Design method and device for longitudinal field coils of fusion device based on semi-analytical magnetic field calculation

Abstract

The application provides a fusion device longitudinal field coil design method and device based on semi-analytical magnetic field calculation. The method first establishes a parameterized geometric model of the longitudinal field coil and global optimization decision variables; based on the semi-analytical magnetic field integral method, the electromagnetic field coupling calculation of the coil unit is carried out, thereby avoiding the calculation burden of grid partitioning in the traditional numerical method; an electromagnetic mechanics coupled tension fluctuation evaluation model is constructed; a global closed loop optimization is carried out by using a differential evolution algorithm, and a global optimal variable set that minimizes the tension fluctuation rate is output; finally, the accurate analytical trajectory and manufacturing parameters of the optimal coil configuration are generated. The technical effect of the application lies in that the calculation efficiency and accuracy of the longitudinal field coil design are significantly improved, the tension fluctuation in the coil operation is effectively reduced, the operation stability and coil structure reliability of the fusion device are improved, and the accurate geometric parameters for manufacturing can be directly output, thereby shortening the design cycle.

Description

Technical Field

[0001] This invention relates to the technical field of nuclear fusion device design, specifically to a method and apparatus for designing longitudinal field coils for fusion devices based on semi-analytical magnetic field calculations. Background Technology

[0002] In the design of nuclear fusion devices, the longitudinal field coil, as a core component for generating the strong magnetic field required for confined plasma, directly determines the device's operational performance and structural safety. Current technologies face three major bottlenecks in the shape design of longitudinal field coils. First, at the geometric modeling level, traditional designs often rely on free curves or complex spline functions to describe the coil's centerline. While theoretically flexible, this results in a large number of parameters and a lack of clear physical constraints, leading to an excessively high dimensionality in the optimization search space. This makes it prone to getting trapped in local optima, and the generated shape often fails to simultaneously meet the engineering requirements of "ease of fabrication" and "uniform stress distribution." For example, abrupt changes in curve curvature can cause local stress concentration. Second, in the electromagnetic force assessment stage, mainstream methods rely on commercial finite element software (such as ANSYS and COMSOL) for three-dimensional magnetic field and force simulation. While these software programs offer high accuracy, solving for the electromagnetic field distribution of a complete coil system takes approximately ten minutes, and completing a full optimization requires at least thousands of calculations. Finally, regarding optimization strategies, existing technologies lack a global optimization algorithm that can directly embed geometric manufacturability (e.g., the radius of the arc must increase incrementally to avoid processing interference) and physical rationality (e.g., ordered polar angles) as hard constraints into the search process. This often results in distorted solutions that are impractical to manufacture or physically unreasonable, requiring significant manual intervention and post-processing corrections. Therefore, there is an urgent need for a method that can quickly and accurately assess the coil stress and automatically generate a longitudinal field coil shape design that balances manufacturability and stress uniformity. Summary of the Invention

[0003] Based on this, in order to solve the technical problems of low computational efficiency, long iteration cycle and difficulty in quickly optimizing coil geometric parameters and current distribution while ensuring magnetic field accuracy, which rely on full numerical simulation for the design of longitudinal field coils in existing fusion devices, a design method and device for longitudinal field coils of fusion devices based on semi-analytical magnetic field calculation is proposed.

[0004] This invention protects a design method for longitudinal field coils in a fusion device based on semi-analytical magnetic field calculations, comprising: establishing a parameterized geometric model and global optimization decision variables for the longitudinal field coils; performing electromagnetic field coupling calculations on the coil units in the parameterized geometric model based on a semi-analytical magnetic field integration method; constructing an electromagnetic-mechanical coupling tension fluctuation evaluation model; performing global closed-loop optimization based on a differential evolution algorithm, outputting a globally optimal variable set that minimizes the tension fluctuation rate; generating an optimal coil configuration based on the globally optimal variable set, and accurately analyzing the trajectory of the centerline of the optimal coil configuration, and outputting the geometric parameters for manufacturing the longitudinal field coils.

[0005] Further, the steps for establishing the parametric geometric model and global optimization decision variables of the longitudinal field coil include: modeling the upper half of the coil above the equatorial plane in cylindrical coordinates using symmetry; defining the centerline of the upper half as a vertical straight line whose inner leg is continuously tangent to M segments of circular arcs; defining geometric control variables, including: half-height of the inner leg straight segment, polar angle dividing points of each circular arc segment, and radius of curvature of each circular arc segment; establishing geometric constraint relationships through recursive formulas and boundary conditions where the centerline is closed outside the equatorial plane, analytically eliminating two non-independent variables; extracting the set of independent variables as decision variables for subsequent optimization; defining the coil cross-sectional dimensions, and uniformly arraying the two-dimensional contour along the circumferential direction to form a complete longitudinal field coil.

[0006] Furthermore, based on the semi-analytical magnetic field integration method, the steps for electromagnetic field coupling calculation of coil elements in the parameterized geometric model include: establishing a local coordinate system for each coil and transforming the global field point coordinates into the local coordinate system; discretizing a single longitudinal field coil into a straight conductor segment and 2M circular arc conductor elements, wherein the 2M circular arc conductor elements are symmetrically distributed above and below the equatorial plane; for the straight conductor segment, using the analytical solution of the magnetic field of a three-dimensional block conductor to calculate the magnetic field components; for the circular arc conductor segment, performing analytical derivation of the spatial integral of the conductor cross section, transforming the integral with respect to the arc polar angle into a single numerical integral, and calculating the magnetic field components; traversing all coils and elements, vectorizing all magnetic field components, and using a vectorized computational architecture and just-in-time compilation acceleration technology for accelerated computation.

[0007] Furthermore, the steps for constructing an electromagnetically coupled tension fluctuation evaluation model include: sampling N evaluation points at equal intervals along the arc length of the coil centerline in the parametric geometric model; for each evaluation point, calculating the circumferential magnetic induction intensity at that point using a semi-analytical magnetic field integral method, and extracting the local radius of curvature of the evaluation point from the parametric geometric model; calculating the local electromagnetic tension at the evaluation point based on the total coil current, circumferential magnetic induction intensity, and the total electromagnetic current; determining the maximum tension value, minimum tension value, and average tension value based on the tension values ​​of all evaluation points; and defining the tension fluctuation rate as the optimization objective function, which is determined based on the maximum tension value, minimum tension value, and average tension value.

[0008] Furthermore, the steps for global closed-loop optimization based on differential evolution algorithm to output the globally optimal variable set that minimizes tension volatility include: setting a search range for the global optimization decision variables and randomly generating an initial population composed of multiple individuals; performing mutation and crossover operations of differential evolution algorithm on individuals in the initial population to generate new candidate individuals; checking whether the geometric parameters of each candidate individual satisfy the hard constraints of monotonically increasing polar angle, increasing radius of all arcs, and no geometric inflection points; assigning penalty values ​​to candidate individuals that violate the constraints and calculating the tension volatility of candidate individuals that meet the constraints; using a greedy selection strategy to retain candidate individuals whose fitness meets the conditions to enter the next generation, repeating the iteration until the preset convergence condition is reached, and outputting the globally optimal geometric parameters that minimize tension volatility.

[0009] Furthermore, the method also includes: extracting the globally optimal set of variables that minimizes the tension fluctuation rate from the convergent differential evolution algorithm; using geometric constraints, analytically solving the remaining geometric parameters and calculating the center coordinates of all arc segments to obtain the complete analytical trajectory of the coil centerline; and using denser sampling points than in the optimization process to re-evaluate the electromagnetic performance of the reconstructed accurate geometric model and verify the final tension fluctuation rate.

[0010] This invention protects a design device for a longitudinal field coil of a fusion device based on semi-analytical magnetic field calculation, comprising: a first establishment module for establishing a parameterized geometric model of the longitudinal field coil and global optimization decision variables; a first calculation module for performing electromagnetic field coupling calculations on the coil units in the parameterized geometric model based on a semi-analytical magnetic field integration method; a second establishment module for constructing a tension fluctuation evaluation model of electromagnetic coupling; an optimization module for performing global closed-loop optimization based on a differential evolution algorithm, outputting a globally optimal variable set that minimizes the tension fluctuation rate; and a generation module for generating an optimal coil configuration based on the globally optimal variable set, accurately analyzing the trajectory of the center line of the optimal coil configuration, and outputting geometric parameters for manufacturing the longitudinal field coil.

[0011] This invention protects an electronic device, comprising: a processor, a memory, and a bus. The memory stores machine-readable instructions executable by the processor. When the electronic device is running, the processor and the memory communicate via the bus. The machine-readable instructions are executed by the processor to perform the steps of a longitudinal field coil design method for a fusion device based on semi-analytical magnetic field calculation.

[0012] This invention protects a computer-readable storage medium storing a computer program that, when executed by a processor, performs the steps of a method for designing longitudinal field coils for a fusion device based on semi-analytical magnetic field calculations.

[0013] This invention protects a design method for longitudinal field coils in fusion devices based on semi-analytical magnetic field calculations. Its core innovation lies in establishing a parametric geometric model and global optimization decision variables, combining a semi-analytical magnetic field integration method to perform electromagnetic field coupling calculations on coil units, constructing an electromagnetic-mechanical coupling tension fluctuation evaluation model, and then performing global closed-loop optimization based on a differential evolution algorithm. Finally, it outputs the globally optimal variable set that minimizes the tension fluctuation rate and generates the coil configuration and manufacturing parameters with a precise analytical trajectory. The technical benefits of this solution are: significantly improved computational efficiency and accuracy in longitudinal field coil design, avoiding the computational burden of mesh generation in traditional numerical methods, and effectively reducing tension fluctuations in the coil during operation through global optimization, thereby improving the operational stability of the fusion device and the reliability of the coil structure. Furthermore, it can directly output precise geometric parameters for manufacturing, shortening the design cycle. Attached Figure Description

[0014] The accompanying drawings are provided to further illustrate the invention and form part of the specification. They are used in conjunction with embodiments of the invention to explain the invention and do not constitute a limitation thereof. In the drawings:

[0015] Figure 1 A flowchart illustrating a method for designing longitudinal field coils of a fusion device based on semi-analytical magnetic field calculations, provided in an embodiment of this application;

[0016] Figure 2 A schematic diagram of a geometric parameterization model and boundary condition definition for a longitudinal field coil provided in an embodiment of this application;

[0017] Figure 3 A schematic diagram of a three-dimensional configuration of a longitudinal field coil based on parameterization of straight segments and multiple connected arc segments provided in this application embodiment;

[0018] Figure 4 A comparison and verification diagram of the circumferential magnetic field distribution and relative error calculated by a semi-analytical algorithm and commercial finite element software, provided in the embodiments of this application;

[0019] Figure 5 A flowchart of a global optimization design for a longitudinal field coil based on a differential evolution algorithm is provided in an embodiment of this application.

[0020] Figure 6 A comparison diagram of the electromagnetic tension distribution along the radial direction of the longitudinal field coil before and after optimization, provided for embodiments of this application;

[0021] Figure 7 This is a structural block diagram of a longitudinal field coil design device for a fusion device based on semi-analytical magnetic field calculation, provided as an embodiment of this application. Detailed Implementation

[0022] To make the objectives, technical solutions, and advantages of the embodiments of this application clearer, the technical solutions of the embodiments of this application will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of this application, and not all embodiments. The components of the embodiments of this application 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 this application provided in the accompanying drawings is not intended to limit the scope of the claimed application, but merely represents selected embodiments of this application. Based on the embodiments of this application, every other embodiment obtained by those skilled in the art without inventive effort falls within the scope of protection of this application.

[0023] Research has revealed significant technical bottlenecks in existing design methods for longitudinal field coils in fusion devices. In engineering manufacturing, theoretically, an absolute constant tension curve with continuously changing curvature is extremely difficult to fabricate, typically requiring approximation using multiple circular arcs. However, a step change in the radius of curvature at the connection point of adjacent arc segments introduces abrupt changes and fluctuations in local electromagnetic tension. To reduce these tension fluctuations, optimization is needed in a high-dimensional geometric parameter space. However, traditional analytical formula methods for evaluating coil tension neglect the discrete distribution effects of adjacent coils, leading to insufficient accuracy in magnetic field and force calculations. Furthermore, relying on finite element multiphysics simulation software (such as COMSOL and ANSYS) for electromagnetic-mechanical coupling calculations requires regenerating the geometric model, meshing, and solving for each iteration, resulting in exponentially increasing computational complexity. A single optimization often takes several days or even longer, making it difficult to achieve the globally optimal solution for high-dimensional nonlinear parameters within the engineering cycle. Therefore, a longitudinal field coil optimization design method that can overcome the computational barriers between "high-precision force assessment" and "global optimization of high-dimensional parameters" is urgently needed.

[0024] Based on this, please refer to Figure 1 This application provides a method for designing longitudinal field coils of a fusion device based on semi-analytical magnetic field calculations, including:

[0025] Step 101: Establish the parameterized geometric model of the longitudinal field coil and the global optimization decision variables;

[0026] Step 102: Based on the semi-analytical magnetic field integration method, perform electromagnetic field coupling calculations on the coil units in the parameterized geometric model;

[0027] Step 103: Construct an evaluation model for tension fluctuations coupled with electromagnetics;

[0028] Step 104: Perform global closed-loop optimization based on differential evolution algorithm, and output the global optimal variable set that minimizes tension fluctuation rate;

[0029] Step 105: Generate the optimal coil configuration based on the global optimal variable set, and accurately analyze the trajectory of the center line of the optimal coil configuration, and output the geometric parameters for manufacturing the longitudinal field coil.

[0030] This application provides a method for designing longitudinal field coils in a fusion device based on semi-analytical magnetic field calculations. By establishing a parametric geometric model and global optimization decision variables, a dimensionality-reduced description of the coil configuration is achieved, effectively compressing the search space. Electromagnetic field coupling calculations are performed on the coil elements based on a semi-analytical magnetic field integration method, abandoning the cumbersome process of mesh generation and iterative solutions required by traditional finite element methods. Vectorization acceleration technology is used to achieve high-precision evaluation of the magnetic field distribution at the second level, significantly improving computational efficiency. An electromagnetic-mechanical coupling tension fluctuation evaluation model is constructed, which can accurately quantify the coil tension distribution. Non-constancy; global closed-loop optimization based on differential evolution algorithm, freeing it from dependence on the initial design solution, can stably search for the globally optimal variable set that minimizes tension fluctuation rate in multi-dimensional parameter space, avoiding getting trapped in local optima; finally, based on the globally optimal variable set, the optimal coil configuration and the accurate analytical trajectory of the center line are generated, and the geometric parameters for manufacturing the longitudinal field coil are output, thereby reducing the tension fluctuation rate to a minimum range while ensuring engineering manufacturability (multi-segment circular arc structure), significantly reducing the risk of local stress concentration, and achieving an efficient balance between electromagnetic-mechanical performance and manufacturing process.

[0031] Step S101, establishing the parameterized geometric model of the longitudinal field coil and the global optimization decision variables, may specifically include the following sub-steps:

[0032] Sub-step S1011: In cylindrical coordinates, utilizing the axisymmetric property of the longitudinal field coil, only the upper half of the coil above the equatorial plane is parametrically modeled. Sub-step S1012: The centerline of the upper half is defined as a vertical straight line whose inner leg is continuously tangent to segment M in a circular arc. Sub-step S1013: Geometric control variables are defined, including: half-height of the inner leg straight segment, polar angle dividing points of each circular arc segment, and radius of curvature of each circular arc segment. Sub-step S1014: Geometric constraints are established using recursive formulas and boundary conditions where the centerline closes outside the equatorial plane, analytically eliminating two independent variables. Sub-step S1015: The set of independent variables is extracted as decision variables for subsequent optimization. Sub-step S1016: The coil cross-sectional dimensions are defined, and the two-dimensional profile is uniformly arrayed along the circumferential direction to form a complete longitudinal field coil system. Figure 2 This is a schematic diagram of the geometric parameterization model and boundary condition definition of the longitudinal field coil provided in an embodiment of the present invention.

[0033] In step S1011, the upper half of the coil above the equatorial plane is modeled in cylindrical coordinates using symmetry. Specifically, the longitudinal field coil is symmetrical about the equatorial plane in the plane, so only the upper half of the center line needs to be parametrically modeled to simplify the model and reduce the amount of computation.

[0034] In step S1012, the centerline of the upper portion is defined as a vertical straight line whose inner leg is continuously tangent to the M-segment circular arc. The straight inner leg is located inside the coil and extends vertically upwards from the equatorial plane; the M-segment circular arcs are sequentially spliced ​​together tangently, extending from the top of the inner leg to the outer side of the equatorial plane, forming a smooth D-shaped profile. This parametric model considers both engineering manufacturability and the ease of manufacturing, as the multiple circular arcs are easy to process, while the continuous tangency ensures the first-order smoothness of the centerline.

[0035] In an optional embodiment, the step of performing electromagnetic field coupling calculations on the coil elements in the parameterized geometric model based on a semi-analytical magnetic field integration method includes: establishing a local coordinate system for each coil and transforming the global field point coordinates into the local coordinate system; discretizing a single longitudinal field coil into a straight conductor segment and 2M circular arc conductor elements, wherein the 2M circular arc conductor elements are symmetrically distributed above and below the equatorial plane; for the straight conductor segment, calculating the magnetic field components using the analytical solution of the magnetic field of a three-dimensional block conductor; for the circular arc conductor segment, analytically deriving the spatial integral of the conductor cross-section, converting the integral over the arc polar angle into a single numerical integral, and calculating the magnetic field components; traversing all coils and elements, vectorizing all magnetic field components, and accelerating the calculation using a vectorized computation architecture and just-in-time compilation acceleration technology. This step provides fast and high-precision magnetic field data for subsequent tension assessment, avoiding the time-consuming calculations of traditional finite element methods.

[0036] In step S1013, geometric control variables are defined, including: the half-height of the straight section of the inner leg, the polar angle dividing point of each arc segment, and the radius of curvature of each arc segment. Specifically, the half-height of the straight section of the inner leg is denoted as H_leg, representing the vertical distance from the equatorial plane to the top of the inner leg; the polar angle dividing point of each arc segment is denoted as θ_i, where i ranges from 1 to M, the starting polar angle of the first arc segment is 0, and the ending polar angle of the Mth arc segment is π; the radius of curvature of each arc segment is denoted as R_i, where i ranges from 1 to M. These variables collectively determine the geometry of the coil centerline.

[0037] In step S1014, geometric constraints are established using a recursive formula and a boundary condition where the centerline closes outside the equatorial plane, thus analytically eliminating two independent variables. Specifically, for the first arc segment, its center coordinates are determined by the radial coordinates of the inner leg and the polar angle; for subsequent arc segments, the center coordinates are calculated using a recursive formula to ensure that adjacent arc segments are tangent at the connection point. Simultaneously, the centerline must close outside the equatorial plane at the specified radial coordinates of the outer leg, thereby establishing a closed boundary condition. By solving this boundary condition, the radii of curvature of the last two arc segments can be analytically eliminated, thereby reducing the number of optimization variables.

[0038] In an optional embodiment, the method provided in this application further includes: extracting the globally optimal set of variables that minimizes the tension fluctuation rate from a converged differential evolution algorithm; analytically solving the remaining geometric parameters using the geometric constraints, and calculating the center coordinates of all arc segments to obtain the complete analytical trajectory of the coil centerline; and re-evaluating the electromagnetic performance of the reconstructed accurate geometric model using a denser sampling point than in the optimization process to verify the final tension fluctuation rate. This step ensures that the optimization results can be directly used for engineering manufacturing and verifies that its performance meets the design specifications.

[0039] In step S1015, a set of independent variables is extracted as decision variables for subsequent optimization. Specifically, the set of independent variables includes: the half-height H_leg of the inner leg straight section, the polar angle dividing points θ_1 to θ_{M-1} of the first M-1 arc segment, and the radii of curvature R_1 to R_{M-2} of the first M-2 arc segment. These variables constitute the search space of the differential evolution algorithm. By optimizing these variables, the coil configuration that minimizes the tension fluctuation rate can be found.

[0040] In step S1016, the coil cross-sectional dimensions are defined, and the two-dimensional profiles are uniformly arrayed along the circumferential direction to form a complete longitudinal field coil. Specifically, the cross-sectional width and thickness of the coil conductors are set according to engineering constraints. Then, the individual coil profiles of the above-parameterized model are uniformly arrayed around the axis of the device to form a longitudinal field coil system composed of N coils, which is used for subsequent electromagnetic field calculations.

[0041] In step S102, electromagnetic field coupling calculations are performed on the coil units in the parameterized geometric model based on the semi-analytical magnetic field integration method. Specifically, based on the parameterized geometric model established in step S101, the principle of linear superposition of electromagnetic fields and semi-analytical integration techniques are used to achieve accurate and rapid solution of the magnetic induction intensity at any field point in the longitudinal field coil system. First, a local coordinate system is established for each longitudinal field coil, and the field points to be evaluated in the global coordinate system are transformed to the local coordinate system of the corresponding unit through translation and rotation operators. Then, a single longitudinal field coil is discretized along its centerline into a set composed of basic current units. The basic current unit includes a straight conductor segment with a length equal to half the height of the inner leg straight segment and 2M circular arc conductor units distributed on both sides of the equatorial plane and symmetrical about the equatorial plane. Each unit is assigned a rectangular cross-section property. For the inner leg straight conductor element, the analytical solution of the magnetic field of a three-dimensional block conductor is used in the local coordinate system to obtain the magnetic flux density components at the field point. For the circular arc conductor element, a semi-analytical integration strategy is adopted. The double spatial integral of the conductor's rectangular cross-section is pre-derived analytically in the local coordinate system of the circular arc, simplifying the three-dimensional volume integral into a single integral about the arc polar angle. Then, the magnetic flux density components are obtained by numerical integration. Finally, all longitudinal field coils and all their discrete elements are traversed. The magnetic field components calculated by each element in the local coordinate system are inversely transformed back to the global coordinate system and vector superimposed to obtain the total circumferential magnetic flux density at the field point. To support subsequent global optimization, a vectorized computation architecture is adopted. Multiple field points to be evaluated and the coil element array are constructed as a high-dimensional tensor mapping. Just-in-time compilation acceleration technology is used to eliminate instruction-level cyclic redundancy, achieving second-level evaluation of the magnetic field distribution of a large-scale coil system.

[0042] In step S103, an evaluation model for tension fluctuations based on electromagnetic coupling is constructed. Specifically, based on the rapid acquisition of the magnetic field distribution in step S102, this step aims to establish a quantitative mapping relationship between geometric configuration and mechanical properties. By calculating the electromagnetic tension distribution along the coil centerline, an objective function for measuring tension fluctuations is constructed.

[0043] Step S103 may specifically include the following sub-steps:

[0044] Step S1031: Sample N evaluation points at equal intervals along the arc length of the coil centerline in the parameterized geometric model. Equal-interval sampling ensures the consistency of weights between subsequent numerical integration and statistical indicators in geometric space, laying the foundation for accurately evaluating the tension distribution of the entire coil.

[0045] Step S1032: For each evaluation point, the circumferential magnetic induction intensity at that point is calculated using a semi-analytical magnetic field integration method, and the local radius of curvature of the evaluation point is extracted from the parameterized geometric model. Specifically, for each evaluation point, the fast calculation method described in step S102 is first called to obtain the total circumferential magnetic induction intensity at that point; simultaneously, since the evaluation point is located on a certain arc or straight line segment defined in step S101, its local radius of curvature can be directly given by the corresponding arc segment parameter or straight line segment attribute.

[0046] Step S1033: Calculate the local electromagnetic tension at the evaluation point based on the total coil current, the circumferential magnetic induction intensity, and the local radius of curvature. The specific calculation formula is: T = I_total × B_φ × ρ, where I_total is the total ampere-turns of the coil, B_φ is the circumferential magnetic induction intensity at that point, and ρ is the local radius of curvature at that point. This formula, based on the principles of electromagnetism, couples the magnetic field with geometric parameters to quantitatively describe the tension distribution of the coil under electromagnetic force.

[0047] Step S1034: Based on the tension values ​​of all evaluation points, determine the maximum tension value, minimum tension value, and average tension value. Collect the tension calculation results of all N sampling points on the center line to form a global tension distribution set. Extract the maximum value T_max and minimum value T_min of the tension distribution of the entire coil from it, and calculate the arithmetic mean T_avg.

[0048] Step S1035 defines the tension fluctuation rate as the optimization objective function, which is determined based on the maximum tension value, minimum tension value, and average tension value. The specific calculation formula uses the normalized ratio of the range to the mean: σ_T = (T_max - T_min) / T_avg. This formula uses the difference between the maximum and minimum tension values ​​as the numerator, representing the absolute fluctuation range; and the mean tension value as the denominator, providing a normalization benchmark. The fundamental goal of the global optimization algorithm is to search for a set of optimal geometric decision variables under given parametric design space and engineering boundary conditions, minimizing the tension fluctuation rate, thereby minimizing local stress concentration and protecting the current-carrying capacity and mechanical safety of the superconducting material.

[0049] Step S104 involves global closed-loop optimization based on the differential evolution algorithm, outputting the globally optimal set of variables that minimizes the tension fluctuation rate. Building upon the tension fluctuation evaluation model constructed in step S103, this step aims to utilize the global random search capability of the differential evolution algorithm to find the optimal set of geometric variables that minimizes the tension fluctuation rate within the multidimensional parameter space. Step S104 specifically includes the following sub-steps:

[0050] Step S1041: Set the search range for the global optimization decision variables and randomly generate an initial population consisting of multiple individuals. Based on the main radius of the fusion device, magnetic field strength, and engineering space constraints, preset upper and lower search limits for the independent decision variables defined in step S101. Within the multidimensional bounded space, an initial population of N_p individuals is randomly generated, with each individual representing a set of candidate coil geometries.

[0051] Step S1042: Perform mutation and crossover operations using the differential evolution algorithm on the individuals in the initial population to generate new candidate individuals. The mutation operation selects the current best individual from the population and constructs a mutated individual by combining it with a randomly selected differential vector. The mutation factor adopts an adaptive interval to balance global exploration and local exploitation capabilities. The crossover operation sets the crossover probability and performs discrete crossover between the mutated individual and the target individual position by position to generate experimental individuals.

[0052] Step S1043 checks whether the geometric parameters of each candidate individual satisfy the hard constraints of monotonically increasing polar angles, increasing radii of all arcs, and no geometric inflection points. Specifically, it verifies whether the polar angle sub-points at each level satisfy monotonically increasing conditions and the intervals are greater than a preset threshold, and simultaneously verifies whether the arc radii of the entire sequence segment satisfy the strict monotonically increasing characteristic. This topological hard constraint aims to physically conform to the distribution law of the circumferential magnetic field decaying with the spatial radius, forcibly ensuring the smoothness of the geometric convexity of the generated D-shaped coil, and avoiding unrealizable distorted solutions with inflection points.

[0053] Step S1044: A penalty value is assigned to candidate individuals that violate the constraints, and the tension fluctuation rate of candidate individuals that meet the constraints is calculated. For illegal individuals that violate any of the above constraints, the algorithm directly assigns a penalty value much larger than the normal fitness level, forcibly eliminating them in subsequent selection operations. For individuals that pass the legality check, the fast magnetic field calculation engine in step S102 and the mechanical evaluation model in step S103 are called sequentially to return their corresponding tension fluctuation rate.

[0054] Step S1045: A greedy selection strategy is used to retain candidate individuals whose fitness meets the conditions for the next generation. This process is repeated iteratively until the preset convergence condition is met, and the globally optimal geometric parameters that minimize tension volatility are output. The greedy selection strategy compares the fitness values ​​of the experimental individuals with those of the original individuals, retaining the better-performing individuals for the next generation. The algorithm repeatedly executes the mutation, crossover, evaluation, and selection processes. Optimization stops when the maximum preset number of iterations is reached or the improvement of the best individual in the population within several consecutive generations is less than the convergence tolerance. Finally, the globally optimal variable set with the minimum tension volatility is output.

[0055] In step S105, an optimal coil configuration is generated based on the globally optimal variable set, and the precise analytical trajectory of the centerline of the optimal coil configuration is calculated, outputting the geometric parameters for manufacturing the longitudinal field coil. Specifically, after obtaining the globally optimal variable set in step S104, this step aims to transform the optimal variable set into precise geometric parameters that can directly guide the engineering manufacturing of the longitudinal field coil. First, key geometric features are extracted from the optimal individual after convergence of the differential evolution algorithm, including the optimal half-height of the inner leg centerline, the optimal set of polar angle bisectors, and the optimal radius of the front arc. Then, using the boundary condition linear equations established in step S101, the above optimal feature parameters are substituted to analytically solve for the remaining two levels of key radii, thus determining all the radius sequences constituting the continuous tangential arc segments. Subsequently, according to the tangential geometric constraint formula, the center coordinates of each arc segment in the global coordinate system are calculated sequentially. The center coordinate sequence and the radius sequence together define the precise analytical trajectory of the longitudinal field coil centerline. Finally, the reconstructed complete geometric model is input again into the evaluation engine described in steps S102 and S103. A high-fidelity final verification is performed using sampling points with a higher density than in the optimization process. The electromagnetic tension distribution of the entire coil is calculated, and the optimal tension fluctuation rate is recalculated according to the formula to ensure that it meets the engineering design specifications. The geometric parameters used to manufacture the longitudinal field coil are then output.

[0056] To achieve the above-mentioned objectives, this invention provides a method for optimizing the longitudinal field coil design of a fusion device based on semi-analytical magnetic field calculations, comprising the following steps:

[0057] Step 1: Establish the parametric geometric model of the longitudinal field coil and the global optimization decision variables.

[0058] Establish a cylindrical coordinate system The corresponding meridian section (i.e.) (Plane). Utilizing longitudinal field coils in about in the plane The property of axisymmetry applies only to the equatorial plane ( The upper half of the centerline above is parametrically modeled. The upper half of the centerline consists of a vertical straight line segment located on the inside (corresponding to the inner leg) and continuously tangentially spliced... Composed of circular arc segments. The specific parametric definitions are as follows:

[0059] Define geometric control variables:

[0060] The half-height of the straight section of the inner leg, i.e., the centerline from the equatorial plane. The vertical distance to the top of the inner thigh;

[0061] Polar angle division points of each arc segment ( (The initial polar angle of the first arc segment). , No. Cutoff polar angle of a segmented circular arc ;

[0062] : No. The radius of curvature of a circular arc ( ).

[0063] To ensure that adjacent circular arc segments are smoothly tangent at the connection point, the coordinates of the centers of each arc segment are... Determined by the following recursive formula:

[0064] For the first arc segment ( Its center coordinates are:

[0065]

[0066] in, Here are the radial coordinates of the inner leg of the longitudinal field coil.

[0067] For the subsequent arc segment ( The recursive formula for the center coordinates of the circle is:

[0068]

[0069] At the same time, in order to ensure that the centerline closes to the specified outer leg radial coordinates outside the equatorial plane. The geometric parameters must satisfy the following closed boundary conditions:

[0070]

[0071] By solving the above boundary conditions, two non-independent variables (such as the radii of curvature of the last two arc segments) can be eliminated. and Therefore, a set of independent decision variables is extracted for subsequent global optimization using the differential evolution algorithm. :

[0072]

[0073] Finally, define the cross-sectional width of the coil conductor. With thickness Along the circumference ( (Direction) will The above-mentioned parametrically modeled longitudinal field coil winding The axes are uniformly arrayed to complete the overall three-dimensional geometric construction of the longitudinal field coil system of the fusion device.

[0074] Step 2: Fast calculation of multi-source electromagnetic field coupling based on semi-analytical magnetic field integral

[0075] Based on the geometric model constructed in step one, the principle of linear superposition of electromagnetic fields and semi-analytical integration techniques are used to accurately and quickly solve for the magnetic induction intensity at any field point in the longitudinal field coil system. The specific process is as follows:

[0076] (1) Mapping transformation between global and local coordinate systems

[0077] To utilize the analytical formula, for the first... indivual( A local coordinate system is established for each basic current element in the longitudinal field coil. For the field point to be evaluated in the global coordinate system... According to the The circumferential distribution angle of each coil The translation and rotation operators are used to transform it to the local coordinate system of the corresponding element. .

[0078] (2) Decomposition and Discretization of Coil Geometric Units

[0079] Based on the parameterized path determined in step one, a single longitudinal field coil is discretized along its centerline into a set composed of basic current units. Each basic current unit includes: a unit with a length of... The straight conductor segment (corresponding to the inner leg of the coil) and the segments distributed on both sides of the equatorial plane, symmetrical about the equatorial plane. Each element is a circular arc conductor unit. Each unit is assigned a rectangular cross-section property with a width of [missing information]. Thickness is .

[0080] (3) Solving the magnetic field of the conductor segment based on the semi-analytical expression

[0081] For the inner leg straight conductor element, the magnetic field analytical solution of the three-dimensional block conductor is used in the local coordinate system to obtain the magnetic induction components at the field points. For the circular arc conductor element, a semi-analytical integration strategy is adopted. In the local coordinate system of the circular arc, the double spatial integral in the direction of the conductor's rectangular cross-section is analytically derived beforehand, simplifying the three-dimensional volume integral to a function relating to the arc polar angle. The single integral is then used. Finally, the magnetic flux density components are obtained by numerical integration.

[0082] (4) Multi-source superposition and vectorization to accelerate computation

[0083] Traverse all For each longitudinal field coil and all its discrete elements, the magnetic field components calculated by each element in the local coordinate system are inversely transformed back to the global coordinate system and then vector-superimposed to obtain the field point. Total circumferential magnetic induction at the location .

[0084] To support the global optimization in the subsequent step four, a vectorized computing architecture is adopted, which constructs a high-dimensional tensor mapping between multiple field points to be evaluated and the coil unit array. Instruction-level cyclic redundancy is eliminated through just-in-time compilation acceleration technology, enabling second-level evaluation of the magnetic field distribution of a large-scale coil system.

[0085] Step 3: Construct an electromagnetic-mechanical coupled tension fluctuation evaluation model

[0086] This step aims to establish a quantitative mapping relationship between geometric configuration and mechanical properties. By calculating the electromagnetic tension distribution along the center line of the coil, an objective function is constructed to measure tension fluctuations.

[0087] Based on the parameterized centerline generated in step one, discrete sampling is performed at equal intervals along the arc length direction, selecting... Evaluation sites The equidistant sampling ensures the consistency of the weights of subsequent numerical integration and statistical indicators in geometric space.

[0088] For each evaluation site Perform the following operations:

[0089] 1. Using the fast calculation method described in step two, obtain the total circumferential magnetic induction at that point. .

[0090] 2. Extract the point at Local radius of curvature in the plane (The parameters of the corresponding arc segment in step one are given directly.)

[0091] 3. Calculate the local electromagnetic tension at each sampling point using the following formula ( ):

[0092]

[0093] in, This represents the total ampere-turns of the coil.

[0094] To quantitatively measure coil tension fluctuations, all data along the centerline were collected. The tension calculation results at each sampling point constitute a global tension distribution set. The maximum value of the entire coil tension distribution is then extracted from this set. and minimum value .

[0095] Define tension volatility As the objective function for global optimization, its calculation formula adopts the normalized ratio of the range to the mean:

[0096]

[0097] The formula uses the difference between the maximum and minimum tension values ​​as the numerator (characterizing the absolute fluctuation range) and the mean tension value as the denominator (providing a normalization benchmark).

[0098] The fundamental goal of the global optimization algorithm is to search for a set of optimal geometric decision variables and minimize the tension variability under given parametric design space and engineering boundary conditions. This minimizes the occurrence of localized stress concentration.

[0099] Step 4: Global Closed-Loop Optimization Based on Differential Evolution Algorithm

[0100] This step aims to utilize the global random search capability of the differential evolution algorithm to find the tension fluctuation rate within the multidimensional parameter space. Minimize the optimal set of geometric variables The specific execution process is as follows:

[0101] (1) Search space definition and population initialization

[0102] Based on the main radius of the fusion device, magnetic field strength, and engineering space constraints, these are the independent decision variables defined in step one. Preset search upper and lower limits. Within the multidimensional bounded space, randomly generate a size of... (like The initial population of individuals. Each individual represents a set of candidate coil geometries.

[0103] (2) Heuristic mutation and crossover operator operations

[0104] Mutation operation: Select the current best individual from the population and construct a mutated individual by combining it with a randomly selected difference vector. Mutation factor use An adaptive interval is used to balance the algorithm's global exploration and local development capabilities.

[0105] Crossover operation: Set crossover probability (like The mutant individuals and the target individuals are discretely crossed position by position to generate experimental individuals.

[0106] (3) Fitness assessment and hard constraint penalty mechanism

[0107] For each generated experimental individual, the following nested legality verification and fitness calculation process is executed:

[0108] Verify whether the polar quantiles at each level satisfy the condition of monotonically increasing and the interval being greater than a preset threshold. (like Simultaneously, the entire sequence, including the parsed and reconstructed portion, is verified. Segment radius Does it satisfy the strict monotonically increasing characteristic? This topological hard constraint aims to physically conform to the distribution law of the decay of the circumferential magnetic field with the spatial radius, forcibly ensuring the smoothness of the geometric convexity of the generated D-shaped coil, and avoiding the occurrence of distorted solutions that are impossible to achieve in engineering due to inflection points.

[0109] Dynamic penalty logic: For any illegal individual that violates any of the above constraints, the algorithm directly assigns a penalty value much larger than the normal fitness metric (e.g., ...). This forces them to be eliminated in subsequent selection operations, thus ensuring that the search process always converges within the physically realizable geometric domain.

[0110] Performance evaluation: For individuals that pass the legality check, the fast magnetic field calculation engine in step two and the mechanical evaluation model in step three are called in sequence to return their corresponding tension fluctuation rate.

[0111] (4) Iterative evolution and selection convergence

[0112] A greedy selection strategy is employed, comparing the fitness values ​​of experimental individuals with those of the original individuals, retaining those with better performance (i.e., Smaller individuals enter the next generation of the population. The algorithm repeatedly performs the mutation, crossover, evaluation, and selection processes.

[0113] Optimization stops when any of the following termination conditions are met:

[0114] 1. Reach the maximum preset number of iterations. (like )

[0115] 2. The improvement of the best individual in the population over multiple generations is less than the convergence tolerance. (like ).

[0116] Finally, the output is the globally optimal set of variables with the minimum tension volatility. .

[0117] Step 5: Optimal Configuration Generation and Engineering Parameterization

[0118] This step aims to transform the globally optimal set of decision variables obtained in step four. This is converted into precise geometric parameters that can directly guide the engineering manufacturing of the longitudinal field coil. The specific process is as follows:

[0119] (1) Extraction of optimal feature parameters

[0120] Extract key geometric features from the optimal individual after convergence of the differential evolution algorithm, including:

[0121] Optimal inner leg centerline half height ;

[0122] Optimal polar division point set ;

[0123] Optimal front Segment radius .

[0124] (2) Analytical reconstruction of complete geometric configuration

[0125] Using the linear equations of the boundary conditions described in step one, and substituting the optimal characteristic parameters mentioned above, the remaining two levels of critical radii can be analytically solved. and Thus, it constitutes... All radius sequences of continuous tangent circular arcs All confirmed.

[0126] Subsequently, based on the tangent geometric constraint formula, the coordinates of each arc segment in the global coordinate system are calculated sequentially. The coordinates of the center of the circle below The center coordinate sequence and the radius sequence together define the precise analytical trajectory of the centerline of the longitudinal field coil.

[0127] (3) Final verification and evaluation of physical properties

[0128] The reconstructed complete geometric model is then input back into the evaluation engine described in steps two and three for final high-fidelity verification:

[0129] High-density sampling evaluation: using sampling points with a higher density than the optimization process (e.g., ), calculate the electromagnetic tension distribution of the entire coil;

[0130] Indicator verification: according to the formula Recalculate the optimal tension fluctuation rate to ensure it meets the engineering design requirements.

[0131] Compared with the prior art, the present invention has the following significant positive effects:

[0132] 1. The synergy of physical constraint dimensionality reduction and population evolution effectively overcomes the challenge of high-dimensional nonlinear optimization.

[0133] Existing multi-segment circular arc geometric models of longitudinal field coils have high parameter dimensionality. Directly using global optimization algorithms for optimization is not only computationally burdensome but also prone to convergence difficulties in the vast parameter space. This invention innovatively proposes a parameterized geometric model of "straight segments + M continuous tangent circular arcs." Through rigorous physical topological closed boundary conditions, two non-independent radius variables are analytically eliminated, achieving dimensionality reduction of the geometric model from a physical level. In this low-dimensional parameter space, this invention combines a differential evolution (DE) algorithm based on an adaptive mutation strategy to significantly compress the ineffective search space. This collaborative mechanism not only effectively reduces the search dimensionality of the optimizer and eliminates the dependence of traditional gradient algorithms on the initial configuration, but also enables the algorithm to overcome local barriers and converge quickly and stably to the global optimal solution that satisfies engineering constraints, fundamentally improving the quality of the optimization solution. The final output optimization results (center, polar angle, radius) can be directly and seamlessly used for engineering 3D geometric modeling.

[0134] 2. Break through the computational barrier based on finite element iteration to achieve a leapfrog improvement in the efficiency of electromagnetic-mechanical evaluation.

[0135] Traditional global optimization of longitudinal field coils based on finite element co-simulation requires tedious re-generation of 3D geometry, mesh generation, and partial differential equation solving for each mutation iteration, resulting in extremely high time consumption. This invention completely abandons the traditional mesh-dependent path, deeply coupling a semi-analytical magnetic field integral operator with vectorization acceleration technology. This mechanism utilizes low-level matrix operations to completely eliminate instruction-level nested loops in coil circumferential array calculations, achieving parallel synchronous calculation of the entire set of geometric parameters of the mutation population without mesh constraints. The full-space high-fidelity magnetic field and force assessment for millions of field points can be shortened to the second level, thereby significantly reducing the global optimization cycle of the longitudinal field coils in fusion devices from several days to tens of minutes, demonstrating extremely high engineering practical value.

[0136] 3. Achieving an optimal balance between engineering manufacturability and low-tension, non-constant stress state.

[0137] In the actual winding and mold processing of superconducting longitudinal field coils, it is extremely difficult to manufacture an absolutely constant tension curve with theoretically continuous curvature. In engineering, it is usually necessary to use multiple circular arcs for approximation. However, the curvature radius step (i.e., discontinuity of the second derivative) at the connection of adjacent circular arc segments inevitably introduces abrupt changes in local electromagnetic tension. This invention addresses and overcomes this engineering physical limitation by constructing an accurate evaluation model for tension instability (tension fluctuation rate) and precisely searching for the combination of circular arc parameters that minimizes this instability within the dimensionality-reduced parameter space. The optimized coil configuration, while fully retaining the "easy to process and manufacture" advantage of multiple circular arcs, reduces the inherent tension fluctuation rate to an extremely small range, approximating the ideal pure tensile stress state to the greatest extent. This not only significantly reduces the additional bending moment and interlayer shear stress caused by discrete curvature but also effectively protects the current-carrying performance and mechanical safety of the superconducting material.

[0138] The following example illustrates the design method for longitudinal field coils of a fusion device based on semi-analytical magnetic field calculations provided in this application.

[0139] (1) Implementation Case Background and Initialization Parameters

[0140] This specific embodiment uses the longitudinal field (TF) coil system design of a fusion reactor (such as CFETR) as an example. The basic engineering constraint parameters of the device are set as follows:

[0141] outer radius of the center column of the inner leg of the coil Outer leg diameter ;

[0142] Total number of longitudinal field coils Single-turn operating current Total number of turns in a single coil That is, operating current ;

[0143] Coil cross-sectional dimensions: width ,thickness ;

[0144] Parameterized segment number: Define the centerline above the equatorial plane as composed of... It is composed of continuous tangent circular arcs.

[0145] Figure 2 A schematic diagram illustrating the geometric parameterization model and boundary condition definition of the longitudinal field coil. Figure 3 This is a schematic diagram of the three-dimensional configuration of the longitudinal field coil, which is constructed based on the parameterization of straight segments and multiple connected arc segments.

[0146] (2) Specific optimization implementation steps

[0147] Step 1: Construct the initial state of the geometric centerline

[0148] First, determine the decision variables. The search dimensions. In this embodiment, the independent variables include: inner leg half-height. The polar angle bisectors of the first two arc segments and the radius of the first arc .

[0149] By establishing a system of linear equations based on boundary conditions, we can establish an equation regarding the unknown radius. The closed constraint ensures that the coil centerline starts from the top of the inner leg. Starting from there, it eventually smoothly connects to the outer leg equatorial point. .

[0150] Step 2: Configure the semi-analytical magnetic field evaluation engine

[0151] The Numba library is used to accelerate the just-in-time (JIT) compilation of the magnetic field calculation kernel function. For the 16 longitudinal field coils, they are decomposed into... Root straight conductor block and A segmental circular arc conductor element. During the optimization process, it is uniformly generated along the centerline. The circumferential magnetic induction intensity at each sampling point is simultaneously calculated using vectorized matrix operations. .

[0152] Figure 4 The diagram shows a comparison and verification of the circumferential magnetic field distribution and relative error calculated by the semi-analytical algorithm provided in this embodiment and the commercial finite element software (COMSOL).

[0153] Step 3: Establish a mechanical evaluation model

[0154] For each sampling point According to the formula Calculate the local electromagnetic tension (in MN). Then, calculate the arithmetic mean of the tension across the entire coil. And the maximum / minimum tension extreme values, and use these to calculate the objective function:

[0155]

[0156] Step 4: Perform differential evolution for global optimization

[0157] Configure DE algorithm parameters: population size Maximum iteration algebra , variable factor Crossover probability .

[0158] During the iteration process, if a set of geometric variables causes the order of the radius or polar angle subtraction points to violate monotonicity, a penalty mechanism is triggered. The algorithm automatically avoids distorted solutions in multidimensional space and evolves in the direction of minimizing tension fluctuations.

[0159] Figure 5 The flowchart for the global optimization design of the longitudinal field coil based on the differential evolution algorithm is provided for this embodiment.

[0160] Step 5: Optimal Parameter Output and Performance Comparison

[0161] The algorithm stops when it converges. It outputs the optimal set of variables. In this embodiment, as Figure 5 As shown, the optimized tension variability From the initial configuration Significantly reduced to .

[0162] Figure 6 A comparison diagram of the electromagnetic tension distribution along the radial direction of the longitudinal field coil before and after optimization, provided for this embodiment.

[0163] Please see Figure 7 , Figure 7 This is a schematic diagram of a longitudinal field coil design device for a fusion device based on semi-analytical magnetic field calculation, provided as an embodiment of this application. Figure 7 The device shown includes the following functional modules:

[0164] The first module 710 is used to establish the parameterized geometric model and global optimization decision variables of the longitudinal field coil;

[0165] The first calculation module 720 is used to perform electromagnetic field coupling calculations on the coil units in the parameterized geometric model based on the semi-analytical magnetic field integration method.

[0166] The second module 730 is used to construct an evaluation model for tension fluctuations in electromagnetic-mechanical coupling.

[0167] The optimization module 740 is used to perform global closed-loop optimization based on the differential evolution algorithm and outputs the global optimal set of variables that minimizes the tension fluctuation rate.

[0168] The generation module 750 is used to generate an optimal coil configuration based on the global optimal variable set, and to accurately analyze the trajectory of the center line of the optimal coil configuration, and output the geometric parameters for manufacturing the longitudinal field coil.

[0169] Furthermore, the first establishment module is specifically used for:

[0170] In cylindrical coordinates, the upper half of the coil above the equatorial plane is modeled using symmetry.

[0171] The centerline of the upper part is defined as an arc that is continuously tangent to the inner leg of a vertical straight line and segment M.

[0172] Define geometric control variables, including: half height of the straight section of the inner leg, polar angle division point of each arc segment, and radius of curvature of each arc segment;

[0173] By establishing geometric constraints using recursive formulas and boundary conditions where the centerline closes outside the equatorial plane, two non-independent variables are analytically eliminated.

[0174] Extract the set of independent variables as decision variables for subsequent optimization;

[0175] Define the coil cross-sectional dimensions and arrange the two-dimensional profile in a uniform array along the circumferential direction to form a complete longitudinal field coil.

[0176] Furthermore, the first calculation module is specifically used for:

[0177] Establish a local coordinate system for each coil and transform the global field point coordinates to the local coordinate system;

[0178] A single longitudinal field coil is discretized into a straight conductor segment and 2M circular arc conductor units, wherein the 2M circular arc conductor units are symmetrically distributed above and below the equatorial plane;

[0179] For the straight conductor segment, the magnetic field components are calculated using the analytical solution of the magnetic field of a three-dimensional block conductor;

[0180] For the arc conductor segment, the spatial integral of the conductor cross section is analytically derived, and the integral with respect to the arc polar angle is transformed into a single numerical integral to calculate the magnetic field components.

[0181] It iterates through all coils and units, superimposes all magnetic field components into vectors, and uses a vectorized computing architecture and just-in-time compilation acceleration technology to speed up the calculation.

[0182] Furthermore, the second establishment module is specifically used for:

[0183] N evaluation points are sampled at equal intervals along the arc length of the coil centerline in the parametric geometric model;

[0184] For each evaluation point, the circumferential magnetic induction intensity at that point is calculated using a semi-analytical magnetic field integral method, and the local radius of curvature of the evaluation point is extracted from the parameterized geometric model.

[0185] Based on the total coil current, the circumferential magnetic induction intensity, and the calculated local electromagnetic tension at the evaluation point;

[0186] Based on the tension values ​​of all evaluation points, determine the maximum tension value, minimum tension value, and average tension value;

[0187] Tension fluctuation rate is defined as the objective function for optimization, and the tension fluctuation rate is determined based on the maximum tension value, minimum tension value, and average tension value.

[0188] Furthermore, the optimization module is specifically used for:

[0189] The search range is set for the global optimization decision variables, and an initial population consisting of multiple individuals is randomly generated;

[0190] Perform mutation and crossover operations using the differential evolution algorithm on individuals in the initial population to generate new candidate individuals;

[0191] Check whether the geometric parameters of each candidate individual satisfy the hard constraints of monotonically increasing polar angle, increasing radius of all arcs, and no geometric inflection points;

[0192] A penalty value is assigned to candidate individuals that violate the constraints, and the tension volatility of candidate individuals that meet the constraints is calculated.

[0193] A greedy selection strategy is adopted to retain candidate individuals whose fitness meets the conditions to enter the next generation. This process is repeated until the preset convergence condition is met, and the global optimal geometric parameters that minimize the tension fluctuation rate are output.

[0194] Furthermore, the device also includes a verification module, which is used for:

[0195] Extract the globally optimal set of variables that minimizes tension fluctuation from a convergent differential evolution algorithm;

[0196] Using the aforementioned geometric constraints, the remaining geometric parameters are solved analytically, and the center coordinates of all circular arc segments are calculated to obtain the complete analytical trajectory of the coil centerline.

[0197] Using a denser sampling point than in the optimization process, the electromagnetic performance of the reconstructed accurate geometric model is re-evaluated to verify the final tension fluctuation rate.

[0198] The longitudinal field coil design device for fusion devices based on semi-analytical magnetic field calculation provided in this application establishes a parameterized geometric model of the longitudinal field coil and global optimization decision variables; performs electromagnetic field coupling calculations on the coil units in the parameterized geometric model based on a semi-analytical magnetic field integration method; constructs an electromagnetic-mechanical coupling tension fluctuation evaluation model; performs global closed-loop optimization based on a differential evolution algorithm, outputting a globally optimal variable set that minimizes the tension fluctuation rate; generates an optimal coil configuration based on the globally optimal variable set, and outputs the precise analytical trajectory of the centerline of the optimal coil configuration for manufacturing the longitudinal field coil. In this way, designers can quickly obtain the longitudinal field coil configuration with minimal tension fluctuation through parameterized modeling and semi-analytical magnetic field calculations combined with automatic optimization using a differential evolution algorithm, significantly shortening the design cycle of the longitudinal field coil for fusion devices, reducing design complexity, and improving design accuracy.

[0199] This application provides a schematic diagram of the structure of an electronic device. The electronic device includes a processor, a memory, and a bus.

[0200] The memory stores machine-readable instructions executable by the processor. When the electronic device is running, the processor communicates with the memory via a bus. When the machine-readable instructions are executed by the processor, they can perform the operations described above. Figure 1 The steps of the longitudinal field coil design method for fusion devices based on semi-analytical magnetic field calculation in the method embodiment shown are described in detail in the method embodiment, and will not be repeated here.

[0201] This application also provides a computer-readable storage medium storing a computer program, which, when executed by a processor, can perform the above-described actions. Figure 1 The steps of the longitudinal field coil design method for fusion devices based on semi-analytical magnetic field calculation in the method embodiment shown are described in detail in the method embodiment, and will not be repeated here.

[0202] Those skilled in the art will understand that, for the sake of convenience and brevity, the specific working processes of the systems, devices, and units described above can be referred to the corresponding processes in the foregoing method embodiments, and will not be repeated here.

[0203] In the several embodiments provided in this application, it should be understood that the disclosed systems, apparatuses, and methods can be implemented in other ways. The apparatus embodiments described above are merely illustrative. For example, the division of units is only a logical functional division, and in actual implementation, there may be other division methods. Furthermore, multiple units or components may be combined or integrated into another system, or some features may be ignored or not executed. Additionally, the shown or discussed mutual couplings, direct couplings, or communication connections may be through some communication interfaces; indirect couplings or communication connections between devices or units may be electrical, mechanical, or other forms.

[0204] The units described as separate components may or may not be physically separate. The components shown as units may or may not be physical units; that is, they may be located in one place or distributed across multiple network units. Some or all of the units can be selected to achieve the purpose of this embodiment according to actual needs.

[0205] In addition, the functional units in the various embodiments of this application can be integrated into one processing unit, or each unit can exist physically separately, or two or more units can be integrated into one unit.

[0206] If the aforementioned functions are implemented as software functional units and sold or used as independent products, they can be stored in a processor-executable, non-volatile, 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. The aforementioned storage medium includes various media capable of storing program code, such as USB flash drives, portable hard drives, read-only memory (ROM), random access memory (RAM), magnetic disks, or optical disks.

[0207] Finally, it should be noted that the above-described embodiments are merely specific implementations of this application, used to illustrate the technical solutions of this application, and not to limit them. The scope of protection of this application is not limited thereto. Although this application has been described in detail with reference to the foregoing embodiments, those skilled in the art should understand that any person skilled in the art can still modify or easily conceive of changes to the technical solutions described in the foregoing embodiments, or make equivalent substitutions for some of the technical features, within the scope of the technology disclosed in this application. Such modifications, changes, or substitutions do not cause the essence of the corresponding technical solutions to deviate from the spirit and scope of the technical solutions of the embodiments of this application, and should all be covered within the scope of protection of this application. Therefore, the scope of protection of this application should be determined by the scope of the claims.

Claims

1. A method for designing longitudinal field coils in a fusion device based on semi-analytical magnetic field calculations, characterized in that, include: Establish a parameterized geometric model of the longitudinal field coil and global optimization decision variables; Electromagnetic field coupling calculations are performed on the coil units in the parameterized geometric model based on the semi-analytical magnetic field integral method. Construct an evaluation model for tension fluctuations coupled with electromagnetics; The differential evolution algorithm is used to perform global closed-loop optimization, and the output is the global optimal set of variables that minimizes the tension fluctuation rate. The optimal coil configuration is generated based on the global optimal variable set, and the precise analytical trajectory of the center line of the optimal coil configuration is obtained. The geometric parameters for manufacturing the longitudinal field coil are then output.

2. The method according to claim 1, characterized in that, The steps for establishing the parametric geometric model of the longitudinal field coil and the global optimization decision variables include: In cylindrical coordinates, the upper half of the coil above the equatorial plane is modeled using symmetry. The centerline of the upper part is defined as an arc that is continuously tangent to the inner leg of a vertical straight line and segment M. Define geometric control variables, including: half height of the straight section of the inner leg, polar angle division point of each arc segment, and radius of curvature of each arc segment; By establishing geometric constraints using recursive formulas and boundary conditions where the centerline closes outside the equatorial plane, two non-independent variables are analytically eliminated. Extract the set of independent variables as decision variables for subsequent optimization; Define the coil cross-sectional dimensions and arrange the two-dimensional profile in a uniform array along the circumferential direction to form a complete longitudinal field coil.

3. The method according to claim 2, characterized in that, The steps for performing electromagnetic field coupling calculations on the coil elements in the parameterized geometric model based on the semi-analytical magnetic field integration method include: Establish a local coordinate system for each coil and transform the global field point coordinates to the local coordinate system; A single longitudinal field coil is discretized into a straight conductor segment and 2M circular arc conductor units, wherein the 2M circular arc conductor units are symmetrically distributed above and below the equatorial plane; For the straight conductor segment, the magnetic field components are calculated using the analytical solution of the magnetic field of a three-dimensional block conductor; For the arc conductor segment, the spatial integral of the conductor cross section is analytically derived, and the integral with respect to the arc polar angle is transformed into a single numerical integral to calculate the magnetic field components. It iterates through all coils and units, superimposes all magnetic field components into vectors, and uses a vectorized computing architecture and just-in-time compilation acceleration technology for accelerated computation.

4. The method according to claim 1, characterized in that, The steps for constructing an evaluation model for tension fluctuations coupled with electromagnetics include: N evaluation points are sampled at equal intervals along the arc length of the coil centerline in the parametric geometric model; For each evaluation point, the circumferential magnetic induction intensity at that point is calculated using a semi-analytical magnetic field integral method, and the local radius of curvature of the evaluation point is extracted from the parameterized geometric model. Based on the total coil current, the circumferential magnetic induction intensity, and the calculated local electromagnetic tension at the evaluation point; Based on the tension values ​​of all evaluation points, determine the maximum tension value, minimum tension value, and average tension value; Tension fluctuation rate is defined as the objective function for optimization, and the tension fluctuation rate is determined based on the maximum tension value, minimum tension value, and average tension value.

5. The method according to claim 1, characterized in that, The steps for global closed-loop optimization based on the differential evolution algorithm, outputting the globally optimal set of variables that minimizes tension fluctuations, include: The search range is set for the global optimization decision variables, and an initial population consisting of multiple individuals is randomly generated; Perform mutation and crossover operations using the differential evolution algorithm on individuals in the initial population to generate new candidate individuals; Check whether the geometric parameters of each candidate individual satisfy the hard constraints of monotonically increasing polar angle, increasing radius of all arcs, and no geometric inflection points; A penalty value is assigned to candidate individuals that violate the constraints, and the tension volatility of candidate individuals that meet the constraints is calculated. A greedy selection strategy is adopted to retain candidate individuals whose fitness meets the conditions to enter the next generation. This process is repeated until the preset convergence condition is met, and the global optimal geometric parameters that minimize the tension fluctuation rate are output.

6. The method according to claim 2, characterized in that, The method further includes: Extract the globally optimal set of variables that minimizes tension fluctuation from a convergent differential evolution algorithm; Using the aforementioned geometric constraints, the remaining geometric parameters are solved analytically, and the coordinates of the centers of all circular arc segments are calculated to obtain the complete analytical trajectory of the coil centerline. Using a denser sampling point than in the optimization process, the electromagnetic performance of the reconstructed accurate geometric model is re-evaluated to verify the final tension fluctuation rate.

7. A design device for longitudinal field coils of a fusion device based on semi-analytical magnetic field calculation, characterized in that, include: The first module is used to establish the parametric geometric model of the longitudinal field coil and the global optimization decision variables; The first calculation module is used to perform electromagnetic field coupling calculations on the coil units in the parameterized geometric model based on the semi-analytical magnetic field integration method. The second module is used to construct an evaluation model for tension fluctuations in electromagnetic-mechanical coupling. The optimization module is used to perform global closed-loop optimization based on the differential evolution algorithm, and outputs the globally optimal set of variables that minimizes the tension fluctuation rate. The generation module is used to generate the optimal coil configuration based on the global optimal variable set, and to accurately analyze the trajectory of the center line of the optimal coil configuration, and output the geometric parameters for manufacturing the longitudinal field coil.

8. The apparatus according to claim 7, characterized in that, The first module is specifically used for: In cylindrical coordinates, the upper half of the coil above the equatorial plane is modeled using symmetry. The centerline of the upper part is defined as an arc that is continuously tangent to the inner leg of a vertical straight line and segment M. Define geometric control variables, including: half height of the straight section of the inner leg, polar angle division point of each arc segment, and radius of curvature of each arc segment; By establishing geometric constraints using recursive formulas and boundary conditions where the centerline closes outside the equatorial plane, two non-independent variables are analytically eliminated. Extract the set of independent variables as decision variables for subsequent optimization; define the coil cross-sectional dimensions and uniformly array the two-dimensional profile along the circumferential direction to form a complete longitudinal field coil.

9. The apparatus according to claim 8, characterized in that, The first calculation module is specifically used for: Establish a local coordinate system for each coil and transform the global field point coordinates to the local coordinate system; A single longitudinal field coil is discretized into a straight conductor segment and 2M circular arc conductor units, wherein the 2M circular arc conductor units are symmetrically distributed above and below the equatorial plane; For the straight conductor segment, the magnetic field components are calculated using the analytical solution of the magnetic field of a three-dimensional block conductor; For the arc conductor segment, the spatial integral of the conductor cross section is analytically derived, and the integral with respect to the arc polar angle is transformed into a single numerical integral to calculate the magnetic field components. It iterates through all coils and units, superimposes all magnetic field components into vectors, and uses a vectorized computing architecture and just-in-time compilation acceleration technology for accelerated computation.

10. The apparatus according to claim 7, characterized in that, The second establishment module is specifically used for: N evaluation points are sampled at equal intervals along the arc length of the coil centerline in the parametric geometric model; For each evaluation point, the circumferential magnetic induction intensity at that point is calculated using a semi-analytical magnetic field integral method, and the local radius of curvature of the evaluation point is extracted from the parameterized geometric model. Based on the total coil current, the circumferential magnetic induction intensity, and the calculated local electromagnetic tension at the evaluation point; Based on the tension values ​​of all evaluation points, determine the maximum tension value, minimum tension value, and average tension value; Tension fluctuation rate is defined as the objective function for optimization, and the tension fluctuation rate is determined based on the maximum tension value, minimum tension value, and average tension value.

11. An electronic device, characterized in that, include: The device includes a processor, a memory, and a bus. The memory stores machine-readable instructions executable by the processor. When the electronic device is running, the processor communicates with the memory via the bus. The machine-readable instructions are executed by the processor to perform the steps of the longitudinal field coil design method for a fusion device based on semi-analytical magnetic field calculation as described in any one of claims 1 to 6.

12. A computer-readable storage medium, characterized in that, The computer-readable storage medium stores a computer program that, when executed by a processor, performs the steps of the longitudinal field coil design method for a fusion device based on semi-analytical magnetic field calculation as described in any one of claims 1 to 6.

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