Design method of multi-pole magnet based on three-dimensional optimization of extended inverse boundary element

Abstract

The application discloses a multi-pole magnet design method based on three-dimensional optimization of an extended inverse boundary element, relates to the technical field of superconducting magnets, and comprises the following steps: determining a coil distribution surface of a magnet according to actual requirements; performing grid segmentation according to the coil distribution surface to obtain a grid model; defining grid node current density to be solved on grid nodes of the grid model; constructing a linear scalar magnetic field superposition by performing linear scalar magnetic field superposition on a vector target magnetic field; optimizing a function function Phi of the linear scalar magnetic field superposition to solve the grid node current density; and obtaining a multi-pole magnet coil structure according to the distribution of the solved grid node current density. The application takes the magnetic field distribution of the entire three-dimensional target region as an optimization target, improves the axial magnetic field uniformity of the multi-pole magnet, allows the shape of a source point and a field point to be freely defined, is compact and efficient, realizes higher space utilization and a higher target magnetic field, and can take into account the convenience of mechanical structure design and skeleton processing.

Description

Technical Field

[0001] This invention relates to the field of superconducting magnet technology, and in particular to a multipole magnet design method based on extended inverse boundary element three-dimensional optimization. Background Technology

[0002] Superconducting multipole magnets are high-precision magnetic field devices developed based on the low-temperature zero-resistance properties of superconducting materials. They generate specific magnetic field distributions such as dipole, quadrupole, and hexapole through specially configured coils (e.g., saddle-shaped, spiral, and cosine-shaped). The core applications are deflection, focusing, guidance, and nonlinear correction of particle beams. Superconducting multipole magnets are core components of large-scale high-energy physics facilities such as the Large Hadron Collider (LHC) in Europe, the High Intensity Reduction Facility (HIRFL) in Lanzhou, and the Shanghai Synchrotron Radiation Facility (SSRF). Their technological evolution has consistently focused on breaking through field strength limits, improving magnetic field quality, optimizing low-temperature stability, and reducing the risk of quenching. They are one of the core technologies driving the development of high-energy physics research, advanced manufacturing, and precision medicine. Currently, superconducting multipole magnets are based on the approximate design of infinitely long current lines. Various extended coil configurations for multipole magnets have been proposed, such as ordinary coil magnets, Block magnets, and cosine magnets. Among these, cosine distributed magnets are more widely used due to their high magnetic field uniformity and low Lorentz force accumulated on the coils. Furthermore, cosine magnets can be classified into ordinary cosine magnets, tilted cosine (CCT) magnets, discrete cosine (DCT) magnets, and uni-layer cosine magnets.

[0003] However, the aforementioned superconducting multipole magnets are all based on a two-dimensional approximation design method, with further approximation methods used for the structures at both ends of the magnet. Therefore, only the magnetic field quality requirements in the axial midplane of the magnet can be guaranteed. Once away from the axial midplane, the magnetic field quality generated by this type of magnet decreases rapidly, resulting in severe distortion of the magnetic field quality at both ends of the magnet. On the other hand, limited by current design methods, most coil frames are restricted to cylindrical or curved cylindrical structures, which cannot be well matched with elliptical beam cross-sections. This leads to lower space utilization of the coils and makes it difficult to achieve higher field strengths in the target region. It also brings inconvenience to frame fabrication and structural design, and the frame fabrication cost is high. Summary of the Invention

[0004] This invention provides a multipole magnet design method based on extended inverse boundary element three-dimensional optimization. This method addresses the problems in existing technologies where the two-dimensional approximation method leads to severe distortion of the magnetic field quality at both ends of the magnet, and where the coil frame is limited to cylindrical or curved cylindrical structures, which cannot be well matched with the elliptical beam cross-section, resulting in low space utilization of the coil, difficulty in achieving higher field strength in the target area, inconvenience for frame processing and structural design, and high frame processing costs.

[0005] On one hand, embodiments of the present invention provide a multipole magnet design method based on extended inverse boundary element three-dimensional optimization, including:

[0006] The coil distribution surface of the magnet is determined according to actual needs;

[0007] A mesh model is obtained by meshing the coil distribution surface.

[0008] Define the grid node current density to be solved on the grid nodes of the grid model;

[0009] Constructed by superimposing linear and scalar magnetic fields on the target vector magnetic field:

[0010] The grid node current density is obtained by optimizing the function Φ constructed by the superposition of the linear scalar magnetic fields.

[0011] The multipole magnet coil structure is obtained based on the solved distribution of the grid node current density;

[0012] A multipole magnet is fabricated based on the described multipole magnet coil structure.

[0013] In one possible implementation, defining the grid node current density to be solved on the grid nodes of the grid model includes:

[0014] The grid node current density is defined according to the following formula:

[0015] ;

[0016] in, Spatial location r The current density vector at that location, N This is the total number of grid nodes; n It is the node index, indicating the index of all current nodes traversed, from 1 to... N ; I n It is the first n The undetermined current density at each node, f n ( r ) is the first n The current basis function corresponding to each node is related to the spatial location. r Related functions.

[0017] In one possible implementation, the method involves constructing the vector target magnetic field by superimposing linear scalar magnetic fields, including:

[0018] The superimposed triaxial magnetic flux density, derived from Biot-Saffar's law and the current density at the grid nodes, is shown in the following equation:

[0019] ;

[0020] ;

[0021] ;

[0022] in, It is a point in the derivation space r The x-axis component of the magnetic flux density at that location; r It is the position vector of the magnetic field to be calculated in space. x , y , z It is a venue r The rectangular coordinate components; x’ , y’ , z’ It is the source point r′ The rectangular coordinate components; μ 0 is the permeability of free space; N This is the total number of grid nodes; n It is the node index, indicating the index of all current nodes traversed, from 1 to... N ; The current basis function of the nth node is in x , y , z The components are used to describe the first... n The spatial distribution of current at each node; This represents the distance from the field point to the source point, which is the straight-line distance between the point in space where the magnetic field to be calculated and the current node.

[0023] The target magnetic field distribution to be optimized is defined as three magnetic field components. B x (r), B y (r), B z Any combination of (r) is shown in the following equation:

[0024] ;

[0025] in, The target is a superimposed magnetic field that needs to be optimized; a , b , c It is a component adjustment coefficient, used to control... B x , B y , B z The weights of these three magnetic field components in the target magnetic field, These are the magnetic induction intensities at spatial point r, respectively. x ,y , z Quantity.

[0026] In one possible implementation, the optimization of the function Φ constructed by the superposition of the linear scalar magnetic fields is performed using the least squares method.

[0027] In one possible implementation, the optimized function Φ is shown in the following equation:

[0028] ;

[0029] in, These are adjustment coefficients, each responsible for adjusting the magnet inductance during the optimization process. L Wire consumption for magnet coils P , x Torque in direction M x , y Torque in direction M y and z Torque in direction M z Importance percentage; W For different positions r k Weighting coefficients at each location; The target magnetic field distribution is known. The magnetic field distribution is calculated based on the grid node current density. K It represents the total number of grid nodes around the magnet. k It is the sequence number of the grid node surrounding the magnet.

[0030] In one possible implementation, the multipole magnet coil structure is obtained based on the solved distribution of the grid node current density, including:

[0031] The three-dimensional coil structure of the multipole magnet coil is obtained by dividing the obtained grid node current density distribution into contour lines.

[0032] In one possible implementation, fabricating a multipole magnet based on the multipole magnet coil structure involves fabricating a real multipole magnet coil based on the three-dimensional coil structure.

[0033] The multipole magnet is assembled based on the actual multipole magnet coil.

[0034] The multipole magnet design method based on extended inverse boundary element three-dimensional optimization in this invention has the following advantages:

[0035] (1) Taking the magnetic field distribution of the entire three-dimensional target region as the optimization target, the complete three-dimensional structure of the coil can be obtained directly through the three-dimensional optimization algorithm, which can significantly improve the axial magnetic field uniformity of the superconducting multipole magnet.

[0036] (2) The extended inverse boundary element algorithm allows for free definition of the shape of the source point and the field point. The new magnet is compact and efficient, achieving higher space utilization and a higher target magnetic field, while also taking into account the convenience of its mechanical structure design and skeleton processing. Attached Figure Description

[0037] To more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are only some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0038] Figure 1 A flowchart of a multipole magnet design method based on extended inverse boundary element three-dimensional optimization provided in this application embodiment;

[0039] Figure 2 A schematic diagram of the multipole magnet coil design process provided in this application embodiment for the multipole magnet design method based on extended inverse boundary element three-dimensional optimization;

[0040] Figure 3 A comparison diagram of the structure of a multipole magnet based on extended inverse boundary element three-dimensional optimization and a binary magnet coil designed by discrete cosine method provided in the embodiments of this application (DCT: discrete cosine method, EIBEM: extended inverse boundary element method, hexagon: hexagonal, cylinder: cylindrical).

[0041] Figure 4 A comparison of the axial magnetic fields of a multipole magnet designed based on extended inverse boundary element three-dimensional optimization and a binary magnet designed using the discrete cosine method, provided for embodiments of this application (DCT: Discrete Cosine Method, EIBEM: Extended Inverse Boundary Element Method, hexagon: hexagonal, cylinder: cylindrical).

[0042] Figure 5 A comparison of the axial magnetic field normalization of a multipole magnet designed based on extended inverse boundary element three-dimensional optimization and a binary magnet designed by discrete cosine method, provided for embodiments of this application (DCT: discrete cosine method, EIBEM: extended inverse boundary element method, hexagon: hexagonal, cylinder: cylindrical).

[0043] Figure 6A comparison of the transverse magnetic field at the end of a multipole magnet designed based on extended inverse boundary element three-dimensional optimization and discrete cosine method provided for embodiments of this application (DCT: Discrete cosine method, EIBEM: Extended inverse boundary element method, hexagon: hexagonal, cylinder: cylindrical).

[0044] Figure 7 The diagram shows the current density distribution and coil structure of four-pole and six-pole coils designed based on the extended inverse boundary element three-dimensional optimization method provided in the embodiments of this application. Detailed Implementation

[0045] 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.

[0046] Figure 1 A flowchart illustrating the multipole magnet design method based on extended inverse boundary element three-dimensional optimization provided in this application embodiment; the present invention provides a multipole magnet design method based on extended inverse boundary element three-dimensional optimization, including:

[0047] The coil distribution surface of the magnet is determined according to actual needs;

[0048] A mesh model is obtained by meshing the coil distribution surface.

[0049] Define the grid node current density to be solved on the grid nodes of the grid model;

[0050] Constructed by superimposing linear and scalar magnetic fields on the target vector magnetic field:

[0051] The grid node current density is obtained by optimizing the function Φ constructed by the superposition of the linear scalar magnetic fields.

[0052] The multipole magnet coil structure is obtained based on the solved distribution of the grid node current density;

[0053] A multipole magnet is fabricated based on the described multipole magnet coil structure.

[0054] The grid node current density to be solved is defined on the grid nodes of the grid model, including:

[0055] The grid node current density is defined according to the following formula:

[0056] ;

[0057] in, Spatial location r The current density vector at that location, N This is the total number of grid nodes; n It is the node index, indicating the index of all current nodes traversed, from 1 to... N ; I n It is the first n The undetermined current density at each node, f n ( r ) is the first n The current basis function corresponding to each node is related to the spatial location. r Related functions.

[0058] The construction of a vector target magnetic field by superimposing linear scalar magnetic fields includes:

[0059] The superimposed triaxial magnetic flux density, derived from Biot-Saffar's law and the current density at the grid nodes, is shown in the following equation:

[0060] ;

[0061] ;

[0062] ;

[0063] in, It is a point in the derivation space r The x-axis component of the magnetic flux density at that location; r It is the position vector of the magnetic field to be calculated in space. x , y , z It is a venue r Cartesian coordinate components; x’ , y’ , z’ It is the source point r′ Cartesian coordinate components; μ 0 is the permeability of free space; N This is the total number of grid nodes; n It is the node index, indicating the index of all current nodes traversed, from 1 to... N ; The current basis function of the nth node is in x , y , z The components are used to describe the first... n The spatial distribution of current at each node; This represents the distance from the field point to the source point, which is the straight-line distance between the point in space where the magnetic field to be calculated and the current node.

[0064] The target magnetic field distribution to be optimized is defined as three magnetic field components. B x (r), B y (r), B z Any combination of (r) is shown in the following equation:

[0065] ;

[0066] in, The target is a superimposed magnetic field that needs to be optimized; a , b , c It is a component adjustment coefficient, used to control... B x , B y , B z The weights of these three magnetic field components in the target magnetic field, These are the magnetic induction intensities at spatial point r, respectively. x , y , z Quantity.

[0067] The optimization of the function Φ constructed by the superposition of the linear scalar magnetic fields is performed using the least squares method.

[0068] The optimized function Φ is shown in the following equation:

[0069] ;

[0070] in, These are adjustment coefficients, each responsible for adjusting the magnet inductance during the optimization process. L Wire consumption for magnet coils P , x Torque in direction M x , y Torque in direction M y and z Torque in direction M z Importance percentage; W For different positions r k Weighting coefficients at each location; The target magnetic field distribution is known. The magnetic field distribution is calculated based on the grid node current density. K It represents the total number of grid nodes around the magnet. k It is the sequence number of the grid node surrounding the magnet.

[0071] The multipole magnet coil structure obtained from the solved distribution of the grid node current density includes:

[0072] The three-dimensional coil structure of the multipole magnet coil is obtained by dividing the obtained grid node current density distribution into contour lines.

[0073] The process of fabricating a multipole magnet based on the described multipole magnet coil structure involves creating a real multipole magnet coil based on the described three-dimensional coil structure.

[0074] The multipole magnet is assembled based on the actual multipole magnet coil.

[0075] For example, optimizing the function Φ constructed by the superposition of the linear scalar magnetic fields to solve for the grid node current density includes:

[0076] The target magnetic field distribution to be optimized is defined as three magnetic field components. B x (r), B y (r), B z Any combination of (r) is shown in the following equation:

[0077] ;

[0078] in, The target magnetic field distribution to be optimized; a , b , c It is a component adjustment coefficient, used to control... B x , B y , B z The weights of these three magnetic field components in the target magnetic field, y and z are the x, y, and z components of the magnetic field strength at point r in space, respectively.

[0079] The design of multipolar magnetic fields generally only involves the first two terms. Here, a, b, and c are adjustment coefficients. Then, the function is defined and optimized using the least squares method as shown in the following equation:

[0080] ;

[0081] in, These are adjustment coefficients, each responsible for adjusting the magnet inductance during the optimization process. L Wire consumption for magnet coils P , x Torque in direction M x , yTorque in direction M y and z Torque in direction M z Importance percentage; W For different positions r k Weighting coefficients at each location; The target magnetic field distribution is known. The magnetic field distribution is calculated based on the grid node current density. K It represents the total number of grid nodes around the magnet. k It is the sequence number of the grid node surrounding the magnet.

[0082] The current density I on the grid nodes of the coil distribution surface can be obtained by using the least squares optimization algorithm. n ;

[0083] Furthermore, the coil structure can be obtained by drawing contour lines on the current density distribution at the grid nodes.

[0084] In one possible embodiment, taking a bent diode magnet coil as an example, the process of designing a multipole magnet coil using the extended inverse boundary element algorithm is as follows: Figure 2 As shown:

[0085] (1) Determine the distribution of the coil surface (outer curved cylindrical surface) and the target field points (distribution of the middle ring points);

[0086] (2) Determine the magnetic field distribution of the target field point (e.g., the polar field distribution is a uniform field). B t ( r )= B y );

[0087] (3) The current density distribution on the grid nodes of the coil surface is obtained using an optimization algorithm;

[0088] (4) The results in (3) are divided into contour lines to obtain a two-dimensional distribution map of the coil structure;

[0089] (5) A three-dimensional coil structure is obtained by transforming the two-dimensional coil structure. Finally, a real coil can be obtained through engineering physical design.

[0090] Figure 3 A comparison is presented of straight cylindrical, hexagonal, and discrete cosine coil structures designed based on the extended inverse boundary element (EBElement) 3D optimization algorithm. Due to the inherent 3D optimization nature, the EBElement-based structure is more complex. In particular, the fingerprint-like structure at the coil ends significantly improves the field quality at the coil ends. Figure 4 ,5 and Figure 6 (T value represents the magnetic field strength, specifically the magnetic induction intensity of the area corresponding to the color in the diagram.) This section compares the axial magnetic field and transverse magnetic field at the coil ends produced by different coil structures under the same coil volume and turn spacing constraints. DCT represents a discrete cosine coil structure, EIBEM hexagon represents a hexagonal coil structure designed based on the extended inverse boundary element algorithm, and EIBEM cylinder represents a cylindrical coil structure designed based on the extended inverse boundary element algorithm. It can be seen that the axial magnetic field uniformity produced by the coil structure designed using the extended inverse boundary element 3D optimization algorithm is significantly improved, with the magnetic field uniformity at the coil ends increasing by approximately 20 times. Furthermore, the hexagonal coil structure with an inscribed cylinder produces a center field strength approximately 9% higher than the cylindrical coil structure because the coil is closer to the target area.

[0091] Figure 7 The designs of linear four-pole and six-pole coils based on the extended inverse boundary element method (IB / BEM) 3D optimization algorithm are presented. It can be seen that both coils are planar structures. This means that the coil frame can be fabricated using only flatbed machining followed by assembly, eliminating the need for five-axis machining equipment. Compared to cylindrical coil structures, this planar structure significantly reduces the fabrication difficulty and cost of the coil frame.

[0092] Although preferred embodiments of the invention have been described, those skilled in the art, upon learning the basic inventive concept, can make other changes and modifications to these embodiments. Therefore, the appended claims are intended to be interpreted as including both the preferred embodiments and all changes and modifications falling within the scope of the invention.

[0093] Obviously, those skilled in the art can make various modifications and variations to this invention without departing from its spirit and scope. Therefore, if these modifications and variations fall within the scope of the claims of this invention and their equivalents, this invention also intends to include these modifications and variations.

Claims

1. A multipole magnet design method based on extended inverse boundary element three-dimensional optimization, characterized in that, include: The coil distribution surface of the magnet is determined according to actual needs; A mesh model is obtained by meshing the coil distribution surface. Define the grid node current density to be solved on the grid nodes of the grid model; Constructed by superimposing linear and scalar magnetic fields on the target vector magnetic field: The target magnetic field distribution to be optimized is defined as three magnetic field components. B x (r), B y (r), B z Any combination of (r) is shown in the following equation: ； in, The target is a superimposed magnetic field that needs to be optimized; a , b , c It is a component adjustment coefficient, used to control... B x , B y , B z The weights of these three magnetic field components in the target magnetic field, These are the magnetic induction intensities at spatial point r, respectively. x , y , z Quantity; The grid node current density is obtained by optimizing the function Φ constructed by the superposition of the linear scalar magnetic fields. The optimized function Φ is shown in the following equation: ； in, These are adjustment coefficients, each responsible for adjusting the magnet inductance during the optimization process. L Wire consumption for magnet coils P , x Torque in direction M x , y Torque in direction M y and z Torque in direction M z Importance percentage; W For different positions r k Weighting coefficients at each location; The target magnetic field distribution is known. The magnetic field distribution is calculated based on the grid node current density. K It represents the total number of grid nodes around the magnet. k It is the sequence number of the grid node surrounding the magnet; The multipole magnet coil structure is obtained based on the solved distribution of the grid node current density; A multipole magnet is fabricated based on the described multipole magnet coil structure.

2. The multipole magnet design method based on extended inverse boundary element three-dimensional optimization according to claim 1, characterized in that, The grid node current density to be solved is defined on the grid nodes of the grid model, including: The grid node current density is defined according to the following formula: ； in, Spatial location r The current density vector at that location, N This is the total number of grid nodes; n It is the node index, indicating the index of all current nodes traversed, from 1 to... N ; I n It is the first n The undetermined current density at each node, f n ( r ) is the first n The current basis function corresponding to each node is related to the spatial location. r Related functions.

3. The multipole magnet design method based on extended inverse boundary element three-dimensional optimization according to claim 2, characterized in that, The construction of a vector target magnetic field by superimposing linear scalar magnetic fields also includes: The superimposed triaxial magnetic flux density, derived from Biot-Saffar's law and the current density at the grid nodes, is shown in the following equation: ； ； ； in, It is a point in the derivation space r The x-axis component of the magnetic flux density at that location; r It is the position vector of the magnetic field to be calculated in space. x , y , z It is a venue r Cartesian coordinate components; x’ , y’ , z’ It is the source point r′ Cartesian coordinate components; μ 0 is the permeability of free space; N This is the total number of grid nodes; n It is the node index, indicating the index of all current nodes traversed, from 1 to... N ; The current basis function of the nth node is in x , y , z The components are used to describe the first... n The spatial distribution of current at each node; This represents the distance from the field point to the source point, which is the straight-line distance between the point in space where the magnetic field to be calculated and the current node.

4. The multipole magnet design method based on extended inverse boundary element three-dimensional optimization according to claim 3, characterized in that, The optimization of the function Φ constructed by the superposition of the linear scalar magnetic fields is performed using the least squares method.

5. The multipole magnet design method based on extended inverse boundary element three-dimensional optimization according to claim 1, characterized in that, The multipole magnet coil structure obtained from the solved distribution of the grid node current density includes: The three-dimensional coil structure of the multipole magnet coil is obtained by dividing the obtained grid node current density distribution into contour lines.

6. The multipole magnet design method based on extended inverse boundary element three-dimensional optimization according to claim 5, characterized in that, The process of fabricating a multipole magnet based on the described multipole magnet coil structure involves creating a real multipole magnet coil based on the described three-dimensional coil structure. The multipole magnet is assembled based on the actual multipole magnet coil.

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