Magnetic design method of Halbach magnetic ring based on neural network

Abstract

The invention relates to a magnetic design method for a Halbach magnet ring based on a neural network, and the method can quickly and accurately complete the magnetic design of the Halbach magnet ring according to the needs of a user, and is especially suitable for a thin magnet. Compared with the prior art, the Halbach magnet optimization method is better in callable performance, the Halbach magnet optimization method can be directly integrated into an optimization program of a user to complete optimization of other targets, optimization parameters needing to be adjusted are still size parameters of the Halbach magnet, parameter adjustment is visual and has engineering realizability, and secondary decomposition of intermediate variables is avoided.

Description

Technical Field

[0001] The present application relates to the field of magnet design in accelerator physics, and in particular to a magnetic design method of a Halbach magnetic ring based on a neural network. Background Art

[0002] In 1980, Professor Klaus Halbach of the Lawrence Berkeley National Laboratory in the United States obtained the Halbach magnet by assembling permanent magnets during an electron acceleration experiment. The design goal of this magnet is to arrange permanent magnets with different magnetization directions at a certain angle so that the magnetic field within its inner radius is significantly stronger than that on the outer surface, and the strongest magnetic field is generated within the working target range with the least amount of magnetic blocks. The Halbach magnetic ring is a ring-shaped Halbach magnet used in high-energy physics fields such as large accelerator focusing and deflection systems and magnetic cooling devices. Due to its excellent electromagnetic properties, it has been widely used in industrial fields such as nuclear magnetic resonance systems, magnetic levitation devices, and permanent magnet motors in recent years.

[0003] At present, the research on the magnetic field of Halbach magnetic ring mainly focuses on two-dimensional theoretical methods and three-dimensional finite element simulation methods. et al. derived the magnetic vector potential, magnetic field and magnetic induction intensity of the two-dimensional Halbach magnetic ring based on Maxwell's equations, and compared them with the results obtained by the two-dimensional numerical method. This method is relatively fast and suitable for preliminary evaluation. In 2013, Chen Yin et al. from Southwest Jiaotong University used the surface current to replace the magnetic field generated by the Halbach magnet based on the Ampere circulation hypothesis, and calculated the magnetic field intensity at any point in the two-dimensional plane using the superposition principle. When the axial / radial scale ratio is less than a certain value, the end effect of the magnet cannot be ignored, that is, the influence of the three-dimensional thickness direction on the plane magnetic field distribution needs to be considered. The three-dimensional finite element simulation method can obtain the magnetic induction intensity at any point in the space range by solving the Maxwell equations under the boundary conditions, with high accuracy.

[0004] Currently, various application scenarios have put forward higher and higher requirements on the spatial size, materials, and environmental adaptability of Halbach magnets. However, it is difficult to directly optimize the parameters of the magnets according to the final needs of users with existing methods. They often perform secondary decomposition of intermediate process variables, which is time-consuming and unintuitive. Sometimes it is even difficult to decompose them into parameters with engineering processability. Summary of the invention

[0005] In order to overcome at least one deficiency in the prior art, the present application provides a magnetic design method of a Halbach magnetic ring based on a neural network.

[0006] In a first aspect, a magnetic design method of a Halbach magnetic ring based on a neural network is provided, comprising:

[0007] Constructing a network training data set, the network training data set includes an input set and an output set; the input set is a plurality of sets of magnet size information randomly generated within a set range, and the output set is a correction coefficient corresponding to the input set; the correction coefficient includes a correction coefficient of a key magnetic parameter and a correction coefficient of an effective magnetic path length, and / or a coefficient of variation in the radial direction of the magnetic induction intensity of the transverse central section of the magnet;

[0008] Training the neural network based on the network training data set to obtain a trained neural network;

[0009] Input the magnet size information into the trained neural network to obtain the predicted value of the correction coefficient;

[0010] The two-dimensional key magnetic parameters are calculated based on the magnet size information;

[0011] According to the predicted values ​​of the two-dimensional key magnetic parameters and the correction coefficients, the predicted values ​​of the magnet-related parameters are obtained, and the predicted values ​​of the magnet-related parameters include the predicted values ​​of the key magnetic parameters and the predicted value of the effective magnetic path length, and / or the predicted distribution of the magnetic field-related information in the transverse plane, and the magnetic field-related information includes the magnetic field, the magnetic field gradient or the second-order derivative of the magnetic field.

[0012] In one embodiment, the magnet size information within the set range includes:

[0013] 5mm≤R i ≤120mm

[0014] 10 / 9≤ε≤5 / 2

[0015] 0.1≤w≤4

[0016] 0.9T≤B r ≤1.4T

[0017] Among them, R i is the inner radius, ε is the ratio of the outer radius to the inner radius, w is the ratio of the thickness to the inner radius, B r is the residual magnetic strength.

[0018] In one embodiment, the predicted values ​​of magnet-related parameters are obtained based on the predicted values ​​of the two-dimensional key magnetic parameters and the correction coefficients, including:

[0019] If the magnet is a dipole magnet, the two-dimensional key magnetic parameter is the two-dimensional magnetic field strength in the X direction; the predicted value of the magnetic field strength in the X direction, i.e. the predicted value of the key magnetic parameter, is calculated using the following formula:

[0020] B x预测 =αB x( 2D)

[0021] Among them, α is the correction coefficient of key magnetic parameters, Bx(2D) is the predicted value of the magnetic field strength in the two-dimensional X direction, B x预测 is the predicted value of the magnetic field strength in the X direction;

[0022] If the magnet is a quadrupole magnet, the two-dimensional key magnetic parameter is the magnetic induction intensity gradient at the two-dimensional transverse center point; the predicted value of the magnetic induction intensity gradient at the transverse center point, that is, the predicted value of the key magnetic parameter, is calculated using the following formula:

[0023]

[0024] Where α is the correction coefficient of key magnetic parameters, is the two-dimensional magnetic induction intensity gradient at the transverse center point, is the predicted value of the magnetic induction intensity gradient at the transverse center point;

[0025] To calculate the predicted value of the effective magnetic path length, use the following formula:

[0026] l=(β+w)*R i

[0027] Where l is the predicted value of the effective magnetic path length, β is the correction factor of the effective magnetic path length, w is the ratio of thickness to inner radius, R i is the inner radius;

[0028] The predicted distribution of magnetic field related information in the transverse plane is determined based on the coefficient of variation of the magnetic induction intensity in the radial direction of the transverse central section of the magnet; if the magnet is a dipole magnet, the magnetic field related information is the magnetic field; if the magnet is a quadrupole magnet, the magnetic field related information is the magnetic field gradient.

[0029] In one embodiment, the neural network includes an axial parameter mapping network and / or a radial parameter mapping network, both of which are BP neural network structures; the output set used by the axial parameter mapping network during training includes correction coefficients of key magnetic parameters and effective magnetic path length correction coefficients, and the output set used by the radial parameter mapping network during training includes the coefficient of variation in the radial direction of the magnetic induction intensity of the transverse central section of the magnet.

[0030] In a second aspect, a magnetic design device for a Halbach magnetic ring based on a neural network is provided, comprising:

[0031] A data set construction module is used to construct a network training data set, which includes an input set and an output set; the input set is a plurality of sets of magnet size information randomly generated within a set range, and the output set is a correction coefficient corresponding to the input set; the correction coefficient includes a correction coefficient of a key magnetic parameter and a correction coefficient of an effective magnetic path length, and / or a coefficient of variation in the radial direction of the magnetic induction intensity of the transverse central section of the magnet;

[0032] A network training module is used to train the neural network based on the network training data set to obtain a trained neural network;

[0033] A prediction module is used to input the magnet size information into the trained neural network to obtain a predicted value of the correction coefficient;

[0034] A first calculation module is used to calculate two-dimensional key magnetic parameters according to magnet size information;

[0035] The second calculation module is used to obtain the predicted values ​​of magnet-related parameters according to the predicted values ​​of the two-dimensional key magnetic parameters and the correction coefficients, the predicted values ​​of the magnet-related parameters include the predicted values ​​of the key magnetic parameters and the predicted value of the effective magnetic path length, and / or the predicted distribution of the magnetic field-related information in the transverse plane, the magnetic field-related information includes the magnetic field, the magnetic field gradient or the second-order derivative of the magnetic field.

[0036] In one embodiment, the magnet size information within the set range includes:

[0037] 5mm≤R i ≤120mm

[0038] 10 / 9≤ε≤5 / 2

[0039] 0.1≤w≤4

[0040] 0.9T≤B r ≤1.4T

[0041] Among them, R i is the inner radius, ε is the ratio of the outer radius to the inner radius, w is the ratio of the thickness to the inner radius, B r is the residual magnetic strength.

[0042] In one embodiment, the second computing module is further configured to:

[0043] If the magnet is a dipole magnet, the two-dimensional key magnetic parameter is the two-dimensional magnetic field strength in the X direction; the predicted value of the magnetic field strength in the X direction, i.e. the predicted value of the key magnetic parameter, is calculated using the following formula:

[0044] B x预测 =αB x(2D)

[0045] Among them, α is the correction coefficient of key magnetic parameters, B x(2D) is the predicted value of the magnetic field strength in the two-dimensional X direction, B x预测 is the predicted value of the magnetic field strength in the X direction;

[0046] If the magnet is a quadrupole magnet, the two-dimensional key magnetic parameter is the magnetic induction intensity gradient at the two-dimensional transverse center point; the predicted value of the magnetic induction intensity gradient at the transverse center point, that is, the predicted value of the key magnetic parameter, is calculated using the following formula:

[0047]

[0048] Where α is the correction coefficient of key magnetic parameters, is the two-dimensional magnetic induction intensity gradient at the transverse center point, is the predicted value of the magnetic induction intensity gradient at the transverse center point;

[0049] To calculate the predicted value of the effective magnetic path length, use the following formula:

[0050] l=(β+w)*R i

[0051] Where l is the predicted value of the effective magnetic path length, β is the correction factor of the effective magnetic path length, w is the ratio of thickness to inner radius, R i is the inner radius;

[0052] The predicted distribution of magnetic field related information in the transverse plane is determined based on the coefficient of variation of the magnetic induction intensity in the radial direction of the transverse central section of the magnet; if the magnet is a dipole magnet, the magnetic field related information is the magnetic field; if the magnet is a quadrupole magnet, the magnetic field related information is the magnetic field gradient.

[0053] In one embodiment, the neural network includes an axial parameter mapping network and / or a radial parameter mapping network, both of which are BP neural network structures; the output set used by the axial parameter mapping network during training includes correction coefficients of key magnetic parameters and effective magnetic path length correction coefficients, and the output set used by the radial parameter mapping network during training includes the coefficient of variation in the radial direction of the magnetic induction intensity of the transverse central section of the magnet.

[0054] In a third aspect, a computer-readable storage medium is provided, wherein the computer-readable storage medium stores a computer program, and when the computer program is executed by a processor, the magnetic design method of the Halbach magnetic ring based on a neural network is implemented.

[0055] In a fourth aspect, a computer program product is provided, comprising a computer program / instruction, which, when executed by a processor, implements the above-mentioned magnetic design method of the Halbach magnetic ring based on a neural network.

[0056] Compared with the prior art, the present application has the following beneficial effects: the present application can quickly and accurately complete the magnetic design of the Halbach magnetic ring according to the user's needs, especially when the magnet is relatively thin; the present application has better callability, and it can be directly integrated into the user's optimization program to complete the optimization of other goals, and the optimization parameters that need to be adjusted are still only the size parameters of the Halbach magnet. The adjustment of the parameters is intuitive and has engineering feasibility, avoiding the secondary decomposition of the intermediate variables. BRIEF DESCRIPTION OF THE DRAWINGS

[0057] The present application may be better understood by referring to the following description given in conjunction with the accompanying drawings, which together with the following detailed description are included in this specification and form a part of this specification. In the drawings:

[0058] Figure 1 The magnetization of the Halbach magnetic ring in a two-dimensional plane is shown;

[0059] Figure 2 A flowchart of a design method of a Halbach magnetic ring based on a neural network is shown;

[0060] Figure 3 The topology of the neural network is shown;

[0061] Figure 4 The neural network training errors and correlation coefficients for dipole and quadrupole magnets are shown;

[0062] Figure 5 A comparison diagram of the finite element simulation numerical solution and the neural network fitting solution of the correction coefficient of the dipole magnet in three-dimensional space is shown;

[0063] Figure 6 A comparison diagram of the finite element simulation numerical solution and the neural network fitting solution of the correction coefficient of the quadrupole magnet in three-dimensional space is shown;

[0064] Figure 7 A comparison diagram of the neural network fitting solution and the finite element simulation numerical solution of the magnetic induction intensity of a dipole magnet is shown;

[0065] Figure 8 A comparison diagram of the quadrupole magnet magnetic induction intensity gradient neural network fitting solution and the finite element simulation numerical solution is shown;

[0066] Fig. 9 The initial electron phase diagram and the comparison diagram of the beam spot before and after beam expansion by the quadrupole magnet are shown. DETAILED DESCRIPTION

[0067] The exemplary embodiments of the present application will be described below in conjunction with the accompanying drawings. For the sake of clarity and conciseness, not all features of the actual embodiments are described in the specification. However, it should be understood that many implementation-specific decisions can be made in the process of developing any such actual embodiments in order to achieve the specific goals of the developer, and these decisions may vary from embodiment to embodiment.

[0068] It is also necessary to explain here that, in order to avoid obscuring the present application due to unnecessary details, only the device structure closely related to the scheme according to the present application is shown in the drawings, while other details that are not closely related to the present application are omitted.

[0069] It should be understood that the present application is not limited to the described implementation forms due to the following description with reference to the accompanying drawings. In this article, where feasible, the embodiments can be combined with each other, features between different embodiments can be replaced or borrowed, and one or more features can be omitted in one embodiment.

[0070] The present application provides a design method of a Halbach magnetic ring based on a neural network. The research object is a Halbach type magnetic ring, specifically a split multi-pole permanent magnetic ring: that is, the permanent magnetic ring is divided into N segments according to the orientation, and the orientation angle of each segment relative to the center is 2π / N. Each segment of the magnet is uniformly magnetized, and the angular interval of the magnetization direction is the same. Figure 1 The figure shows the magnetization condition of the Halbach magnetic ring in a two-dimensional plane, where (a) is the size parameter of the magnet in the transverse plane, (b) is the magnetization condition of the dipole magnet, (c) is the magnetization condition of the quadrupole magnet, and (d) is the magnetization condition of the sextupole magnet.

[0071] Figure 2 A flowchart of the design method of the Halbach magnetic ring based on a neural network is shown, see Figure 2 , the method mainly includes the following steps:

[0072] Step S1, constructing a network training data set, the network training data set includes an input set and an output set; the input set is a plurality of sets of magnet size information randomly generated within a set range, and the output set is a correction coefficient corresponding to the input set; the correction coefficient includes a correction coefficient of a key magnetic parameter and a correction coefficient of an effective magnetic path length, and / or a coefficient of variation in the radial direction of the magnetic induction intensity of the transverse center section of the magnet.

[0073] Specifically, the magnet size information within the set range includes:

[0074] 5mm≤R i ≤120mm

[0075] 10 / 9≤ε≤5 / 2

[0076] 0.1≤w≤4

[0077] 0.9T≤B r ≤1.4T

[0078] Among them, R i is the inner radius, ε is the ratio of the outer radius to the inner radius, w is the ratio of the thickness to the inner radius, B r is the residual magnetic strength.

[0079] Specifically, the output set is obtained in the following way:

[0080] For the input set, the spatial magnetic field analytical representation method in the two-dimensional Cartesian coordinate system is used to obtain the two-dimensional key magnetic parameters corresponding to each set of magnet size information in the input set. Here, for a dipole magnet, the two-dimensional key magnetic parameter is the two-dimensional magnetic field intensity in the X direction, and for a quadrupole magnet, the two-dimensional key magnetic parameter is the two-dimensional magnetic induction intensity gradient at the transverse center point. At the same time, after obtaining the two-dimensional key magnetic parameters, the distribution of the two-dimensional magnetic field related information in the transverse plane and the effective magnetic path length can be obtained based on the two-dimensional key magnetic parameters.

[0081] Specifically, for a dipole magnet, the two-dimensional key magnetic parameter is the two-dimensional magnetic field strength B in the X direction. x , calculated using the following formula:

[0082] B x =B r ln(ε)

[0083] Among them, B r is the residual magnetic intensity, v is the ratio of the outer radius to the inner radius, and ln is the natural logarithm.

[0084] For a quadrupole magnet, the two-dimensional key magnetic parameter is the magnetic induction intensity gradient at the two-dimensional transverse center point. The calculation is done using the following formula:

[0085]

[0086] Among them, R i is the inner radius, B r is the residual magnetic intensity, ε is the ratio of the outer radius to the inner radius

[0087] For the input set, the finite element simulation model in the three-dimensional Cartesian coordinate system of the magnetic ring is used to obtain the three-dimensional key magnetic parameters corresponding to each set of magnet size information in the input set, and further obtain the distribution of the three-dimensional magnetic field related information in the transverse plane and the effective magnetic path length. Here, the three-dimensional key magnetic parameters and the two-dimensional key magnetic parameters have the same parameter type but different values.

[0088] Then, the correction coefficients corresponding to the input set can be determined by fitting the three-dimensional parameters and the two-dimensional parameters. The correction coefficients include the correction coefficient α of the key magnetic parameters and the correction coefficient β of the effective magnetic path length, and / or the radial variation coefficients c0, c1, c2 of the magnetic induction intensity of the transverse center section of the magnet.

[0089] Step S2, training the neural network based on the network training data set to obtain a trained neural network.

[0090] here, Figure 3The topological structure of the neural network is shown. The neural network includes an axial parameter mapping network and / or a radial parameter mapping network, both of which are BP neural network structures, including a hidden layer, with a total of 30 neurons. Among them, the output set used by the axial parameter mapping network during training includes the correction coefficients of key magnetic parameters and the effective magnetic path length correction coefficient, and the output set used by the radial parameter mapping network during training includes the coefficient of change in the radial direction of the magnetic induction intensity of the transverse central section of the magnet. The specific combination of the neural network is flexibly combined according to the actual situation, and is not specifically limited here.

[0091] The maximum number of training times is 1000, and the iteration termination condition is to exit the training when there is no improvement in the verification data after 20 times. Figure 4 The neural network training errors and correlation coefficients of dipole and quadrupole magnets are shown, where (a) is the axial neural network training error and correlation coefficient of the dipole magnet, (b) is the radial neural network training error and correlation coefficient of the dipole magnet, (c) is the axial neural network training error and correlation coefficient of the quadrupole magnet, and (d) is the radial neural network training error and correlation coefficient of the quadrupole magnet. The training errors of the training, inspection, and test sets represented by the blue, green, and red lines all show a downward trend with the number of training times, and can basically meet the convergence conditions within 1000 times. For all training results, the root mean square error (MSE) is less than 10 -5 , the correlation coefficient (R) is close to or even equal to 1, indicating that the fitting effect of the neural network is excellent.

[0092] Step S3, inputting the magnet size information into the trained neural network to obtain a predicted value of the correction coefficient.

[0093] Step S4, calculating and obtaining the two-dimensional key magnetic parameters according to the magnet size information; here, the calculation method of the two-dimensional key magnetic parameters refers to the description in step S1.

[0094] Step S5, obtaining predicted values ​​of magnet-related parameters according to the predicted values ​​of the two-dimensional key magnetic parameters and the correction coefficients, wherein the predicted values ​​of the magnet-related parameters include predicted values ​​of the key magnetic parameters and predicted values ​​of the effective magnetic path length, and / or predicted distribution of magnetic field-related information in the transverse plane, wherein the magnetic field-related information includes the magnetic field, the magnetic field gradient or the second-order derivative of the magnetic field.

[0095] Specifically, if the magnet is a dipole magnet, the two-dimensional key magnetic parameter is the two-dimensional magnetic field strength in the X direction; the predicted value of the magnetic field strength in the X direction is calculated, that is, the predicted value of the key magnetic parameter B 预测 , using the following formula:

[0096] B x预测 =αB x(2D)

[0097] Among them, α is the correction coefficient of key magnetic parameters, B x(2D) is the predicted value of the magnetic field strength in the two-dimensional X direction, B x预测 is the predicted value of the magnetic field strength in the X direction;

[0098] If the magnet is a quadrupole magnet, the two-dimensional key magnetic parameter is the magnetic induction intensity gradient at the two-dimensional transverse center point; calculate the predicted value of the magnetic induction intensity gradient at the transverse center point, that is, the predicted value of the key magnetic parameter B 预测 , using the following formula:

[0099]

[0100] Where α is the correction coefficient of key magnetic parameters, is the two-dimensional magnetic induction intensity gradient at the transverse center point, is the predicted value of the magnetic induction intensity gradient at the lateral center point.

[0101] To calculate the predicted value of the effective magnetic path length, use the following formula:

[0102] l=(β+w)*R i

[0103] Where l is the predicted value of the effective magnetic path length, β is the correction factor of the effective magnetic path length, w is the ratio of thickness to inner radius, R i is the inner radius;

[0104] According to the coefficient of variation of the magnetic induction intensity in the radial direction of the transverse central section of the magnet, the predicted distribution of the magnetic field related information in the transverse plane is determined. If the magnet is a dipole magnet, the magnetic field related information is the magnetic field; if the magnet is a quadrupole magnet, the magnetic field related information is the magnetic field gradient; if the magnet is a sextupole magnet, the magnetic field related information is the second-order derivative of the magnetic field.

[0105] Here, the predicted distribution of the magnetic field-related information in the transverse plane is determined according to the following formula:

[0106] E=(c0·ρ 2 +c1·ρ+c2)*B 预测

[0107] Where E is the predicted distribution of magnetic field related information in the transverse plane, c0, c1, c2 are the coefficients of variation of the magnetic induction intensity in the transverse central section of the magnet in the radial direction, where 0≤ρ≤1 is the normalized radial position. 预测 is the predicted value of the key magnetic parameters. For a two-pole magnet, B 预测 =B x预测 , for a quadrupole magnet,

[0108] Figure 5A comparison diagram of the finite element simulation numerical solution and the neural network fitting solution of the correction coefficient of the dipole magnet in three-dimensional space is shown, wherein (a) is a comparison diagram of the finite element simulation numerical solution and the neural network fitting solution of the correction coefficient of the key magnetic parameters, (b) is a comparison diagram of the finite element simulation numerical solution and the neural network fitting solution of the correction coefficient of the effective magnetic path length, and (c) is a comparison diagram of the finite element simulation numerical solution and the neural network fitting solution of the radial variation coefficient of the magnetic induction intensity of the transverse central section of the magnet. The correlation between α and ε is not obvious, but α tends to 1 as w increases. The physical explanation is that when the thickness of the Halbach magnetic ring is thicker, the magnetic field on its central section can be expressed by the analytical solution of the two-dimensional theory. β increases with the increase of ε, and tends to 0 as w increases. The physical explanation is that when the thickness of the Halbach magnetic ring is thicker, the effective magnetic path length can be approximately regarded as its thickness. In the radial direction, the predicted distribution of the magnetic field in the transverse plane is expressed as E=(c0·ρ 2 +c1·ρ+c2)*B x预测 , where 0≤ρ≤1 is the normalized radial position. It can be seen that for different sizes of Halbach magnetic rings, c0 varies widely, between 0 and 0.6, c1 is approximately 0, and c2 is approximately 1.

[0109] Figure 6 A comparison diagram of the finite element simulation numerical solution and the neural network fitting solution of the correction coefficient of the quadrupole magnet in three-dimensional space is shown, where (a) is a comparison diagram of the finite element simulation numerical solution and the neural network fitting solution of the correction coefficient of the key magnetic parameters, (b) is a comparison diagram of the finite element simulation numerical solution and the neural network fitting solution of the correction coefficient of the effective magnetic path length, and (c) is a comparison diagram of the finite element simulation numerical solution and the neural network fitting solution of the radial variation coefficient of the magnetic induction intensity of the transverse central section of the magnet. The correlation between α and ε is still not obvious. α tends to 1 as w increases. The physical explanation is that when the thickness of the Halbach magnetic ring is thicker, the magnetic field on its central section can be expressed by the analytical solution of the two-dimensional theory. β increases with the increase of ε and tends to 0 as w increases. The physical explanation is that when the thickness of the Halbach magnetic ring is thicker, the effective magnetic path length can be approximately regarded as its thickness. In the radial direction, the predicted distribution of the magnetic field gradient in the transverse plane is expressed as Where 0≤ρ≤1 is the normalized radial position. It can be seen that for different sizes of Halbach magnetic rings, c0 varies widely, between 0 and 3, c1 is approximately 0, and c2 is approximately 1.

[0110] Figure 5 and Figure 6 For Halbach magnetic rings represented by dipole and quadrupole magnets, a table lookup method is provided to find the approximate correction coefficient.

[0111] For a certain two-pole magnet, its inner radius is 28 mm, its outer radius is 56 mm, its thickness is 84 mm, and its material is a samarium cobalt magnet with a magnetization intensity of 0.92 T and a magnetic permeability of 1.03. Figure 7 The figure shows the comparison between the neural network fitting solution and the finite element simulation numerical solution of the magnetic induction intensity of the dipole magnet. Figure 7 As shown, the magnetic field intensity B in the X direction at the center of the central section calculated by the neural network is x =0.503T, and the numerical solution of the simulation is B x =0.505T, with an error of 4‰. It can be seen that the method of this application is not effective in calculating the spatial distribution of the magnetic field of a dipole magnet. The reason is that the aforementioned setting method is only applicable to the characteristics of physical quantities with rotational symmetry in the polar coordinate system. For a very narrow region (the range of x is around 0), B x The distribution characteristics along the y direction can be well described using the method of the present application.

[0112] For a certain quadrupole magnet, its inner radius is 14.9 mm, its outer radius is 25.3 mm, its thickness is 25.7 mm, and its material is a samarium cobalt magnet with a magnetization intensity of 0.92 T and a magnetic permeability of 1.03. Figure 8 The figure shows the comparison between the neural network fitting solution of the magnetic induction intensity gradient of the quadrupole magnet and the finite element simulation numerical solution. Figure 8 As shown, the magnetic induction intensity gradient at the transverse center point calculated by the neural network The numerical solution of the simulation is The error is 3‰. Since the magnetic induction intensity gradient has the characteristics of rotational symmetry in the polar coordinate system, this method is more effective in calculating the spatial distribution of the magnetic field of a quadrupole magnet. From the center to the periphery, the magnetic induction intensity gradient increases slowly.

[0113] In the field of beam optics, quadrupole magnets are usually used to achieve the focusing and divergence effects of high-energy electron beams. The optimized embodiment of the high-energy electron beam expansion magnet implemented by the present application is as follows:

[0114] Device entrance electrons: The electron beam center energy is 10.03MeV, 90% of the electron energy is scattered within 2%, the emittance is 0.6mmmrad, and the radius of the beam spot (defined as 90% of the electron envelope) is 1.18mm;

[0115] Expected effect: Using two sets of quadrupole magnets, the beam spot radius after beam expansion (defined as 90% electron envelope) is 15mm and the size difference in the two directions is within 5%, and the device beam line length is no more than 0.5m (the distance from the device to the screen is 0.2m).

[0116] By using the Halbach neural network mapping relationship provided in this application and integrating it directly into the beam optical genetic algorithm optimization program, the size parameters and relative position relationship of the quadrupole magnet can be obtained as follows:

[0117] Table 1 Quadrupole magnet size and relative position relationship

[0118]

[0119] Effect: Fig. 9 The initial electron phase diagram and the comparison diagram of the beam spot before and after the quadrupole magnet beam expansion are shown, where (a) is the initial electron phase diagram, and (b) is the comparison diagram of the beam spot before and after the quadrupole magnet beam expansion. Fig. 9 As shown, the red and blue beam spots represent the beam before and after expansion, and the effect is very obvious. After expansion, the beam spot radius is 15.2m, the size difference in the two directions is 2%, and the beam line length is 487mm, which meets the design requirements.

[0120] Using the same inventive concept as the magnetic design method of the Halbach magnetic ring based on the neural network, this embodiment also provides a corresponding magnetic design device of the Halbach magnetic ring based on the neural network, including:

[0121] A data set construction module is used to construct a network training data set, which includes an input set and an output set; the input set is a plurality of sets of magnet size information randomly generated within a set range, and the output set is a correction coefficient corresponding to the input set; the correction coefficient includes a correction coefficient of a key magnetic parameter and a correction coefficient of an effective magnetic path length, and / or a coefficient of variation in the radial direction of the magnetic induction intensity of the transverse central section of the magnet;

[0122] A network training module is used to train the neural network based on the network training data set to obtain a trained neural network;

[0123] A prediction module is used to input the magnet size information into the trained neural network to obtain a predicted value of the correction coefficient;

[0124] A first calculation module is used to calculate two-dimensional key magnetic parameters according to magnet size information;

[0125] The second calculation module is used to obtain the predicted values ​​of magnet-related parameters according to the predicted values ​​of the two-dimensional key magnetic parameters and the correction coefficients, the predicted values ​​of the magnet-related parameters include the predicted values ​​of the key magnetic parameters and the predicted value of the effective magnetic path length, and / or the predicted distribution of the magnetic field-related information in the transverse plane, the magnetic field-related information includes the magnetic field, the magnetic field gradient or the second-order derivative of the magnetic field.

[0126] The magnetic design device of the Halbach magnetic ring based on neural network in this embodiment has the same inventive concept as the magnetic design method of the Halbach magnetic ring based on neural network mentioned above. Therefore, the specific implementation method of the device can be seen in the implementation example part of the magnetic design method of the Halbach magnetic ring based on neural network in the above text, and its technical effect corresponds to the technical effect of the above method, which will not be repeated here.

[0127] An embodiment of the present application provides a computer-readable storage medium, which stores a computer program. When the computer program is executed by a processor, the magnetic design method of the Halbach magnetic ring based on the neural network is implemented.

[0128] An embodiment of the present application provides a computer program product, including a computer program / instruction. When the computer program / instruction is executed by a processor, the above-mentioned magnetic design method of the Halbach magnetic ring based on neural network is implemented.

[0129] The above are only various implementations of the present application, but the protection scope of the present application is not limited thereto. Any person skilled in the art who is familiar with the present technical field can easily think of changes or substitutions within the technical scope disclosed in the present application, which should be included in the protection scope of the present application. Therefore, the protection scope of the present application should be based on the protection scope of the claims.

Claims

1. A magnetic design method for Halbach magnetic ring based on neural network, characterized in that: include: Constructing a network training data set, the network training data set includes an input set and an output set; the input set is a plurality of sets of magnet size information randomly generated within a set range, and the output set is a correction coefficient corresponding to the input set; the correction coefficient includes a correction coefficient of a key magnetic parameter and a correction coefficient of an effective magnetic path length, and / or a coefficient of variation in the radial direction of the magnetic induction intensity of a transverse central section of the magnet; Training the neural network based on the network training data set to obtain a trained neural network; Inputting the magnet size information into the trained neural network to obtain a predicted value of the correction coefficient; Calculate two-dimensional key magnetic parameters according to the magnet size information; According to the predicted values ​​of the two-dimensional key magnetic parameters and the correction coefficients, the predicted values ​​of the magnet-related parameters are obtained, and the predicted values ​​of the magnet-related parameters include the predicted values ​​of the key magnetic parameters and the predicted value of the effective magnetic path length, and / or the predicted distribution of the magnetic field-related information in the transverse plane, and the magnetic field-related information includes the magnetic field, the magnetic field gradient or the second-order derivative of the magnetic field.

2. The method according to claim 1, characterized in that The magnet size information within the setting range includes: 5mm≤R i ≤120mm 10 / 9≤ε≤5 / 2 0.1≤w≤4 0.9T≤B r ≤1.4T Among them, R i is the inner radius, ε is the ratio of the outer radius to the inner radius, w is the ratio of the thickness to the inner radius, B r is the residual magnetic strength.

3. The method according to claim 1, characterized in that According to the predicted values ​​of the two-dimensional key magnetic parameters and the correction coefficients, the predicted values ​​of the magnet-related parameters are obtained, including: If the magnet is a dipole magnet, the two-dimensional key magnetic parameter is the two-dimensional magnetic field strength in the X direction; the predicted value of the magnetic field strength in the X direction, i.e., the predicted value of the key magnetic parameter, is calculated using the following formula: B x预测 =αB x(2D) Among them, α is the correction coefficient of key magnetic parameters, B x(2D) is the predicted value of the magnetic field strength in the two-dimensional X direction, B x预测 is the predicted value of the magnetic field strength in the X direction; If the magnet is a quadrupole magnet, the two-dimensional key magnetic parameter is the magnetic induction intensity gradient at the two-dimensional transverse center point; the predicted value of the magnetic induction intensity gradient at the transverse center point, that is, the predicted value of the key magnetic parameter, is calculated using the following formula: Where α is the correction coefficient of key magnetic parameters, is the two-dimensional magnetic induction intensity gradient at the transverse center point, is the predicted value of the magnetic induction intensity gradient at the transverse center point; The predicted value of the effective magnetic path length is calculated using the following formula: l=(β+w)*R i Where l is the predicted value of the effective magnetic path length, β is the correction factor of the effective magnetic path length, w is the ratio of thickness to inner radius, R i is the inner radius; The predicted distribution of magnetic field related information in the transverse plane is determined according to the coefficient of variation of the magnetic induction intensity in the radial direction of the transverse central section of the magnet; if the magnet is a dipole magnet, the magnetic field related information is the magnetic field; if the magnet is a quadrupole magnet, the magnetic field related information is the magnetic field gradient.

4. The method according to claim 1, characterized in that The neural network includes an axial parameter mapping network and / or a radial parameter mapping network, both of which are BP neural network structures; the output set used by the axial parameter mapping network during training includes correction coefficients of key magnetic parameters and effective magnetic path length correction coefficients, and the output set used by the radial parameter mapping network during training includes a coefficient of variation in the radial direction of the magnetic induction intensity of the transverse central section of the magnet.

5. A magnetic design device for Halbach magnetic ring based on neural network, characterized in that: include: A data set construction module is used to construct a network training data set, wherein the network training data set includes an input set and an output set; the input set is a plurality of sets of magnet size information randomly generated within a set range, and the output set is a correction coefficient corresponding to the input set; the correction coefficient includes a correction coefficient of a key magnetic parameter and a correction coefficient of an effective magnetic path length, and / or a coefficient of variation in the radial direction of the magnetic induction intensity of the transverse central section of the magnet; A network training module, used to train the neural network based on the network training data set to obtain a trained neural network; A prediction module, used for inputting magnet size information into the trained neural network to obtain a predicted value of the correction coefficient; A first calculation module, used for calculating two-dimensional key magnetic parameters according to the magnet size information; The second calculation module is used to obtain the predicted values ​​of magnet-related parameters according to the predicted values ​​of the two-dimensional key magnetic parameters and the correction coefficients, wherein the predicted values ​​of the magnet-related parameters include the predicted values ​​of the key magnetic parameters and the predicted value of the effective magnetic path length, and / or the predicted distribution of the magnetic field-related information in the transverse plane, wherein the magnetic field-related information includes the magnetic field, the magnetic field gradient or the second-order derivative of the magnetic field.

6. The device according to claim 5, characterized in that The magnet size information within the setting range includes: 5mm≤R i ≤120mm 10 / 9≤ε≤5 / 2 0.1≤w≤4 0.9T≤B r ≤1.4T Among them, R i is the inner radius, ε is the ratio of the outer radius to the inner radius, w is the ratio of the thickness to the inner radius, B r is the residual magnetic strength.

7. The device according to claim 5, characterized in that The second computing module is further used for: If the magnet is a dipole magnet, the two-dimensional key magnetic parameter is the two-dimensional magnetic field strength in the X direction; the predicted value of the magnetic field strength in the X direction, i.e., the predicted value of the key magnetic parameter, is calculated using the following formula: B x预测 =αB x(2D) Among them, α is the correction coefficient of key magnetic parameters, B x(2D) is the predicted value of the magnetic field strength in the two-dimensional X direction, B x预测 is the predicted value of the magnetic field strength in the X direction; If the magnet is a quadrupole magnet, the two-dimensional key magnetic parameter is the magnetic induction intensity gradient at the two-dimensional transverse center point; the predicted value of the magnetic induction intensity gradient at the transverse center point, that is, the predicted value of the key magnetic parameter, is calculated using the following formula: Where α is the correction coefficient of key magnetic parameters, is the two-dimensional magnetic induction intensity gradient at the transverse center point, is the predicted value of the magnetic induction intensity gradient at the transverse center point; The predicted value of the effective magnetic path length is calculated using the following formula: l=(β+w)*R i Where l is the predicted value of the effective magnetic path length, β is the correction factor of the effective magnetic path length, w is the ratio of thickness to inner radius, R i is the inner radius; The predicted distribution of magnetic field related information in the transverse plane is determined according to the coefficient of variation of the magnetic induction intensity in the radial direction of the transverse central section of the magnet; if the magnet is a dipole magnet, the magnetic field related information is the magnetic field; if the magnet is a quadrupole magnet, the magnetic field related information is the magnetic field gradient.

8. The device according to claim 5, characterized in that The neural network includes an axial parameter mapping network and / or a radial parameter mapping network, both of which are BP neural network structures; the output set used by the axial parameter mapping network during training includes correction coefficients of key magnetic parameters and effective magnetic path length correction coefficients, and the output set used by the radial parameter mapping network during training includes a coefficient of variation in the radial direction of the magnetic induction intensity of the transverse central section of the magnet.

9. A computer-readable storage medium, characterized in that: The computer-readable storage medium stores a computer program, and when the computer program is executed by a processor, the magnetic design method of the Halbach magnetic ring based on a neural network as described in any one of claims 1 to 4 is implemented.

10. A computer program product, characterized in that It includes a computer program / instruction, which, when executed by a processor, implements the magnetic design method of the Halbach magnetic ring based on a neural network as described in any one of claims 1 to 4.

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