A method and system for designing an electron beam expansion magnet based on an intelligent algorithm

Abstract

An electron beam expander magnet design method and system based on intelligent algorithms is proposed. Based on intelligent algorithms, the global optimal value of design parameters can be found within a specified range. By using the spatial distribution theory of the magnetic field of a four-level magnet, the geometric parameters and spatial position information of the magnet are directly introduced into the optimization process, resulting in optimization results that are more conducive to engineering implementation. The design method can quickly, flexibly and accurately obtain the optimal parameters based on the phase space information of the electron beam at the accelerator exit and the beam expansion requirements.

Description

Technical Field

[0001] This invention relates to a design method and system for electron beam expander magnets based on intelligent algorithms, belonging to the field of beam spot expansion technology in accelerator physics. Background Technology

[0002] Electron beam technology is a general term for technologies that use electromagnetic means to accelerate electrons to higher energies, and then use these high-energy electrons to explore the structure of matter or for other applications. Because of this, this technology has very important and wide-ranging applications in industrial and agricultural production, medical and health care, science and technology, and national defense. In some large electron accelerators, the electron beam needs to be transported over long distances, and the beam often diverges from its center, leading to an increase in the envelope radius of the target beam spot, a decrease in flux density, and a significant reduction in working efficiency.

[0003] To address this issue, an electron beam expander is typically added at the accelerator exit to compress the divergence angle of the incident electron beam. Current beam expander magnet assemblies are usually optimized based on prior experience or using finite element method (FE) simulations, resulting in significant computational resource waste and time-consuming trial-and-error costs. For beam expander magnet assemblies composed of multiple quadrupole magnets, the number of optimization parameters is large and the optimization is challenging. Relying on the aforementioned methods for beam expander magnet design usually involves changing single, local variables, often failing to obtain the globally optimal solution for the design parameters, thus leaving considerable room for optimization. Summary of the Invention

[0004] The technical problem solved by this invention is that, in the existing technology, the traditional method of adding an electron beam expander to compress the divergence angle of the incident electron beam has low working efficiency and it is difficult to obtain the global optimal solution of the design parameters. Therefore, an electron beam expander magnet design method based on intelligent algorithm is proposed.

[0005] The present invention solves the above-mentioned technical problem through the following technical solution:

[0006] A design method for electron beam expander magnets based on intelligent algorithms, comprising:

[0007] Quadrupole magnets are arranged sequentially along the beam line to form a beam expander magnet group;

[0008] Determine the transverse magnetic field gradient of the central section of each quadrupole magnet, calculate the effective magnetic path length, and determine the beam transmission matrix of the quadrupole magnet segment based on the transverse magnetic field gradient of the central section and the effective magnetic path length.

[0009] The beam drift segment transmission matrix is ​​determined based on the drift segment length between the quadrupole magnets;

[0010] The target electronic state phase space vector is determined by the initial electronic state phase space vector and the beam transport matrix of the quadrupole magnet segment.

[0011] The optimal beam expansion mode and optimal design parameters are determined by using optimization algorithms in combination with actual processing capabilities and working conditions.

[0012] The quadrupole magnets are positioned between drift sections. The number of quadrupole magnets arranged is even. In the beam expanding magnet group, half of the quadrupole magnets are used to control the size of the beam envelope in the X and Y directions of the beam expanding magnet group, and the other half of the quadrupole magnets are used to control the size of the beam divergence angle in the X and Y directions of the beam expanding magnet group.

[0013] The method for calculating the transverse magnetic field gradient of the central cross section is as follows:

[0014]

[0015] In the formula, the ε parameter includes ε1 to ε n R is the ratio of the inner and outer diameters of each quadrupole magnet. i Parameters include inner diameter R i1 ~R in ω represents the inner diameter of each quadrupole magnet, and the parameter ω includes the ratio of the actual pole face length to the radius of each quadrupole magnet, ω1~ω n B rem Here, C represents the magnetic parameter, and C is the theoretical deviation correction amount.

[0016] The effective magnetic circuit length L is calculated as follows:

[0017] L=(η+ω)R i

[0018] In the formula, η is a parameter related to the thickness of the quadrupole magnet.

[0019] The transverse magnetic field gradient and effective magnetic circuit length of the central section are both based on R. i The parameters ω and ω define the range of parameters. The effective magnetic path length L is used to correct for the difference between the magnetic path length and the actual pole face length L caused by edge effects. Q The deviation between them, where L Q =ωR i .

[0020] The quadrupole magnet segment beam transmission matrix includes the transmission matrix corresponding to the quadrupole magnet focusing in the X direction and the transmission matrix corresponding to the quadrupole magnet diverging in the Y direction, specifically:

[0021]

[0022]

[0023]

[0024]

[0025] In the formula, the transverse forces in the X and Y directions experienced by the electron in the quadrupole magnet are F and F, respectively. x F y The value of k is a parameter related to the focusing intensity of the magnet, which varies along the electron propagation direction within the range of the pole face length and is controlled and corrected by the effective magnetic circuit length of each quadrupole magnet.

[0026] In the quadrupole magnet beam transmission matrix, if the electron is subjected to a defocusing force in the X direction and a focusing force in the Y direction, then the transmission matrix corresponding to focusing in the X direction and the transmission matrix corresponding to diverging in the Y direction are interchanged.

[0027] The beam expander magnet assembly consists of quadrupole magnets and drift sections connected end to end. The drift section transmission matrix is ​​determined based on the drift section length as follows:

[0028]

[0029] The drift segment lengths are d1 to d2. n ;

[0030] Each quadrupole magnet is equipped with a quadrupole magnetic lens with an inner diameter parameter of R. i1 ~R in The ratio of the polar surface length to the inner diameter is ω1~ω n The state variables flag2, flag3, and flag4, which determine whether focusing is enabled or disabled, are all set to either 1 or -1. The initial electronic state phase space vector is then multiplied by the beam drift segment transfer matrix to determine the target electronic state phase space vector. Specifically:

[0031] U x =N4·(X4·(N3·(X3·(N2·(X2·(N1·(X1·(N0·U)) 0x ))))))))

[0032] U y =N4·(Y4·(N3·(Y3·(N2·(Y2·(N1·(Y1·(N0·U 0y ))))))))

[0033] In the formula, U x U is the phase space vector of the electrons at the exit of the magnet assembly in the X direction. y U is the phase space vector of the electron in the Y direction at the exit. 0x U is the phase space vector of the electron at the entrance in the X direction. 0y Let N be the phase space vector of the electron at the entrance in the Y direction, and N0 be the transfer matrix corresponding to the first drift segment.

[0034] The optimization algorithm includes, but is not limited to, genetic algorithm, annealing algorithm, and swarm intelligence algorithm. The optimization range of the design parameters in the optimization algorithm is determined according to the actual engineering processing capability of electron beam expansion and equipment installation requirements. After optimization by a specified number of optimization algorithms, the reciprocal of the average distance from the electron at the exit to the beam center is determined as the fitness function, and the magnet parameter corresponding to the largest fitness function is taken as the optimal design parameter.

[0035] The quadrupole magnets are made of NdFeB N50 toroidal Helbach magnetic rings, arranged in an even number of pairs, at least 4 groups, with an inter-group drift length d greater than 0.1m and an inner-outer diameter ratio ε1~ε1. n The range is between 0.7 and 0.9.

[0036] An electron beam expander magnet based on an intelligent algorithm includes a beamline and a quadrupole magnet, wherein:

[0037] The quadrupole magnets are arranged sequentially on the beam line, and a drift section is provided between the quadrupole magnets. The electron beam is transported through the beam line and the beam expander magnet group composed of the quadrupole magnets. The quadrupole magnets are used to control the size of the beam envelope in the X and Y directions of the beam expander magnet group, and at the same time, they are used to control the size of the beam divergence angle in the X and Y directions of the beam expander magnet group.

[0038] The quadrupole magnets are made of NdFeB N50 toroidal Helbach magnetic rings, arranged in an even number of pairs, at least 4 groups, with an inter-group drift length d greater than 0.1m and an inner-outer diameter ratio ε1~ε1. n The range is between 0.7 and 0.9.

[0039] The advantages of this invention compared to the prior art are:

[0040] This invention provides a design method for electron beam expander magnets based on intelligent algorithms. Compared to existing finite element simulation-assisted design methods, this invention, based on intelligent algorithms, can find the globally optimal values ​​of design parameters within a specified range. Furthermore, by directly incorporating the geometric parameters and spatial location information of the magnet into the optimization process through the spatial distribution theory of the four-level magnet magnetic field, the optimized results are more conducive to engineering implementation. Traditional design methods rely heavily on the long-term accumulated debugging experience of experts or on computational resources, often resulting in significant computation time or debugging costs. The design method proposed in this invention can quickly, flexibly, and accurately obtain optimal parameters based on the electron beam phase space information at the accelerator exit and the beam expansion requirements. Attached Figure Description

[0041] Figure 1 A schematic diagram of the beam-expanding magnet assembly device provided for the invention;

[0042] Figure 2A schematic diagram of the geometric dimensions of a quadrupole magnet provided for the invention;

[0043] Figure 3 A schematic diagram of the genetic optimization algorithm provided for the invention;

[0044] Figure 4 A schematic diagram of the electron phase space image in the X and Y directions at the entrance provided for the invention;

[0045] Figure 5 A schematic diagram of the X and Y direction electron beams to the target phase space without processing by the beam expander magnet assembly, provided for the invention;

[0046] Figure 6 A schematic diagram of the X and Y direction electron beams to the target phase space after being processed by the beam-expanding magnet assembly, provided for the invention;

[0047] Figure 7 A schematic diagram illustrating the design steps of an electron beam expander magnet based on an intelligent algorithm, provided for the invention. Detailed Implementation

[0048] An electron beam expander magnet design method and system based on intelligent algorithms is proposed. Based on intelligent algorithms, the global optimal value of design parameters can be found within a specified range. By using the spatial distribution theory of the magnetic field of a four-level magnet, the geometric parameters and spatial position information of the magnet are directly introduced into the optimization process, resulting in optimization results that are more conducive to engineering implementation. The design method can quickly, flexibly and accurately obtain the optimal parameters based on the phase space information of the electron beam at the accelerator exit and the beam expansion requirements.

[0049] The specific process of designing electron beam expander magnets is as follows:

[0050] Quadrupole magnets are arranged sequentially along the beam line to form a beam expander magnet group;

[0051] Determine the transverse magnetic field gradient of the central section of each quadrupole magnet, calculate the effective magnetic path length, and determine the beam transmission matrix of the quadrupole magnet segment based on the transverse magnetic field gradient of the central section and the effective magnetic path length.

[0052] The beam drift segment transmission matrix is ​​determined based on the drift segment length between the quadrupole magnets;

[0053] The target electronic state phase space vector is determined by the initial electronic state phase space vector and the beam transport matrix of the quadrupole magnet segment.

[0054] The optimal beam expansion mode and optimal design parameters are determined by using optimization algorithms in combination with actual processing capabilities and working conditions.

[0055] The space between the quadrupole magnets is a drift section. The number of quadrupole magnets is arranged in an even number. In the beam expanding magnet group, half of the quadrupole magnets are used to control the size of the beam envelope in the X and Y directions of the beam expanding magnet group, and the other half of the quadrupole magnets are used to control the size of the beam divergence angle in the X and Y directions of the beam expanding magnet group.

[0056] The method for calculating the transverse magnetic field gradient at the central cross section is as follows:

[0057]

[0058] In the formula, the ε parameter includes ε1 to ε n R is the ratio of the inner and outer diameters of each quadrupole magnet. i Parameters include inner diameter R i1 ~R in ω represents the inner diameter of each quadrupole magnet, and the parameter ω includes the ratio of the actual pole face length to the radius of each quadrupole magnet, ω1~ω n B rem Here, C is a magnetic parameter used to correct theoretical deviations, and can be expressed as:

[0059]

[0060] The effective magnetic circuit length L is calculated as follows:

[0061] L=(η+ω)R i

[0062] In the formula, η is a parameter related to the thickness of the quadrupole magnet, and its value is expressed as:

[0063] η = -0.03082w 3 +0.2975w 2 -0.9872w +1.181

[0064] The transverse magnetic field gradient and effective magnetic circuit length of the central section are both based on R. i The parameters ω and ω define the range of parameters. The effective magnetic circuit length L is used to correct for the difference between the magnetic circuit length and the actual pole face length L caused by edge effects. Q The deviation between them, where L Q =ωR i ;

[0065] The beam transmission matrix of the quadrupole magnet segment includes the transmission matrix corresponding to the quadrupole magnet focusing in the X direction and the transmission matrix corresponding to the quadrupole magnet diverging in the Y direction, specifically:

[0066]

[0067]

[0068]

[0069]

[0070] In the formula, the transverse forces in the X and Y directions experienced by the electron in the quadrupole magnet are F and F, respectively. x F y The value of k is a parameter related to the focusing intensity of the magnet, which varies along the electron propagation direction within the range of the pole face length and is controlled and corrected by the effective magnetic circuit length of each quadrupole magnet.

[0071] In the beam transmission matrix of the quadrupole magnet segment, if the electron is subjected to a defocusing force in the X direction and a focusing force in the Y direction, then the transmission matrix corresponding to focusing in the X direction and the transmission matrix corresponding to diverging in the Y direction are interchanged.

[0072] The beam expander magnet assembly consists of quadrupole magnets connected before and after the drift section. The drift section transmission matrix is ​​determined based on the drift section length:

[0073]

[0074] The drift segment lengths are d1 to d2. n ;

[0075] Each quadrupole magnet is equipped with a quadrupole magnetic lens with an inner diameter parameter of R. i1 ~R in The ratio of the polar surface length to the inner diameter is ω1~ω n The state variables flag2, flag3, and flag4, which determine whether focusing is enabled or disabled, are all set to either 1 or -1. The initial electronic state phase space vector is then multiplied by the beam drift segment transfer matrix to determine the target electronic state phase space vector. Specifically:

[0076] U x =N4·(X4·(N3·(X3·(N2·(X2·(N1·(X1·(N0·U)) 0x ))))))))

[0077] U y =N4·(Y4·(N3·(Y3·(N2·(Y2·(N1·(Y1·(N0·U 0y ))))))))

[0078] In the formula, U x U is the phase space vector of the electrons at the exit of the magnet assembly in the X direction. y U is the phase space vector of the electron in the Y direction at the exit. 0x U is the phase space vector of the electron at the entrance in the X direction. 0y Let N be the phase space vector of the electron at the entrance in the Y direction, and N0 be the transfer matrix corresponding to the first drift segment;

[0079] The optimization algorithm includes, but is not limited to, genetic algorithm, annealing algorithm, and swarm intelligence algorithm. The optimization range of the design parameters in the optimization algorithm is determined according to the actual engineering processing capacity and equipment installation requirements of electron beam expansion. After optimization by a specified number of optimization algorithms, the reciprocal of the average distance from the electron at the exit to the beam center is determined as the fitness function, and the magnet parameter corresponding to the largest fitness function is taken as the optimal design parameter.

[0080] The quadrupole magnets use N50 neodymium iron boron toroidal Helbach magnetic rings, arranged in an even number of pairs, at least 4 groups, with an inter-group drift length d greater than 0.1m and an inner-outer diameter ratio ε1~ε1. n The range is between 0.6 and 0.9;

[0081] The electron beam expander magnet based on intelligent algorithms includes a beamline and a quadrupole magnet. The quadrupole magnets are arranged sequentially on the beamline, and drift sections are set between the quadrupole magnets. The electron beam is transported through the beam expander magnet group composed of the beamline and the quadrupole magnets. The quadrupole magnets are used to control the size of the beam envelope in the X and Y directions of the beam expander magnet group, and at the same time, they are used to control the size of the beam divergence angle in the X and Y directions of the beam expander magnet group.

[0082] The following description, in conjunction with the accompanying drawings and preferred embodiments, provides further details:

[0083] In the current embodiment, the electron beam expander magnet design method based on intelligent algorithms is as follows: Figure 7 As shown, the specific steps are as follows:

[0084] Multiple sets of quadrupole magnets and drift sections between the magnets are arranged sequentially along the beam line, together forming a beam expanding magnet group, such as... Figure 1 As shown. This device minimizes the divergence angle of the output beam in the X and Y directions, allowing the beam to travel long distances and converge at the target spot;

[0085] like Figure 2 As shown, based on the geometry of a quadrupole magnet (inner diameter R) i The ratio of inner to outer diameter ε, the ratio of pole length to inner diameter ω), and magnetic parameters (remanence B) rem (where the value is a constant), the transverse magnetic field gradient at the central cross section is determined using theoretical methods. Considering the edge effect of the magnet, determine the effective magnetic path length (L=(η+ω)R). i , where ω is the ratio of the actual pole face length to the inner diameter of the magnet, and the beam transmission matrix of the quadrupole magnet segment is determined based on the above parameters;

[0086] The beam drift segment transmission matrix is ​​derived based on the drift segment length d. The target electronic state phase space vector is obtained by combining the initial electronic state phase space vector and the quadrupole magnet segment beam transmission matrix.

[0087] The range of magnet optimization parameters is determined based on actual processing capacity and equipment operating conditions, and the optimal beam expansion mode and best design parameters are determined using a genetic algorithm.

[0088] The quadrupole magnets are N50 neodymium iron boron toroidal Helbach magnetic rings, arranged in an even number of pairs, at least four sets. Two sets control the beam envelope size in the X and Y directions to be as close as possible, while the other two sets control the beam divergence angle in the X and Y directions to be as small as possible.

[0089] The magnetic field gradient at the center cross-section of a quadrupole magnet is given by the theoretical formula. The value of C (which represents a correction to the two-dimensional theoretical model considering the magnet thickness) is determined without relying on finite element simulation. The adjusted magnet parameters include the inner diameter R. i1 ~R in , the ratio of inner and outer diameter ε1~ε n The ratio of the actual pole face length to the radius of the magnet is ω1~ω n The drift distance between magnets is d1~d n The flags flag2 to flag2 control the focus and divergence modes. n There are 5n-1 parameters;

[0090] The drift segment length d is greater than 0.1m, and the ratio of the inner to outer diameter is ε1~ε. n The target electron state phase space vector is in the range of 0.6 to 0.9 and is determined by the aforementioned parameters. This set of parameters can be optimized according to the target electron beam spot requirements.

[0091] Intelligent algorithms are not limited to genetic algorithms; they also include annealing algorithms, swarm intelligence algorithms, and other optimization algorithms. The optimization range of the design parameters for intelligent algorithms is determined by actual engineering processing capabilities and equipment installation requirements. Taking a genetic algorithm as an example, the optimization steps are as follows: Figure 3 As shown;

[0092] For lightweight structural design considerations, a beam-expanding magnet group consisting of 4 sets of quadrupole magnets is provided;

[0093] The electron beam cross-section envelope contains 5000 electrons, and the state vector space vector of each electron in this electron group is [x]. n0 ,x n0 ′] T With [y n0 ,y n0 ′] T The beam spot radius is 1 mm, the divergence angle is 0.001, and the minimum beam spot radius is required after the beam propagates for 10 km. The initial phase space image of this electron beam is as follows. Figure 4 As shown.

[0094] In the inner radius circular region of an ideal quadrupole magnet, the derivative of the magnetic flux density in the orthogonal directions is: The specific value depends only on the inner diameter R. i The ratio of inner to outer diameter ε, the ratio of pole length to inner diameter ω, and remanence B. rem Related. The length of the pole face of a quadrupole magnet is L. Q Due to the edge effect, the value of K is not constant along the electron propagation direction within the range of the polar surface length. To correct this effect, an effective length L = (η + ω)R is used here. i Make corrections, L Q =ωR i The transverse forces in the X and Y directions experienced by an electron in a quadrupole magnet can be expressed as follows: This makes The transfer matrix corresponding to a quadrupole magnet when focused in the X direction is:

[0095]

[0096] Correspondingly, its effect on electrons in the Y direction is divergent, and the corresponding transfer matrix can be expressed as:

[0097]

[0098] If the electron is subjected to a defocusing force in the X direction and a focusing force in the Y direction, the matrix can be interchanged. The beam expander magnet assembly consists of several components and drift segments connected before and after. For the beam expander magnet assembly designed in this scheme, it contains 5 drift segments with lengths d1, d2, d3, d4, and d5, where d5 is the known propagation distance of 10km. The transmission matrix of the drift segment is:

[0099]

[0100] Four quadrupole magnetic lenses, their inner diameters are divided into R... i1 ,R i2 ,R i3 ,R i4 The ratios of their inner and outer diameters are ε1, ε2, ε3, and ε4, respectively; the ratios of the pole length to the inner diameter are ω1, ω2, ω3, and ω4, respectively; and the state variables flag2, flag3, and flag4 (with values ​​of 1 or -1) control whether focusing occurs. Therefore, there are a total of 19 design parameters that need to be optimized. The effect of the beam-expanding magnet assembly on the incident electrons can be obtained by multiplying the phase space vectors sequentially by the transfer matrix.

[0101] U x =N4·(X4·(N3·(X3·(N2·(X2·(N1·(X1·(N0·U)) 0x ))))))))

[0102] U y=N4·(Y4·(N3·(Y3·(N2·(Y2·(N1·(Y1·(N0·U 0y ))))))))

[0103] The optimal design parameters for different focusing and diverging modes can be obtained using a genetic algorithm. Due to the crossover and mutation operations, the optimization results of the genetic algorithm are uncertain. Therefore, to obtain a more stable and reasonable result, it is necessary to run the algorithm multiple times and compare the results. The beam-expanding mode with the largest average fitness function is the optimal beam-expanding mode. The set of parameters corresponding to the largest fitness function (the reciprocal of the average distance from the electron to the zero point) under this beam-expanding mode is the optimal parameter, as shown in Table 1.

[0104] Table 1. Geometric and positional information of the beam expander magnet assembly

[0105]

[0106] If the electron beam is transported directly without being processed by the beam expander magnet assembly, the phase space image from 10km to the target will be as follows: Figure 5 As shown, after processing by the beam-expanding magnet group designed in the embodiments of the present invention, the phase space image of the target beam spot under the same conditions is as follows: Figure 6 As shown. By comparison, it can be found that the beam-expanding magnet assembly designed in this embodiment can compress the beam spot radius in the X direction by 12 times and the beam spot radius in the Y direction by 12 times, increasing the flux density to the target beam spot by more than 144 times, which is a significant effect.

[0107] Although the present invention has been disclosed above with reference to preferred embodiments, it is not intended to limit the present invention. Any person skilled in the art can make possible changes and modifications to the technical solutions of the present invention by utilizing the methods and techniques disclosed above without departing from the spirit and scope of the present invention. Therefore, any simple modifications, equivalent changes and alterations made to the above embodiments based on the technical essence of the present invention without departing from the content of the technical solutions of the present invention shall fall within the protection scope of the technical solutions of the present invention.

[0108] The contents not described in detail in this specification are common knowledge to those skilled in the art.

Claims

1. A design method for electron beam expander magnets based on intelligent algorithms, characterized in that... include: Multiple sets of quadrupole magnets and drift sections between magnets are arranged sequentially on the beam line to form a beam expanding magnet group. The space between the quadrupole magnets is a drift section. The number of quadrupole magnets is arranged in an even number. In the beam expanding magnet group, half of the quadrupole magnets are used to control the size of the beam envelope in the X and Y directions of the beam expanding magnet group, and the other half of the quadrupole magnets are used to control the size of the beam divergence angle in the X and Y directions of the beam expanding magnet group. Quadrupole magnets are arranged sequentially along the beam line to form a beam expander magnet group; Determine the transverse magnetic field gradient of the central section of each quadrupole magnet, calculate the effective magnetic path length, and determine the beam transmission matrix of the quadrupole magnet segment based on the transverse magnetic field gradient of the central section and the effective magnetic path length. The beam drift segment transmission matrix is ​​determined based on the drift segment length between the quadrupole magnets; The target electronic state phase space vector is determined by the initial electronic state phase space vector and the beam transport matrix of the quadrupole magnet segment. The optimal beam expansion mode and optimal design parameters are determined by using optimization algorithms in combination with actual processing capabilities and working conditions.

2. The design method for an electron beam expander magnet based on an intelligent algorithm according to claim 1, characterized in that: The method for calculating the transverse magnetic field gradient of the central cross section is as follows: In the formula, Parameters include , where is the ratio of the inner and outer diameters of each quadrupole magnet. Parameters include inner diameter , where is the inner diameter of each quadrupole magnet. The parameters include the ratio of the actual pole face length to the radius of each quadrupole magnet. , Here, C represents the magnetic parameter, and C is the theoretical deviation correction amount. The effective magnetic circuit length The calculation method is as follows: In the formula, These are the parameters related to the thickness of the quadrupole magnet.

3. The design method for an electron beam expander magnet based on an intelligent algorithm according to claim 2, characterized in that: The transverse magnetic field gradient and effective magnetic circuit length of the central section are both based on... parameter, The range of parameters is determined, including the effective magnetic circuit length. Used to correct for the difference between the magnetic circuit length and the actual pole length caused by edge effects. The deviation between them, .

4. The design method for an electron beam expander magnet based on an intelligent algorithm according to claim 3, characterized in that: The quadrupole magnet segment beam transmission matrix includes the transmission matrix corresponding to the quadrupole magnet focusing in the X direction and the transmission matrix corresponding to the quadrupole magnet diverging in the Y direction, specifically: In the formula, the transverse forces in the X and Y directions experienced by the electron in the quadrupole magnet are respectively , , The value is a parameter related to the magnet focusing intensity, which varies along the electron propagation direction within the range of the pole face length, and is controlled and corrected by the effective magnetic circuit length of each quadrupole magnet.

5. The design method for an electron beam expander magnet based on an intelligent algorithm according to claim 4, characterized in that: In the quadrupole magnet beam transmission matrix, if the electron is subjected to a defocusing force in the X direction and a focusing force in the Y direction, then the transmission matrix corresponding to focusing in the X direction and the transmission matrix corresponding to diverging in the Y direction are interchanged.

6. The design method for an electron beam expander magnet based on an intelligent algorithm according to claim 5, characterized in that: The beam expander magnet assembly consists of quadrupole magnets and drift sections connected end to end. The drift section transmission matrix is ​​determined based on the drift section length as follows: The drift segment lengths are respectively ; Each quadrupole magnet is equipped with a quadrupole magnetic lens with an inner diameter parameter of [missing information]. The ratio of the polar surface length to the inner diameter is Determine the state variables for whether or not to control focus. All values ​​are 1 or -1. The initial electronic state phase space vector is determined by multiplying the beam drift segment transfer matrix sequentially on the left to determine the target electronic state phase space vector, specifically: In the formula, Let X be the phase space vector of the electrons at the exit of the magnet assembly in the X direction. Let be the phase space vector of the electron at the exit in the Y direction. Let X be the phase space vector of the electron at the entrance in the X direction. Let be the phase space vector of the electron at the entrance in the Y direction. This is the transfer matrix corresponding to the first drift segment.

7. The design method for an electron beam expander magnet based on an intelligent algorithm according to claim 6, characterized in that: The optimization algorithm includes, but is not limited to, genetic algorithm, annealing algorithm, and swarm intelligence algorithm. The optimization range of the design parameters in the optimization algorithm is determined according to the actual engineering processing capability of electron beam expansion and equipment installation requirements. After optimization by a specified number of optimization algorithms, the reciprocal of the average distance from the electron at the exit to the beam center is determined as the fitness function, and the magnet parameter corresponding to the largest fitness function is taken as the optimal design parameter.

8. The design method for an electron beam expander magnet based on an intelligent algorithm according to claim 7, characterized in that: The quadrupole magnets are made of NdFeB N50 toroidal Helbach magnetic rings, arranged in an even number of pairs, at least 4 groups, with an inter-group drift length of... Greater than 0.1 m, ratio of inner to outer diameter The range is between 0.7 and 0.

9.

9. An electron beam expander magnet implemented according to the intelligent algorithm-based electron beam expander magnet design method as described in claim 8, characterized in that: Including beamlines and quadrupole magnets, among which: The quadrupole magnets are arranged sequentially on the beam line, and a drift section is provided between the quadrupole magnets. The electron beam is transported through the beam line and the beam expander magnet group composed of the quadrupole magnets. The quadrupole magnets are used to control the size of the beam envelope in the X and Y directions of the beam expander magnet group, and at the same time, they are used to control the size of the beam divergence angle in the X and Y directions of the beam expander magnet group. The quadrupole magnets are made of NdFeB N50 toroidal Helbach magnetic rings, arranged in an even number of pairs, at least four groups, with an inter-group drift length of [missing information]. Greater than 0.1 m, ratio of inner to outer diameter The range is between 0.7 and 0.9.

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