Permanent magnet type axial uniform magnetic field generating device and design method thereof

Abstract

The application belongs to the technical field of uniform magnetic field device design, and particularly relates to a permanent magnet type axial uniform magnetic field generating device and a design method thereof. The device comprises two conical permanent magnets, the vertexes of the two conical permanent magnets are oppositely arranged, the two conical permanent magnets are radially magnetized, and the magnetization directions of the two conical permanent magnets are opposite. The application aims at the problems of large volume and low magnetic field utilization rate of the traditional permanent magnet type axial uniform magnetic field generating device.

Description

Technical Field

[0001] This invention belongs to the field of uniform magnetic field device design technology, specifically relating to a permanent magnet type axial uniform magnetic field generator and its design method. Background Technology

[0002] In a uniform magnetic field, charged particles in a particle beam are deflected by the Lorentz force. Therefore, by adjusting the appropriate magnetic field amplitude and direction, the trajectory of the particle beam can be precisely controlled, thereby converging and focusing the particle beam, improving its collimation, and meeting the needs of different application scenarios. An axially uniform magnetic field can be easily generated using a solenoid coil. However, solenoid coils require an external power supply, and in applications requiring a large magnetic field amplitude, even a cooling device is needed, significantly increasing the system's cost and size. Permanent magnets possess strong magnetic properties and do not require an external power supply or cooling device. Therefore, permanent magnet magnetic field generators are simple in structure and small in size.

[0003] Traditional permanent magnet axial uniform magnetic field generators employ a long circular ring structure and are axially magnetized to produce a uniform axial magnetic field along its axis. However, most of the magnetic field generated by this structure diffuses outward, with only a small portion entering the axis. Therefore, it suffers from drawbacks such as large device size and low magnetic field utilization. Summary of the Invention

[0004] This invention provides a permanent magnet axial uniform magnetic field generator and its design method, which addresses the problems of large size and low magnetic field utilization of traditional permanent magnet axial uniform magnetic field generators.

[0005] This invention is achieved through the following technical solution:

[0006] A permanent magnet axial uniform magnetic field generator for particle beam transmission is disclosed. The device includes two conical permanent magnets with their vertices facing each other. The two conical permanent magnets are radially magnetized and their magnetization directions are opposite.

[0007] A design method for a permanent magnet axial uniform magnetic field generator for particle beam transmission is provided. The design method is as follows: based on Ampere's circuital law and Stokes' theorem, an integral formula for the magnetic field strength generated by the permanent magnet axial uniform magnetic field generator is obtained; based on the symmetry of the structure and considering the constitutive relation of the material, and assuming the air gap magnetic flux density and the core permeability in the axial direction, an expression for the magnetic flux density generated by the permanent magnet axial uniform magnetic field generator is obtained.

[0008] Furthermore, by Ampere's circuital law, the following formula can be derived:

[0009]

[0010] In the formula, H is the magnetic field strength and J is the current density;

[0011] Since there is no current in the device, the right side is equal to zero. Integrating equation (1) yields...

[0012]

[0013] In the formula, Ω is the region surrounded by the red border, and dS is the differential unit that constitutes this region;

[0014] Using Stokes' theorem, the above equation can be transformed into

[0015]

[0016] In the formula, Γ is the closed path formed by the red border, and dl is the differential unit that constitutes the path;

[0017] Equation (3) means that the integral of the magnetic field strength along the path of the magnetic field lines is zero, and can be written in the following form:

[0018]

[0019] In the formula, H a H b H iron and H pm Representing path l a Magnetic field strength and path l b magnetic field

[0020] Strength, magnetic field strength along the iron core path and magnetic field strength inside the permanent magnet.

[0021] Furthermore, due to the symmetry of the device, l b Magnetic field strength H along the path b The value is 0; considering the material constitutive properties

[0022] Assuming that the air gap magnetic flux density along the axial direction is uniform, equation (4) can be written in the following form:

[0023]

[0024] In the formula, B δ It is the air gap magnetic flux density, μ0 is the air permeability, and B iron The magnetic flux density inside the iron core, μ iron It is the magnetic permeability of the iron core.

[0025] Since the permeability of the iron core is much greater than that of air, the second term in equation (5) can be ignored. Therefore, we have

[0026]

[0027] In a permanent magnet, the magnetic flux density (magnetic flux density) is generated by the applied magnetic field and the magnetization of the permanent magnet itself.

[0028] B δ =μ0(H pm +M) (7)

[0029] In the formula, M is the remanent magnetization of the permanent magnet;

[0030] From (6) and (7), we can obtain the expression for the air gap magnetic flux density:

[0031]

[0032] make

[0033]

[0034] Then equation (8) becomes,

[0035]

[0036] As can be seen from equation (10), as long as α remains unchanged, the air gap magnetic flux density will remain unchanged.

[0037] Furthermore, as can be seen from equation (10), the amplitude of the air gap magnetic field is related to α; therefore, a permanent magnet pole surface can be designed so that α is larger at the center and gradually decreases as it moves away from the center point, thereby making the magnetic field generated by the device at the axis more uniform, and obtaining the relationship between α and z coordinates. Through the relationship between α and z coordinates, straight line segments can be used to transition at the end and center line respectively. The permanent magnet pole surface curve drawn through the relationship between α and z coordinates cuts the original conical surface, cutting to the intersection of the curve and the original oblique line.

[0038] Furthermore, to ensure the axial length and outer diameter of the device are consistent, a curve is drawn that passes through the center point of the device and is 40% of the axial length of the device from the center symmetry line. At the center point z = 0.1, l a and l b Since both are close to infinitesimal, we can define an initial ratio α0 = 0.4. Then, we take the product of α0 / (α0+1) and the magnetic field amplitude at z = 0.1 as the base and divide by... Figure 5 The magnetic field at other locations on the curve is used to obtain the relationship curve between α / (α+1) and the z coordinate.

[0039] Furthermore, based on the relationship curve, let

[0040]

[0041] therefore,

[0042]

[0043] The relationship between the α and z coordinates can be obtained through equation (12).

[0044] Furthermore, when the axial length of the device is small compared to its outer diameter, i.e., axial length / diameter < 2.5, straight line segments are used for transition at the end and center line respectively; the permanent magnet pole surface curve drawn by the relationship between the α and z coordinates is used to cut the original conical surface, cutting to the intersection of the curve and the original oblique line.

[0045] Furthermore, when the ratio of the axial length to the outer diameter of the device is large, i.e., axial length / diameter ≥ 2.5, a conical pole permanent magnet scheme is adopted.

[0046] A permanent magnet type axial uniform magnetic field generator, wherein the device adopts the structure described above, is used for particle beam transmission.

[0047] The beneficial effects of this invention are:

[0048] This invention employs a conical pole surface permanent magnet scheme when the length-to-diameter ratio is large.

[0049] This invention employs a novel pole-face permanent magnet scheme when the length-to-diameter ratio is small.

[0050] The permanent magnet magnetic field generator of the present invention has a simple structure and small size. Attached Figure Description

[0051] Figure 1 This is a schematic diagram of the structure of the present invention.

[0052] Figure 2 It is a traditional permanent magnet type axial uniform magnetic field generator.

[0053] Figure 3 This is a comparison diagram of the magnetic fields generated by the traditional and new schemes.

[0054] Figure 4 This is a magnetic field distribution diagram of the novel scheme of the present invention when the aspect ratio is 0.66.

[0055] Figure 5 This is a magnetic field distribution diagram on the cut line segment of the present invention.

[0056] Figure 6 This is a graph showing the variation of α / (α+1) in this invention.

[0057] Figure 7 This is a graph showing the variation of α with the z-coordinate in this invention.

[0058] Figure 8 This is a graph showing the variation of α with the z-coordinate in this invention.

[0059] Figure 9 This is a diagram of the permanent magnet axial uniform magnetic field generator of the present invention after changing the pole face.

[0060] Figure 10 This is a comparison diagram between the conical pole surface of the present invention and the novel pole surface. Detailed Implementation

[0061] In the following description, specific details such as particular system architectures and techniques are set forth for illustrative purposes and not for limitation, in order to provide a thorough understanding of the embodiments of this application. However, those skilled in the art will understand that this application may also be implemented in other embodiments without these specific details. In other instances, detailed descriptions of well-known systems, apparatuses, circuits, and methods are omitted so as not to obscure the description of this application with unnecessary detail.

[0062] It should be understood that, when used in this specification and the appended claims, the term "comprising" indicates the presence of the described features, integrals, steps, operations, elements and / or components, but does not exclude the presence or addition of one or more other features, integrals, steps, operations, elements, components and / or collections thereof.

[0063] It should also be understood that the terminology used in this application specification is for the purpose of describing particular embodiments only and is not intended to limit the application. As used in this application specification and the appended claims, the singular forms “a,” “an,” and “the” are intended to include the plural forms unless the context clearly indicates otherwise.

[0064] The following is in conjunction with the appendix to this application specification. Figure 1-10 The technical solutions in the embodiments of this application are clearly and completely described. Obviously, the described embodiments are only a part of the embodiments of this application, and not all of the embodiments. Based on the embodiments in this application, all other embodiments obtained by those of ordinary skill in the art without creative effort are within the scope of protection of this application.

[0065] Many specific details are set forth in the following description in order to provide a full understanding of this application. However, this application may also be implemented in other ways different from those described herein. Those skilled in the art can make similar extensions without departing from the spirit of this application. Therefore, this application is not limited to the specific embodiments disclosed below.

[0066] Implementation Method 1

[0067] This embodiment provides a permanent magnet axial uniform magnetic field generator for particle beam transmission. The device includes two conical permanent magnets, with their vertices facing each other. The two conical permanent magnets are radially magnetized, and their magnetization directions are opposite. Figure 1 As shown, Figure 1 The image shows a circumferential cross-section, which, when rotated 360 degrees around an axis, forms the complete device.

[0068] Implementation Method 2

[0069] This embodiment provides a design method for a permanent magnet axial uniform magnetic field generator for particle beam transmission. The design method is as follows: based on Ampere's circuital law and Stokes' theorem, an integral formula for the magnetic field strength generated by the permanent magnet axial uniform magnetic field generator is obtained; based on the symmetry of the structure and considering the constitutive relation of the material, and assuming the air gap magnetic flux density and the core permeability in the axial direction, an expression for the magnetic flux density generated by the permanent magnet axial uniform magnetic field generator is obtained.

[0070] Furthermore, by Ampere's circuital law, the following formula can be derived:

[0071]

[0072] In the formula, H is the magnetic field strength and J is the current density;

[0073] Since there is no current in the device, the right side is equal to zero. Integrating equation (1) yields...

[0074]

[0075] In the formula, Ω is the region surrounded by the red border, and dS is the differential unit that constitutes this region;

[0076] Using Stokes' theorem, the above equation can be transformed into

[0077]

[0078] In the formula, Γ is the closed path formed by the red border, and dl is the differential unit that constitutes the path;

[0079] Equation (3) means that the integral of the magnetic field strength along the path of the magnetic field lines is zero, and can be written in the following form:

[0080]

[0081] In the formula, H a H b H iron and H pm Representing path l a Magnetic field strength and path l bmagnetic field

[0082] Strength, magnetic field strength along the iron core path and magnetic field strength inside the permanent magnet.

[0083] Furthermore, due to the symmetry of the device, l b Magnetic field strength H along the path b The value is 0; considering the material constitutive properties

[0084] Assuming that the air gap magnetic flux density along the axial direction is uniform, equation (4) can be written in the following form:

[0085]

[0086] In the formula, B δ It is the air gap magnetic flux density, μ0 is the air permeability, and B iron The magnetic flux density inside the iron core, μ iron It is the magnetic permeability of the iron core.

[0087] Since the permeability of the iron core is much greater than that of air, the second term in equation (5) can be ignored. Therefore, we have

[0088]

[0089] In a permanent magnet, the magnetic flux density (magnetic flux density) is generated by the applied magnetic field and the magnetization of the permanent magnet itself.

[0090] B δ =μ0(H pm +M) (7)

[0091] In the formula, M is the remanent magnetization of the permanent magnet;

[0092] From (6) and (7), we can obtain the expression for the air gap magnetic flux density:

[0093]

[0094] make

[0095]

[0096] Then equation (8) becomes,

[0097]

[0098] As can be seen from equation (10), as long as α remains unchanged, the air gap magnetic flux density will remain unchanged.

[0099] Furthermore, comparing the magnetic field distribution generated along the axis of the two structural schemes (ensuring the axial length and outer diameter of the device are consistent), it can be seen that the new structural scheme generates a larger magnetic field amplitude and a larger uniform area while using fewer permanent magnets. Figure 3 As shown.

[0100] However, when the aspect ratio (the ratio of axial length to outer diameter) of the device is low, the uniform magnetic field region along its axis will be distorted, such as... Figure 4 As shown, the magnetic field distribution at the center of the axis is a curve with poor uniformity.

[0101] As can be seen from equation (10), the amplitude of the air gap magnetic field is related to α. Therefore, a permanent magnet pole can be designed such that α is larger at the center and gradually decreases as it moves away from the center, thereby making the magnetic field generated by the device along the axis more uniform.

[0102] The next question is how to obtain the relationship between the α and z coordinates. Draw two auxiliary lines in the diagram: one is the line of symmetry passing through the center point of the device, and the other is 40% of the axial length of the device from the center line of symmetry. Extract the magnetic field curve between the two auxiliary lines, as shown below. Figure 5 As shown.

[0103] At the center point of the device, z = 0.1, l a and l b Since both are close to infinitesimal, we can define an initial ratio α0 = 0.4. Then, we take the product of α0 / (α0+1) and the magnetic field amplitude at z = 0.1 as the base and divide by... Figure 5 The relationship curve between α / (α+1) and the z-coordinate at other locations in the magnetic field is obtained, as shown in the figure. Figure 6 As shown.

[0104] Furthermore, based on the relationship curve, let

[0105]

[0106] therefore,

[0107]

[0108] Through equation (12), the relationship between the changes in α and the z coordinates can be obtained, such as Figure 7 As shown.

[0109] Thus, by utilizing the relationship between the α and z coordinates, the pole surface curve of the permanent magnet can be drawn on the cross-section of the conical permanent magnet base, as shown below. Figure 8 As shown.

[0110] Furthermore, Figure 8In the process, considering the actual processing technology, the permanent magnet does not adopt a completely triangular cross section. When the axial length of the device is small compared with the outer diameter, that is, when the axial length / diameter is less than 2.5, straight line segments are used to transition at the end and the center line respectively. The permanent magnet pole surface curve drawn by the relationship between the α and z coordinates cuts the original conical surface, cutting to the intersection of the curve and the original oblique line.

[0111] Furthermore, when the ratio of the axial length to the outer diameter of the device is large, i.e., axial length / diameter ≥ 2.5, a conical pole permanent magnet scheme is adopted.

[0112] Implementation Method 3

[0113] This embodiment provides a permanent magnet type axial uniform magnetic field generator, which adopts the structure described in Embodiment 1 and is used for particle beam transmission.

Claims

1. A design method for a permanent magnet type axial uniform magnetic field generator, characterized in that, The device includes two conical permanent magnets, with their vertices facing each other. The two conical permanent magnets are radially magnetized, and their magnetization directions are opposite. The design method is as follows: based on Ampere's circuital law and Stokes' theorem, the integral formula of the magnetic field strength generated by the permanent magnet axial uniform magnetic field generator is obtained; based on the symmetry of the structure and considering the constitutive relation of the material, and assuming the air gap magnetic flux density and the core permeability in the axial direction, the magnetic flux density expression of the permanent magnet axial uniform magnetic field generator is obtained. Depend on (10) It can be seen that the amplitude of the air gap magnetic field is related to α Relevant, as long as it remains α If it remains unchanged, the air gap magnetic flux density will remain unchanged. (9), of which It is the air gap magnetic flux density. M It is the remanent magnetization of the permanent magnet. μ 0 is the permeability of air. l a It is the transverse path of the magnetic field lines in a closed path formed by closed loops along the magnetic field lines. l b It is the vertical path of the magnetic field lines in a closed path formed by closed loops along the magnetic field lines; Therefore, a permanent magnet pole face can be designed such that the center... α Larger, and as it moves further away from the center point α By gradually decreasing the size, the magnetic field generated by the device along the axis becomes more uniform, thus obtaining... α and z The relationship between coordinates is achieved through... α and z The relationship between coordinates can be transitioned using straight line segments at the ends and centerline, respectively. α and z The permanent magnet pole surface curve, plotted by the relationship between coordinates, is cut off from the original conical surface, to the point where the curve intersects the original oblique line. To ensure the axial length and outer diameter of the device are consistent, a curve is drawn that passes through the center point of the device and is 40% of the axial length of the device from the center line of symmetry. At the center point of the device... z =0.1, l a and l b Since both are close to infinitesimal, an initial ratio can be defined. α 0 = 0.4, then, α 0 / ( α 0+1) and z The product of the magnetic field amplitudes at =0.1 is used as the base, and then divided by the magnetic field amplitudes at other positions on the curve to obtain the result. α / ( α +1) and z The relationship curve between coordinates; Based on the relationship curve, let （11） therefore, （12） Through equation (12), we can obtain α and z The relationship between coordinates; When the ratio of the axial length to the outer diameter of the device is small, i.e., axial length / diameter < 2.5, straight transitions are used at the ends and centerline respectively; through α and z The permanent magnet pole surface curve, plotted by the relationship between coordinates, is cut off from the original conical surface, to the point where the curve intersects the original oblique line. When the ratio of the axial length to the outer diameter of the device is large, i.e., axial length / diameter ≥ 2.5, a conical pole permanent magnet scheme is adopted.

2. The design method according to claim 1, characterized in that, By Ampere's circuital law, the following formula can be derived: （1） In the formula, H It is the magnetic field strength. J It is the current density; Since there is no current in the device, the right side equals zero; Integrating equation (1) yields （2） In the formula, Ω is the region enclosed by a closed loop along the magnetic field lines, and d S It is the differential unit that constitutes this region; Using Stokes' theorem, the above equation can be transformed into: （3） In the formula, Γ is the closed path formed by a closed loop along the magnetic field lines, and d l It is the differential unit that constitutes the path; Equation (3) means that the integral of the magnetic field strength along the path of the magnetic field lines is zero, and can be written in the following form: （4） In the formula, H a , H b , H iron and H pm These represent the transverse paths of the magnetic field lines in a closed path formed by closed loops along the magnetic field lines. l a The magnetic field strength on the surface, and the vertical path of the magnetic field lines in the closed path formed by the closed loop along the magnetic field lines. l b Magnetic field strength and core path l iron The magnetic field strength on the surface and the magnetic field strength inside the permanent magnet.

3. The design method according to claim 2, characterized in that, Due to the symmetry of the device, l b Magnetic field strength along the path H b The value is 0; considering the material constitutive relation and assuming that the air gap magnetic flux density is uniform along the axial direction, equation (4) can be written in the following form: （5） In the formula, B δ It is the air gap magnetic flux density. μ 0 is the permeability of air. B iron Magnetic density inside the iron core μ iron It is the magnetic permeability of the iron core; Since the permeability of the iron core is much greater than that of air, the second term in equation (5) can be ignored, therefore we have （6） In a permanent magnet, the magnetic flux density is generated by the applied magnetic field and the magnetization of the permanent magnet itself. （7） In the formula, M It is the remanent magnetization of the permanent magnet; From (6) and (7), the expression for the air gap magnetic flux density can be obtained: （8）。 4. A permanent magnet type axial uniform magnetic field generator, characterized in that, The device is obtained by using the design method of the permanent magnet axial uniform magnetic field generator as described in any one of claims 1-3, and is used for particle beam transmission.

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