A method for magnetic design of a Halbach magnetic ring based on a neural network

Abstract

The application relates to a magnetic design method of a Halbach magnetic ring based on a neural network, which can quickly and accurately complete the magnetic design of the Halbach magnetic ring according to the needs of a user, and is particularly suitable for the case that the magnet is relatively thin; the application has better callability, can be directly integrated into an optimization program of the user to complete the optimization of other targets, 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 realizability, and secondary decomposition of intermediate variables is avoided.

Description

Technical Field

[0001] This application relates to the field of magnet design in accelerator physics, and more specifically, to a magnetic design method for a Heilbeck magnetic ring based on a neural network. Background Technology

[0002] In 1980, Professor Klaus Halbach of Lawrence Berkeley National Laboratory in the United States obtained the Helbeck magnet by assembling permanent magnets during electron acceleration experiments. The design goal of this magnet was to arrange permanent magnets with different magnetization directions at a certain angle, so that the magnetic field within its inner radius was significantly stronger than that on the outer surface, generating the strongest magnetic field within the target working range with the minimum amount of magnetic blocks. The Helbeck magnetic ring is a toroidal Helbeck 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 also been widely used in industrial fields such as nuclear magnetic resonance systems, magnetic levitation devices, and permanent magnet motors in recent years.

[0003] Current research on the magnetic field of Hellbeck magnetic rings mainly focuses on two-dimensional theoretical methods and three-dimensional finite element simulation methods. (2010, Technical University of Denmark) Based on Maxwell's equations, researchers derived the magnetic vector potential, magnetic field, and magnetic flux density of a two-dimensional Hellbeck magnetic ring and compared the results with those obtained by two-dimensional numerical methods. This method is relatively fast and suitable for preliminary evaluation. In 2013, Chen Yin et al. from Southwest Jiaotong University, starting from the Ampere circulation hypothesis, used surface current to replace the magnetic field generated by the Hellbeck magnet and calculated the magnetic field strength at any point in a 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, meaning the influence of the three-dimensional thickness direction on the planar magnetic field distribution needs to be considered. Three-dimensional finite element simulation, by solving Maxwell's equations under boundary conditions, can obtain the magnetic flux density at any point in space with high accuracy.

[0004] Currently, various application scenarios are placing increasingly higher demands on the spatial dimensions, materials, and environmental adaptability of Heilbeck magnets. However, existing methods are difficult to directly optimize the magnet parameters based on the user's final needs. They often involve secondary decomposition of intermediate process variables, which is time-consuming and not intuitive. Sometimes, it is even difficult to decompose them into parameters that are engineering-processable. Summary of the Invention

[0005] To overcome at least one deficiency in the prior art, this application provides a magnetic design method for a Heilbeck magnetic ring based on a neural network.

[0006] Firstly, a magnetic design method for Heilbeck magnetic rings based on neural networks is provided, including:

[0007] constructing a network training data set, the network training data set comprising an input set and an output set; the input set being a plurality of groups of magnet size information randomly generated within a set range, the output set being correction coefficients corresponding to the input set; the correction coefficients comprising correction coefficients of key magnetic parameters and correction coefficients of effective magnetic path length, and / or variation coefficients of magnetic induction intensity in the radial direction 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] inputting the magnet size information into the trained neural network to obtain a predicted value of the correction coefficients;

[0010] calculating two-dimensional key magnetic parameters according to the magnet size information;

[0011] obtaining a predicted value of magnet-related parameters according to the two-dimensional key magnetic parameters and the predicted value of the correction coefficients, the predicted value of the magnet-related parameters comprising a predicted value of the key magnetic parameters and a predicted value of the effective magnetic path length, and / or a predicted distribution of magnetic field-related information in the transverse plane, the magnetic field-related information comprising magnetic field, magnetic field gradient or magnetic field second derivative.

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

[0013] 5mm≤R i ≤120mm

[0014] 10 / 9≤ε≤5 / 2

[0015] 0.1≤w≤4

[0016] 0.9T≤B r ≤1.4T

[0017] wherein 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, and B r is the residual magnetism.

[0018] In one embodiment, the predicted value of the magnet-related parameters obtained according to the two-dimensional key magnetic parameters and the predicted value of the correction coefficients comprises:

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

[0020] B x预测 =αB x( 2D)

[0021] wherein α is the correction coefficient of the key magnetic parameters, and Bx(2D) Bx is the predicted value of the magnetic field strength in the X direction, x预测 Bx is the predicted value of the magnetic field strength in the X direction;

[0022] If the magnet is a four-pole magnet, the two-dimensional key magnetic parameter is the magnetic flux density gradient at the transverse center point; the predicted value of the magnetic flux density gradient at the transverse center point, i.e., the predicted value of the key magnetic parameter, is calculated using the following formula:

[0023]

[0024] wherein a is the correction coefficient of the key magnetic parameter, Bx is the magnetic flux density gradient at the transverse center point, Bx is the predicted value of the magnetic flux density gradient at the transverse center point;

[0025] The predicted value of the effective magnetic path length is calculated using the following formula:

[0026] l = (β + w) * R i

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

[0028] According to the radial variation coefficient of the magnetic flux density of the transverse center section of the magnet, the predicted distribution of the magnetic field related information in the transverse plane is determined; if the magnet is a two-pole magnet, the magnetic field related information is the magnetic field, and if the magnet is a four-pole 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 the correction coefficient of the key magnetic parameter and the correction coefficient of the effective magnetic path length, and the output set used by the radial parameter mapping network during training includes the radial variation coefficient of the magnetic flux density of the transverse center 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, including:

[0031] A data set construction module is configured to construct a network training data set, the network training data set including 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 radial variation coefficient of the magnetic flux density of a transverse center section of a magnet;

[0032] a network training module, configured to train the neural network based on a network training dataset to obtain a trained neural network;

[0033] a prediction module, configured 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, configured to calculate a two-dimensional key magnetic parameter according to the magnet size information;

[0035] a second calculation module, configured to obtain a predicted value of a magnet-related parameter according to the two-dimensional key magnetic parameter and the predicted value of the correction coefficient, the predicted value of the magnet-related parameter including a predicted value of the key magnetic parameter and a predicted value of an effective magnetic path length, and / or a predicted distribution of magnetic field-related information in a transverse plane, the magnetic field-related information including a magnetic field, a magnetic field gradient or a second-order derivative of the magnetic field.

[0036] In one embodiment, the magnet size information in a certain 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] wherein R i is an inner radius, ε is a ratio of an outer radius to the inner radius, w is a ratio of a thickness to the inner radius, and B r is a residual magnetism.

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

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

[0044] B x预测 =αB x(2D)

[0045] wherein α is a correction coefficient of the key magnetic parameter, B x(2D) is the predicted value of the two-dimensional X-direction magnetic field strength, and B x预测 is the predicted value of the X-direction magnetic field strength.

[0046] if the magnet is a quadrupole magnet, the two-dimensional key magnetic parameter is a two-dimensional magnetic induction strength gradient at a transverse center point; a predicted value of the magnetic induction strength gradient at the transverse center point, i.e., a predicted value of the key magnetic parameter, is calculated using the following formula:

[0047]

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

[0049] a predicted value of an effective magnetic path length is calculated using the following formula:

[0050] l = (β + w) * R i

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

[0052] a predicted distribution of the magnetic field related information in the transverse plane is determined according to the variation coefficient of the magnetic induction intensity in the radial direction of the transverse center section of the magnet; if the magnet is a dipole magnet, the magnetic field related information is the magnetic field, and 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 the correction coefficient of the key magnetic parameter and the effective magnetic path length correction coefficient, and the output set used by the radial parameter mapping network during training includes the variation coefficient of the magnetic induction intensity in the radial direction of the transverse center section of the magnet.

[0054] In a third aspect, a computer readable storage medium is provided, the computer readable storage medium storing a computer program, the computer program being executed by a processor to implement the above-mentioned magnetic design method for a Halbach magnet ring based on a neural network.

[0055] In a fourth aspect, a computer program product is provided, including computer programs / instructions, the computer programs / instructions being executed by a processor to implement the above-mentioned magnetic design method for a Halbach magnet 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 a Halbach magnet ring according to user needs, and is still applicable when the magnet is relatively thin; the present application has better callability, can be directly integrated into a user's optimization program to complete optimization of other targets, 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 realizability, avoiding secondary decomposition of intermediate variables. BRIEF DESCRIPTION OF DRAWINGS

[0057] The present application can be better understood with reference to the following description taken in connection with the accompanying drawings, which are included as part of the present specification and represent the best presently contemplated embodiment of the present application. In the drawings:

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

[0059] Figure 2 The flow chart of the design method of the Halbach magnetic ring based on neural network is shown;

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

[0061] Figure 4 The neural network training error and correlation coefficient of the dipole magnet and the quadrupole magnet are shown;

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

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

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

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

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

[0067] In the following, exemplary embodiments of the present application will be described with reference to the drawings. In the specification, not all the features of the actual embodiments have been described for the sake of clarity and conciseness. It should be appreciated, however, that many embodiment-specific decisions can be made in the process of developing any such actual embodiments in order to achieve the specific goals of the developers, and these decisions can vary from embodiment to embodiment.

[0068] It should also be noted here that, in order to avoid obscuring the present application with unnecessary details, only the device structures closely related to the scheme according to the present application are shown in the drawings, and other details not closely related to the present application are omitted.

[0069] It should be understood that the present application is not limited to the described embodiments by virtue of the description with reference to the drawings. In this context, the embodiments can be combined with each other, features can be replaced or borrowed between different embodiments, one or more features can be omitted in an embodiment, as far as this is possible.

[0070] The 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 azimuth, the azimuth angle occupied by each segment relative to the center is 2π / N, each segment of the magnet is uniformly magnetized, and the angle interval of the magnetization direction is the same, Figure 1 The magnetization of the Halbach magnetic ring in a two-dimensional plane is shown, wherein (a) is the size parameter in the transverse plane of the magnet, (b) is the magnetization of the dipole magnet, (c) is the magnetization of the quadrupole magnet, and (d) is the magnetization of the sextupole magnet.

[0071] Figure 2 A flowchart of the design method of the Halbach magnetic ring based on the neural network is shown, referring to 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 groups of magnet size information randomly generated in 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 an effective magnetic path length correction coefficient, and / or a change coefficient of the magnetic induction intensity in the radial direction of the transverse center section of the magnet.

[0073] Specifically, the magnet size information in 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] Wherein, 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 magnetism.

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

[0080] For the input set, the spatial magnetic field analytical expression method under the two-dimensional Cartesian coordinate system is adopted to obtain the two-dimensional key magnetic parameters corresponding to the size information of each group of magnets in the input set. Here, for the dipole magnet, the two-dimensional key magnetic parameter is the two-dimensional X-direction magnetic field strength, and for the quadrupole magnet, the two-dimensional key magnetic parameter is the two-dimensional transverse center point magnetic induction intensity gradient. 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 according to the two-dimensional key magnetic parameters.

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

[0082] B x =B r ln(ε)

[0083] Where B r is the residual magnetism, v is the ratio of the outer radius to the inner radius, and ln is the natural logarithm.

[0084] For the quadrupole magnet, the two-dimensional key magnetic parameter is the two-dimensional transverse center point magnetic induction intensity gradient , which is calculated by the following formula:

[0085]

[0086] Where R i is the inner radius, B r is the residual magnetism, and ε is the ratio of the outer radius to the inner radius

[0087] For the input set, the three-dimensional Cartesian coordinate system finite element simulation model of the magnetic ring can be used to obtain the three-dimensional key magnetic parameters corresponding to the size information of each group of magnets 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 are consistent with the two-dimensional key magnetic parameters in terms of parameter type, but different in value.

[0088] Then, the three-dimensional parameters and two-dimensional parameters are fitted to determine the correction coefficients corresponding to the input set. The correction coefficients include the key magnetic parameter correction coefficient α and the effective magnetic path length correction coefficient β, and / or the magnetic induction intensity radius direction variation coefficients c0, c1, and c2 of the transverse center section of the magnet.

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

[0090] Here, Figure 3The topology 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, and each contains one hidden layer with a total of 30 neurons. Among them, the output set adopted by the axial parameter mapping network during training includes the correction coefficient of the key magnetic parameter and the correction coefficient of the effective magnetic path length, and the output set adopted by the radial parameter mapping network during training includes the variation coefficient of the magnetic induction intensity in the radial direction of the transverse central section of the magnet. The specific combination mode of the neural network is flexibly combined according to the actual situation, which 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 for 20 times. Figure 4 The neural network training error and correlation coefficient of the dipole magnet and the quadrupole magnet are shown, wherein (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, test and test set training errors represented by the blue line, green line and red line all show a downward trend with the number of training times, and can basically meet the convergence condition within 1000 times. For all training results, the root mean square error (MSE) is less than 10 -5 , and the correlation coefficient (R) is close to or equal to 1, indicating that the fitting effect of the neural network is excellent.

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

[0093] Step S4: calculate the two-dimensional key magnetic parameters according to the magnet size information; here, the calculation method of the two-dimensional key magnetic parameters is described in step S1.

[0094] Step S5: according to the two-dimensional key magnetic parameters and the predicted value of the correction coefficient, the predicted value of the magnet related parameters is obtained, which includes the predicted value 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 magnetic field second derivative.

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

[0096] B x预测 =αB x(2D)

[0097] wherein a is the correction coefficient of the key magnetic parameter, B x(2D) is the predicted value of the magnetic field strength in the 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 four-pole magnet, the two-dimensional key magnetic parameter is the magnetic induction gradient at the transverse center point; the predicted value of the magnetic induction gradient at the transverse center point, i.e. the predicted value of the key magnetic parameter B 预测 , is calculated using the following formula:

[0099]

[0100] wherein a is the correction coefficient of the key magnetic parameter, is the two-dimensional magnetic induction gradient at the transverse center point, is the predicted value of the magnetic induction gradient at the transverse center point.

[0101] The predicted value of the effective magnetic path length is calculated using the following formula:

[0102] l = (β + w) * R i

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

[0104] The predicted distribution of the magnetic field related information in the transverse plane is determined according to the radial variation coefficient of the magnetic induction at the transverse center section of the magnet. If the magnet is a two-pole magnet, the magnetic field related information is the magnetic field, if the magnet is a four-pole magnet, the magnetic field related information is the magnetic field gradient, and if the magnet is a six-pole 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] wherein E is the predicted distribution of the magnetic field related information in the transverse plane, c0, c1, c2 are the radial variation coefficients of the magnetic induction at the transverse center section of the magnet, wherein 0 ≤ ρ ≤ 1 is the normalized radial position. B 预测 is the predicted value of the key magnetic parameter, for a two-pole magnet, B 预测 = B x预测 , for a four-pole magnet,

[0108] Figure 5Figures showing the comparison of the finite element simulation numerical solution and the neural network fitted solution of the correction factors of dipole magnets in three-dimensional space, where (a) is the comparison of the finite element simulation numerical solution and the neural network fitted solution of the correction factors of key magnetic parameters, (b) is the comparison of the finite element simulation numerical solution and the neural network fitted solution of the correction factor of effective magnetic path length, (c) is the comparison of the finite element simulation numerical solution and the neural network fitted solution of the variation coefficient of the radial direction of the magnetic induction intensity of the transverse central section of the magnet. The correlation between a and e is not obvious, but a tends to 1 more and more as w increases, and the physical explanation is that when the thickness of the Halbach magnet ring is thick, the magnetic field on the central section can be represented by the analytical solution of the two-dimensional theory. Beta increases as epsilon increases, and tends to 0 more and more as w increases, and the physical explanation is that when the thickness of the Halbach magnet ring is thick, the effective magnetic path length can be approximately considered as its thickness. In the radial direction, the predicted distribution of the magnetic field in the transverse plane is represented as E = (c0·p 2 +c1·p+c2)*B x预测 , where 0≤p≤1 is the normalized radial position. It can be seen that for Halbach magnet rings of different sizes, c0 varies in a large range, between 0 and 0.6, c1 is about 0, and c2 is about 1.

[0109] Figure 6 Figures showing the comparison of the finite element simulation numerical solution and the neural network fitted solution of the correction factors of quadrupole magnets in three-dimensional space, where (a) is the comparison of the finite element simulation numerical solution and the neural network fitted solution of the correction factors of key magnetic parameters, (b) is the comparison of the finite element simulation numerical solution and the neural network fitted solution of the correction factor of effective magnetic path length, (c) is the comparison of the finite element simulation numerical solution and the neural network fitted solution of the variation coefficient of the radial direction of the magnetic induction intensity of the transverse central section of the magnet. The correlation between a and e is still not obvious, a tends to 1 more and more as w increases, and the physical explanation is that when the thickness of the Halbach magnet ring is thick, the magnetic field on the central section can be represented by the analytical solution of the two-dimensional theory. Beta increases as epsilon increases, and tends to 0 more and more as w increases, and the physical explanation is that when the thickness of the Halbach magnet ring is thick, the effective magnetic path length can be approximately considered as its thickness. In the radial direction, the predicted distribution of the magnetic field gradient in the transverse plane is represented as , where 0≤p≤1 is the normalized radial position. It can be seen that for Halbach magnet rings of different sizes, c0 varies in a large range, between 0 and 3, c1 is about 0, and c2 is about 1.

[0110] Figure 5 and Figure 6 provide a table lookup method to find the approximate correction factors for Halbach magnet rings represented by dipole magnets and quadrupole magnets.

[0111] For a certain dipole magnet, its inner radius is 28mm, its outer radius is 56mm, its thickness is 84mm, and its material is a samarium cobalt magnet with a magnetization intensity of 0.92T and a permeability of 1.03. Figure 7 A comparison diagram is shown between the neural network fitting solution and the finite element simulation numerical solution for the magnetic induction intensity of a dipolar magnet, as follows: Figure 7 As shown, the magnetic field strength B in the X direction at the center of its central cross-section is calculated by a neural network. x =0.503T, while the simulated numerical solution is B. x =0.505T, with an error of 4‰. It can be seen that the method in this application is not effective in calculating the spatial distribution of the magnetic field of a dipole magnet. This is because the aforementioned method is only applicable to physical quantities that have rotational symmetry in polar coordinates. For a very narrow region (x varies around 0), B x The distribution characteristics along the y-direction can be well described using the method of this 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 permeability of 1.03. Figure 8 A comparison diagram is shown between the neural network fitting solution and the numerical solution from finite element simulation of the magnetic induction intensity gradient of a quadrupole magnet, as follows: Figure 8 As shown, the magnetic field strength gradient at the transverse center point is calculated by the neural network. The numerical solution from the simulation is The error is within 3‰. Due to the rotational symmetry of the magnetic flux density gradient in the polar coordinate system, this method is effective in calculating the spatial distribution of the magnetic field of a quadrupole magnet, where the magnetic flux density gradient increases slowly from the center to the periphery.

[0113] In the field of beam optics, quadrupole magnets are typically used to focus and diverge high-energy electron beams. An optimized embodiment of the high-energy electron beam expander magnet implemented in this application is as follows:

[0114] The electron beam at the device entrance has a central energy of 10.03 MeV, with 90% of the electrons scattered within 2%, an emittance of 0.6 mm rad, and an exit beam spot (defined as the 90% electron envelope) radius of 1.18 mm.

[0115] Desired effect: Using two sets of quadrupole magnets, achieve a beam spot radius (defined as 90% electron envelope) of 15mm after beam expansion with a dimensional difference of less than 5% in both directions, and a beam length of no more than 0.5m (distance from device to screen is 0.2m).

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

[0117] Table 1 Size and relative position relationship of quadrupole magnet

[0118]

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

[0120] The same inventive concept as the magnetic design method of the Halbeek magnetic ring based on the neural network is adopted, and the embodiment also provides a magnetic design device of the Halbeek magnetic ring based on the neural network corresponding thereto, comprising:

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

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

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

[0124] A first calculation module is configured to calculate a two-dimensional key magnetic parameter based on the magnetic size information;

[0125] A second calculation module is configured to obtain a predicted value of a magnetic related parameter based on the two-dimensional key magnetic parameter and the predicted value of the correction coefficient, the predicted value of the magnetic related parameter comprising a predicted value of the key magnetic parameter and a predicted value of the effective magnetic path length, and / or a predicted distribution of magnetic field related information in the transverse plane, the magnetic field related information comprising a magnetic field, a magnetic field gradient or a magnetic field second derivative.

[0126] The neural network-based magnetic design device of the Halbach magnetic ring of the embodiment has the same inventive concept as the neural network-based magnetic design method of the Halbach magnetic ring described above, and thus the specific embodiments of the device can be seen in the embodiment part of the neural network-based magnetic design method of the Halbach magnetic ring described above, and the technical effects thereof correspond to those of the method described above, which will not be described here again.

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

[0128] The embodiment of the present application provides a computer program product, which includes computer programs / instructions. The computer programs / instructions are executed by a processor to implement the neural network-based magnetic design method of the Halbach magnetic ring.

[0129] The above is only various embodiments of the present application, but the protection scope of the present application is not limited thereto. Any person skilled in the art can easily think of changes or replacements within the technical range disclosed in the present application, which should be covered in the protection scope of the present application. Therefore, the protection scope of the present application should be subject to the protection scope of the claims.

Claims

1. A magnetic design method for Heilbeck magnetic rings based on neural networks, characterized in that, include: Construct a network training dataset, which includes an input set and an output set; the input set consists of multiple sets of magnet size information randomly generated within a set range, and the output set consists of correction coefficients corresponding to the input set; the correction coefficients include correction coefficients for key magnetic parameters and correction coefficients for effective magnetic circuit length, and / or the coefficient of variation of the magnetic induction intensity radius of the transverse central cross section of the magnet. The neural network is trained based on the aforementioned network training dataset to obtain the trained neural network; The magnet size information is input into the trained neural network to obtain the predicted value of the correction coefficient; Two-dimensional key magnetic parameters are calculated based on the magnet size information; Based on the predicted values ​​of the two-dimensional key magnetic parameters and the correction coefficients, the predicted values ​​of magnet-related parameters are obtained. The predicted values ​​of magnet-related parameters include the predicted values ​​of key magnetic parameters and the predicted values ​​of effective magnetic path length, and / or the predicted distribution of magnetic field-related information in the transverse plane. The magnetic field-related information includes the magnetic field, magnetic field gradient, or magnetic field second derivative.

2. The method as described in claim 1, characterized in that, The magnet size information within the specified 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 Let B be the inner radius, ε be the ratio of the outer radius to the inner radius, w be the ratio of the thickness to the inner radius, and B be the inner radius. r Remanence is the magnetic field strength.

3. The method as described in claim 1, characterized in that, Based on the predicted values ​​of the two-dimensional key magnetic parameters and the correction coefficients, predicted values ​​of magnet-related parameters are obtained, including: If the magnet is a dipolar magnet, the two-dimensional key magnetic parameter is the magnetic field strength in the X-direction of the two dimensions; 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) Where α is the correction coefficient for the key magnetic parameter, and B x(2D) B is the predicted value of the magnetic field strength in the two-dimensional X direction. x预测 This 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 flux density gradient at the transverse center point of the two-dimensional magnetochemical system. The predicted value of the magnetic flux density gradient at the transverse center point, i.e., the predicted value of the key magnetic parameter, is calculated using the following formula: Where α is the correction coefficient for the key magnetic parameter. The magnetic field strength gradient at the two-dimensional transverse center point is denoted as . This is the predicted value of the magnetic field strength gradient at the transverse center point; The predicted value of the effective magnetic circuit length is calculated using the following formula: l=(β+w)*R i Where l is the predicted effective magnetic circuit length, β is the effective magnetic circuit length correction factor, w is the ratio of thickness to inner radius, and R i The inner radius; Based on the coefficient of variation of the magnetic induction intensity radius of the transverse central section of the magnet, the predicted distribution of 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.

4. The method as described in 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 for key magnetic parameters and correction coefficients for effective magnetic path length. The output set used by the radial parameter mapping network during training includes the coefficient of variation of the magnetic induction intensity in the radial direction of the transverse central cross section of the magnet.

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

6. The apparatus as claimed in claim 5, characterized in that, The magnet size information within the specified 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 Let B be the inner radius, ε be the ratio of the outer radius to the inner radius, w be the ratio of the thickness to the inner radius, and B be the inner radius. r Remanence is the magnetic field strength.

7. The apparatus as claimed in claim 5, characterized in that, The second calculation module is also used for: If the magnet is a dipolar magnet, the two-dimensional key magnetic parameter is the magnetic field strength in the X-direction of the two dimensions; 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) Where α is the correction coefficient for the key magnetic parameter, and B x(2D) B is the predicted value of the magnetic field strength in the two-dimensional X direction. x预测 This 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 flux density gradient at the transverse center point of the two-dimensional magnetochemical system. The predicted value of the magnetic flux density gradient at the transverse center point, i.e., the predicted value of the key magnetic parameter, is calculated using the following formula: Where α is the correction coefficient for the key magnetic parameter. The magnetic field strength gradient at the two-dimensional transverse center point is denoted as . This is the predicted value of the magnetic field strength gradient at the transverse center point; The predicted value of the effective magnetic circuit length is calculated using the following formula: l=(β+w)*R i Where l is the predicted effective magnetic circuit length, β is the effective magnetic circuit length correction factor, w is the ratio of thickness to inner radius, and R i The inner radius; Based on the coefficient of variation of the magnetic induction intensity radius of the transverse central section of the magnet, the predicted distribution of 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.

8. The apparatus as claimed in 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 for key magnetic parameters and correction coefficients for effective magnetic path length. The output set used by the radial parameter mapping network during training includes the coefficient of variation of the magnetic induction intensity in the radial direction of the transverse central cross section of the magnet.

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

10. A computer program product, characterized in that, Includes a computer program / instruction, which, when executed by a processor, implements the magnetic design method for a neural network-based Helbeck magnetic ring as described in any one of claims 1-4.

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