Static magnetic field magnet structure optimization method for nuclear magnetic resonance imaging

Abstract

The invention discloses a static magnetic field magnet structure optimization method for nuclear magnetic resonance imaging, relates to a magnet structure optimization method, and provides a trial-and-error-free design method aiming at the problem of lack of magnetic steel quantity optimization guidance in Halbach annular magnet design. And calculating the magnetic induction intensity, amplitude uniformity and directivity uniformity of the central area, and revealing the nonlinear relationship between the number of the magnetic steels and the magnetic field performance. According to the method, the optimal number and arrangement scheme of magnetic steel are rapidly determined according to the requirements of nuclear magnetic resonance equipment, and balance optimization of magnetic induction intensity, amplitude uniformity and directivity uniformity of a central area is achieved. A traditional trial and error method is avoided, the research and development period is remarkably shortened, and the magnetic field quality is improved.

Description

Technical Field

[0001] The present invention relates to a method for optimizing a magnet structure, in particular to a method for optimizing a static magnetic field magnet structure for nuclear magnetic resonance imaging. Background Art

[0002] Equipment such as magnetic resonance imaging (MRI) requires a high-intensity and highly uniform static magnetic field within the imaging area. Currently, most MRI systems use superconducting electromagnets or large permanent magnets to generate high field strengths, but these systems are expensive and bulky. The Halbach permanent magnet array is a magnet arrangement proposed by physicist Klaus Halbach that can generate an enhanced magnetic field on one side of the array while significantly canceling the magnetic field on the other side. The Halbach ring magnet (also known as the "magic ring" magnet) is composed of multiple permanent magnetic steels in a circular ring. The magnetization direction is carefully arranged to generate a nearly uniform and consistent magnetic field inside the ring. The aluminum sheets used for spacing make the magnetic field more uniform. It has important applications in fields such as MRI and nuclear magnetic resonance spectroscopy. Compared with traditional magnets, the Halbach ring array can achieve high magnetic field strength without an iron core, while having less magnetic leakage to the surrounding environment.

[0003] However, the design of Halbach ring magnets still faces challenges in practical applications. First, the number of magnetic steel blocks that make up the ring and their magnetization direction will significantly affect the magnetic induction intensity and uniformity in the central area: too few magnetic steel blocks will lead to uneven magnetic field distribution, while too many magnetic steel blocks will increase cost and assembly complexity. Second, the discrete Halbach array formed by different numbers of magnetic steel blocks can only approximate a continuously distributed magnetic source, which may introduce certain field intensity fluctuations and directional deviations.

[0004] The existing technology lacks a systematic guide for determining the number of magnets required to meet both field strength and uniformity requirements for a specific size. Therefore, it is necessary to provide a design method that quantitatively analyzes the variations in magnetic induction intensity, directional uniformity, and amplitude uniformity of the central magnetic field for different numbers of magnets, thereby helping engineers select the optimal Halbach ring magnet structure. Summary of the Invention

[0005] The present invention aims to provide a method for optimizing the structure of a static magnetic field magnet for nuclear magnetic resonance imaging. This method selects an appropriate number of magnetic steel blocks and aluminum blocks to form a Halbach array based on the requirements of nuclear magnetic resonance equipment. The aluminum blocks improve the uniformity of the magnet, thereby achieving the desired magnetic induction intensity, amplitude uniformity, and directional uniformity in the central imaging area of ​​the magnet. This results in stronger magnetic induction, better directionality, and better uniformity in the central working area.

[0006] The purpose of the present invention is achieved through the following technical solutions:

[0007] A method for optimizing the structure of a static magnetic field magnet for nuclear magnetic resonance imaging, comprising: a magnet comprising a plurality of permanent magnets arranged in a ring structure according to a Halbach array; determining required magnetic field parameter indicators, including central magnetic flux density (B0), amplitude uniformity, and directional uniformity requirements; establishing Halbach ring magnet models consisting of different numbers N of magnetic steels (N=4, 8, 12, 16), and solving the magnetic field distribution in the central region by analytical calculation or finite element simulation; calculating the magnetic flux density, amplitude uniformity, and amplitude directionality of the central region of each model and comparing them with predetermined requirements; selecting the number of magnetic steels and the arrangement scheme based on the comparison results to achieve magnetic field performance optimization; wherein the amplitude uniformity is characterized by the ratio (unit: ppm) of the difference between the maximum and minimum magnetic flux density in the central region and the magnetic flux density at the center point, and the directional uniformity is characterized by the ratio of the vertical component to the main direction component.

[0008] In the static magnetic field magnet structure optimization method for nuclear magnetic resonance imaging, the relationship between the number of magnetic steels N and the magnetic field performance is as follows: as the number of magnetic steels N increases, the magnetic induction intensity B0 in the central area shows an approximately nonlinear decreasing trend;

[0009] The amplitude uniformity and directional uniformity overall showed a characteristic of first improving and then stabilizing. Specifically, when the number of magnets N increased from 4 to 8, the amplitude uniformity decreased from 18121ppm to 9919ppm, an improvement of 45.3%; the directional uniformity decreased from 10744ppm to 7027ppm, still remaining within an acceptable range. When the number of magnets N further increased to 12 and 16, the amplitude uniformity was 11021ppm and 12031ppm, respectively, a slight rebound compared to the case of 8 magnets; the directional uniformity also increased.

[0010] In the static magnetic field magnet structure optimization method for nuclear magnetic resonance imaging, the amplitude uniformity calculation formula is:

[0011]

[0012] in, is the magnetic flux density vector, is the magnetic flux density vector at the center point, Uni represents the uniformity of the magnetic field; the directional uniformity calculation formula is:

[0013]

[0014] in, represents the directionality of the magnetic field, is the x-axis component of the magnetic flux density, is the z-axis component of the magnetic flux density, is the y-axis component of the magnetic flux density.

[0015] In the method for optimizing the static magnetic field magnet structure for nuclear magnetic resonance imaging, the magnetic steel blocks of the Halbach ring magnet model are evenly distributed along the circumference, and the magnetization directions of the magnetic steel blocks are rotated in sequence to form a Halbach magnetic array, so that an enhanced and uniform magnetic field is obtained inside the ring structure, and the magnetic field outside the ring structure is weakened.

[0016] The static magnetic field magnet structure optimization method for nuclear magnetic resonance imaging uses finite element simulation and mathematical analysis to obtain central area magnetic field characteristic data of configurations with different numbers of magnetic steels, and constructs a relationship curve between the number of magnetic steels and the magnetic field intensity, uniformity and directionality as a basis for selecting the optimal number of magnetic steels.

[0017] The significant features and positive effects of the present invention are:

[0018] The data provided by this invention is normalized and plotted on a single graph to convert data of different dimensions and ranges to a similar scale. This allows designers to intuitively balance magnetic field performance with magnet complexity and determine the optimal number of magnet blocks based on specific application requirements. By applying the method of this invention, magnet design for nuclear magnetic resonance equipment will be more targeted, avoiding blind trial and error, thereby reducing R&D costs and improving magnetic field quality. BRIEF DESCRIPTION OF THE DRAWINGS

[0019] Figure 1 Schematic diagram of a ring unit structure of four types of Halbach magnets in an embodiment of the present invention;

[0020] Figure 2 Schematic diagram of the longitudinal direction of each column of four Halbach magnets in an embodiment of the present invention;

[0021] Figure 3 Schematic diagram of the magnetic induction intensity, directional uniformity and amplitude uniformity in the central area of ​​four Halbach magnets as the number of magnetic steels increases in an embodiment of the present invention. DETAILED DESCRIPTION

[0022] The method steps and principles of the present invention are described in detail below with reference to specific embodiments and drawings.

[0023] The design process of a Halbach ring magnet of the present invention includes the following steps:

[0024] The first step is to determine the target magnetic field parameters, including the required central magnetic induction intensity B0, amplitude uniformity index, and directional uniformity control requirements;

[0025] The second step is to construct a Halbach ring magnet model composed of different numbers of N magnetic steels, where N is a positive integer, preferably N=4, 8, 12, and 16. The model can use analytical modeling or finite element simulation to obtain magnetic field distribution data in the central area;

[0026] The third step is to extract the performance indicators such as magnetic induction intensity, amplitude uniformity (ppm), and directional uniformity (ppm) of the central area based on the simulation results of the model;

[0027] The fourth step is to compare the obtained performance indicators with the preset magnetic field requirements to determine whether they meet the application needs, and then determine the number N of magnetic steel blocks and their arrangement so that the designed magnet can achieve the best balance between magnetic field strength and uniformity in the central area.

[0028] The core of the method of the present invention is to reveal the functional relationship between the number of magnets N and the central magnetic field performance, which is specifically manifested as follows: as N increases, the magnetic induction intensity B in the central area shows an approximately linear decreasing trend, while the amplitude uniformity and directional uniformity are significantly improved, which is reflected in a more uniform magnetic field distribution and smaller directional deviation; when the number of magnets increases from N=4 to N=8, the amplitude uniformity is improved to the greatest extent; and when N further increases from 12 to 16, the uniformity and directionality improvement effects tend to saturate, and the performance improvement is significantly reduced.

[0029] The present invention relates to four models, which are respectively composed of 32, 64, 96 and 128 rectangular parallelepiped magnets bonded together. Each model contains 8 groups of annular unit magnets, each ring contains the same number of magnets, and the residual magnetism and magnetization direction of each ring magnet are consistent. The magnetization direction can be set along any 30 mm direction. For the four-magnet magnet model, it is divided into 8 groups, each group contains 4 magnets. These 4 magnets are arranged in the same plane to form an annular unit. Specifically, the 4 magnets are located at the front, back, left and right positions of the ring, of which the magnetization direction of the two magnets at the front and back positions is forward, while the magnetization direction of the two magnets at the left and right positions is backward, thereby generating a uniformly distributed horizontal main static magnetic field in the center area of ​​the ring. For the eight-magnet magnet model, it is also divided into 8 groups, each group contains 8 magnets. These 8 magnets are arranged in the same plane to form an annular unit. Specifically, the 8 magnets are located at the front, back, left, right and 45° diagonal positions of the ring. The two magnets in the front and rear positions are magnetized forward, while the two magnets in the left and right positions are magnetized backward. The magnets in the right front and left rear positions are magnetized rightward, while those in the right rear and left front positions are magnetized leftward. The closed magnetic flux density curve determines the magnetization direction of the diagonally opposite magnets, generating a uniformly distributed horizontal main static magnetic field in the center of the ring. For the twelve-magnet magnet model, it is divided into eight groups, each containing 12 magnets. These 12 magnets are arranged coplanarly to form a ring unit. Specifically, the 12 magnets are located at 30° intervals around the ring. The magnet blocks are arranged in a circular pattern, but the diagonal magnet blocks are rotated due to the closed magnetic flux lines. For example, magnet blocks 19 and 20 are sandwiched between magnet blocks 15 and 18. Magnet blocks 19 and 20 bisect the 180° angle, so the magnet blocks need to be rotated accordingly. The magnetization directions are shown in the figure. Ultimately, a uniformly distributed horizontal main static magnetic field is generated in the center of the ring. For the sixteen-magnet magnet model, it is divided into eight groups, each containing 16 magnets. These 16 magnets are arranged coplanarly to form a ring unit. Specifically, the 16 magnets are located at intervals of 22.5° around the ring. The center points of the magnet blocks are arranged in a circular pattern, but the oblique magnet blocks rotate due to the influence of closed magnetic flux lines, similar to the principle of the aforementioned model. For example, magnet blocks 32, 33, and 34 are sandwiched between magnet blocks 28 and 31. Magnet blocks 32, 33, and 34 divide 180° equally, so the magnet blocks need to be rotated by the corresponding angle, with the magnetization direction shown in the figure. Ultimately, a uniformly distributed horizontal main static magnetic field is generated in the center of the ring. Gaps are left between the eight ring-shaped units. Each ring structure has gaps between each of the eight rings, and aluminum alloy flat blocks are embedded in the gaps. The gaps between adjacent rings gradually decrease in thickness from the center of symmetry of the NMR permanent magnet toward its ends. The thickness of the aluminum alloy flat blocks also gradually decreases from the center of symmetry of the NMR permanent magnet toward its ends. The aluminum alloy blocks are embedded to make the magnet's magnetic field more uniform.

[0030] Generally speaking, for two identical cubic magnets, assuming the side length is a meter and the residual magnetic flux density is B r Tesla, then when the two are close, the maximum mutual attraction F can be expressed as:

[0031]

[0032] In the formula, μ0 is the magnetic permeability in vacuum. From this, it can be calculated that when the residual magnetic flux density B r When the value of the magnet is 1.42 Tesla and the side length a is 10 mm, the maximum attraction is about 80.23 Newtons; when a is 30 mm, the maximum attraction can reach 722.07 Newtons.

[0033] The directional uniformity of the magnetic field generated by a magnet in the surrounding space is defined as:

[0034]

[0035] Where, Indicates the directional uniformity of the magnetic field, is the x-axis component of the magnetic flux density, is the z-axis component of the magnetic flux density, is the y-axis component of the magnetic flux density.

[0036] The amplitude uniformity generated by a magnet in the surrounding space is defined as:

[0037]

[0038] Where, is the magnetic flux density vector, is the magnetic flux density vector at the center point, and Uni represents the amplitude uniformity of the magnetic field.

[0039] The remanence of the magnetic steel in the present invention is 1.42 Tesla. Simulation and calculation show that the magnetic induction intensity in the central area of ​​the four-magnet magnet is 0.600734 Tesla, the directional uniformity is 10744 ppm, and the amplitude uniformity is 18121 ppm; the magnetic induction intensity in the central area of ​​the eight-magnet magnet is 0.552215 Tesla, the directional uniformity is 7027 ppm, and the amplitude uniformity is 9919 ppm; the magnetic induction intensity in the central area of ​​the twelve-magnet magnet is 0.394573 Tesla, the directional uniformity is 9121 ppm, and the amplitude uniformity is 11021 ppm; the magnetic induction intensity in the central area of ​​the sixteen-magnet magnet is 0.227585 Tesla, the directional uniformity is 9146 ppm, and the amplitude uniformity is 12031 ppm.

[0040] Example

[0041] Figure 1In the figure, 1-4 are the front, back, left, and right magnets of the four-steel magnet; 5 is the solution domain within the center of the four-steel magnet. 6-9 are the front, back, left, and right magnets of the eight-steel magnet; 10-13 are the four corner magnets of the eight-steel magnet; and 14 is the solution domain within the center of the eight-steel magnet. 15-18 are the front, rear, left and right magnetic blocks of the twelve-magnet steel magnet respectively; 19 is a magnetic block with an angle of 60° between the 15th and 20th magnetic blocks; 20 is a magnetic block with an angle of 60° between the 19th and 18th magnetic blocks; 21 is a magnetic block with an angle of 60° between the 18th and 22th magnetic blocks; 22 is a magnetic block with an angle of 60° between the 21st and 16th magnetic blocks; 23 is a magnetic block with an angle of 60° between the 16th and 24th magnetic blocks; 24 is a magnetic block with an angle of 60° between the 23rd and 17th magnetic blocks; 25 is a magnetic block with an angle of 60° between the 17th and 26th magnetic blocks; 26 is a magnetic block with an angle of 60° between the 25th and 15th magnetic blocks; 27 is the solution domain at the center of the twelve-magnet steel magnet. 28-31 are the front, rear, left and right magnetic blocks of the sixteen-magnet steel magnet respectively; 32 is a magnetic block with an angle of 45° to the 28 and 33 magnetic blocks; 33 is a magnetic block with an angle of 45° to the 32 and 34 magnetic blocks; 34 is a magnetic block with an angle of 45° to the 33 and 31 magnetic blocks; 35 is a magnetic block with an angle of 45° to the 36 and 31 magnetic blocks; 36 is a magnetic block with an angle of 45° to the 37 and 35 magnetic blocks; 37 is a magnetic block with an angle of 45° to the 29 and 36 magnetic blocks The magnets are arranged at a 45° angle; 38 is at a 45° angle with magnets 39 and 29; 39 is at a 45° angle with magnets 40 and 38; 40 is at a 45° angle with magnets 30 and 39; 41 is at a 45° angle with magnets 42 and 30; 42 is at a 45° angle with magnets 43 and 31; 43 is at a 45° angle with magnets 28 and 42; 44 is the internal center solution domain of the sixteen-magnet magnet. The center points of these magnets lie on the same circle and bisect the circle. The magnetization direction also follows the distribution of magnetic flux lines, forming a closed loop.

[0042] Figure 2 In the figure, 45 is positive to the fourth magnetic ring, 46 is positive to the third magnetic ring, 47 is positive to the second magnetic ring, 48 is positive to the first magnetic ring, 49 is negative to the first magnetic ring, 50 is negative to the second magnetic ring, 51 is negative to the third magnetic ring, 54 is negative to the fourth magnetic ring, 53 is positive to the second aluminum alloy gap, 54 is positive to the first aluminum alloy gap, 55 is middle aluminum alloy gap, 56 is negative to the first aluminum alloy gap, and 57 is negative to the second aluminum alloy gap.

[0043] Figure 3The figure shows a line graph of the raw data after normalization and logarithmic transformation, which is used to illustrate the trend of the normalized values ​​of the three indicators, center point magnetic flux density, uniformity, and directionality, as the number of Halbach magnets changes. The figure uses black and white colors, and the solid line of dots, the dashed line of squares, and the dotted line of diamonds represent the normalized values ​​of center point magnetic flux density, uniformity, and directionality, respectively. As the number of Halbach magnets increases, the normalized value of center point magnetic flux density decreases overall, while the normalized values ​​of uniformity and directionality show an upward or stable trend. The raw data is normalized and logarithmically transformed to unify the dimensions of each indicator and eliminate differences in orders of magnitude. This enhances the comparability between indicators with different physical meanings, allowing them to be intuitively compared in the same figure.

[0044] The four example models used in the present invention are respectively composed of 32 rectangular magnets and 20 non-magnetic aluminum alloy flat blocks; 64 rectangular magnets and 40 non-magnetic aluminum alloy flat blocks; 96 rectangular magnets and 60 non-magnetic aluminum alloy flat blocks; and 128 rectangular magnets and 80 non-magnetic aluminum alloy flat blocks. The length, width and height of each magnet are 30 mm × 30 mm × 10 mm, and the length and width of each aluminum alloy flat block are 30 mm × 30 mm. The height of the second positive aluminum alloy gap and the second negative aluminum alloy gap is 3.06 mm, the height of the first positive aluminum alloy gap and the first negative aluminum alloy gap is 3.75 mm, and the height of the middle aluminum alloy gap is 3.39 mm. A circular array is formed by 4 magnets, 8 magnets, 12 magnets and 16 magnets, respectively. Figure 2 shown. Figure 1As shown, the four magnets of the four-steel magnet are located at the front, back, left, and right positions of the ring. The two magnets at the front and back are magnetized forward, while the two magnets at the left and right are magnetized backward, generating a uniform magnetic field in the center area 5 of the ring unit. The eight magnets of the eight-steel magnet are located at the front, back, left, right, and 45° diagonal positions of the ring unit. The two magnets at the front and back are magnetized forward, while the two magnets at the left and right are magnetized backward. The magnets at the right front and left rear are magnetized to the right, while those at the right rear and left front are magnetized to the left. The closed magnetic induction intensity curve determines the magnetization direction of the diagonally located magnets, generating a uniform magnetic field in the center area 14 of the ring unit. The 12 magnets of the twelve-steel magnet are located at 30° intervals around the ring. The center points of the magnets are arranged in a circle, but the diagonal magnets rotate due to the influence of the closed magnetic flux lines. For example, between magnet blocks No. 15 and No. 18, magnet blocks No. 19 and No. 20 are sandwiched, and magnet blocks No. 19 and No. 20 divide the angle of 180° in half. Therefore, the magnet blocks need to be rotated at a corresponding angle. Finally, a uniformly distributed horizontal main static magnetic field is generated in the annular center area 27. The 16 magnets of the sixteen-magnet magnet are located at positions every 22.5° in the ring. The center points of the magnet blocks are arranged in a circle, but the oblique magnet blocks rotate due to the influence of the closed magnetic flux lines, and the principle is similar to the aforementioned model. For example, between magnet blocks No. 28 and No. 31, magnet blocks No. 32, 33 and 34 are sandwiched, and magnet blocks No. 32, 33 and 34 divide the angle of 180° in half. Therefore, the magnet blocks need to be rotated at a corresponding angle. The magnetization directions of the four magnets are as follows: Figure 1 As shown in FIG. , a uniformly distributed horizontal main static magnetic field is generated in the center of the ring, which becomes the example model used in the present invention. Figure 2As shown, gaps are left between the eight ring units. Each structure has gaps between the eight rings, and aluminum alloy flat blocks are embedded in the gaps. The gaps between adjacent rings gradually decrease from the center of symmetry of the magnet toward the ends, and the thickness of the aluminum alloy flat blocks also gradually decreases from the center of symmetry of the magnet toward the ends. The embedded aluminum alloy blocks are intended to make the magnet's magnetic field more uniform. The eight magnetic ring units are stacked longitudinally to form the magnet model of the present invention. When stacked, the magnetic field of each magnetic ring unit has the same direction. The positive direction of the magnet of the present invention is defined as upward, and negative, based on the central aluminum alloy gap 55. The positive direction includes the positive first magnetic ring 45, the positive second magnetic ring 46, the positive third magnetic ring 47, and the positive fourth magnetic ring 48; the negative direction includes the negative first magnetic ring 49, the negative second magnetic ring 50, the negative third magnetic ring 51, and the negative fourth magnetic ring 52. The distances between adjacent ring-shaped magnet units are, from top to bottom, 0 mm, 3.06 mm, 3.75 mm, 3.39 mm, 3.75 mm, 3.06 mm, and 0 mm, forming aluminum alloy gaps. The second aluminum alloy gap 53 in the positive direction is 3.06 mm, the first aluminum alloy gap 54 in the positive direction is 3.75 mm, the middle aluminum alloy gap 55 is 3.39 mm, the first aluminum alloy gap 56 in the negative direction is 3.75 mm, and the second aluminum alloy gap 57 in the negative direction is 3.06 mm. The aluminum alloy gaps are filled with 30 mm x 30 mm aluminum alloy flat blocks of the corresponding spacing thickness. The thickness of the aluminum alloy flat block inserted into the second positive aluminum alloy gap 53 is 3.06 mm, the thickness of the aluminum alloy flat block inserted into the first positive aluminum alloy gap 54 is 3.75 mm, and the thickness of the aluminum alloy flat block inserted into the middle aluminum alloy gap 55 is 3.39 mm. The thickness of the aluminum alloy flat block inserted into the first negative aluminum alloy gap 56 is 3.75 mm, and the thickness of the aluminum alloy flat block inserted into the second negative aluminum alloy gap 57 is 3.06 mm. The insertion of the aluminum alloy flat blocks can significantly improve the uniformity of the magnet.

[0045] The core of this example is based on finite element simulation (COMSOL) and data analysis (Matlab), comparing the magnetic field characteristics in the central area of ​​Halbach ring magnets composed of 4, 8, 12, and 16 permanent magnets. All four models assume the use of the same specifications of NdFeB permanent magnet material and geometric dimensions, and only the number of magnet blocks N and their arrangement angle on the circumference are different. For each structure, the three-dimensional magnetic flux density distribution B(x, y, z) of the central sphere area with a radius of approximately 7.5 mm is calculated, and the following indicators are evaluated based on this:

[0046] Magnetic induction intensity in the central area |B center |: That is, the magnitude of the magnetic flux density at the geometric center point of the central area.

[0047] Amplitude uniformity Uni(ppm): defined as the maximum value of magnetic flux density in the central area With minimum value The difference relative to the center point magnetic flux density The ratio of

[0048]

[0049] The smaller the value, the more uniform the magnetic field.

[0050] Directivity uniformity (ppm): To characterize the consistency of the magnetic field direction, this article uses the ratio of the x- and z-direction magnetic flux density components to the y-direction magnetic flux density component to express it. Calculate the directivity value of each point And pay attention to its maximum value, which is the degree to which the magnetic field deviates from the main direction at the most unfavorable position. The smaller the value, the more uniform the magnetic field direction is.

[0051] Using the above definitions, the main magnetic field parameters calculated for Halbach ring magnets with four different numbers of magnets (4, 8, 12, and 16) are summarized in the following table:

[0052]

[0053] From the above data, we can see that the magnetic field intensity in the center area of ​​the Halbach ring magnet shows a typical "magnetic field concentration effect", and its change trend shows a nonlinear decreasing relationship with the number of magnets. The specific manifestations are:

[0054] When the number of magnets is 4, the central magnetic induction modulus reaches a maximum value of 0.600734T, showing the optimal magnetic flux density concentration effect;

[0055] When the number of magnets increases to 8, the central magnetic field intensity drops to 0.552215T (about 8.1% lower than that of 4 magnets), proving that increasing the number of magnets weakens the effective contribution of a single magnet.

[0056] When the number of magnets further increased to 12 and 16, the magnetic field strength sharply decreased to 0.394573 T (a decrease of 34.4%) and 0.227585 T (a decrease of 62.0%).

[0057] It can be seen that under the size and arrangement parameters of this embodiment, a small number of magnets can form a stronger magnetic field concentration effect. When the number of magnets exceeds a critical value (such as 8 pieces), the superposition of adjacent magnetic poles causes the magnetic field lines to diverge, resulting in a "field strength dilution effect."

[0058] Figure 3 The figure shows a line graph of the original data after normalization and logarithmic transformation, which is used to show the trend of the normalized values ​​of the three indicators of magnetic induction intensity, amplitude uniformity and directional uniformity in the central area under different numbers of Halbach magnets as the number of magnets changes.

[0059] The magnetic field uniformity of the Halbach ring magnet shows a non-monotonic change characteristic of first improving and then deteriorating. Specific data show that:

[0060] When there are 4 magnets, the amplitude uniformity is 1.8121×104 (i.e. 18121ppm), which is the benchmark level.

[0061] When there are 8 magnets, the amplitude uniformity is optimized to 0.9919×104 (i.e. 9919ppm), an improvement of 45.3%;

[0062] When the number of magnets increases to 12 and 16, the amplitude uniformity rebounds to 1.1021×104 (11021ppm) and 1.2031×104 (12031ppm) respectively.

[0063] The above results show that the optimal balance point of amplitude uniformity is formed when 8 magnets are configured. When the number of magnets exceeds 8, the local interference effect caused by oversaturation of the magnetic field leads to the degradation of amplitude uniformity.

[0064] The directional uniformity index of the Halbach ring magnet (defined as the ratio of the vertical component to the main direction component) shows a "low-high-low" oscillation characteristic as the number of magnetic steels changes.

[0065] When there are four magnets, the directional uniformity is 1.0744×104ppm, and the field lines in the edge area deviate significantly from the main direction;

[0066] When there are 8 magnets, the directional uniformity drops to the optimal value of 0.7027×104ppm (34.6% improvement), proving that the magnetic field focusing effect is the best;

[0067] When there are 12 and 16 magnets, the directional uniformity returns to 0.9121×104ppm and 0.9146×104ppm, respectively, showing a slight increase but both are better than the 4-piece configuration.

[0068] The above data reveal that the directionality of the magnetic field is closely related to the degree of magnetic steel interference, and the 8-piece and 16-piece configurations can effectively suppress the deviation of the edge field lines.

[0069] Based on the above experimental data and analysis, this embodiment summarizes the three major laws of the magnetic field characteristics of the Halbach ring magnet, and accordingly extracts the trial-free design rules, which are as follows:

[0070] Optimization law of magnetic induction intensity in the central area

[0071] High-intensity demand scenarios (such as magnetic sensors and nuclear magnetic resonance): When the goal is to maximize the central magnetic field strength, the four-magnet configuration (central magnetic induction intensity 0.600734T) should be preferred. Although the uniformity is lower (18121ppm), it can meet the needs of high-intensity applications.

[0072] Strength and uniformity balance scenario: If you need to improve amplitude uniformity while ensuring a certain strength, you can choose an 8-magnet configuration (strength 0.5522T, amplitude uniformity 9919ppm). Its strength is only 0.21% lower than the 4-magnet configuration, but the uniformity is significantly improved by 45.3%.

[0073] Amplitude uniformity optimization law

[0074] Scenarios requiring high uniformity (such as particle accelerators and precision measurements): When the goal is to minimize magnetic field inhomogeneity, the 8-magnet configuration is the optimal solution (uniformity 9919ppm), which is 45.3% better than the 4-magnet configuration, while maintaining good directionality (7027ppm).

[0075] Configurations to avoid: When the number of magnets exceeds 8 (12 / 16), the uniformity rebounds (11021ppm / 12031ppm), indicating that the high number of magnets causes local interference and should be avoided.

[0076] Directional uniformity optimization law

[0077] Scenarios requiring high focusing (such as directional magnetic therapy and magnetic levitation): The eight-magnet configuration has the best directionality (7027ppm), a 34.6% improvement over the four-magnet configuration (10744ppm), meeting the needs of high-precision directional control.

[0078] Edge field line control: Although the uniformity of 12 / 16 magnets rebounds, the directionality (9121ppm / 9146ppm) is still better than the 4-piece configuration, which is suitable for scenarios where strength requirements are not high but edge effects need to be controlled.

[0079] Based on the above rules, this embodiment proposes a three-step trial-free design rule: first, clarify the optimization target: determine the priority of magnetic induction intensity, amplitude uniformity, and directional uniformity; second, select the benchmark configuration: magnetic induction intensity priority → 4 magnets; amplitude uniformity priority → 8 magnets; comprehensive balance → 8 magnets; third, special scenario adjustment: if higher intensity is required, fine-tune the magnet arrangement on the basis of 8 magnets (such as angle optimization); if lower uniformity is required, add a magnetic shielding structure on the basis of 12 magnets.

[0080] The adaptation suggestions of the embodiments are as follows: Embodiment 1 (high-intensity type): suitable for equipment such as magnetic sensors, it adopts a 4-piece magnet configuration, and the central magnetic field strength reaches 0.600734T, meeting the high-intensity requirements. Embodiment 2 (balanced type): suitable for equipment such as particle accelerators, it adopts an 8-piece magnet configuration, and achieves the best balance between intensity (0.552215T), amplitude uniformity (9919ppm), and directionality uniformity (7027ppm). Embodiment 3 (high-focus type): suitable for directional magnetic therapy equipment, it adopts an 8-piece magnet configuration, the directionality is optimized to 7027ppm, and the edge field line deviation is minimized.

[0081] It should be pointed out that the design framework of the present invention is not only applicable to the above-mentioned specific numerical values. In practical applications, designers can combine this method to optimize the design based on the magnetic steel material, structural dimensions and application scenarios. For example, a multi-layer Halbach laminated structure can be used to enhance the field strength, or magnetic pole compensation technology can be used to improve the amplitude uniformity and directional uniformity. In short, the present invention provides a set of flexible and effective analysis and optimization paths, providing theoretical and engineering basis for the customized design of Halbach magnets in the fields of nuclear magnetic resonance, precision sensing, electromagnetic drive, etc.

Claims

1. A method for optimizing the structure of a static magnetic field magnet for nuclear magnetic resonance imaging, characterized in that: The magnet of the method comprises a plurality of permanent magnets arranged in a ring structure according to a Halbach array; and the required magnetic field parameter indicators are determined, including the central magnetic induction intensity (B0), amplitude uniformity, and directional uniformity requirements; a Halbach ring magnet model consisting of different numbers N of magnetic steels (N=4, 8, 12, 16) is established, and the magnetic field distribution in the central area is solved by analytical calculation or finite element simulation; the magnetic induction intensity, amplitude uniformity, and amplitude directionality of the central area of ​​each model are calculated and compared with predetermined requirements; the number of magnetic steels and the arrangement scheme are selected based on the comparison results to achieve magnetic field performance optimization; wherein the amplitude uniformity is represented by the ratio of the difference between the maximum and minimum magnetic flux density in the central area and the magnetic flux density at the center point (unit: ppm), and the directional uniformity is represented by the ratio of the vertical component to the main direction component.

2. The method for optimizing the static magnetic field magnet structure for nuclear magnetic resonance imaging according to claim 1, wherein: The relationship between the number of magnetic steels N and the magnetic field performance is as follows: as the number of magnetic steels N increases, the magnetic induction intensity B0 in the central area shows an approximately nonlinear decreasing trend; The amplitude uniformity and directional uniformity overall showed a characteristic of first improving and then stabilizing. Specifically, when the number of magnets N increased from 4 to 8, the amplitude uniformity decreased from 18121ppm to 9919ppm, an improvement of 45.3%; the directional uniformity decreased from 10744ppm to 7027ppm, still remaining within an acceptable range. When the number of magnets N further increased to 12 and 16, the amplitude uniformity was 11021ppm and 12031ppm, respectively, a slight rebound compared to the case of 8 magnets; the directional uniformity also increased.

3. The method for optimizing the static magnetic field magnet structure for nuclear magnetic resonance imaging according to claim 1, wherein: The amplitude uniformity calculation formula is: in, is the magnetic flux density vector, is the magnetic flux density vector at the center point, Uni represents the uniformity of the magnetic field; the directional uniformity calculation formula is: in, represents the directionality of the magnetic field, is the x-axis component of the magnetic flux density, is the z-axis component of the magnetic flux density, is the y-axis component of the magnetic flux density.

4. The method for optimizing the static magnetic field magnet structure for nuclear magnetic resonance imaging according to claim 1, wherein: The magnetic steel blocks of the Halbach annular magnet model are evenly distributed along the circumference, and the magnetization directions of the magnetic steel blocks rotate in sequence to form a Halbach magnetic array, so that an enhanced and uniform magnetic field is obtained inside the annular structure, and the magnetic field outside the annular structure is weakened.

5. The method for optimizing the static magnetic field magnet structure for nuclear magnetic resonance imaging according to claim 1, wherein: The method uses finite element simulation and mathematical analysis to obtain central area magnetic field characteristic data of configurations with different numbers of magnetic steels, and constructs a relationship curve between the number of magnetic steels and the magnetic field intensity, uniformity and directionality as a basis for selecting the optimal number of magnetic steels.

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