulting in poor design flexibility and difficulty in supporting rapid iterative optimization. Third, manual modeling struggles to accurately characterize the fine geometric features of superconducting conductor edges and interlayer transitions, easily introducing geometric discontinuities or dimensional deviations. These errors will propagate to subsequent multiphysics simulations, affecting the accuracy of magnetic field calculations and thus reducing the overall design reliability. Finally, during multiphysics coupling analysis, electromagnetic field calculation results (such as electromagnetic force and Joule heating) need to be manually exported and imported to the thermo-mechanical analysis module. Data connection relies on intermediate files, which is not only cumbersome but also prone to information distortion due to mesh mismatch or unit inconsistencies, severely impacting the accuracy and efficiency of coupling calculations. Summary of the Invention

[0004] In view of this, this disclosure provides a method for rapid modeling of superconducting magnets based on two-dimensional cross-sectional equations and three-dimensional trajectories, which can at least partially solve the above-mentioned technical problems.

[0005] This disclosure provides a method for rapid modeling of superconducting magnets based on two-dimensional cross-sectional equations and three-dimensional trajectories, including: determining the two-dimensional cross-sectional point set data of the coil based on the Biot-Savart law, the critical magnetic field characteristics of the superconducting material, and the target magnetic field distribution requirements; processing each point in the two-dimensional cross-sectional point set data of the coil to generate three-dimensional spatial trajectory data; creating a sweep path and the cross-sectional contour of the superconducting conductor based on the three-dimensional spatial trajectory data and performing a sweep operation to generate a solid model of the coil.

[0006] According to embodiments of this disclosure, the two-dimensional cross-sectional point set data of the coil is determined based on the Biot-Savart law, the critical magnetic field characteristics of the superconducting material, and the target magnetic field distribution requirements. This includes: constructing a two-dimensional cross-sectional parameterized equation of the coil based on the target magnetic field distribution requirements and the critical magnetic field characteristics of the superconducting material, combined with the Biot-Savart law; and determining the two-dimensional cross-sectional point set data of the coil based on the preset parameters of the coil and the two-dimensional cross-sectional parameterized equation.

[0007] According to embodiments of this disclosure, based on preset parameters of the coil and a two-dimensional cross-section parameterization equation, the two-dimensional cross-section point set data of the coil is determined, including: determining the normal offset of the inner and outer boundaries of the superconducting conductor relative to the reference circle on the cross-section according to the coil reference radius, the cross-sectional size parameters of the superconducting conductor, the interlayer offset, and the two-dimensional cross-section parameterization equation; and determining the coordinates of the inner boundary point and the outer boundary point according to the normal offset and a preset angle sequence to generate the two-dimensional cross-section point set data.

[0008] According to embodiments of this disclosure, the preset angle sequence is an equally spaced or non-uniform array of angles.

[0009] According to an embodiment of this disclosure, each point in the two-dimensional cross-sectional point set data of the coil is processed to generate three-dimensional spatial trajectory data, including: rotating each point in the two-dimensional cross-sectional point set data around a preset axis of symmetry, and discretely sampling the azimuth angle used for rotation within a preset range to generate three-dimensional spatial trajectory data corresponding to each turn of the superconducting conductor.

[0010] According to embodiments of this disclosure, creating a sweep path and a cross-sectional profile of a superconducting conductor based on three-dimensional spatial trajectory data, and performing a sweep operation to generate a coil solid model includes: importing three-dimensional spatial trajectory data into a computer-aided design system; calling the programmatic modeling interface of the computer-aided design system to create a sweep path and a cross-sectional profile of the superconducting conductor, and performing a one-time sweep operation to generate a coil solid model.

[0011] According to embodiments of this disclosure, the method further includes: importing the coil physical model into a multiphysics simulation platform, and performing multiphysics coupling calculations based on the property parameters of the superconducting material and preset boundary conditions.

[0012] According to embodiments of this disclosure, a coil physical model is imported into a multiphysics simulation platform, and multiphysics coupling calculations are performed based on the property parameters of the superconducting material and preset boundary conditions. This includes: importing the coil physical model into the multiphysics simulation platform, calculating the electromagnetic force based on the property parameters of the superconducting material and preset boundary conditions; and performing electromagnetic-thermal-mechanical coupling analysis based on the electromagnetic force under preset liquid helium cooling parameters and mechanical constraints, outputting the temperature field, deformation displacement field, and stress field distribution of the coil.

[0013] According to embodiments of this disclosure, the property parameters of the superconducting material include the electromagnetic properties of the superconducting material and the excitation current.

[0014] According to embodiments of this disclosure, the method further includes: readjusting the preset parameters of the coil when the temperature field, deformation displacement field, and stress field distribution of the coil exceed the preset parameters of the superconducting material; and updating the two-dimensional cross-sectional point set data of the coil based on the preset parameters.

[0015] The method for rapid modeling of superconducting magnets based on two-dimensional section equations and three-dimensional trajectories according to embodiments of this disclosure has at least the following technical effects:

[0016] This invention combines the Biot-Savart law, the critical magnetic field characteristics of superconducting materials, and the target magnetic field distribution requirements to directly construct a two-dimensional cross-sectional point set data for generating coil geometry. This achieves an automatic conversion from physical design goals to geometric descriptions, avoiding the trial-and-error process of repeatedly adjusting structural parameters based on manual experience, and significantly shortening the modeling cycle. Furthermore, by performing spatial mapping processing on the two-dimensional cross-sectional point set, three-dimensional spatial trajectory data is automatically generated. Based on this trajectory data, a sweep path and the cross-sectional profile of the superconducting conductor are created. A complete coil solid model can be obtained by performing a single sweep operation, effectively solving the problems of low efficiency and geometric discontinuity caused by manual segmented modeling in traditional methods. Attached Figure Description

[0017] The above and other objects, features and advantages of this disclosure will become clearer from the following description of embodiments with reference to the accompanying drawings, in which:

[0018] Figure 1 A flowchart illustrating a rapid modeling method for superconducting magnets based on two-dimensional section equations and three-dimensional trajectories according to an embodiment of the present disclosure is shown.

[0019] Figure 2 A schematic cross-sectional view of a skeleton according to an embodiment of the present disclosure is shown;

[0020] Figure 3 A schematic cross-sectional view of a coil according to an embodiment of the present disclosure is shown;

[0021] Figure 4 A schematic diagram of a three-dimensional trajectory of a coil according to an embodiment of the present disclosure is shown.

[0022] Figure 5 A flowchart illustrating a multiphysics coupling calculation according to an embodiment of the present disclosure is shown schematically. Detailed Implementation

[0023] The embodiments of the present disclosure will now be described with reference to the accompanying drawings. However, it should be understood that these descriptions are exemplary only and are not intended to limit the scope of the disclosure. In the following detailed description, numerous specific details are set forth to provide a thorough understanding of the embodiments of the present disclosure for ease of explanation. However, it will be apparent that one or more embodiments may be practiced without these specific details. Furthermore, descriptions of well-known structures and techniques are omitted in the following description to avoid unnecessarily obscuring the concepts of the present disclosure.

[0024] The terminology used herein is for the purpose of describing particular embodiments only and is not intended to limit this disclosure. The terms “comprising,” “including,” etc., as used herein indicate the presence of the stated features, steps, operations, and / or components, but do not exclude the presence or addition of one or more other features, steps, operations, or components.

[0025] All terms used herein (including technical and scientific terms) have the meanings commonly understood by those skilled in the art, unless otherwise defined. It should be noted that the terms used herein are to be interpreted in a manner consistent with the context of this specification, and not in an idealized or overly rigid way.

[0026] Figure 1 A flowchart illustrating a method for rapid modeling of superconducting magnets based on two-dimensional section equations and three-dimensional trajectories according to an embodiment of the present disclosure is shown.

[0027] Figure 2 A schematic cross-sectional view of a skeleton according to an embodiment of the present disclosure is shown.

[0028] Figure 3 A schematic cross-sectional view of a coil according to an embodiment of the present disclosure is shown. Figure 1 As shown, this embodiment includes operations S110 to S130:

[0029] In operation S110, the two-dimensional cross-sectional point set data of the coil is determined based on the Biot-Savart law, the critical magnetic field characteristics of the superconducting material, and the target magnetic field distribution requirements.

[0030] Furthermore, based on the Biot-Savart law, the critical magnetic field characteristics of superconducting materials, and the target magnetic field distribution requirements, the two-dimensional cross-sectional point set data of the coil is determined, including: constructing the two-dimensional cross-sectional parameterized equation of the coil based on the target magnetic field distribution requirements and the critical magnetic field characteristics of the superconducting material, combined with the Biot-Savart law; and determining the two-dimensional cross-sectional point set data of the coil based on the preset parameters of the coil and the two-dimensional cross-sectional parameterized equation.

[0031] Furthermore, based on the preset parameters of the coil and the two-dimensional cross-section parameterization equation, the two-dimensional cross-section point set data of the coil is determined, including: determining the normal offset of the inner and outer boundaries of the superconducting conductor relative to the reference circle on the cross-section according to the coil reference radius, the cross-sectional size parameters of the superconducting conductor, the interlayer offset, and the two-dimensional cross-section parameterization equation; determining the coordinates of the inner boundary point and the outer boundary point according to the normal offset and the preset angle sequence, and generating the two-dimensional cross-section point set data.

[0032] In operation S120, each point in the two-dimensional cross-section point set data of the coil is processed to generate three-dimensional spatial trajectory data.

[0033] In operation S130, a sweep path and the cross-sectional profile of the superconducting conductor are created based on the three-dimensional spatial trajectory data, and a sweep operation is performed to generate a coil solid model.

[0034] In the embodiments of this disclosure, the Biot-Savart law is used to calculate the magnetic induction intensity generated by any current-carrying conductor at a point in space, and is the theoretical basis for magnetic field inversion design.

[0035] Critical magnetic field characteristics of superconducting materials: refers to the maximum magnetic field value at which a superconductor can maintain its superconducting state at a specific temperature. Exceeding this value will cause it to lose its superconductivity, which is a safety constraint in design.

[0036] Two-dimensional cross-sectional point set data: Under the assumption of axisymmetry, the set of discrete boundary points of the coil on the rz two-dimensional plane, representing the spatial occupancy range of the conductor.

[0037] 3D spatial trajectory data: A list of points describing the continuous path of each turn of the conductor in 3D space; it is the path input for sweep modeling.

[0038] First, based on the Biot-Savart law and combined with the critical magnetic field characteristics of superconducting materials (such as the maximum allowable working magnetic field and critical current density), a two-dimensional cross-sectional parameterized equation for the coil that satisfies the target magnetic field distribution (such as the center field strength and the size of the uniform region) is established. The expression of this equation is as follows:

[0039]

[0040] Where B(x,y) is the magnetic flux density vector at a point (x,y) in space; μ0 is the permeability of free space; and r is the displacement vector of the current element dI pointing towards the field point (x,y).

[0041] The equation takes the coil's reference radius, conductor cross-sectional dimensions, and interlayer offset as input variables, and accurately calculates the coordinates of the inner and outer boundary points on the cross-section using trigonometric functions. Subsequently, a Python program is used to automatically solve the equation, outputting an ordered set of two-dimensional coordinate points (i.e., "two-dimensional cross-sectional point set data"), which serves as the basis for subsequent modeling. This process supports real-time adjustment of design parameters (such as the number of turns and radius), enabling rapid adaptation to different topologies (such as solenoids and double-pane coils).

[0042] like Figure 2 The diagram shown is a cross-sectional view of the skeleton, which illustrates the geometric contour of the centerline path of the superconducting conductor and reflects the relative positional relationship of each turn of the coil in the axial and radial directions. However, it does not include the actual cross-sectional dimensions of the conductor and is used to make a preliminary judgment on the winding density and path continuity.

[0043] For example, constructing a skeleton cross-section model:

[0044] Set the characteristic dimensions of the superconducting conductor: r=R, and set the reference radius of the coil: RD1=D.

[0045] Calculate the normal offset using a fixed layer offset of 3:

[0046] Inner offset angle ;

[0047] Inner normal offset ;

[0048] Outer offset angle ;

[0049] Outer normal offset .

[0050] Define angle sequence .

[0051] Calculate the starting point The outer boundary coordinates (x141, y141) are used as the starting point of the path;

[0052] Calculate the endpoint The outer boundary coordinates (x13END, y13END) are used as the path endpoint.

[0053] Traverse each index i of the angle sequence TT:

[0054] Calculate the benchmark point ;

[0055] Calculate the inner point (x11, y11):

[0056] ;

[0057] .

[0058] Calculate the outer point (x14, y14):

[0059] ;

[0060] .

[0061] like (If not the last turn), then pre-calculate the next angle point. , used for path connection or interpolation.

[0062] Output all path points to form a simplified 2D skeleton outline.

[0063] like Figure 3 The image shown is a cross-sectional view of the coil, illustrating the geometric shape of the conductor's cross-section and its spatial arrangement. Each "rectangular block" represents the actual cross-sectional projection of a turn of conductor, reflecting the conductor thickness and interlayer spacing. Compared to... Figure 2 , Figure 3 It is more physically realistic and can be used to calculate important parameters such as coil volume and current density distribution.

[0064] For example, construct a realistic coil cross-section model that includes the conductor thickness:

[0065] Set the characteristic dimensions of the superconducting conductor: r=R, set the reference radius of the coil: RD1=D, and set the interlayer offset d to control the spacing between the inner and outer layers.

[0066] Calculate the inner normal offset:

[0067] Offset angle ;

[0068] Normal offset .

[0069] Calculate the outer normal offset:

[0070] Offset angle ;

[0071] Normal offset .

[0072] Iterate through each angle i in the angle sequence TT:

[0073] Calculate the coordinates of the corresponding point on the reference circle: .

[0074] Calculate the inner boundary point (x11, y11):

[0075] ;

[0076] .

[0077] Calculate the outer boundary point (x13, y13) and subtract an additional correction term of 0.2:

[0078] ;

[0079] .

[0080] Output the coordinates of all inner / outer boundary points to form a complete two-dimensional cross-sectional profile of the coil.

[0081] After obtaining the two-dimensional cross-sectional point set, three-dimensional spatial trajectory data is automatically generated by spatial mapping of the two-dimensional cross-sectional point set. Based on this trajectory data, a sweep path and the cross-sectional profile of the superconducting conductor are created. A complete coil solid model can be obtained by performing a single sweep operation, effectively solving the problems of low efficiency and geometric discontinuity caused by manual segmented modeling in traditional methods. At the same time, since the two-dimensional cross-sectional point set is accurately derived based on electromagnetic theory and material constraints, its boundary coordinates can accurately reflect the actual spatial occupancy of the superconducting conductor, thus ensuring geometric accuracy in the modeling stage and providing a reliable foundation for subsequent high-fidelity simulation.

[0082] According to embodiments of this disclosure, the preset angle sequence is an equally spaced or non-uniform array of angles.

[0083] In the embodiments of this disclosure, when an equidistant angle sequence is used, the angle points are uniformly distributed on the reference circumference, which is suitable for modeling solenoid coils with constant axial length and uniform turn density. When a non-uniform angle sequence is used, the angle interval can be locally densified or sparsed according to the magnetic field optimization requirements or the geometric complexity of the end transition region. For example, the angle sampling density can be increased in the coil end region to more accurately characterize the conductor arrangement of the curved transition section, thereby improving magnetic field uniformity or reducing local stress concentration. By flexibly configuring the distribution of the angle sequence, this disclosure can ensure modeling efficiency while taking into account the different requirements of different superconducting magnet structures for geometric accuracy and magnetic field performance.

[0084] Figure 4 A schematic diagram of a three-dimensional trajectory of a coil according to an embodiment of the present disclosure is shown.

[0085] like Figure 4 As shown, according to an embodiment of this disclosure, each point in the two-dimensional cross-sectional point set data of the coil is processed to generate three-dimensional spatial trajectory data, including: rotating each point in the two-dimensional cross-sectional point set data around a preset axis of symmetry, and discretely sampling the azimuth angle used for rotation within a preset range to generate three-dimensional spatial trajectory data corresponding to each turn of the superconducting conductor.

[0086] In the embodiments of this disclosure, each two-dimensional point is spatially mapped using a discretization algorithm: the point is considered as the projection of a turn of conductor onto its circumferential average position, rotated around the device's axis of symmetry (z-axis), and subjected to equally spaced or adaptively discrete sampling (e.g., 36 points per turn) within the azimuth angle interval [0, 2π), generating a closed three-dimensional spatial trajectory curve. This process is automatically completed by a Python script, outputting multiple three-dimensional coordinate sequences (x, y, z), each sequence corresponding to the spatial orientation of a turn of superconducting conductor. This method avoids the subjective errors of manually drawing paths, ensuring that the trajectory is strictly consistent with the original cross-section, laying the foundation for high-precision modeling.

[0087] According to embodiments of this disclosure, creating a sweep path and a cross-sectional profile of a superconducting conductor based on three-dimensional spatial trajectory data, and performing a sweep operation to generate a coil solid model includes: importing three-dimensional spatial trajectory data into a computer-aided design system; calling the programmatic modeling interface of the computer-aided design system to create a sweep path and a cross-sectional profile of the superconducting conductor, and performing a one-time sweep operation to generate a coil solid model.

[0088] In the embodiments of this disclosure, 3D trajectory data generated by Python and a preset cross-sectional profile of a superconducting conductor (such as a rectangle or D-shape) are imported into SolidWorks (a mainstream 3D CAD software), and a sweep path and cross-sectional sketch are automatically created through its application programming interface (API). The system calls the sweep command to make the cross-section move continuously along the trajectory while maintaining normal alignment, generating a complete multi-layer, multi-turn coil solid model in one go. Compared with traditional manual segmented modeling, this method eliminates geometric discontinuities such as seams and misalignments, significantly improving model integrity and simulation applicability, and reducing modeling time from several hours to minutes.

[0089] Figure 5 A flowchart illustrating a multiphysics coupling calculation according to an embodiment of the present disclosure is shown schematically.

[0090] like Figure 5 As shown, the method also includes: importing the coil entity model into a multiphysics simulation platform and performing multiphysics coupling calculations based on the property parameters of the superconducting material and preset boundary conditions.

[0091] Furthermore, the coil solid model is imported into a multiphysics simulation platform, and multiphysics coupling calculations are performed based on the property parameters of the superconducting material and preset boundary conditions. This includes: importing the coil solid model into the multiphysics simulation platform, calculating the electromagnetic force based on the property parameters of the superconducting material and preset boundary conditions; and performing electromagnetic-thermal-mechanical coupling analysis based on the electromagnetic force under preset liquid helium cooling parameters and mechanical constraints, outputting the temperature field, deformation displacement field, and stress field distribution of the coil.

[0092] The property parameters of superconducting materials include the electromagnetic properties of the superconducting material and the excitation current.

[0093] In the embodiments of this disclosure, the generated coil solid model is imported into Maxwell (electromagnetic field simulation software) for electromagnetic analysis: the electromagnetic properties of the superconducting conductor (such as conductivity and relative permeability) and excitation current boundary conditions are applied to solve for the Lorentz force density and Joule heat source distribution. Subsequently, through the software interaction mechanism between Maxwell and Workbench (ANSYS multiphysics platform), the electromagnetic calculation results (such as volume forces and heat sources) are automatically mapped to the structural mechanics and heat conduction modules in Workbench, without the need for manual export / import of intermediate files. Liquid helium cooling parameters (such as 4.2K ambient temperature and convective heat transfer coefficient) and mechanical constraints (such as end fixation and interlayer preload) are applied in Workbench to perform a fully coupled electromagnetic-thermal-mechanical analysis, outputting the temperature field, deformation displacement field, and stress field distribution for evaluating the thermal stability and structural safety of the magnet.

[0094] According to embodiments of this disclosure, the method further includes: readjusting the preset parameters of the coil when the temperature field, deformation displacement field, and stress field distribution of the coil exceed the preset parameters of the superconducting material; and updating the two-dimensional cross-sectional point set data of the coil based on the preset parameters.

[0095] In the embodiments of this disclosure, after completing the multiphysics coupling simulation, the system acquires the temperature field, deformation displacement field, and stress field distribution results of the coil. These physical fields reflect the thermo-mechanical response state of the superconducting magnet under actual operating conditions (such as strong electromagnetic loads and liquid helium cooling environments). Subsequently, the above calculation results are compared with the preset safety indicators of the superconducting material, which include, but are not limited to, the critical temperature threshold, the maximum allowable stress, and the maximum allowable deformation. If any field exceeds the corresponding preset indicator, it is determined that the current design scheme has a risk of thermal instability. At this time, the key preset parameters of the coil are readjusted, such as the coil reference radius, conductor cross-sectional dimensions, interlayer offset, turns density, or end transition curvature. The updated parameters are sent back to the front end of the modeling process to re-execute the two-dimensional cross-sectional equation solution and generate the corrected two-dimensional cross-sectional point set data of the coil. This then drives the subsequent three-dimensional trajectory generation, solid modeling, and multiphysics simulation, forming an iterative closed loop of "modeling-simulation-evaluation-optimization". This mechanism enables automated feedback from performance verification to design correction, avoiding the inefficient trial-and-error mode of relying on human experience in traditional design. It significantly improves the structural integrity and operational reliability of superconducting magnets under high electromagnetic loads and extreme low temperature environments, while supporting rapid convergence to the optimal geometric scheme that satisfies multiphysics constraints.

[0096] The embodiments of this disclosure have been described above. However, these embodiments are for illustrative purposes only and are not intended to limit the scope of this disclosure. Although various embodiments have been described above, this does not mean that the measures in the various embodiments cannot be used advantageously in combination. The scope of this disclosure is defined by the appended claims and their equivalents. Various substitutions and modifications can be made by those skilled in the art without departing from the scope of this disclosure, and all such substitutions and modifications should fall within the scope of this disclosure.

Claims

1. A method for rapid modeling of superconducting magnets based on two-dimensional section equations and three-dimensional trajectories, characterized in that, include: Based on the Biot-Savart law, the critical magnetic field characteristics of superconducting materials, and the target magnetic field distribution requirements, the two-dimensional cross-sectional point set data of the coil is determined. Each point in the two-dimensional cross-section point set data of the coil is processed to generate three-dimensional spatial trajectory data; Based on the three-dimensional spatial trajectory data, a sweep path and the cross-sectional profile of the superconducting conductor are created, and a sweep operation is performed to generate a coil solid model.

2. The method according to claim 1, characterized in that, The determination of the two-dimensional cross-sectional point set data of the coil, based on the Biot-Savart law, the critical magnetic field characteristics of superconducting materials, and the target magnetic field distribution requirements, includes: Based on the target magnetic field distribution requirements and the critical magnetic field characteristics of superconducting materials, a two-dimensional cross-sectional parameterized equation for the coil is constructed using the Biot-Savart law. Based on the preset parameters of the coil and the parameterized equation of the two-dimensional cross-section, the point set data of the two-dimensional cross-section of the coil is determined.

3. The method according to claim 2, characterized in that, The determination of the coil's two-dimensional cross-section point set data based on the coil's preset parameters and the two-dimensional cross-section parameterized equation includes: Based on the coil reference radius, the cross-sectional dimensions of the superconducting conductor, the interlayer offset, and the two-dimensional cross-sectional parameterization equation, the normal offsets of the inner and outer boundaries of the superconducting conductor relative to the reference circle on the cross-section are determined. Based on the normal offset and the preset angle sequence, the coordinates of the inner boundary point and the outer boundary point are determined, and the two-dimensional cross-sectional point set data is generated.

4. The method according to claim 3, characterized in that, The preset angle sequence is an equally spaced or non-uniform angle array.

5. The method according to claim 1, characterized in that, The step of processing each point in the two-dimensional cross-section point set data of the coil to generate three-dimensional spatial trajectory data includes: Each point in the two-dimensional cross-sectional point set data is spatially rotated around a preset axis of symmetry, and the azimuth angle used for rotation is discretely sampled within a preset range to generate three-dimensional spatial trajectory data corresponding to each turn of the superconducting conductor.

6. The method according to claim 1, characterized in that, The process of creating a sweep path and superconducting conductor cross-sectional profile based on the three-dimensional spatial trajectory data, and performing a sweep operation to generate a coil solid model includes: Import the three-dimensional spatial trajectory data into a computer-aided design system; The programmatic modeling interface of the computer-aided design system is invoked to create the sweep path and the cross-sectional profile of the superconducting conductor, and a one-time sweep operation is performed to generate the coil solid model.

7. The method according to claim 1, characterized in that, Also includes: The coil physical model is imported into a multiphysics simulation platform, and multiphysics coupling calculations are performed based on the property parameters of the superconducting material and the preset boundary conditions.

8. The method according to claim 7, characterized in that, The step of importing the coil physical model into a multiphysics simulation platform and performing multiphysics coupling calculations based on the property parameters of the superconducting material and preset boundary conditions includes: The coil physical model is imported into a multiphysics simulation platform, and the electromagnetic force is calculated based on the property parameters of the superconducting material and the preset boundary conditions. Under preset liquid helium cooling parameters and mechanical constraints, electromagnetic-thermal-mechanical coupling analysis is performed based on the electromagnetic force to output the temperature field, deformation displacement field, and stress field distribution of the coil.

9. The method according to claim 7, characterized in that, The property parameters of the superconducting material include the electromagnetic properties of the superconducting material and the excitation current.

10. The method according to claim 8, characterized in that, Also includes: If the temperature field, deformation displacement field, and stress field distribution of the coil exceed the preset parameters of the superconducting material, the preset parameters of the coil are readjusted. The two-dimensional cross-sectional point set data of the coil is updated based on the preset parameters.

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