Superconducting coils with superelliptic curve structures, superconducting magnet systems and their design methods

Abstract

This application belongs to the field of superconducting magnet technology, specifically disclosing a superconducting coil with a superelliptic curve structure, a superconducting magnet system, and its design method. By using a superelliptic curve instead of the traditional straight-side segment, the entire coil has a finite curvature. This allows for effective tension application to the conductor and reinforcing materials during winding and reinforcement. Under the combined effect of winding tension and reinforcing materials, the coil's mechanical structure is more stable, and its resistance to deformation under strong magnetic field conditions is significantly enhanced. Optimizing the coil structure with a superelliptic curve improves the coil's mechanical stability, reduces stress concentration, and lowers manufacturing costs while maintaining the aperture size and magnetic field strength. This results in a superconducting magnet system that, while increasing magnetic field strength, possesses superior mechanical stability and lower manufacturing costs, making it widely applicable in vertical ring magnetic separators, wind turbines, and other fields, and providing new technical support for other applications requiring large-aperture, strong magnetic fields.

Description

Technical Field

[0001] This application belongs to the field of superconducting magnet technology, and more specifically, relates to superconducting coils with superelliptic curve structures, superconducting magnet systems, and their design methods. Background Technology

[0002] Superconducting magnets are widely used in industrial fields due to their ability to generate strong magnetic fields and low energy consumption. In magnetic separation equipment, superconducting magnets are used for the efficient separation of minerals and other materials, and their magnetic field strength and stability directly affect the magnetic separation effect. In wind turbines, the application of superconducting magnets can improve energy conversion efficiency and reduce system weight. Applications such as vertical ring magnetic separators and wind turbines have relatively lower requirements for magnetic field uniformity; it is only necessary to ensure that the magnetic field strength exceeds a certain threshold.

[0003] In industrial applications such as vertical ring magnetic separators and wind turbines, the most common superconducting magnet coil structure is the racetrack-shaped coil. This structure consists of two straight sections and two curved ends, providing a large central aperture to meet the structural requirements of magnetic separators or generators.

[0004] However, the traditional racetrack-shaped superconducting coil structure has certain limitations in practical applications: (1) In the traditional racetrack-shaped coil, since the straight side cannot be tensioned during the winding process, the wires are difficult to be arranged compactly along the predetermined straight path, and large gaps will be left between the wires; (2) The commonly used circumferential reinforcement method is also difficult to apply tension to the straight side, which leads to the problem of the straight side being difficult to reinforce in terms of mechanical structure. Under strong magnetic field environment, it is easy to be affected by electromagnetic force and undergo mechanical deformation, which in turn leads to stress concentration, local reduction of superconducting characteristics, or even structural damage; (3) In the traditional racetrack-shaped coil, since the straight side is difficult to apply winding tension and reinforcement stress, large gaps will be left between the wires. This will lead to the stress of the straight side being transferred to the end under the action of electromagnetic force, and stress concentration areas often form at the connection between the straight side and the bend. Stress concentration not only increases the risk of material fatigue, but also directly affects the stability of the superconducting critical current. Both of these increase the risk of local quench failure of the coil. (4) Stress concentration will reduce the critical current of the superconducting material, resulting in the actual current that can be carried being far lower than the performance limit of the material itself. To compensate for this loss, traditional solutions often require increasing the amount of superconducting materials used, resulting in waste of raw materials and increased costs. Summary of the Invention

[0005] In view of the shortcomings of the prior art, the purpose of this application is to provide a superconducting coil with a superelliptic curve structure, a superconducting magnet system and its design method, which aims to solve the problem that the straight side section of the existing racetrack-shaped superconducting coil is difficult to strengthen in terms of mechanical structure, and is easily affected by electromagnetic force in a strong magnetic field environment, which leads to deformation, stress concentration, local reduction of superconducting properties or even structural damage.

[0006] In a first aspect, this application provides a superconducting coil with a superelliptic curve structure. The superconducting coil is formed by winding superconducting wire into a single closed superelliptic curve structure or a splicing structure of multiple superelliptic curve segments. Adjacent superelliptic curve segments have the same curvature value at the connection point, making the entire superconducting coil smooth and continuous.

[0007] Preferably, the expression for the hyperelliptic curve is as follows:

[0008]

[0009] Among them, parameters and The horizontal and vertical centers of the hyperelliptic curve are controlled separately, and parameters A and B control the horizontal and vertical scales of the hyperelliptic curve, respectively. The exponent... Used to adjust the shape of hyperelliptic curves, ensuring a smooth transition between them. This represents the absolute value operator.

[0010] Preferably, the superconducting coils are uniformly distributed between layers, and the coil conductors are equidistantly extended along the normal direction.

[0011] Preferably, the superconducting coil is wound from NbTi, Nb3Sn, BSCCO, ReBCO, MgB2 or an iron-based superconductor.

[0012] In a second aspect, this application provides a superconducting magnet system, including a superconducting coil as described in the first aspect.

[0013] Preferably, the system also includes current leads, a cold shield, a vacuum container, a cryogenic refrigeration component, a support structure, a quench protection component, a power supply component, and a monitoring and control component. The power supply component is connected to the superconducting magnet coil via the current leads. The coil is mounted on the support structure and placed entirely within the vacuum container. The cold shield is installed inside the vacuum container, enclosing the superconducting magnet and part of the current leads. The cryogenic refrigeration component is connected to both the cold shield and the coil. The quench protection component and the monitoring and control component are distributed at key nodes in the system, collecting data and forming a closed-loop feedback to ensure timely response in abnormal situations.

[0014] Preferably, the superconducting magnet system is applied to a vertical ring magnetic separator or a wind turbine.

[0015] Thirdly, this application provides a design method for a superconducting coil with a superelliptic curve structure as described in the first aspect, comprising:

[0016] The cross-sectional curve of the superconducting coil is parameterized;

[0017] For the case of a single closed hyperelliptic curve structure, multiple parameters of the hyperelliptic curve are used as optimization quantities, with the goal of maximizing the central magnetic field generation efficiency, and aperture and curvature constraints are set. For the case of a structure with multiple hyperelliptic curve segments continuously spliced ​​together, multiple parameters of each hyperelliptic curve segment and the connection point angle parameters of adjacent hyperelliptic curve segments in parameter space are used as optimization quantities, with the goal of maximizing the central magnetic field generation efficiency, and aperture, curvature, axis perpendicularity, and connection smoothness constraints are set. Among them, the aperture constraint ensures that the aperture size meets the user's requirements, the curvature constraint ensures the conductor performance and winding tension, the axis perpendicularity constraint ensures the coil symmetry, and the connection smoothness constraint ensures that the coordinates and slopes of adjacent hyperelliptic segments are completely consistent at the connection point.

[0018] Solving for the parameters of the hyperelliptic curve that satisfy the objective and all constraints yields the solution.

[0019] Preferably, the objective function is as follows:

[0020]

[0021] in, The objective function value, The discrete integral of the central magnetic field is obtained by numerically integrating the axial magnetic field at the origin for all discrete line elements using the Biot–Savart method. Let be the total length of the coil wire, and be the penalty function for soft penalties applied to violations of constraints. These serve as weighting factors to ensure strict control over constraints during the optimization process. This represents the absolute value operator.

[0022] Preferably, the solution is obtained using the continuous least squares algorithm, particle swarm optimization algorithm, or genetic algorithm.

[0023] Overall, the technical solutions conceived in this application have the following beneficial effects compared with the prior art:

[0024] (1) This application proposes a superconducting coil with a superelliptic curve structure. The superelliptic curve replaces the traditional straight side section, making the entire coil have a finite curvature. It can effectively apply tension to the conductor and reinforcing material during the winding and reinforcement process. Under the combined action of winding tension and reinforcing material, the mechanical structure of the coil is more stable and its resistance to deformation under strong magnetic field environment is significantly enhanced.

[0025] (2) This application proposes a superconducting coil with a superelliptic curve structure. The superelliptic curve structure enables the coil to obtain winding prestress and effective reinforcement, eliminates stress transmission, and optimizes the stress distribution of the coil. On the other hand, the design ensures the curvature continuity of each curve segment and strictly controls the slope consistency at the splicing point, so that the overall coil structure is smooth, continuous and without abrupt change points, effectively reducing stress concentration.

[0026] (3) This application proposes a superconducting coil with a superelliptic curve structure. Through structural design, the stress distribution is optimized, effectively increasing the critical current of the superconducting coil and thus significantly reducing the amount of material required per unit magnetic field. Furthermore, the use of a superelliptic curve simplifies the winding process, avoiding multiple tightening and adjustments at bends, and significantly reducing the error rate and rework rate of the coil during manufacturing. In mass industrial manufacturing, this plays a decisive role in controlling production costs and improving product consistency.

[0027] (4) This application proposes a superconducting magnet system. By optimizing the coil structure through superelliptic curves, it can improve the mechanical stability of the coil, reduce stress concentration, and lower manufacturing costs while ensuring the aperture size and magnetic field strength. This makes the superconducting magnet system have better mechanical stability and lower manufacturing costs while increasing the magnetic field strength. It can be widely used in vertical ring magnetic separators, wind turbines, and other fields, and provides new technical support for other application scenarios that require large aperture and strong magnetic field.

[0028] (5) This application proposes a design method for a superconducting coil with a superelliptic curve structure, which involves carefully designing each segment... , The parameters A, B, and n are used to ensure that adjacent hyperelliptic curve segments have the same curvature value at the connection point, thereby achieving a smooth and continuous transition. The hyperelliptic coil structure constructed by the above method not only eliminates the straight-side segment problem of traditional racetrack-shaped coils, but also effectively reduces the local stress concentration phenomenon caused by electromagnetic force and improves the mechanical strength of the coil. Attached Figure Description

[0029] Figure 1 This is a schematic diagram of a superconducting coil with a superelliptic curve structure provided in an embodiment of this application.

[0030] Figure 2 This is a schematic diagram of a single hyperelliptic curve structure designed according to an embodiment of this application.

[0031] Figure 3 This is a schematic diagram of the multi-hyperelliptic curve structure designed according to the embodiments of this application. Detailed Implementation

[0032] To make the objectives, technical solutions, and advantages of this application clearer, the following detailed description is provided in conjunction with the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are merely illustrative and not intended to limit the scope of this application.

[0033] In this application, the term "and / or" describes the relationship between related objects, indicating that three relationships can exist. For example, A and / or B can represent three cases: A existing alone, A and B existing simultaneously, and B existing alone. In this application, the symbol " / " indicates that the related objects are in an "or" relationship, for example, A / B means A or B.

[0034] The terms "first" and "second," etc., used in the specification and claims of this application are used to distinguish different objects, not to describe a specific order of objects. For example, "first response message" and "second response message," etc., are used to distinguish different response messages, not to describe a specific order of response messages.

[0035] In the embodiments of this application, the terms "exemplary" or "for example" are used to indicate that something is an example, illustration, or description. Any embodiment or design that is described as "exemplary" or "for example" in the embodiments of this application should not be construed as being more preferred or advantageous than other embodiments or design. Specifically, the use of the terms "exemplary" or "for example" is intended to present the relevant concepts in a specific manner.

[0036] In the description of the embodiments of this application, unless otherwise stated, "multiple" means two or more, for example, multiple processing units means two or more processing units, multiple elements means two or more elements, etc.

[0037] The embodiments of this application are described below with reference to the accompanying drawings.

[0038] Firstly, such as Figure 1 As shown, this application provides a superconducting coil with a superelliptic curve structure. The superconducting coil is formed by winding superconducting wire into a single closed superelliptic curve structure or a splicing structure of multiple superelliptic curve segments. Adjacent superelliptic curve segments have the same curvature value at the connection point, making the entire superconducting coil smooth and continuous.

[0039] Theoretically, the more segments there are, the better the results will be; however, a larger number of segments will also make the design process more complex. Preferably, the number of hyperelliptic curve segments is [2, 10].

[0040] The entire coil has finite curvature. The minimum curvature depends on the minimum bending radius of the conductor material; for example, this value is typically 10-15 mm for YBCO tape. The maximum curvature depends on the maximum curvature at which winding tension can be effectively applied during winding; this value is usually no more than 3 m based on engineering experience.

[0041] Preferably, the expression for the hyperelliptic curve is as follows:

[0042]

[0043] Among them, parameters and The horizontal and vertical centers of the hyperelliptic curve are controlled separately, and parameters A and B control the horizontal and vertical scales of the hyperelliptic curve, respectively. The exponent... Used to adjust the shape of hyperelliptic curves, ensuring a smooth transition between them. This represents the absolute value operator.

[0044] The superconducting coil designed based on the aforementioned superelliptic curve structure will also be wound using one or more continuous superelliptic curve structures. The coil winding frame is machined into a superelliptic curve shape, so the innermost layer of conductors will be wound strictly according to the superelliptic curve. The winding frame is typically made of aluminum alloy or stainless steel. Preferably, the layers of the superconducting coil are uniformly distributed, and the coil conductors are equidistantly extended along the normal direction.

[0045] Preferably, the superconducting coil is wound from NbTi, Nb3Sn, BSCCO, ReBCO, MgB2 or an iron-based superconductor.

[0046] In a second aspect, this application provides a superconducting magnet system, including a superconducting coil as described in the first aspect.

[0047] Preferably, the system also includes current leads, a cold shield, a vacuum container, a cryogenic refrigeration component, a support structure, a quench protection component, a power supply component, and a monitoring and control component. The power supply component is connected to the superconducting magnet coil via the current leads. The coil is mounted on the support structure and placed entirely within the vacuum container. The cold shield is installed inside the vacuum container, enclosing the superconducting magnet and part of the current leads. The cryogenic refrigeration component is connected to both the cold shield and the coil. The quench protection component and the monitoring and control component are distributed at key nodes in the system, collecting data and forming a closed-loop feedback to ensure timely response in abnormal situations.

[0048] Current leads are used to transfer current from an external power source to the superconducting coil in a cryogenic environment. A cold shield is positioned between room temperature and cryogenic temperature to reduce thermal radiation load. A vacuum container provides a high-vacuum environment to suppress gas heat transfer. Cryogenic cooling components maintain the superconducting state of the magnet using liquid helium Dewars or cryogenic systems. A support structure ensures the mechanical stability of the superconducting coil in the cryogenic environment, a quench protection component prevents quenching accidents, and a power supply component provides a stable DC current. Monitoring and control components use various sensors to acquire and control parameters such as temperature, pressure, voltage, and current in real time, ensuring the safe and stable operation of the system.

[0049] Preferably, the superconducting magnet system is applied to a vertical ring magnetic separator or a wind turbine.

[0050] Thirdly, this application provides a design method for a superconducting coil with a superelliptic curve structure as described in the first aspect, comprising:

[0051] The cross-sectional curve of the superconducting coil is parameterized;

[0052] For the case of a single closed hyperelliptic curve structure, multiple parameters of the hyperelliptic curve are used as optimization quantities, with the goal of maximizing the central magnetic field generation efficiency, and aperture and curvature constraints are set. For the case of a structure with multiple hyperelliptic curve segments continuously spliced ​​together, multiple parameters of each hyperelliptic curve segment and the connection point angle parameters of adjacent hyperelliptic curve segments in parameter space are used as optimization quantities, with the goal of maximizing the central magnetic field generation efficiency, and aperture, curvature, axis perpendicularity, and connection smoothness constraints are set. Among them, the aperture constraint ensures that the aperture size meets the user's requirements, the curvature constraint ensures the conductor performance and winding tension, the axis perpendicularity constraint ensures the coil symmetry, and the connection smoothness constraint ensures that the coordinates and slopes of adjacent hyperelliptic segments are completely consistent at the connection point.

[0053] Solving for the parameters of the hyperelliptic curve that satisfy the objective and all constraints yields the solution.

[0054] Preferably, the objective function is as follows:

[0055]

[0056] in, The objective function value, The discrete integral of the central magnetic field is obtained by numerically integrating the axial magnetic field at the origin for all discrete line elements using the Biot–Savart method. Let be the total length of the coil wire, and be the penalty function for soft penalties applied to violations of constraints. These serve as weighting factors to ensure strict control over constraints during the optimization process. This represents the absolute value operator.

[0057] Preferably, the solution is obtained using the continuous least squares algorithm, particle swarm optimization algorithm, or genetic algorithm.

[0058] Example 1 (Single Hyperelliptic Curve)

[0059] This embodiment provides a design method for superconducting coils based on a single superelliptic curve structure. The goal is to maximize the efficiency of the central magnetic field generation while meeting constraints such as aperture and curvature, thereby improving the overall performance of the magnet system.

[0060] The coil designed in this embodiment requires an aperture length greater than X0 = 3.0 m and a width greater than Y0 = 2.0 m, and the conductor material is selected as NbTi superconducting wire.

[0061] To achieve the above objectives, the following design steps are adopted:

[0062] 1. Parametric modeling

[0063] The coil cross-section is parameterized using a single closed hyperelliptic curve, and its parametric equation is as follows:

[0064]

[0065] In the formula, the parameter A , B Control the horizontal and vertical dimensions of the curve separately. n This is a shape index used to adjust the flatness of the curve. This represents the absolute value operator. In this embodiment, the center of the hyperellipse must be at the origin, i.e. = =0.

[0066] 2. Definition of the objective function

[0067] After discretizing the parameterized hyperelliptic curve, the Biot–Savart method is used to measure the axial magnetic field at the origin for all discrete line elements. Perform numerical integration and simultaneously calculate the total length of the coil wire. L .

[0068] Construct the objective function:

[0069]

[0070] Among them, the penalty term 𝑃 applies a soft penalty to violations of constraints, and 𝜆 is a weighting factor to ensure strict control over constraints during the optimization process. This represents the absolute value operator.

[0071] 3. Setting Constraints

[0072] 3.1 Aperture Constraint: Ensures that the point (X0 / 2, Y0 / 2) lies inside the hyperelliptic curve, which is equivalent to... .

[0073] 3.2 Curvature Constraint:

[0074] Calculate the radius of curvature at any position along the curve and guarantee Among them, based on the properties of superconducting materials and the requirements of the winding process, , This is to ensure the manufacturability and structural stability of the coil.

[0075] 4. Optimization process

[0076] Define the variable to be optimized as The solution is obtained using a nonlinear optimization algorithm such as SLSQP (Sequential Least Squares Programming) or a global optimization algorithm (such as particle swarm optimization or genetic algorithm). For each candidate parameter combination as input, the following steps are performed:

[0077] ① Discrete generation of hyperelliptic curve point sequences ;

[0078] ② Calculate the magnetic field integral of the discrete linear element and total length L ;

[0079] The central magnetic field is expressed using Biot–Savart's law. The continuous integral is:

[0080]

[0081] Curve C is given by the parametric equation of the hyperelliptic curve, and the vacuum permeability is... The value is .

[0082] The continuous integral is discretized into N points using the composite Simpson integral. :

[0083]

[0084] Similarly, the total length of the curve L The continuous integral form is:

[0085]

[0086] Discrete approximation is performed using the complex Simpson integral:

[0087]

[0088] ③ Calculate the penalty term based on the constraints. P ;

[0089]

[0090] in, Indicates each penalty item, For aperture constraint penalty, Penalty for minimum curvature constraint, Penalty for maximum curvature constraint; The weights of each constraint penalty function.

[0091] The aperture constraint penalty function is established as follows:

[0092]

[0093] The curvature constraint penalty function is established as follows:

[0094]

[0095]

[0096] in, and They represent The minimum and maximum values, The distribution of the radius of curvature of the curve:

[0097]

[0098] ④ Evaluate the objective function ;

[0099] ⑤ Iterate until convergence, then select the option that makes convergence possible. The minimum parameter combination is taken as the final design result.

[0100] 5. Optimization Results

[0101] Through the above calculations and optimizations, the following optimal parameter combinations are obtained: .

[0102] At this time, the coil's central magnetic field generation efficiency reaches [percentage missing] under a 1 A current excitation. .

[0103] This set of parameters, while satisfying all constraints, achieves optimal central magnetic field generation efficiency, and the corresponding hyperelliptic curve exhibits good smoothness and structural continuity, making it suitable for winding with NbTi superconducting wire. The designed hyperelliptic coil curve is shown below. Figure 2 As shown.

[0104] This embodiment demonstrates that by employing a single hyperelliptic curve structure and combining Biot-Savart numerical integration with multi-constraint optimization, both magnetic field efficiency and manufacturing feasibility can be improved under complex constraints, demonstrating significant engineering practical value.

[0105] Example 2 (Multiple Hyperelliptic Curves)

[0106] This embodiment provides a design method for superconducting coils based on a double superelliptic curve structure. The goal is to maximize the efficiency of the central magnetic field generation while satisfying multiple constraints such as perpendicularity to the coordinate axes, smooth connection, internal point wrapping, and curvature manufacturability, thereby further improving the overall performance of the magnet system.

[0107] The coil designed in this embodiment requires an aperture length greater than X0 = 3.0 m and a width greater than Y0 = 2.0 m, and the conductor material is selected as NbTi superconducting wire.

[0108] To achieve the above objectives, the following design steps are adopted:

[0109] 1. Parametric modeling

[0110] Because the coil structure is centrally symmetrical, only the curve parameters in the first quadrant are considered for design. Clearly, the curve will be perpendicular to both the X and Y axes; therefore, the coil cross-section curve is divided into two hyperelliptic curves—the center of the first segment is set at... The parameters are The center of the second paragraph is set at The parameters are The connection point between two segments in the parameter space is determined by the angular parameter. , The descriptions and their parametric equations are as follows:

[0111]

[0112] 2. Definition of the objective function

[0113] After discretizing the two curve segments, the Biot–Savart method is used to measure the axial magnetic field of all discrete line elements at the origin. Perform numerical integration and simultaneously calculate the total length of the coil wire. L .

[0114] Construct the objective function:

[0115]

[0116] Among them, the penalty term 𝑃 applies a soft penalty to violations of constraints, and 𝜆 is a weighting factor to ensure strict control of constraints during the optimization process.

[0117] 3. Setting Constraints

[0118] 3.1 Axis Perpendicular Constraint: Ensures that segment 1 is perpendicular to the axis. When perpendicular to the Y-axis, segment 2 is in It is perpendicular to the X-axis.

[0119] 3.2 Connection Smoothness Constraint: Ensures that the coordinates and slopes of the two segments are completely consistent at the connection point.

[0120]

[0121] 3.3 Aperture constraint: Ensure that the point (X0 / 2, Y0 / 2) lies inside the hyperelliptic curve.

[0122] 3.4 Curvature Constraint: Calculate the radius of curvature at any position along the curve. And ensure that it falls Within the range.

[0123] 4. Optimization process

[0124] Define the variable to be optimized as The objective function is iteratively minimized using the SLSQP nonlinear optimization algorithm or a global optimization algorithm (such as particle swarm optimization or genetic algorithm), combined with the aforementioned equality and inequality constraints. Each iteration generates two hyperelliptic curves based on the current parameters and performs discrete calculations. , L The system also includes penalty measures, which are then fed back to the optimizer.

[0125] 5. Optimization Results

[0126] Through the above calculations and optimizations, the following optimal parameter combinations are obtained:

[0127]

[0128] At this time, the coil's central magnetic field generation efficiency reaches [percentage missing] under a 1 A current excitation. .

[0129] This set of parameters, while satisfying all constraints, achieves optimal central magnetic field generation efficiency, and the corresponding hyperelliptic curve exhibits good smoothness and structural continuity, making it suitable for winding with NbTi superconducting wire. The designed hyperelliptic coil curve is shown below. Figure 3 As shown.

[0130] This embodiment demonstrates that by employing a double hyperelliptic curve structure and introducing multiple equality / inequality constraints for optimization, the optimal balance between magnetic field efficiency, geometric continuity, and manufacturing feasibility can be achieved simultaneously in a complex design space. Furthermore, compared to a single hyperelliptic curve structure, it possesses a greater central magnetic field generation efficiency and has significant engineering application value.

[0131] It should be understood that the above-described device is used to execute the methods in the above embodiments. The implementation principle and technical effect of the corresponding program modules in the device are similar to those described in the above methods. The working process of the device can be referred to the corresponding process in the above methods, and will not be repeated here.

[0132] Based on the methods in the above embodiments, this application provides an electronic device that may include a processor, a communications interface, a memory, and a communication bus, wherein the processor, communications interface, and memory communicate with each other via the communication bus. The processor may invoke logical instructions stored in the memory to execute the methods in the above embodiments.

[0133] Furthermore, the logical instructions in the aforementioned memory can be implemented as software functional units and, when sold or used as independent products, can be stored in a computer-readable storage medium. Based on this understanding, the technical solution of this application, in essence, or the part that contributes to the prior art, or a portion of the technical solution, can be embodied in the form of a software product. This computer software product is stored in a storage medium and includes several instructions to cause a computer device (which may be a personal computer, server, or network device, etc.) to execute all or part of the steps of the methods described in the various embodiments of this application.

[0134] Based on the methods in the above embodiments, this application provides a computer-readable storage medium storing a computer program that, when run on a processor, causes the processor to execute the methods in the above embodiments.

[0135] Based on the methods in the above embodiments, this application provides a computer program product that, when run on a processor, causes the processor to execute the methods in the above embodiments.

[0136] It is understood that the processor in the embodiments of this application can be a central processing unit (CPU), or other general-purpose processors, digital signal processors (DSPs), application-specific integrated circuits (ASICs), field-programmable gate arrays (FPGAs), or other programmable logic devices, transistor logic devices, hardware components, or any combination thereof. A general-purpose processor can be a microprocessor or any conventional processor.

[0137] The method steps in this application embodiment can be implemented in hardware or by a processor executing software instructions. The software instructions can consist of corresponding software modules, which can be stored in random access memory (RAM), flash memory, read-only memory (ROM), programmable read-only memory (PROM), erasable programmable read-only memory (EPROM), electrically erasable programmable read-only memory (EEPROM), registers, hard disks, portable hard disks, CD-ROMs, or any other form of storage medium known in the art. An exemplary storage medium is coupled to the processor, enabling the processor to read information from and write information to the storage medium. Of course, the storage medium can also be a component of the processor. The processor and the storage medium can reside in an ASIC.

[0138] In the above embodiments, implementation can be achieved entirely or partially through software, hardware, firmware, or any combination thereof. When implemented using software, it can be implemented entirely or partially as a computer program product. The computer program product includes one or more computer instructions. When the computer program instructions are loaded and executed on a computer, all or part of the processes or functions described in the embodiments of this application are generated. The computer can be a general-purpose computer, a special-purpose computer, a computer network, or other programmable device. The computer instructions can be stored in a computer-readable storage medium or transmitted through the computer-readable storage medium. The computer instructions can be transmitted from one website, computer, server, or data center to another website, computer, server, or data center via wired (e.g., coaxial cable, fiber optic, digital subscriber line (DSL)) or wireless (e.g., infrared, wireless, microwave, etc.) means. The computer-readable storage medium can be any available medium that a computer can access or a data storage device such as a server or data center that integrates one or more available media. The available medium can be a magnetic medium (e.g., floppy disk, hard disk, magnetic tape), an optical medium (e.g., DVD), or a semiconductor medium (e.g., solid-state disk (SSD)).

[0139] It is understood that the various numerical designations used in the embodiments of this application are merely for the convenience of description and are not intended to limit the scope of the embodiments of this application.

[0140] Those skilled in the art will readily understand that the above description is merely a preferred embodiment of this application and is not intended to limit this application. Any modifications, equivalent substitutions, and improvements made within the spirit and principles of this application should be included within the scope of protection of this application.

Claims

1. A superconducting coil of hyper-elliptical curve structure, characterized by, The superconducting coil is wound by superconducting wire into a single closed super-elliptic curve structure or a plurality of super-elliptic curve segment splicing structures. The super-elliptic curve structure is designed by the following method: The cross-sectional curve of the superconducting coil is parameterized. For the case of a single closed super-elliptic curve structure, a plurality of parameters of the super-elliptic curve are taken as optimization variables, the maximum central magnetic field generation efficiency is taken as the target, and aperture constraints and curvature constraints are set. For the case of a plurality of super-elliptic curve segment continuous splicing structures, a plurality of parameters of each super-elliptic curve segment and an angle parameter of a connection point of adjacent super-elliptic curve segments in the parameter space are taken as optimization variables, the maximum central magnetic field generation efficiency is taken as the target, and aperture constraints, curvature constraints, axis vertical constraints and connection smoothness constraints are set. The super-elliptic curve parameters satisfying the target and all constraints are solved. The target function is as follows: wherein is the objective function value, is the discrete integral of the central magnetic field, which is obtained by numerically integrating the axial magnetic field at the origin of all discrete line elements using the Biot-Savart law, is the total wire length of the coil, is a penalty function that soft penalizes the violation of the constraint, is a weight factor that ensures a strict control of the constraint during the optimization process, denotes the absolute value operator; The aperture constraints ensure that the aperture size meets the user's requirements, the curvature constraints ensure the conductor performance and winding tension, the axis vertical constraints ensure the symmetry of the coil, and the connection smoothness constraints ensure that the coordinates and slopes of adjacent super-elliptic curve segments at the connection point are completely consistent.

2. The superconducting coil of claim 1, wherein, The expression of the super-elliptic curve is as follows: wherein the parameters and control the horizontal and vertical center of the super-elliptical curve, respectively, the parameters A and B control the horizontal and vertical scale of the super-elliptical curve, respectively, and the exponent are used to adjust the shape of the super-elliptical curve such that it smoothly transitions between the individual super-elliptical curves, denotes the absolute value operator.

3. The superconducting coil of claim 1, wherein, The superconducting coil is uniformly distributed between layers, and the coil conductor is expanded equidistantly along the normal direction.

4. The superconducting coil of claim 1, wherein, The superconducting coil is wound by NbTi, Nb3Sn, BSCCO, ReBCO, MgB2 or iron-based superconductor.

5. The superconducting coil of claim 1, wherein, The continuous least squares method algorithm, particle swarm optimization algorithm or genetic algorithm is used for solving.

6. A superconducting magnet system characterized by, The superconducting coil includes the superconducting coil according to any one of claims 1 to 5.

7. The superconducting magnet system of claim 6, wherein, It also includes current leads, a cold shield, a vacuum container, a low-temperature refrigeration assembly, a support structure, a quench protection assembly, a power supply assembly and a monitoring and control assembly. The power supply assembly is connected to the superconducting magnet coil through the current leads. The coil is mounted on the support structure and placed in the vacuum container as a whole. The cold shield is mounted inside the vacuum container and wraps the superconducting magnet and part of the current leads. The low-temperature refrigeration assembly is connected to the cold shield and the coil, respectively. The quench protection assembly and the monitoring and control assembly are distributed at key nodes in the system, collect data and form a closed loop feedback to ensure timely response in abnormal conditions.

8. The superconducting magnet system of claim 6 or 7, wherein, The superconducting magnet system is applied to a vertical ring magnetic separator or a wind turbine.

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