A design method and system for the centerline of the toroidal field coil in a fusion device

Abstract

This invention discloses a design method and system for the centerline of a fusion device's toroidal field coil, relating to the technical field of low-temperature and / or high-temperature superconducting magnet design. The design method specifically involves: initializing the centerline based on input toroidal field coil parameters; calculating the radius of curvature of the current centerline; establishing a toroidal field coil model and calculating the magnetic field on the current centerline; calculating the tension and tension instability of the current centerline; if the tension instability does not meet design requirements, correcting and updating the geometry of the current centerline, calculating the updated centerline, and continuing the iteration until the tension instability meets design requirements, thus completing the design of the optimized D-shaped centerline of the toroidal field coil. Based on accurate calculation of the centerline's magnetic field, this invention designs an optimized D-shaped centerline with higher tension constancy, which can reduce the tension non-uniformity on the centerline of the fusion device's toroidal field coil.

Description

TECHNICAL FIELD

[0001] The present application relates to the technical field of low temperature and / or high temperature superconducting magnet design, and particularly to a design method and system of a fusion device toroidal field coil center line. BACKGROUND

[0002] With the development of fusion technology, fusion power generation will become an important option to solve the human energy problem. The toroidal field coil of a fusion device is generally wound by superconducting conductors according to a specific shaped center line, which is very important for realizing the stable confinement of plasma. The toroidal field coil conductor carrying current will bear a huge electromagnetic force under the action of the toroidal magnetic field. This electromagnetic force causes the superconducting conductor to bear tension. The ideal toroidal field coil center line should make the tension borne by the toroidal field coil conductor constant, thereby avoiding performance degradation of the toroidal field coil conductor caused by excessive local tension. At present, the Princeton D-shaped or modified D-shaped center line is adopted in the design of most fusion device toroidal field coils. However, since the magnetic field used in the design of the two D-shaped center lines deviates from the real magnetic field, the variation range of the tension borne by the conductor is large and the constancy is poor.

[0003] The center line in the fusion field mainly refers to the center line of the toroidal field coil, which can be regarded as a geometric shape obtained by sweeping a cross section perpendicular to the center line around the center line. SUMMARY

[0004] In order to overcome the defects in the prior art, one of the purposes of the present application is to provide a design method of a fusion device toroidal field coil center line, which designs an optimized D-shaped center line with higher tension constancy on the basis of accurate calculation of the center line magnetic field, so as to reduce the non-uniformity of the tension on the fusion device toroidal field coil center line.

[0005] To achieve the above purpose, the present application adopts the following technical solutions, comprising:

[0006] A design method of a fusion device toroidal field coil center line, comprising the following steps:

[0007] S1, initializing the center line z(s) according to the input toroidal field coil parameters; wherein s is the arc length of the center line;

[0008] S2, calculating the curvature radius of the current center line ;

[0009] S3, establishing a toroidal field coil model to calculate the magnetic field on the current center line ;

[0010] S4, calculating the tension of the current center line ;

[0011] S5, calculate the tension instability of the current centerline. If the tension instability does not meet the design requirements, proceed to step S6; if the tension instability meets the design requirements, end the iteration and proceed to step S7.

[0012] S6, correct the geometry of the current centerline, that is, update the geometric coordinates of the current centerline, calculate the updated centerline, and then return to step S2 to continue iterating, that is, calculate the radius of curvature, tension, and tension instability of the updated centerline based on the updated centerline, and determine whether the tension instability meets the design requirements.

[0013] S7, the centerline whose output tension inconstancy meets the design requirements, and the design of the optimized D-shaped centerline of the circumferential field coil are completed.

[0014] Preferably, the detailed process of step S2 is as follows:

[0015] S21. For the current centerline, a fitting algorithm is used to fit the radial coordinate r and axial coordinate z of the centerline into functions r(s) and z(s) about the arc length s of the centerline.

[0016] S22, based on the r(s) and z(s) functions, calculate the radius of curvature of the current centerline using the plane curve curvature calculation formula. ;

[0017] The formula for calculating the curvature of a plane curve is:

[0018]

[0019] in, and These are the first and second derivatives of the function r(s) with respect to the arc length s of the centerline, respectively. and These are the first and second derivatives of the z(s) function with respect to the arc length s of the center line, respectively.

[0020] Preferably, in step S21, the fitting algorithm includes, but is not limited to, least squares fitting and cubic spline interpolation fitting.

[0021] The boundary conditions for the centerline are as follows: at the inner leg radius r1 of the centerline, the first derivatives of the functions r(s) and z(s) with respect to the arc length s of the centerline are 0 and 1, respectively; at the outer leg radius r2 of the centerline, the first derivatives of the functions r(s) and z(s) with respect to the arc length s of the centerline are 0 and -1, respectively.

[0022] Preferably, in step S3, the finite element method is used to establish a finite element model of the circumferential field coil based on the current centerline, and the magnetic field on the current centerline is calculated. ;

[0023] Alternatively, a semi-analytical method can be used to establish a circumferential field coil model based on the trapezoidal prism current, and then the magnetic field on the current centerline can be calculated using the analytical formula for the magnetic field of the trapezoidal prism current. .

[0024] Preferably, a semi-analytical method is used to calculate the magnetic field on the current centerline. The detailed process is as follows:

[0025] S31. After establishing the circumferential field coil model based on the current of the trapezoidal prism, the field points on the center line are transformed from the global coordinate system to the local coordinate system where the trapezoidal prism is located by translation and rotation.

[0026] S32, in the local coordinate system, the magnetic field at each field point is calculated using the analytical formula for the magnetic field of the current in the trapezoidal prism;

[0027] S33 transforms the magnetic field calculated in the local coordinate system to the global coordinate system through rotation transformation; in the global coordinate system, for each field point, the magnetic fields of all trapezoidal prism currents are accumulated to obtain the magnetic field of that field point.

[0028] Preferably, the detailed process of step S6 is as follows:

[0029] S61, define the following characteristic function. :

[0030]

[0031] S62, Based on the constant tension principle and the boundary conditions of the centerline, the geometry of the current centerline is corrected, and the updated radius of curvature is calculated in the same manner as in step S2. ;

[0032] The constant tension principle is as follows:

[0033]

[0034] Where I is the total operating current of the circumferential field coil;

[0035] S63, based on the updated radius of curvature and characteristic function The definition is used to calculate the updated feature function. ;

[0036] S64, based on the updated radius of curvature and updated characteristic functions The updated centerline is calculated. :

[0037] .

[0038] Preferably, in step S4, the tension of the current centerline The calculation is as follows:

[0039]

[0040] Where I is the total operating current of the circumferential field coil.

[0041] Preferably, the calculation method and design requirements for the tension inconstancy in step S5 are as follows:

[0042]

[0043] in, Indicates the maximum tension along the center line; This indicates the minimum tension on the center line; This indicates the average tension along the center line;

[0044] If the tension instability is greater than α%, it means that the tension instability does not meet the design requirements; if the tension instability is less than or equal to α%, it means that the tension instability meets the design requirements; where α≤0.1.

[0045] Preferably, in step S7, the centerline whose tension instability meets the design requirements is fitted using the least squares method with three or more tangent circular arcs, and the center coordinates, radius and angle of the three or more tangent circular arcs are output as parameters for optimizing the D-shaped centerline, thus obtaining the design result of the optimized D-shaped centerline.

[0046] The second objective of this invention is to provide a system applicable to the design method of the center line of the toroidal field coil in a fusion device, for implementing the design method of the center line of the toroidal field coil in a fusion device.

[0047] To achieve the above objectives, the present invention adopts the following technical solution, and the system includes the following components:

[0048] Parameter input module: Used to input the parameters of the circumferential field coil and initialize the center line;

[0049] Curvature radius calculation module: Used to calculate the curvature radius of the current centerline;

[0050] Magnetic field calculation module: used to calculate the magnetic field of the circumferential field coil system formed by the current centerline on the centerline;

[0051] Tension Calculation Module: Used to calculate the tension on the current centerline;

[0052] Tension Instability Evaluation Module: Used to evaluate whether the tension instability on the current centerline meets the design requirements;

[0053] Geometry correction module: used to correct the geometry of the current centerline according to the constant tension principle, so as to obtain an updated centerline;

[0054] Parameter output module: Used to perform least squares fitting on the centerline that meets the design requirements for tension instability, and outputs the center coordinates, radius and angle of the tangent arc obtained by fitting as parameters for optimizing the D-shaped centerline.

[0055] The advantages of this invention are:

[0056] (1) Based on the principle of constant tension, the present invention can achieve rapid optimization of the shape of the center line according to the input parameters.

[0057] (2) The magnetic field calculation method based on finite element method and semi-analytical magnetic field calculation method based on prism current of the present invention provides a solid foundation for the subsequent optimization of centerline tension through more accurate magnetic field calculation.

[0058] (3) Based on the accurate calculation of the magnetic field of the center line, the present invention designs an optimized D-shaped center line with higher tension constantness, thereby reducing the non-uniformity of tension on the center line of the circumferential field coil of the fusion device.

[0059] (4) The present invention uses the finite element method or semi-analytical method to establish the trapezoidal prism model of the circumferential field coil to achieve a more accurate calculation of the magnetic field of the center line; then, based on the constant tension principle and the integral form of the center line geometry correction formula, the shape of the center line is corrected, the shape of the center line is iterated, the tension instability is gradually reduced, and finally an optimized D-shaped center line with a tension instability of less than or equal to 0.1% is given.

[0060] (5) The present invention can perform least squares fitting of multiple arcs in the form of the optimized D-shaped center line of the iterative output, and quickly output the center coordinates, arc radius and arc angle of the tangent arc obtained by fitting as relevant parameters for the center line design, so as to realize the parameterized output of the optimized D-shaped center line. Attached Figure Description

[0061] Figure 1 This is a flowchart illustrating a design method for the centerline of a circumferential field coil in a fusion device according to the present invention.

[0062] Figure 2 This is the mesh model of the circumferential field coil based on the finite element method of the present invention.

[0063] Figure 3 This is the circumferential field coil model based on the current of a trapezoidal prism, as described in this invention.

[0064] Figure 4 This is a schematic diagram of the coordinate transformation used in the magnetic field calculation of this invention.

[0065] Figure 5 This is a comparison diagram of the analytical magnetic field and the real magnetic field along the center line of the Princeton D-shape and the modified D-shape based on the traditional design method.

[0066] Figure 6 This is a comparison diagram of the magnetic field on the center line obtained by the semi-analytical method of the present invention and the magnetic field on the center line obtained by the finite element method.

[0067] Figure 7 This is a comparison diagram of the tension distribution on the center line of the optimized D-shape obtained by the method of this invention with the tension distribution on the center lines of the Princeton D-shape and the modified D-shape obtained by the traditional method.

[0068] Figure 8 This is a schematic diagram showing that the center line of the present invention is fitted with multiple tangent circular arcs.

[0069] Figure 9 This is a system architecture diagram of the design of the center line of the circumferential field coil of a fusion device according to the present invention. Detailed Implementation

[0070] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0071] Depend on Figure 1 As shown, the design method for the centerline of the circumferential field coil of a fusion device according to the present invention is an iterative process, specifically including the following steps:

[0072] S1, the user inputs the basic parameters of the toroidal field coils for the fusion device design, including: the number of toroidal field coils N, the inner leg radius r1 of the toroidal field coil centerline, the outer leg radius r2 of the toroidal field coil centerline, the width w and thickness d of the toroidal field coil winding cross-section, and the total operating current I of a single toroidal field coil, etc. Then, based on the input data, the centerline... Initialize as a semicircle. Where s represents the arc length of the centerline.

[0073] S2, calculate the radius of curvature of the current centerline. .

[0074] S3. Calculate the magnetic field along the current centerline using the finite element method or a semi-analytical method. .

[0075] S4, Calculate the tension of the current centerline according to the tension calculation formula. .

[0076] S5. Based on the tension calculated in step S4, calculate the tension instability and determine whether the tension instability meets the design requirements. If the tension instability is greater than 0.1%, i.e. does not meet the design requirements, proceed to step S6; if the tension instability is less than or equal to 0.1%, i.e. meets the design requirements, end the iteration and proceed to step S7.

[0077] S6. Based on the constant tension principle, the geometry of the current centerline is corrected, i.e., the geometric coordinates of the current centerline are updated, and the updated centerline is calculated. Then, return to step S2 and continue iterating.

[0078] S7. For centerlines with a tension instability of less than or equal to 0.1%, the least squares method is used to fit three or more tangent circular arcs, and the centerline design result composed of the center coordinates, radius and angle of the three or more tangent circular arcs is output. Thus, the design of the optimized D-shaped centerline of the present invention is completed.

[0079] Currently, the magnetic field error of the centerline used in the design of the circumferential field coil of a fusion device is relatively large, resulting in a significant instability in the centerline tension. Therefore, this invention employs the finite element method or a semi-analytical method based on prism currents to establish a circumferential field coil model, enabling accurate calculation of the centerline magnetic field. Then, based on the geometric shape correction formula of the centerline, the shape of the centerline is iteratively adjusted to gradually reduce its tension instability, ultimately yielding an optimized D-shaped centerline with a tension instability of less than or equal to 0.1%.

[0080] Specifically, the detailed process of step S2 is as follows:

[0081] S21. For the current centerline, use the least squares method or cubic spline interpolation and other fitting algorithms to fit the r coordinates and z coordinates of the centerline into functions r(s) and z(s) about the arc length s of the centerline.

[0082] The centerline can be viewed as a curve located in the rz plane, where r represents the radial direction and z represents the axial direction. Therefore, the centerline can be described using its radial coordinates r and axial coordinates z. Once the r and z coordinates of the centerline are determined, its geometry is also determined. Furthermore, for ease of derivation of subsequent formulas, curves in the plane are often described using parametric equations with the arc length s of the centerline as a parameter.

[0083] S22, based on the r(s) and z(s) functions, the radius of curvature of the current centerline is calculated using the plane curve curvature calculation formula, as follows. :

[0084]

[0085] in, and These are the first and second derivatives of the function r(s) with respect to the arc length s of the centerline, respectively. and These are the first and second derivatives of the z(s) function with respect to the arc length s of the center line, respectively.

[0086] The fitting algorithm and boundary conditions used in step S2 are as follows:

[0087] The fitting algorithm can be selected from, but is not limited to, least squares fitting and cubic spline interpolation.

[0088] The boundary conditions for the centerline are as follows: at the inner leg radius r1 of the centerline, the first derivatives of the centerline's r(s) function and z(s) function with respect to the centerline's arc length s are 0 and 1, respectively; at the outer leg radius r2 of the centerline, the first derivatives of the centerline's r(s) function and z(s) function with respect to the centerline's arc length s are 0 and -1, respectively.

[0089] Specifically, the calculation of the magnetic field on the center line in step S3 includes two methods:

[0090] Method 1: From Figure 2 As shown, the finite element method is used to establish a finite element model of the circumferential field coil and calculate the magnetic field on the center line.

[0091] Method 2: From Figure 3 As shown, a semi-analytical method is used to establish a trapezoidal prism current model for the circumferential field coil. The magnetic field analysis formula for the trapezoidal prism current is then used to calculate the magnetic field along the center line. Figure 4 The following is a schematic diagram of the coordinate transformations used, and the detailed process of the semi-analytical method is as follows:

[0092] S31. After establishing the trapezoidal prism current model of the circumferential field coil, the field points on the center line are transformed from the global coordinate system to the local coordinate system where the trapezoidal prism is located by translation and rotation.

[0093] S32, in the local coordinate system, calculate the magnetic field at each field point using the analytical formula for the magnetic field of the current in the trapezoidal prism.

[0094] S33 transforms the magnetic field calculated in the local coordinate system to the global coordinate system through rotation. In the global coordinate system, for each field point, the magnetic fields of all trapezoidal prism currents are summed to obtain the magnetic field at that point.

[0095] Figure 5 The diagram shows the assumed magnetic field of the Princeton D-shaped centerline and the modified D-shaped centerline design, compared to their accurate magnetic field; a significant deviation is evident. Figure 5The curve of the magnetic field along the center line as a function of the radial coordinate r was plotted. The reason for plotting the change of the magnetic field with the radial coordinate r is that the geometry of the circumferential field coil determines that its magnetic field is not highly correlated with the longitudinal coordinate z, but highly correlated with the radial coordinate r.

[0096] Figure 6 The figure shows the centerline magnetic field calculated by the two magnetic field calculation methods described in this invention: the finite element method and the semi-analytical method. As can be seen from the figure, the centerline magnetic field calculated by the two methods is basically the same.

[0097] In step S3, after calculating the magnetic field on the center line, algorithms including but not limited to least squares method or cubic spline interpolation are used to numerically fit the magnetic field on the center line to obtain the magnetic field fitting function. .

[0098] Specifically, in step S4, the tension of the centerline is calculated according to the following formula:

[0099]

[0100] Specifically, in step S5, the tension instability is calculated based on the tension obtained in step S4 using the following formula:

[0101]

[0102] in, Indicates the maximum tension along the center line; This indicates the minimum tension on the center line; This indicates the average tension along the center line.

[0103] Specifically, the detailed process of step S6 is as follows:

[0104] S61, Define the characteristic function :

[0105]

[0106] According to the constant tension principle, the product of the magnetic field at any point on the center line and the radius of curvature at that point is... :

[0107]

[0108] We can obtain:

[0109]

[0110] Where s2 is the arc length of the centerline from radius r1 to radius r2; the arc length s of the centerline is 0 at r1 and s2 at r2.

[0111] S62, based on the constant tension principle and the boundary conditions of the centerline, the geometry of the current centerline is corrected, and the updated radius of curvature is calculated in the same manner as in step S2. .

[0112] Based on the constant tension principle—that is, the product of the magnetic field and the radius of curvature at each point on the centerline is constant—the updated radius of curvature is determined using the boundary conditions at the two endpoints (radial coordinates r1 and r2) and the vertex of the centerline. However, the constant tension principle only determines that the product of the radius of curvature and the magnetic field is constant; to determine the specific value of this constant, boundary conditions are needed. Therefore, calculating the updated radius of curvature also requires the corresponding boundary conditions on the centerline.

[0113] S63, based on the updated radius of curvature and characteristic functions The definition is used to calculate the updated feature function. .

[0114] S64, based on the updated radius of curvature and updated characteristic functions The updated centerline is calculated using the following formula. :

[0115]

[0116] Figure 7 The diagram shows a comparison of the tension distribution of the optimized D-shaped centerline calculated using the method of this invention, compared with the Princeton D-shaped centerline and the modified D-shaped centerline. It is evident that the tension constancy of the optimized D-shaped centerline calculated using the method of this invention is superior to that of the Princeton D-shaped centerline and the modified D-shaped centerline.

[0117] Figure 8 The results show an optimized D-shaped centerline calculated for this invention, fitted with three tangent circular arcs.

[0118] Depend on Figure 9 As shown, a design system for the centerline of the circumferential field coil of a fusion device according to the present invention includes:

[0119] Parameter input module: Used to input the parameters of the circumferential field coil and initialize the center line.

[0120] Curvature radius calculation module: Used to calculate the curvature radius of the current centerline.

[0121] Magnetic field calculation module: used to calculate the magnetic field of the toroidal field coil system formed by the current centerline on the centerline.

[0122] Tension Calculation Module: Used to calculate the tension on the current centerline.

[0123] Tension Instability Evaluation Module: Used to evaluate whether the tension instability on the current centerline meets the error requirements.

[0124] The geometry correction module is used to correct and update the geometry of the current centerline according to the constant tension principle, thus obtaining an updated centerline. The geometry correction module includes: a radius of curvature update unit, a characteristic function update unit, and a centerline update unit.

[0125] Parameter output module: Used to perform least squares fitting on the centerline that meets the design requirements for tension instability, and outputs the center coordinates, radius and angle of the tangent arc obtained by fitting as parameters for optimizing the D-shaped centerline.

[0126] The above are merely preferred embodiments of the present invention and are not intended to limit the scope of the present invention. Any modifications, equivalent substitutions, and improvements made within the spirit and principles of the present invention should be included within the scope of protection of the present invention.

Claims

1. A method of designing a central line of a toroidal field coil of a fusion device, characterized by, The method comprises the following steps: S1, initializing the center line z(s) according to the input toroidal field coil parameters; wherein s is the arc length of the center line; S2, calculate the radius of curvature of the current centerline ; S3, establish a toroidal field coil model, calculate the magnetic field on the current center line ; S4, calculate the tension of the current centerline ; S5, calculating the tension non-constant degree of the current center line, if the tension non-constant degree does not meet the design requirement, then entering step S6; if the tension non-constant degree meets the design requirement, then ending iteration, entering step S7; S6, correcting the geometric shape of the current center line, i.e. updating the geometric coordinates of the current center line, calculating the updated center line, and then returning to step S2 for continuous iteration, i.e. calculating the radius of curvature, tension, and tension non-constant degree of the updated center line according to the updated center line, and judging whether the tension non-constant degree meets the design requirement; S7, outputting the center line with the tension non-constant degree meeting the design requirement, and completing the design of the optimized D-shaped center line of the toroidal field coil; The detailed process of step S2 is shown as follows: S21, for the current center line, using a fitting algorithm to fit the radial coordinate r and the axial coordinate z of the center line into functions r(s), z(s) about the arc length s of the center line; S22, according to r(s) and z(s) functions, the current center line curvature radius is calculated by using a plane curve curvature calculation formula ; The plane curve curvature calculation formula is: wherein and are the first and second derivatives of the function r(s) with respect to the centerline arc length s, respectively; and are the first and second derivatives of the function z(s) with respect to the centerline arc length s, respectively.

2. The method of designing a tokamak poloidal field coil centerline according to claim 1, wherein, In step S21, the fitting algorithm includes but is not limited to the least square fitting method and the cubic spline interpolation fitting method; The boundary condition of the center line is that the first derivatives of the functions r(s), z(s) about the arc length s of the center line are 0 and 1 respectively at the inner leg radius r1 of the center line, and the first derivatives of the functions r(s), z(s) about the arc length s of the center line are 0 and -1 respectively at the outer leg radius r2 of the center line.

3. The method of designing a poloidal field coil center line of a fusion device according to claim 1, wherein In step S3, a finite element method is used to establish a finite element model of the toroidal field coil based on the current central line, and the magnetic field on the current central line is calculated ; Alternatively, a semi-analytical method is used to establish a toroidal field coil model based on trapezoidal prism current, and then the magnetic field analytical formula of trapezoidal prism current is used to calculate the magnetic field on the current center line .

4. The method of designing a poloidal field coil center line of a fusion device according to claim 3, wherein Semi-analytical method is used to calculate the magnetic field on the current centerline The detailed procedure is shown below: S31, after establishing the toroidal field coil model based on the trapezoidal prism current, the field points on the center line are transformed from the global coordinate system to the local coordinate system in which the trapezoidal prism is located through translation and rotation; S32, in the local coordinate system, the magnetic fields of the field points are calculated through the magnetic field analytical formula of the trapezoidal prism current; S33, the magnetic fields calculated in the local coordinate system are transformed to the global coordinate system through rotation transformation; in the global coordinate system, the magnetic fields of all the trapezoidal prism currents are accumulated for each field point, so as to obtain the magnetic field of the field point.

5. The method of designing a poloidal field coil center line of a fusion device according to claim 1 or 2, wherein The detailed process of step S6 is shown as follows: S61, a characteristic function defined as follows : S62, based on the constant tension principle and the boundary condition of the center line, the geometry of the current center line is corrected, and the updated curvature radius is calculated in the manner of step S2 ; The constant tension principle is shown as follows: Wherein I is the total operating current of the toroidal field coil. S63, based on the updated radius of curvature and the characteristic function are calculated based on the definition of the updated characteristic function ; S64, based on the updated radius of curvature and the updated feature function , the updated centerline is calculated : 。 6. The method of designing a tokamak poloidal field coil centerline of claim 1, wherein, In step S4, the tension of the current center line is calculated as shown below: Wherein I is the total operating current of the toroidal field coil.

7. The method of designing a tokamak poloidal field coil centerline of claim 1, wherein, In step S5, the calculation method of the tension non-constant degree and the design requirement are shown as follows: wherein, represents the maximum tension on the centerline; represents the minimum tension on the centerline; represents the average tension on the centerline; If the tension non-constant degree is greater than a%, it indicates that the tension non-constant degree does not meet the design requirement; if the tension non-constant degree is less than or equal to a%, it indicates that the tension non-constant degree meets the design requirement; wherein a≤0.

1.

8. The method according to claim 1, in step S7, the center line with the tension non-constant degree meeting the design requirement is fitted by using the least square method with 3 or more tangent circular arcs, and the center coordinates, the circular arc radius and the circular arc angle of the 3 or more tangent circular arcs are output as the parameters of the optimized D-shaped center line, so as to obtain the design result of the optimized D-shaped center line.

9. A system for use in a method of designing a centerline for a toroidal field coil of a fusion device as defined in claim 1, wherein, The method comprises the following components: A parameter input module for inputting the parameters of the toroidal field coil and initializing the center line; a curvature radius calculation module for calculating the curvature radius of the current center line; a magnetic field calculation module for calculating the magnetic field of the toroidal field coil system formed by the current center line on the center line; a tension calculation module for calculating the tension on the current center line; a tension inconstancy evaluation module for evaluating whether the tension inconstancy on the current center line meets the design requirement; a geometry correction module for correcting the geometry of the current center line according to the constant tension principle to obtain an updated center line; a parameter output module for least square fitting of the center line whose tension inconstancy meets the design requirement, and outputting the center coordinates, the arc radius and the arc angle of the fitted tangent circular arc as the parameters of the optimized D-shaped center line.

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