A method and system for analyzing and optimizing electromagnetic force of a toroidal field coil of a stellarator

Abstract

The present application relates to a kind of star simulator annular field coil electromagnetic force analysis structure optimization method and system, it is related to star simulator annular field coil electromagnetic force structure optimization technical field, including according to the spatial constraint of vacuum chamber geometric characteristics and external modular coil, determine the arrangement scheme parameter of star simulator annular field coil;Utilize arrangement scheme parameter to construct coil three-dimensional geometric model, solve electromagnetic volume force distribution;Identify peak load area and extract single-turn coil equivalent load;Through cable deflection experiment, the equivalent Young's modulus of composite cable is determined, the equivalent elastic modulus parameter of cable is obtained;Equivalent load and equivalent elastic modulus parameter are combined with single-turn coil, establish fixture-cable coupling finite element model, determine the key structure size of fixture and verify strength criterion.The present application has beneficial effect for significantly improving the installation reliability and anti-electromagnetic force ability of annular field coil, ensure the accuracy of magnetic field configuration and the stability of device operation.

Description

Technical Field

[0001] This invention relates to the field of electromagnetic force structure optimization technology for stellarator circumferential field coils, and more specifically, to a method and system for analyzing and optimizing the electromagnetic force structure of stellarator circumferential field coils. Background Technology

[0002] Quasi-toroidal stellarators, due to their inherent steady-state operation capabilities, have become important devices for magnetic confinement fusion research. Their toroidal field coils (TFCs) play a crucial role in regulating the toroidal magnetic field strength and influencing plasma rotation transformation. In existing technologies, TFCs are typically located outside the vacuum chamber, requiring them to simultaneously meet multiple constraints such as avoiding the outer modular coils, being close to the plasma to improve magnetic field efficiency, and adapting to complex curved surface installations. This results in limited installation space and complex support surface shapes.

[0003] During operation, TFC is subjected to significant normal and subnormal electromagnetic forces. Existing support structures mostly use empirical estimation methods based on simplified models to determine the clamp spacing. At the same time, for composite cables composed of multi-strand copper wires, insulation layers and sheaths, existing technologies lack precise means to measure their equivalent mechanical parameters, resulting in a mismatch between the support structure design and the actual stress state, making it difficult to effectively suppress coil deformation, and thus affecting the accuracy of the magnetic field configuration and the stability of the device operation. Summary of the Invention

[0004] The purpose of this invention is to provide a method and system for optimizing the electromagnetic force analysis structure of a stellarator's circumferential field coil, thereby improving the aforementioned problems. To achieve this objective, the technical solution adopted by this invention is as follows: In a first aspect, this application provides a method for optimizing the electromagnetic force analysis structure of a stellarator's circumferential field coil, including: Based on the geometric characteristics of the vacuum chamber and the spatial constraints of the external modular coils, the arrangement parameters of the stellarator circumferential field coils are determined so that the coils are wound in close contact with the outer surface of the vacuum chamber. A three-dimensional geometric model of the coil is constructed using the layout parameters. The distribution of the coil's self-magnetic field is calculated and superimposed with the magnetic field of the modular coil to form a joint magnetic field model. The distribution of electromagnetic volume force is then solved. Based on the electromagnetic volume force distribution, the coil is discretized into several arc segments along the center line. The volume force density is decomposed into normal and subnormal components and integrated to obtain the normal and subnormal forces of each arc segment. The peak load region is identified and the equivalent load of a single-turn coil is extracted. To address the stiffness requirements of the cable under the equivalent load of a single-turn coil, the equivalent Young's modulus of the composite cable was determined through cable deflection experiments, thereby obtaining the cable's equivalent elastic modulus parameters. By combining the equivalent load and equivalent elastic modulus parameters of a single-turn coil, a finite element model of clamp-cable coupling is established. The contact conditions and load boundaries between conductors are set, the clamp spacing and number of clamps are optimized, the key structural dimensions of the clamps are determined, and the strength criteria are verified.

[0005] Preferably, the step of determining the arrangement parameters of the stellarator circumferential field coil based on the geometric characteristics of the vacuum chamber and the spatial constraints of the external modular coil, so that the coil is wound close to the outer surface of the vacuum chamber, includes: Obtain the structural details of the outer surface of the vacuum chamber and the installation position of the modular coils, analyze the available installation gaps and mechanical interference constraints, and obtain the boundary of the area where the coils can be arranged. Based on the boundary of the coil placement area, the stellarator circumferential field coils are designed as multiple planar coils arranged along the circumferential direction, and the number of coils and coverage area are determined. According to the number of coils and coverage area, a grouped cyclic arrangement method is adopted to determine the geometric shape variation law of the coils in each group. By utilizing the geometric shape variation law of the coils in each group, the center line of the coil is defined as a similar curve with a fixed offset distance relative to the outer surface of the vacuum chamber, and the spatial path parameters of the coil are obtained. Using the spatial path parameters of the coil, the coil is wound in a way that directly adheres to the outer surface of the vacuum chamber, and is formed by winding multiple strands of cable around the outer wall of the vacuum chamber multiple times.

[0006] Preferably, based on the boundary of the coil arrangement area, the stellarator circumferential field coils are designed as multiple planar coils arranged circumferentially, determining the number of coils and the coverage area, including: The stellarator's circumferential field coils are designed as twelve planar coils arranged circumferentially, using four groups of cyclical arrangement. Each group covers a 90° circumferential range, and each group contains three different geometric shapes of circumferential field coils: the first circumferential field coil, the second circumferential field coil, and the third circumferential field coil.

[0007] Preferably, the step of constructing a three-dimensional geometric model of the coil using the arrangement parameters, calculating the coil's self-magnetic field distribution, and superimposing it with the modular coil's magnetic field to form a joint magnetic field model, and solving for the electromagnetic volume force distribution, includes: Using the coil spatial path parameters, number of coils, coil grouping method, and spatial relationship between the coils and the vacuum chamber as inputs, a three-dimensional geometric model of the stellarator circumferential field coil is constructed. The coil cross-section is equivalent to a circular cross-section to obtain the coil geometric model. By applying corresponding operating currents to coils with different geometric shapes in the coil geometric model, and solving for the magnetic field distribution generated by the coil based on the Biot-Savart law, the self-magnetic field distribution of the coil is obtained. A joint magnetic field model is constructed by superimposing the self-magnetic field distribution of the coil with the magnetic field generated by the modular coil. The coil region is divided into grids. Based on the above magnetic field model, the volume force density is calculated using the electromagnetic force density formula. The electromagnetic volume force distribution is obtained under the conditions of only the stellarator circumferential field coil operating and the stellarator circumferential field coil and the modular coil operating simultaneously.

[0008] Preferably, based on the electromagnetic volume force distribution, the coil is discretized into several arc segments along the centerline, the volume force density is decomposed into normal and subnormal components and integrated to obtain the normal and subnormal forces of each arc segment, the peak load region is identified and the equivalent load of a single-turn coil is extracted, including: Based on the electromagnetic volume force distribution, the stellarator circumferential field coil is divided into several geometrically continuous arc segments along its centerline. The force on each arc segment is decomposed into normal and subnormal components in the local coordinate system to obtain the distribution of normal and subnormal forces in each arc segment. The normal component corresponds to the circumferential tension in the coil plane, and the subnormal component corresponds to the lateral tension difference of the coil. Multiply the cross-sectional area of ​​the coil by the length of each arc segment to obtain the volume of each arc segment; use the volume of each arc segment as the integration region, perform volume integrals on the normal and subnormal components of the volume force density to obtain the total force on the normal and subnormal components of each arc segment. Based on the distribution of normal and secondary normal forces in each arc segment, the peak force region is identified, and the total force of the arc segment is converted into the equivalent force of a single-turn coil to obtain the equivalent load of a single-turn coil.

[0009] Preferably, to address the cable stiffness requirement due to the equivalent load of a single-turn coil, the equivalent Young's modulus of the composite cable is determined through a cable deflection test to obtain the cable's equivalent elastic modulus parameters, including: The two ends of the cable are fixed to form a simply supported beam structure. A vertical load is applied at the center of the span, and the deflection change of the cable under the load is measured to obtain load-deflection data. Multiple sets of experimental conditions with different fixed lengths and different loads were set up, and the load-deflection data of each set of experiments were linearly fitted to obtain the slope of the deflection-load curve. The equivalent Young's modulus of the cable is calculated based on the slope of the deflection-load curve using the simple supported beam bending theory. The equivalent Young's modulus calculated from all experimental groups was averaged to obtain the final equivalent elastic modulus parameter of the cable.

[0010] Preferably, the step of establishing a clamp-cable coupling finite element model by combining the equivalent load and equivalent elastic modulus parameters of a single-turn coil, setting the contact conditions and load boundaries between conductors, and optimizing the clamp spacing and number of clamps includes: Based on the equivalent load and equivalent elastic modulus parameters of a single-turn coil, a finite element analysis model of the clamp and multiple cables is established, and contact constraints between conductors are set to obtain a clamp-cable coupling finite element model. Normal and subnormal electromagnetic force components are applied as load boundaries to the clamp-cable coupled finite element model. The cable deflection response under different clamp spacings is analyzed to obtain the relationship curve between clamp spacing and deflection. Based on the relationship curve between clamp spacing and deflection, the maximum allowable clamp spacing is determined with the deflection limit as a constraint, and the optimized clamp spacing is obtained. Based on the optimized clamp spacing and the actual arc length of the coil, the number of clamps is calculated so that the clamps are evenly distributed along the entire length of the coil.

[0011] Preferably, the determination of key structural dimensions of the fixture and verification of strength criteria includes: Based on the optimized fixture spacing and number of fixtures, a detailed model of the fixture structure is established; electromagnetic loads are applied to the detailed model of the fixture structure for strength analysis to obtain the stress distribution of the fixture; Based on the stress distribution of the fixture, the key parameters of the cover plate thickness and weld size were optimized to obtain the optimized fixture structure dimensions, and the optimized fixture structure dimensions were verified to meet the strength criteria.

[0012] Preferably, the process of determining the key structural dimensions of the fixture and verifying the strength criteria further includes: During coil operation, the coil temperature distribution is monitored to obtain real-time monitoring data; The system compares real-time monitoring data with preset thresholds. When the data exceeds the preset threshold, an alert is issued; otherwise, monitoring continues.

[0013] Secondly, this application also provides a stellarator circumferential field coil electromagnetic force analysis and structural optimization system, comprising: Determining module: Used to determine the arrangement parameters of the stellarator circumferential field coil based on the geometric characteristics of the vacuum chamber and the spatial constraints of the external modular coil, so that the coil is wound in close contact with the outer surface of the vacuum chamber. Calculation module: Used to construct a three-dimensional geometric model of the coil using the layout parameters, calculate the coil's self-magnetic field distribution, and superimpose it with the modular coil magnetic field to form a joint magnetic field model, and solve for the electromagnetic volume force distribution; Decomposition module: Based on the electromagnetic volume force distribution, the coil is discretized into several arc segments along the center line, the volume force density is decomposed into normal and subnormal components and integrated to obtain the normal and subnormal forces of each arc segment, the peak load region is identified and the equivalent load of a single-turn coil is extracted. The module is used to determine the equivalent Young's modulus of the composite cable by measuring the equivalent elastic modulus of the cable through cable deflection experiments, based on the cable stiffness requirements of the equivalent load of a single-turn coil. Establish an optimization module: This module combines the equivalent load and equivalent elastic modulus parameters of a single-turn coil to establish a finite element model of the clamp-cable coupling, set the contact conditions and load boundaries between conductors, optimize the clamp spacing and number of clamps, determine the key structural dimensions of the clamps, and verify the strength criteria.

[0014] Thirdly, this application also provides a device for analyzing and optimizing the electromagnetic force of a stellarator's circumferential field coil, comprising: Memory, used to store computer programs; A processor is used to implement the steps of the stellarator circumferential field coil electromagnetic force analysis structure optimization method when executing the computer program.

[0015] Fourthly, this application also provides a readable storage medium storing a computer program, which, when executed by a processor, implements the steps of the above-described structural optimization method based on the electromagnetic force analysis of a stellarator circumferential field coil.

[0016] The beneficial effects of this invention are as follows: This invention constructs a design method for a quasi-toroidal symmetric stellarator circumferential field coil that can be engineered, achieving a balance between magnetic field performance, structural strength, and installation feasibility. By using 12 planar coils arranged in 4 groups and directly wound on the outer surface of the vacuum chamber, mechanical interference with external modular coils is avoided, and the coils are brought as close to the plasma as possible, thereby improving the efficiency of magnetic field utilization.

[0017] This invention solves the problem of directly calculating electromagnetic forces on complex curved surfaces by discretizing the coil into several arc segments and performing volume force integration. It accurately obtains the normal and subnormal force distribution per unit length and identifies dangerous electromagnetic loads up to 37,000 N / m, providing a reliable basis for structural design. Addressing the lack of theoretical mechanical parameters for composite cables, the equivalent Young's modulus of the cable is experimentally measured to be 1 GPa, enabling finite element analysis to incorporate real material inputs.

[0018] This invention is based on a finite element model of a cable-clamp system. Taking into account various contact conditions, the clamp spacing is determined to be 140mm, and the clamps are uniformly arranged along the entire length of the coil accordingly, effectively suppressing coil deflection caused by electromagnetic force. Through stress analysis of the clamps, the cover plate thickness is ultimately determined to be 8mm and the weld leg size to be 5mm, ensuring the structural safety of the clamps under complex loads. Furthermore, during vacuum chamber baking and coil operation, heat conduction may cause the coil temperature to exceed the insulation material's tolerance limit, and existing solutions lack effective monitoring and protection measures for coil temperature.

[0019] Other features and advantages of the invention will be set forth in the following description, and will be apparent in part from the description, or may be learned by practicing embodiments of the invention. The objects and other advantages of the invention may be realized and obtained by means of the structures particularly pointed out in the written description, claims, and drawings. Attached Figure Description

[0020] To more clearly illustrate the technical solutions of the embodiments of the present invention, the accompanying drawings used in the embodiments will be briefly introduced below. It should be understood that the following drawings only show some embodiments of the present invention and should not be regarded as a limitation on the scope. For those skilled in the art, other related drawings can be obtained based on these drawings without creative effort.

[0021] Figure 1 The diagram below shows the CFQS device in the electromagnetic force analysis structure optimization method for the circumferential field coil of the stellarator described in this embodiment of the invention: (a) is the main structure; (b) is the modular coil; and (c) is the circumferential field coil. Figure 2 This is a diagram showing the distribution of magnetic field lines generated by the circumferential field coil in the stellarator electromagnetic force analysis and structural optimization method described in this embodiment of the invention. Figure 3 This is a schematic diagram of the volume force density distribution of the circumferential field coil in the stellarator electromagnetic force analysis structure optimization method described in this embodiment of the invention. Figure 4 This is a schematic diagram of the segmented model and normal and sub-normal directions of the circumferential field coil in the electromagnetic force analysis structure optimization method for the stellarator circumferential field coil described in this embodiment of the invention. Figure 5 This is a schematic diagram of the cable deflection testing device in the stellarator circumferential field coil electromagnetic force analysis and structural optimization method described in this embodiment of the invention; Figure 6 This is a cable load-deflection curve in the structural optimization method for electromagnetic force analysis of the stellarator circumferential field coil described in this embodiment of the invention. Figure 7 This is a finite element model diagram of the circumferential field coil clamp in the stellarator circumferential field coil electromagnetic force analysis structure optimization method described in this embodiment of the invention; Figure 8 This is a graph showing the relationship between clamp spacing and deformation in the electromagnetic force analysis structure optimization method for the circumferential field coil of the stellarator described in this embodiment of the invention. Figure 9 This is a diagram of the clamp structure strength analysis model in the stellarator circumferential field coil electromagnetic force analysis structure optimization method described in this embodiment of the invention; Figure 10This is a diagram showing the stress analysis results of the fixture in the structural optimization method for electromagnetic force analysis of the stellarator circumferential field coil described in this embodiment of the invention. Figure 11 This is a schematic diagram of the structural optimization method for electromagnetic force analysis of the stellarator circumferential field coil described in this embodiment of the invention; Figure 12 This is a schematic diagram of the electromagnetic force analysis and optimization system for the stellarator circumferential field coil described in this embodiment of the invention. Figure 13 This is a schematic diagram of the structure optimization device for electromagnetic force analysis of the stellarator circumferential field coil described in this embodiment of the invention.

[0022] In the diagram: 701, Determination Module; 702, Calculation Module; 703, Decomposition Module; 704, Acquisition Module; 705, Establishment and Optimization Module; 800, Stellarator Circular Field Coil Electromagnetic Force Analysis and Structural Optimization Equipment; 801, Processor; 802, Memory; 803, Multimedia Components; 804, I / O Interface; 805, Communication Components. Detailed Implementation

[0023] To make the objectives, technical solutions, and advantages of the embodiments of the present invention clearer, 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, not all, of the embodiments of the present invention. The components of the embodiments of the present invention described and shown in the accompanying drawings can generally be arranged and designed in various different configurations. Therefore, the following detailed description of the embodiments of the present invention provided in the accompanying drawings is not intended to limit the scope of the claimed invention, but merely to illustrate selected embodiments of the invention. All other embodiments obtained by those skilled in the art based on the embodiments of the present invention without inventive effort are within the scope of protection of the present invention.

[0024] It should be noted that similar reference numerals and letters in the following figures indicate similar items; therefore, once an item is defined in one figure, it does not need to be further defined and explained in subsequent figures. Furthermore, in the description of this invention, terms such as "first," "second," etc., are used only to distinguish descriptions and should not be construed as indicating or implying relative importance.

[0025] Example 1:

[0026] To address the shortcomings of existing technologies, this invention provides a method and system for optimizing the electromagnetic force analysis structure of a stellarator's circumferential field coil. The method involves constructing a joint magnetic field model of the circumferential field coil and modular coils to accurately solve for the electromagnetic volume force distribution. Based on this distribution, the coil is discretized along its centerline into several arc segments for volume integration to obtain the force on each segment and identify peak load regions. The equivalent Young's modulus of the composite cable is determined through cable deflection experiments, providing real material parameters for structural analysis. Furthermore, a clamp-cable coupled finite element model is established to optimize the clamp spacing, number of clamps, and key structural dimensions, achieving precise installation and reliable support of the coil on complex curved surfaces. This effectively suppresses deformation caused by electromagnetic forces, improving magnetic field stability and device operational reliability.

[0027] This embodiment provides a method for optimizing the electromagnetic force analysis structure of a stellarator circumferential field coil.

[0028] See Figure 11 The figure shows that the method includes steps S100, S200, S300, S400 and S500.

[0029] S100. Based on the geometric characteristics of the vacuum chamber and the spatial constraints of the external modular coil, determine the arrangement parameters of the stellarator circumferential field coil so that the coil is wound close to the outer surface of the vacuum chamber.

[0030] It is understood that step S100 includes S101, S102, and S103, wherein: S101. Obtain the structural details of the outer surface of the vacuum chamber and the installation position of the modular coil, analyze the available installation gap and mechanical interference constraints, and obtain the boundary of the area where the coil can be arranged. S102. Based on the boundary of the coil placement area, the stellarator circumferential field coil is designed as multiple planar coils arranged along the circumferential direction, and the number of coils and coverage range are determined. According to the number of coils and coverage range, a grouped cyclic arrangement method is adopted to determine the geometric shape change law of the coils in each group. S103. Utilizing the geometric shape variation patterns of the coils within each group, the coil centerline is defined as a similar curve with a fixed offset distance relative to the outer surface of the vacuum chamber, thus obtaining the coil spatial path parameters. Using these parameters, the coil is wound in a manner directly attached to the outer surface of the vacuum chamber, formed by multiple turns of multi-strand cable wound along the outer wall of the vacuum chamber. Figure 1 As shown.

[0031] It should be noted that in this embodiment, the electromagnetic effects experienced by the coil under operating conditions are accurately assessed, and the reliability design of the support structure is completed accordingly, thereby effectively suppressing coil deformation and improving the stability of the device operation. This includes the following steps: Step 1: The design of the circumferential field coils begins by determining the arrangement area based on the three-dimensional geometric features of the outer surface of the stellarator's vacuum chamber and the spatial constraints of external components. By analyzing the complete external shape data of structural details such as window openings, weld protrusions, and supports on the outer surface of the vacuum chamber, combined with the installation positions of the external modular coils (MCs) and available installation gaps, a spatial constraint analysis is performed on the coil placement area. Based on this, to ensure the circumferential magnetic field is continuous and uniform within a 360° range, and to avoid mechanical interference between the coils and the outer surface of the vacuum chamber or external components, the circumferential field coils are designed as twelve planar coils arranged circumferentially, using four groups of cyclical arrangement. Each group contains three coils with different geometric shapes: the first circumferential field coil, the second circumferential field coil, and the third circumferential field coil (TFC10, TFC32, TFC70). Each group covers a 90° circumferential range, enabling the twelve coils to achieve periodic repetition and geometric continuity throughout the entire circumferential direction. The coils are wound by directly contacting the outer surface of the vacuum chamber. Each coil is made by winding a cable around the outer wall of the vacuum chamber sixteen times, and the shape of the vacuum chamber is used as a natural support surface to ensure that the coils maintain a stable geometric position during installation.

[0032] S200. Construct a three-dimensional geometric model of the coil using the layout parameters, calculate the coil's self-magnetic field distribution, and superimpose it with the modular coil's magnetic field to form a joint magnetic field model, and solve for the electromagnetic volume force distribution.

[0033] It is understood that step S200 includes S201, S202, S203, and S204, wherein: S201. Using the coil spatial path parameters, number of coils, coil grouping method, and spatial relationship between the coil and the vacuum chamber as input, construct a three-dimensional geometric model of the stellarator circumferential field coil, and equate the coil cross-section to a circular cross-section to obtain the coil geometric model. S202. Apply corresponding operating currents to coils with different geometric shapes in the coil geometric model, and solve for the magnetic field distribution generated by the coil based on the Biot-Savart law to obtain the coil's self-magnetic field distribution. The calculation formula in the form of infinitesimal elements is as follows: In the formula, This represents the minute magnetic induction intensity produced by a current element at a certain point in space. It is the vacuum permeability. It is the current intensity in the conductor. It is a tiny length element vector along the direction of the current. Pi It is the position vector pointing from the current element to the desired field point. It is the straight-line distance from the current element to the field point; S203. Superimpose the self-magnetic field distribution of the coil with the magnetic field generated by the modular coil to construct a joint magnetic field model; S204. The coil region is meshed. Based on the above magnetic field model, the volume force density is calculated using the electromagnetic force density formula. The electromagnetic volume force distribution is obtained under the conditions of only the stellarator circumferential field coil operating and the stellarator circumferential field coil and the modular coil operating simultaneously. The formula for calculating the volume force density is as follows: In the formula, For volume force density, It is the current density vector. is the magnetic induction intensity vector.

[0034] Specifically, in step two, based on the circumferential field coil arrangement results obtained in step one, the coil center path, number of coils, coil grouping method, and spatial relationship between the coils and the vacuum chamber are used as inputs for geometric modeling to construct a three-dimensional geometric model of the circumferential field coils. Since the circumferential field coils are arranged to fit against the outer surface of the vacuum chamber, to ensure the model reflects the actual spatial position of the coils while maintaining the efficiency of electromagnetic field calculation, the coil cross-section is equivalent to a circular cross-section with a diameter of 40mm, where 40mm represents the outer diameter of the equivalent conductor, used to replace the actual multi-strand composite cable structure. In the coil path construction, the coil centerline is defined as a similar curve offset by 20mm relative to the outer surface of the vacuum chamber, where the 20mm offset represents the minimum normal distance between the coil centerline and the outer surface of the vacuum chamber. After completing the three-dimensional geometric model, operating currents are applied to the three types of coils, and the magnetic field distribution generated by the coils is solved using electromagnetic field simulation software to verify the rationality of the coil arrangement in step one. The magnetic field calculation is based on the Biot-Saffar law, and its infinitesimal form is: in, It represents the tiny magnetic induction intensity (i.e., the elementary magnetic field) generated by a current element at a certain point in space. It is the vacuum permeability; It is the current intensity in the conductor; It is a tiny length element vector along the direction of the current. Pi; It is the position vector pointing from the current element to the desired field point; It is the straight-line distance from the current element to the field point (i.e. (Modulus length). By integrating over the entire coil path, the magnetic field distribution of the circumferential field coil in space can be obtained.

[0035] Step 3: Based on the magnetic field distribution of the toroidal field coil (TFC) obtained in Step 2, it is superimposed with the magnetic field generated by the modular coil (MC) of the device to construct a TFC-MC joint magnetic field model. This joint magnetic field model is imported into ANSYS / Maxwell, and the coil region is automatically meshed with over 10,000 mesh elements to ensure spatial resolution and numerical accuracy for electromagnetic force density calculation. Based on this, by applying the electromagnetic volume force vector to the mesh elements used in structural analysis, the volume force vector distribution under the TFC-only operation condition and the TFC system volume force vector distribution under the simultaneous operation condition of TFC and MC are obtained. The volume force density is calculated based on the electromagnetic force density formula: In the formula, This is the volume force density (vector), which is the electromagnetic force per unit volume. It is the current density vector. is the magnetic induction intensity vector.

[0036] S300. Based on the electromagnetic volume force distribution, the coil is discretized into several arc segments along the center line. The volume force density is decomposed into normal and subnormal components and integrated to obtain the normal and subnormal forces of each arc segment. The peak load region is identified and the equivalent load of a single-turn coil is extracted.

[0037] It is understood that step S300 includes S301, S302, and S303, wherein: S301. Based on the electromagnetic volume force distribution, the stellarator circumferential field coil is divided into several geometrically continuous arc segments along its centerline, and the number of arc segments and the length of each arc segment are determined; the cross-sectional area of ​​the coil is multiplied by the length of each arc segment to obtain the volume of each arc segment. S302. Decompose the force on each arc segment into normal and subnormal components in the local coordinate system to obtain the distribution of normal and subnormal forces on each arc segment. The normal component corresponds to the circumferential tension in the coil plane, and the subnormal component corresponds to the lateral tension difference of the coil. Using the volume of each arc segment as the integration region, perform volume integration of the volume force density in the normal and subnormal squares to obtain the normal and subnormal forces on each arc segment. S303. Based on the distribution of normal force and sub-normal force in each arc segment, identify the peak force region, convert the total force of the arc segment into the equivalent force of a single-turn coil, and obtain the equivalent load of a single-turn coil.

[0038] S400: To address the cable stiffness requirements of the equivalent load of a single-turn coil, the equivalent Young's modulus of the composite cable is determined through a cable deflection test to obtain the cable's equivalent elastic modulus parameters.

[0039] It is understood that in this step, S400 includes S401, S402, S403, and S404, wherein: S401. Fix both ends of the cable to form a simply supported beam structure, apply a vertical load at the center of the span, measure the deflection change of the cable under the load, and obtain load-deflection data. S402. Set up multiple sets of experimental conditions with different fixed lengths and different loads, perform linear fitting on the load-deflection data of each set of experiments, and obtain the slope of the deflection-load curve. S403. Using the simply supported beam bending theory, the equivalent Young's modulus of the cable is calculated based on the slope of the deflection-load curve. The calculation formula is as follows: In the formula, L is the fixed length at both ends of the cable. δ is the moment of inertia of the cable cross section, W is the cable deflection, E is the Young's modulus, D is the cable diameter, and π is pi. S404. The equivalent Young's modulus calculated from all experimental groups is averaged to obtain the final equivalent elastic modulus parameter of the cable.

[0040] Specifically, in step four, based on the volumetric force density distribution under the two operating conditions obtained in step three, the circumferential field coil is divided into several geometrically continuous arc segments of appropriate length along its centerline, and the volume of each arc segment is used as the integration region. To verify the rationality of the arc segment division, the integrated force is divided by the cross-sectional area of ​​the coil to obtain the equivalent volumetric force density, which is then compared with the volumetric force density directly calculated in step three. The two are consistent in spatial distribution and order of magnitude, thus proving that the arc segment division meets the accuracy requirements of force analysis. In terms of force direction processing, the volumetric force density is decomposed into two components in the local coordinate system: the normal direction and the subnormal direction. The normal direction represents the circumferential tension direction of the planar coil within its own plane, and the subnormal direction represents the direction of the tension difference between the left and right sides of the coil. Through coordinate transformation of the volumetric force density, the normal component and the subnormal component can be obtained separately, and the total force vector of the arc segment can be obtained through volume integration, the infinitesimal form of which is: Where d is the differential symbol, This is the volume force density (vector), which is the electromagnetic force per unit volume. It is the current density vector. Let V be the magnetic flux density vector, and V be the volume. For volume force The projection component in the normal direction n For volume force The projection component in the subnormal direction b, where i is the number of each component. , The components are subjected to forces in the normal and subnormal directions after being divided. The volume of this component. The length of the component, , This represents the normal and subnormal forces acting on the component per unit length. By analyzing the normal and subnormal forces across all arc segments, the peak force is identified. Based on this, it is determined whether clamps need to be placed on the coil to limit its displacement. Dividing by 16 yields the equivalent maximum force on a single-turn coil, providing input for subsequent support structure design.

[0041] S500, combining the equivalent load and equivalent elastic modulus parameters of a single-turn coil, establish a clamp-cable coupling finite element model, set the contact conditions and load boundaries between conductors, optimize the clamp spacing and arrangement quantity, determine the key structural dimensions of the clamp, and verify the strength criteria.

[0042] It is understood that in this step, S500 includes S501, S502, and S503, wherein: S501. Based on the equivalent load and equivalent elastic modulus parameters of a single-turn coil, a finite element analysis model of the clamp and multiple cables is established, and contact constraint conditions between conductors are set to obtain the clamp-cable coupling finite element model. S502. Apply normal and subnormal electromagnetic force components as load boundaries to the clamp-cable coupling finite element model, analyze the cable deflection response under different clamp spacings, and obtain the relationship curve between clamp spacing and deflection. S503. Based on the relationship curve between clamp spacing and deflection, determine the maximum allowable clamp spacing with the deflection limit as a constraint to obtain the optimized clamp spacing; based on the optimized clamp spacing and the actual arc length of the coil, calculate the number of clamps so that the clamps are evenly distributed along the entire length of the coil.

[0043] It should be noted that the determination of key structural dimensions of the fixture and verification of strength criteria include: Based on the optimized fixture spacing and number of fixtures, a detailed model of the fixture structure is established; electromagnetic loads are applied to the detailed model of the fixture structure for strength analysis to obtain the stress distribution of the fixture; Based on the stress distribution of the fixture, the key parameters of the cover plate thickness and weld size were optimized to obtain the optimized fixture structure dimensions, and the optimized fixture structure dimensions were verified to meet the strength criteria.

[0044] After determining the key structural dimensions of the fixture and verifying the strength criteria, the process also includes: During coil operation, the coil temperature distribution is monitored to obtain real-time monitoring data; The system compares real-time monitoring data with preset thresholds. When the data exceeds the preset threshold, an alert is issued; otherwise, monitoring continues.

[0045] Specifically, in step five, based on the segmented stress results of the coil obtained in step four, to accurately reflect the true deformation behavior of the circumferential field coil under electromagnetic force in the structural finite element analysis, it is also necessary to obtain the equivalent Young's modulus of the actual cable used in the coil. Since this cable is a commercially available standard composite cable, composed of multiple materials such as copper stranded wire, insulation layer, and outer sheath, its overall mechanical properties cannot be directly described by a single material parameter. Therefore, it is necessary to determine the equivalent Young's modulus of the actual cable through experimental methods. To this end, a simple mechanical experimental setup is constructed, fixing both ends of the cable to form a simply supported beam structure with a span of L. A vertical load W is applied at the center of the span, and the deflection δ generated by the cable under load is measured, thereby obtaining the deflection-load-length relationship of the actual cable under stress. To improve the stability and representativeness of the experimental results, several sets of experimental conditions with different fixed lengths L and different loads W are set. The deflection-load curve of each set of experiments is linearly fitted to obtain the slope δ / W, and the equivalent Young's modulus E of the actual cable is calculated accordingly. The formula for calculating the equivalent Young's modulus is: Where L is the fixed length at both ends of the cable, I is the moment of inertia of the cable section, δ is the cable deflection, W is the load, E is Young's modulus, and D is the cable diameter. Let π be the mathematical constant pi. The equivalent Young's modulus of the real cable is obtained by averaging the Young's moduli calculated from all experimental groups.

[0046] Step Six: Based on the coil stress obtained in Step Four, derive the equivalent maximum force of a single-turn coil and the equivalent Young's modulus of the cable obtained in Step Five. Establish several clamps and place at least two cables on one side of each clamp to form a finite element analysis model. Establish two contact conditions between conductors: fully bonded and non-separated. Define the two contact conditions between conductors: fully bonded and non-separated. In the fully bonded type, adjacent cables are bonded at the surface with no relative displacement. In the non-separated type, adjacent cables are in contact, but they may slip without friction. Apply normal force components and sub-normal force components to the two contact conditions respectively, and set the equivalent Young's modulus of the cable and assume the Young's modulus of the clamps. Perform finite element simulation analysis to analyze the relationship between clamp spacing and deflection. The actual working condition is between the fully bonded and non-separated types, with a greater bias towards the fully bonded type. Considering that excessive coil deformation may affect the magnetic field distribution generated by the circumferential field coil, the clamp spacing with a cable deflection of less than 1.0 mm under the fully bonded condition is taken as the maximum allowable spacing to meet the design requirements. After determining the maximum allowable clamp spacing, in order to ensure the uniformity of the clamp arrangement along the entire length of the coil, the number of clamps is calculated based on the actual arc length of the circumferential field coil, so that the clamps are evenly distributed along the entire coil path, thereby ensuring the overall stability and force consistency of the coil under electromagnetic force.

[0047] Step 7: Based on the clamp spacing and number of clamps determined in Step 6, establish a three-dimensional clamp structure model including the clamp body, clamp cover plate, and the coil cable in contact with it. Apply the normal force and sub-normal force obtained in Step 6 as structural loads to the model. Perform finite element analysis on the entire clamp structure to obtain the stress distribution under electromagnetic force. The analysis results show that the stress is mainly concentrated in the middle of the clamp cover plate and the fillet weld area at the connection between the cover plate and the clamp body. The stress in other structural areas is significantly lower than the allowable stress of the material.

[0048] Based on this, the focus of structural optimization was placed on two key parameters: the thickness of the fixture cover plate and the size of the fillet weld leg. Parametric simulations were performed on different size combinations to determine the structural dimensions capable of withstanding the corresponding strain requirements. To prevent the coil temperature from exceeding the insulation material's tolerance limit (180℃) due to heat conduction during vacuum chamber baking and coil operation, a real-time temperature monitoring system based on a type K thermocouple was constructed. A type K thermocouple was selected as the temperature sensor, and the thermocouple compensation wires used a glass fiber insulation layer, as glass fiber has excellent high-temperature resistance. Polyimide high-temperature tape (temperature resistance above 200℃) was used to fix the thermocouple sensing end to the coil surface, ensuring a tight fit between the thermocouple and the measured surface.

[0049] To improve temperature measurement accuracy, thermally conductive silicone grease is applied between the thermocouple sensing end and the coil surface during installation to fill tiny gaps and improve thermal contact. In each coil group, temperature monitoring points are set at the midpoint between two adjacent clamps, on the left and right sides of the coil, and between the layers of two coils, respectively, thus achieving comprehensive monitoring of the coil temperature during vacuum chamber baking and normal coil operation. Fiberglass insulated compensating wires transmit the thermocouple signals to the data acquisition module of the central monitoring system, displaying the temperature at each measuring point in real time and including a temperature change rate monitoring function. Based on the maximum temperature resistance of 180℃ for the circumferential field coil insulation material, when the temperature at any measuring point reaches 160℃, the system issues an alarm signal, prompting the operator to pay attention to the temperature change trend and reduce the baking heating power; when the temperature reaches or exceeds 180℃, the system immediately cuts off the baking heating power, stops vacuum chamber heating, issues an alarm, and marks the over-temperature location on the monitoring interface.

[0050] Example 2:

[0051] In this embodiment, the design of the circumferential field coils is first based on the three-dimensional geometric features of the outer surface of the stellarator vacuum chamber and the spatial constraints of external components to determine the arrangement area. By analyzing the complete external shape data of structural details such as window openings, weld protrusions, and supports on the outer surface of the vacuum chamber, combined with the installation position of the external modular coils (MCs) and available installation gaps, a spatial constraint analysis is performed on the coil arrangement area. Based on this, to ensure the circumferential magnetic field is continuous and uniform within a 360° range, and to avoid mechanical interference between the coils and the outer surface of the vacuum chamber or external components, the circumferential field coils are designed as twelve planar coils arranged circumferentially, using four groups of cyclical arrangement. Each group contains three coils with different geometric shapes: the first circumferential field coil, the second circumferential field coil, and the third circumferential field coil (TFC10, TFC32, TFC70). Each group covers a 90° circumferential range, enabling the twelve coils to achieve periodic repetition and geometric continuity throughout the entire circumferential direction. The coils are wound by directly contacting the outer surface of the vacuum chamber. Each coil is made by winding a cable around the outer wall of the vacuum chamber sixteen times, and the shape of the vacuum chamber is used as a natural support surface to ensure that the coils maintain a stable geometric position during installation.

[0052] Based on the obtained circumferential field coil arrangement results, the coil center path, number of coils, coil grouping method, and spatial relationship between the coils and the vacuum chamber were used as inputs for geometric modeling to construct a three-dimensional geometric model of the circumferential field coils. Since the circumferential field coils are arranged to fit against the outer surface of the vacuum chamber, to ensure the model reflects the actual spatial position of the coils while maintaining the efficiency of electromagnetic field calculations, the coil cross-section was equivalent to a circular cross-section with a diameter of 40mm, where 40mm represents the outer diameter of the equivalent conductor, used to replace the complex composite cable structure actually composed of multiple copper strands, insulation layers, and sheaths. In the coil path construction, the coil centerline was defined as a similar curve offset by 20mm relative to the outer surface of the vacuum chamber, where the 20mm offset represents the minimum normal distance between the coil centerline and the outer surface of the vacuum chamber. After completing the three-dimensional geometric model, operating currents were applied to three types of coils: 32kA for TFC10, 48kA for TFC32, and 48kA for TFC70. Electromagnetic field simulation software was used to solve for the magnetic field distribution generated by the coils to verify the rationality of the coil arrangement in step one. The magnetic field calculation is based on the Biot-Saffar law, and its infinitesimal form is: in, It represents the tiny magnetic induction intensity (i.e., the elementary magnetic field) generated by a current element at a certain point in space. It is the vacuum permeability; It is the current intensity in the conductor; It is a tiny length element vector along the direction of the current. Pi; It is the position vector pointing from the current element to the desired field point; It is the straight-line distance from the current element to the field point (i.e. (Modulus length). By integrating over the entire coil path, the magnetic field distribution of the circumferential field coil in space can be obtained. The results are as follows: Figure 2 As shown, TFC generates a magnetic field distribution in the vacuum chamber that is predominantly circumferential.

[0053] Based on the obtained magnetic field distribution of the toroidal field coil (TFC), it was superimposed with the magnetic field generated by the modular coil (MC) of the device (MC coil current set to 312.5kA) to construct a TFC-MC joint magnetic field model. This joint magnetic field model was imported into ANSYS / Maxwell, and the coil region was automatically meshed with over 10,000 mesh elements to ensure spatial resolution and numerical accuracy for electromagnetic force density calculation. Furthermore, by applying the electromagnetic volume force vector to the mesh elements used in structural analysis, the volume force vector distribution under the TFC-only operating condition and the TFC system's volume force vector distribution under the simultaneous operation of TFC and MC were obtained. Figure 3This only shows an example of the volume force vector under TFC operating conditions. The calculation of the volume force density is based on the electromagnetic force density formula: This is the volume force density (vector), which is the electromagnetic force per unit volume. It is the current density vector. is the magnetic induction intensity vector.

[0054] Secondly, to derive the requirements of the support structure, it is necessary to analyze the force distribution integrated on the coil cross-section. However, ANSYS / Maxwell does not have the ability to integrate three-dimensional vectors on complex surfaces. Therefore, the coil is divided into 10 suitable large components, and the force volume integration is performed on each component. The model shape of each TFC divided into 10 components is as follows: Figure 4 As shown in Table 1, the node coordinates of the TFC are divided into several parts. Each node corresponds to the arc length of each element in the TFC. These models are simplified to understand the characteristics of the electromagnetic force distribution. Each TFC is divided into 10 parts. Here, n is the normal vector, corresponding to the hoop force; b is the subnormal vector, corresponding to the toroidal force. N1~N10 are the names of the nodes, and P1~P10 are the names of each element after TFC division. In terms of force direction, the volume force density is decomposed into two components in the local coordinate system: the normal direction and the subnormal direction. The normal direction represents the hoop force direction of the planar coil within its own plane, and the subnormal direction represents the direction of the tension difference between the left and right sides of the coil. Through coordinate transformation of the volume force density, the normal component and the subnormal component can be obtained separately, and the total force vector of the arc segment can be obtained through volume integrals. Its infinitesimal form is: Where d is the differential symbol, This is the volume force density (vector), which is the electromagnetic force per unit volume. It is the current density vector. Let V be the magnetic flux density vector, and V be the volume. For volume force The projection component in the normal direction n For volume force The projection component in the subnormal direction b, where i is the number of each component. , The components are subjected to forces in the normal and subnormal directions after being divided. The volume of this component. The length of the component, , This refers to the forces acting on the component per unit length in the normal and subnormal directions.

[0055] The total force obtained by integration is then divided by the cross-sectional area of ​​the coil to obtain the equivalent volumetric force density. This is compared with the volumetric force density calculated directly earlier. The two are consistent in spatial distribution and order of magnitude, proving that the arc segment division meets the accuracy requirements of force analysis. Subsequently, by analyzing the normal and sub-normal forces of all arc segments, the peak force regions are identified, and it is determined whether clamps need to be placed in these regions to restrict coil displacement. This provides input for the subsequent design of the support structure, as shown in Table 1 below: Table 1. Coordinates of TFC Segment Nodes The electromagnetic force analysis results are shown in Tables 2 and 3. The total force vector was obtained using the volume integral function in ANSYS / Maxwell. The surface force density was calculated through coordinate transformation. n f represents the normal component. b This represents the subnormal component. The normal component is the circumferential tension of the planar coil, while the subnormal component is the difference between the left and right tensions of the coil.

[0056] Table 2 shows the electromagnetic force distribution when only TFC is running (for temperature rise tests, etc.). Normal force f n It may act on the coil. It has a directional component that causes the coil to expand; it is a self-load. For example... Figure 4 As shown, the outer side of TFC10, TFC32, and the entire TFC70 have convex surfaces similar to those of a typical circular coil. Normal loads acting on these convex surfaces can likely be easily supported by the tensile stiffness of the conductors alone. The inner sides of TFC10 and TFC32 have concave surfaces. Since the conductor stiffness may be ineffective against these concave surfaces, clamps are required to secure the conductors to the vacuum chamber. Furthermore, since the maximum load of 2200 N / m is not very large, deformation is expected to be easily reduced by utilizing the conductor stiffness or by using clamps to secure the coils.

[0057] Table 3 shows the electromagnetic force distribution when TFC and MC currents operate simultaneously. The polarity of the TFC current increases with the rotational transformation of the MC current. In this case, the normal force component is negative, meaning the coil will be pressed against the vacuum chamber. Furthermore, due to the substantial maximum load of 37,000 N / m, the coil may displace relative to the vacuum chamber in both the circumferential and normal directions. Strengthening the structure is crucial to reducing coil deformation, as shown in Tables 2 and 3 below: Table 2 Electromagnetic force distribution under TFC operating conditions only Table 3 Electromagnetic force distribution under simultaneous operation of TFC and MC The only possibility to achieve this function is to use clamps to secure the 16 cables to the vacuum chamber. The cables must be clamped to the vacuum chamber at appropriate intervals to suppress deflection. However, it is necessary to determine the clamp spacing that will keep the deflection below a suitable value.

[0058] In other words, assessing cable deflection requires knowing the cable's Young's modulus. However, since cables are composed of composite materials (copper strands, insulation, and sheath), and there is no formula for calculating their physical properties for such a complex structure, such data is unavailable. Therefore, a commercially available standard cable was procured, and the equivalent Young's modulus was obtained experimentally from the relationship between load and deflection. The stranded CV cable used for TFC has an outer diameter of 11 mm. CV is an abbreviation for cross-linked polyethylene insulation and PVC sheath. Because it is easily bent by hand, it is expected to be easy to wind. To measure the relationship between cable deflection and load, a simple device was developed, such as... Figure 5 As shown, the cable is fixed at both ends, and an upward tension is applied to the middle of the cable. The magnitude of the force and coil deformation are measured, and the relationship between deflection, load, and cable length is studied. To improve the stability and representativeness of the experimental results, several sets of experimental conditions with different fixed lengths L and different loads W are set. The deflection-load curves of each set of experiments are linearly fitted to obtain the slope δ / W, and the equivalent Young's modulus E of the real cable is calculated based on this. The formula for calculating the equivalent Young's modulus is: Where L is the fixed length at both ends of the cable, I is the moment of inertia of the cable section, δ is the cable deflection, W is the load, E is Young's modulus, and D is the cable diameter. Let π be the mathematical constant pi. The equivalent Young's modulus of the real cable is obtained by averaging the Young's moduli calculated from all experimental groups.

[0059] Among them, the measurement results of deflection are as follows: Figure 6 As shown. The slope δ / W of the linear equation is approximated within a small δ range. In practical applications, the cable may experience deflections of less than 1 mm. Based on the slope of the linear equation, the Young's modulus estimated using a beam model with concentrated loads fixed at both ends is 1 GPa.

[0060] Finite element analysis was used to evaluate the relationship between electromagnetic force and cable deflection. Five clamps, each 30 mm wide, were constructed, with two cables placed on one side of each clamp. Figure 7This is an FEM model. Two contact conditions between conductors were assumed, and the analysis results were compared. One is the AB (fully bonded) type, where adjacent cables are bonded at the surface with no relative displacement. The other is the NS (non-separated) type, where adjacent cables are in contact but may slip without friction. The contact conditions of the actual coil can be estimated to be between NS and AB. Assuming the equivalent Young's modulus of the cable is 1 GPa and that of the clamp is 200 GPa, the normal force Fn = 2300 N / m is set based on 1 / 16 of 37000 N / m (approximately 2300 N / m), and the secondary normal force Fb = 1300 N / m is set based on 1 / 16 of 21000 N / m (approximately 1300 N / m). Based on these settings, the relationship between clamp spacing and deflection was evaluated. The results are as follows... Figure 8 As shown in the figure, the deflection varies by approximately three times depending on the contact conditions. Given the significant friction between the conductors in the actual coil, the result is expected to be closer to case AB.

[0061] Considering that excessive coil deformation might affect the magnetic field distribution generated by the circumferential field coil, the clamp spacing with a cable deflection of less than 1.0 mm under fully bonded conditions was taken as the maximum allowable spacing to meet the design requirements. At this point, the normal force is Fn = 2300 N / m, which is 1 / 16 of the maximum electromagnetic force of TFC32 in the normal force component of each cable. To meet this condition, the clamp spacing must be less than 160 mm. Based on this result, the design value of the clamp spacing was determined, as shown in Table 4. A clamp spacing of 140 mm was designed to meet the requirements. When Fn = 2300 N / m, the cable deflection is estimated to be between 0.6 mm and 2.0 mm. The worst-case deflection is estimated to be 2 mm, but since there is sufficient dimensional margin between the vacuum chamber and the modular coil, it is assumed that the TFC will not come into contact with the modular coil. Table 4 is shown below: Table 4. Statistics on TFC Fixture Configuration A fixture for fixing 16 conductors was designed and verified. Finite element analysis was performed to ensure the effectiveness of the design. Figure 9 The analysis model is shown, where the width and height of the fixture slot must meet the requirement of accommodating 16 conductors. The fixture is 152mm long, 30mm wide, and 31mm high. The internal groove for accommodating 16 cables is 88mm long, the cover plate is 8mm long, and the fillet weld is 5mm long. To simulate the stress in the fillet weld, a triangular protrusion is provided at the end of the fixture as a fixed point in the finite element analysis.

[0062] Finite element analysis results as follows Figure 10As shown, the maximum stress on the fixture cover plate is 87 MPa when the normal electromagnetic force component Fn is applied. The maximum stress on the fillet weld is 50 MPa when the secondary normal electromagnetic force component Fb is applied. These stresses are below the design criterion of 137 MPa, therefore the fixture parameters are reasonable.

[0063] In summary, this invention achieves accurate electromagnetic force analysis and reliable structural design of the circumferential field coil on complex curved surfaces, effectively solving the problems of insufficient coil deformation suppression and coil temperature exceeding the tolerance limit of the insulating material in the prior art, and significantly improving the operational safety and stability of the device.

[0064] Example 3:

[0065] like Figure 12 As shown, this embodiment provides a stellarator circumferential field coil electromagnetic force analysis and structural optimization system. See [link to documentation]. Figure 12 The system includes: Determine module 701: Used to determine the arrangement parameters of the stellarator circumferential field coil based on the geometric characteristics of the vacuum chamber and the spatial constraints of the external modular coil, so that the coil is wound in close contact with the outer surface of the vacuum chamber. Calculation module 702: Used to construct a three-dimensional geometric model of the coil using the layout parameters, calculate the coil's self-magnetic field distribution, and superimpose it with the modular coil magnetic field to form a joint magnetic field model, and solve for the electromagnetic volume force distribution; Decomposition module 703: Based on the electromagnetic volume force distribution, the coil is discretized into several arc segments along the center line, the volume force density is decomposed into normal and subnormal components and integrated to obtain the normal and subnormal forces of each arc segment, the peak load region is identified and the equivalent load of a single-turn coil is extracted. Module 704: Used to determine the equivalent Young's modulus of the composite cable through cable deflection tests to meet the cable stiffness requirements of the equivalent load of a single-turn coil, and obtain the equivalent elastic modulus parameters of the cable. Establish optimization module 705: It is used to combine the equivalent load and equivalent elastic modulus parameters of a single-turn coil to establish a clamp-cable coupling finite element model, set the contact conditions and load boundaries between conductors, optimize the clamp spacing and number of clamps, determine the key structural dimensions of the clamps, and verify the strength criteria.

[0066] It should be noted that the specific methods by which each module performs operations in the system described in the above embodiments have been described in detail in the embodiments related to the method, and will not be elaborated here.

[0067] Example 4:

[0068] Corresponding to the above method embodiments, this embodiment also provides a stellarator circumferential field coil electromagnetic force analysis structure optimization device. The stellarator circumferential field coil electromagnetic force analysis structure optimization device described below and the stellarator circumferential field coil electromagnetic force analysis structure optimization method described above can be referred to in correspondence.

[0069] Figure 13 This is a block diagram illustrating a stellarator circumferential field coil electromagnetic force analysis and structure optimization device 800 according to an exemplary embodiment. Figure 13 As shown, the stellarator toroidal field coil electromagnetic force analysis and structure optimization device 800 includes a processor 801 and a memory 802. The stellarator toroidal field coil electromagnetic force analysis and structure optimization device 800 also includes one or more of a multimedia component 803, an I / O interface 804, and a communication component 805.

[0070] The processor 801 controls the overall operation of the stellarator circumferential field coil electromagnetic force analysis and structure optimization device 800 to complete all or part of the steps in the aforementioned stellarator circumferential field coil electromagnetic force analysis and structure optimization method. The memory 802 stores various types of data to support the operation of the stellarator circumferential field coil electromagnetic force analysis and structure optimization device 800. This data may include, for example, instructions for any application or method operating on the stellarator circumferential field coil electromagnetic force analysis and structure optimization device 800, as well as application-related data, such as contact data, sent and received messages, images, audio, video, etc. The memory 802 can be implemented using any type of volatile or non-volatile storage device or a combination thereof, such as Static Random Access Memory (SRAM), Electrically Erasable Programmable Read-Only Memory (EEPROM), Erasable Programmable Read-Only Memory (EPROM), Programmable Read-Only Memory (PROM), Read-Only Memory (ROM), magnetic storage, flash memory, magnetic disk, or optical disk. The multimedia component 803 may include a screen and an audio component. The screen may be, for example, a touchscreen, and the audio component is used to output and / or input audio signals. For example, the audio component may include a microphone for receiving external audio signals. The received audio signals may be further stored in the memory 802 or transmitted via the communication component 805. The audio component also includes at least one speaker for outputting audio signals. I / O interface 804 provides an interface between processor 801 and other interface modules, such as a keyboard, mouse, or buttons. These buttons can be virtual or physical. Communication component 805 is used for wired or wireless communication between the stellarator toroidal field coil electromagnetic force analysis structure optimization device 800 and other devices. Wireless communication includes, for example, Wi-Fi, Bluetooth, Near Field Communication (NFC), 2G, 3G, or 4G, or one or more combinations thereof. Therefore, the corresponding communication component 805 may include a Wi-Fi module, a Bluetooth module, or an NFC module.

[0071] In an exemplary embodiment, the stellarator toroidal field coil electromagnetic force analysis and structure optimization device 800 may be implemented by one or more application-specific integrated circuits (ASICs), digital signal processors (DSPs), digital signal processing devices (DSPDs), programmable logic devices (PLDs), field-programmable gate arrays (FPGAs), controllers, microcontrollers, microprocessors, or other electronic components to perform the stellarator toroidal field coil electromagnetic force analysis and structure optimization method described above.

[0072] In another exemplary embodiment, a computer-readable storage medium including program instructions is also provided. When executed by a processor, these program instructions implement the steps of the stellarator toroidal field coil electromagnetic force analysis structure optimization method described above. For example, the computer-readable storage medium may be the memory 802 including the program instructions described above. These program instructions may be executed by the processor 801 of the stellarator toroidal field coil electromagnetic force analysis structure optimization device 800 to complete the stellarator toroidal field coil electromagnetic force analysis structure optimization method described above.

[0073] Example 5:

[0074] Corresponding to the above method embodiments, this embodiment also provides a readable storage medium. The readable storage medium described below can be referred to in conjunction with the stellarator circumferential field coil electromagnetic force analysis structure optimization method described above.

[0075] A computer program is stored on a readable storage medium, and when the computer program is executed by a processor, it implements the steps of the stellarator circumferential field coil electromagnetic force analysis structure optimization method of the above method embodiments.

[0076] Specifically, the readable storage medium can be a USB flash drive, external hard drive, read-only memory (ROM), random access memory (RAM), magnetic disk, or optical disk, or any other readable storage medium capable of storing program code.

[0077] The above description is merely a preferred embodiment of the present invention and is not intended to limit the present invention in any way. Although the present invention has been disclosed above with reference to preferred embodiments, it is not intended to limit the present invention. Any person skilled in the art can make some modifications or alterations to the above-disclosed technical content to create equivalent embodiments without departing from the scope of the present invention. Any simple modifications, equivalent changes and alterations made to the above embodiments based on the technical essence of the present invention without departing from the scope of the present invention shall still fall within the scope of the present invention.

Claims

1. A method for optimizing the electromagnetic force analysis structure of a stellarator's circumferential field coil, characterized in that, include: Based on the geometric characteristics of the vacuum chamber and the spatial constraints of the external modular coils, the arrangement parameters of the stellarator circumferential field coils are determined so that the coils are wound in close contact with the outer surface of the vacuum chamber. A three-dimensional geometric model of the coil is constructed using the layout parameters. The distribution of the coil's self-magnetic field is calculated and superimposed with the magnetic field of the modular coil to form a joint magnetic field model. The distribution of electromagnetic volume force is then solved. Based on the electromagnetic volume force distribution, the coil is discretized into several arc segments along the center line. The volume force density is decomposed into normal and subnormal components and integrated to obtain the normal and subnormal forces of each arc segment. The peak load region is identified and the equivalent load of a single-turn coil is extracted. To address the stiffness requirements of the cable under the equivalent load of a single-turn coil, the equivalent Young's modulus of the composite cable was determined through cable deflection experiments, thereby obtaining the cable's equivalent elastic modulus parameters. By combining the equivalent load and equivalent elastic modulus parameters of a single-turn coil, a finite element model of clamp-cable coupling is established. The contact conditions and load boundaries between conductors are set, the clamp spacing and number of clamps are optimized, the key structural dimensions of the clamps are determined, and the strength criteria are verified.

2. The method for analyzing and optimizing the electromagnetic force of the circumferential field coil of a stellarator according to claim 1, characterized in that, The arrangement parameters of the stellarator circumferential field coils are determined based on the geometric characteristics of the vacuum chamber and the spatial constraints of the external modular coils, so that the coils are wound close to the outer surface of the vacuum chamber. This includes: Obtain the structural details of the outer surface of the vacuum chamber and the installation position of the modular coils, analyze the available installation gaps and mechanical interference constraints, and obtain the boundary of the area where the coils can be arranged. Based on the boundary of the coil placement area, the stellarator circumferential field coils are designed as multiple planar coils arranged along the circumferential direction, and the number of coils and coverage area are determined. According to the number of coils and coverage area, a grouped cyclic arrangement method is adopted to determine the geometric shape variation law of the coils in each group. By utilizing the geometric shape variation law of the coils in each group, the center line of the coil is defined as a similar curve with a fixed offset distance relative to the outer surface of the vacuum chamber, and the spatial path parameters of the coil are obtained. Using the spatial path parameters of the coil, the coil is wound in a way that directly adheres to the outer surface of the vacuum chamber, and is formed by winding multiple strands of cable around the outer wall of the vacuum chamber multiple times.

3. The method for analyzing and optimizing the electromagnetic force of the circumferential field coil of a stellarator according to claim 2, characterized in that, Based on the boundary of the coil placement area, the stellarator circumferential field coils are designed as multiple planar coils arranged circumferentially, determining the number of coils and their coverage area, including: The stellarator's circumferential field coils are designed as twelve planar coils arranged circumferentially, using four groups of cyclical arrangement. Each group covers a 90° circumferential range, and each group contains three different geometric shapes of circumferential field coils: the first circumferential field coil, the second circumferential field coil, and the third circumferential field coil.

4. The method for analyzing and optimizing the electromagnetic force of the circumferential field coil of a stellarator according to claim 1, characterized in that, The process involves constructing a three-dimensional geometric model of the coil using layout parameters, calculating the coil's self-magnetic field distribution, and superimposing this model with the modular coil's magnetic field to form a joint magnetic field model. This model is then used to solve for the electromagnetic volume force distribution, including: Using the coil spatial path parameters, number of coils, coil grouping method, and spatial relationship between the coils and the vacuum chamber as inputs, a three-dimensional geometric model of the stellarator circumferential field coil is constructed. The coil cross-section is equivalent to a circular cross-section to obtain the coil geometric model. By applying corresponding operating currents to coils of different geometric shapes in the coil geometric model, and solving for the magnetic field distribution generated by the coil based on the Biot-Saffar law, the self-magnetic field distribution of the coil is obtained. The calculation formula in the form of infinitesimal elements is as follows: In the formula, This represents the minute magnetic induction intensity produced by a current element at a certain point in space. It is the vacuum permeability. It is the current intensity in the conductor. It is a tiny length element vector along the direction of the current. Pi It is the position vector pointing from the current element to the desired field point. It is the straight-line distance from the current element to the field point; A joint magnetic field model is constructed by superimposing the self-magnetic field distribution of the coil with the magnetic field generated by the modular coil. The coil region was meshed, and the volume force density was calculated using the electromagnetic force density formula based on the magnetic field model. The electromagnetic volume force distribution was obtained under the following conditions: only the stellarator circumferential field coil was operating, and both the stellarator circumferential field coil and the modular coil were operating simultaneously. The formula for calculating the volume force density is as follows: In the formula, For volume force density, It is the current density vector. is the magnetic induction intensity vector.

5. The method for analyzing and optimizing the electromagnetic force of the circumferential field coil of a stellarator according to claim 1, characterized in that, Based on the electromagnetic volume force distribution, the coil is discretized into several arc segments along the centerline. The volume force density is decomposed into normal and subnormal components and integrated to obtain the normal and subnormal forces in each arc segment. The peak load region is identified and the equivalent load of a single-turn coil is extracted, including: Based on the electromagnetic volume force distribution, the stellarator's circumferential field coil is divided into several geometrically continuous arc segments along its centerline, and the number of arc segments and the length of each arc segment are determined. The forces on each arc segment are decomposed into normal and subnormal components in the local coordinate system to obtain the distribution of normal and subnormal forces on each arc segment. The normal component corresponds to the circumferential tension in the coil plane, and the subnormal component corresponds to the lateral tension difference of the coil. The cross-sectional area of ​​the coil is multiplied by the length of each arc segment to obtain the volume of each arc segment. Using the volume of each arc segment as the integration region, the volume force density is integraled on the normal and subnormal components to obtain the total force on the normal and subnormal components of each arc segment. Based on the distribution of normal and secondary normal forces in each arc segment, the peak force region is identified, and the total force of the arc segment is converted into the equivalent force of a single-turn coil to obtain the equivalent load of a single-turn coil.

6. The method for analyzing and optimizing the electromagnetic force of the circumferential field coil of a stellarator according to claim 1, characterized in that, To address the cable stiffness requirement due to the equivalent load of a single-turn coil, the equivalent Young's modulus of the composite cable is determined through cable deflection experiments to obtain the cable's equivalent elastic modulus parameters, including: The two ends of the cable are fixed to form a simply supported beam structure. A vertical load is applied at the center of the span, and the deflection change of the cable under the load is measured to obtain load-deflection data. Multiple sets of experimental conditions with different fixed lengths and different loads were set up, and the load-deflection data of each set of experiments were linearly fitted to obtain the slope of the deflection-load curve. Using the bending theory of simply supported beams, the equivalent Young's modulus of the cable is calculated based on the slope of the deflection-load curve. The calculation formula is as follows: In the formula, L is the fixed length at both ends of the cable. δ is the moment of inertia of the cable cross section, W is the cable deflection, E is the Young's modulus, D is the cable diameter, and π is pi. The equivalent Young's modulus calculated from all experimental groups was averaged to obtain the final equivalent elastic modulus parameter of the cable.

7. The method for analyzing and optimizing the electromagnetic force of the circumferential field coil of a stellarator according to claim 1, characterized in that, The method combines the equivalent load and equivalent elastic modulus parameters of a single-turn coil to establish a clamp-cable coupling finite element model, sets the contact conditions between conductors and load boundaries, and optimizes the clamp spacing and number of clamps, including: Based on the equivalent load and equivalent elastic modulus parameters of a single-turn coil, a finite element analysis model of the clamp and multiple cables is established, and contact constraints between conductors are set to obtain a clamp-cable coupling finite element model. Normal and subnormal electromagnetic force components are applied as load boundaries to the clamp-cable coupled finite element model. The cable deflection response under different clamp spacings is analyzed to obtain the relationship curve between clamp spacing and deflection. Based on the relationship curve between clamp spacing and deflection, the maximum allowable clamp spacing is determined with the deflection limit as a constraint, and the optimized clamp spacing is obtained. Based on the optimized clamp spacing and the actual arc length of the coil, the number of clamps is calculated so that the clamps are evenly distributed along the entire length of the coil.

8. The method for analyzing and optimizing the electromagnetic force of the circumferential field coil of a stellarator according to claim 7, characterized in that, The determination of key structural dimensions of the fixture and verification of strength criteria include: Based on the optimized fixture spacing and number of fixtures, a detailed model of the fixture structure is established; electromagnetic loads are applied to the detailed model of the fixture structure for strength analysis to obtain the stress distribution of the fixture; Based on the stress distribution of the fixture, the key parameters of the cover plate thickness and weld size were optimized to obtain the optimized fixture structure dimensions, and the optimized fixture structure dimensions were verified to meet the strength criteria.

9. The method for analyzing and optimizing the electromagnetic force of the circumferential field coil of a stellarator according to claim 1, characterized in that, After determining the key structural dimensions of the fixture and verifying the strength criteria, the process also includes: During coil operation, real-time monitoring data is obtained by monitoring the coil temperature distribution; The system compares real-time monitoring data with preset thresholds. When the data exceeds the preset threshold, an alert is issued; otherwise, monitoring continues.

10. A stellarator circumferential field coil electromagnetic force analysis and structure optimization system, based on the stellarator circumferential field coil electromagnetic force analysis and structure optimization method according to claim 1, characterized in that, include: Determining module: Used to determine the arrangement parameters of the stellarator circumferential field coil based on the geometric characteristics of the vacuum chamber and the spatial constraints of the external modular coil, so that the coil is wound in close contact with the outer surface of the vacuum chamber. Calculation module: Used to construct a three-dimensional geometric model of the coil using the layout parameters, calculate the coil's self-magnetic field distribution, and superimpose it with the modular coil magnetic field to form a joint magnetic field model, and solve for the electromagnetic volume force distribution; Decomposition module: used for Based on the electromagnetic volume force distribution, the coil is discretized into several arc segments along the center line. The volume force density is decomposed into normal and subnormal components and integrated to obtain the normal and subnormal forces of each arc segment. The peak load region is identified and the equivalent load of a single-turn coil is extracted. The module is used to determine the equivalent Young's modulus of the composite cable by measuring the equivalent elastic modulus of the cable through cable deflection experiments, based on the cable stiffness requirements of the equivalent load of a single-turn coil. Establish an optimization module: This module combines the equivalent load and equivalent elastic modulus parameters of a single-turn coil to establish a finite element model of the clamp-cable coupling, set the contact conditions and load boundaries between conductors, optimize the clamp spacing and number of clamps, determine the key structural dimensions of the clamps, and verify the strength criteria.

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