Double-layer spherical self-shielding uniform field coil and design method

Abstract

The invention discloses a double-layer spherical self-shielding uniform field coil and a design method, and relates to the field of electromagnetic design. The problems that due to the line width of an existing spherical coil, as the number of turns increases, the actually-machined coil can not meet spherical distribution constraint possibly, and consequently the actual result does not conform to theoretical analysis are solved. The method comprises the following steps: on the basis of a constructed double-layer spherical self-shielding uniform field coil, the magnitude of a magnetic field generated by an ith pair of coils in a space (x, y, z) is calculated according to the Bios-Savart law, and the magnetic field of the double-layer spherical self-shielding uniform field coil is obtained by accumulating the magnetic fields of the coils; describing the uniformity of the magnetic field through a relative error, describing the self-shielding effect of the coil through a ratio, and setting a non-uniform error and an attenuation coefficient constant threshold; a constrained nonlinear multi-objective optimization problem is constructed and is further converted into a single-objective optimization problem through a weighting mode, and optimization calculation is carried out based on a genetic algorithm.

Description

Technical Field

[0001] The present invention relates to the technical field of electromagnetic design, and in particular to a double-layer spherical self-shielding uniform field coil and a design method thereof. Background Art

[0002] Self-shielded uniform-field coils are a special type of uniform-field coil. They exhibit a uniform internal magnetic field and rapidly decaying external magnetic fields, minimizing magnetic field interference with the coil's external environment. This makes them valuable for precision measurement and magnetic field control in weak magnetic fields.

[0003] Currently, most self-shielding uniform-field coils typically utilize square coils, solenoid coils, saddle coils, and other similar designs. These previous coil structures presented two challenges: first, the uniformity and self-shielding properties of the coil's magnetic field were limited by the coil structure, making further improvements difficult; second, the production of a three-axis coil required greater space. Compared to traditional structures, spherical coils generate a more uniform magnetic field internally. By constructing a double-layer spherical structure, they achieve a self-shielding effect with rapid external magnetic field attenuation while maintaining the original uniform internal magnetic field. Furthermore, the unique structural advantages of double-layer spherical coils make it easier to create a three-axis coil by nesting multiple layers.

[0004] Therefore, this application proposes a double-layer spherical self-shielding uniform field coil and design method. However, due to the different coil line widths, as the number of turns increases, the actually processed coil may be difficult to meet the spherical coil distribution constraints, resulting in actual results being inconsistent with theoretical analysis.

[0005] Furthermore, when the primary and secondary coil pairs (U and V) are variables, the optimization problem becomes a dynamic dimensional optimization problem, significantly increasing the computational complexity. Furthermore, the uniformity and self-shielding properties of spherical coils are closely related to the number of coils. Increasing the number of coils increases the search domain for the optimization solution, potentially leading to a better solution. However, this also increases the dimensionality of the optimization variables, further increasing the computational cost. Summary of the Invention

[0006] In order to improve the internal magnetic field uniformity of the self-shielding coil and the self-shielding performance of the external magnetic field, the present invention solves the problem that due to the line width of the spherical coil, as the number of turns increases, the actually processed coil may be difficult to meet the spherical distribution constraints, resulting in the actual results being inconsistent with the theoretical analysis.

[0007] To solve the above technical problems, the present invention is achieved through the following technical solutions:

[0008] Solution 1: The present invention proposes a double-layer spherical self-shielding uniform field coil. The double-layer spherical self-shielding uniform field coil is implemented using a double-layer nested spherical coil structure. The double-layer nested structure includes an inner spherical coil and an outer spherical coil. The inner spherical coil is a primary coil, which is fed with a forward current to generate a uniform magnetic field in the central area; the outer spherical coil is a secondary shielding coil, which is fed with a reverse current to offset the magnetic field generated by the inner coil on the outside.

[0009] The inner spherical coils are composed of U pairs, distributed at a radius of R p On the sphere, the radius of the i-th pair of coils is r pi , the position plane is z=±d pi , ampere-turns is n pi I p , then

[0010] The outer spherical coils are composed of V pairs, distributed at a radius of R s On the sphere, the radius of the i-th pair of coils is r si , the position plane is z=±d si , ampere-turns is n si I s , then

[0011] Solution 2: A design method for a double-layer spherical self-shielding uniform field coil. The design method is based on the double-layer spherical self-shielding uniform field coil described in Solution 1 and includes the following steps:

[0012] Step 1: Based on the constructed double-layer spherical self-shielded uniform field coil, calculate the magnitude of the magnetic field generated by the i-th pair of coils at the space (x, y, z) according to the Biot-Savart law. The magnetic field of the double-layer spherical self-shielded uniform field coil is obtained by summing the magnetic fields of each coil.

[0013] Step 2: Based on the magnetic field size generated by the i-th pair of coils at the space (x, y, z) calculated in step 1, the uniformity of the magnetic field is described by the relative error ε and the self-shielding effect of the coil is described by the ratio δ, and the uneven error ε is set. max and the attenuation coefficient constant threshold δ max The ratio of the magnetic field area within the good field region that meets the corresponding threshold conditions is used to describe the uniformity and self-shielding effects of the coil;

[0014] Step 3: Based on the relative error ε described in step 2 to describe the uniformity of the magnetic field and the self-shielding effect of the coil, a constrained nonlinear multi-objective optimization problem is constructed, and it is further transformed into a single-objective optimization problem through a weighted approach, and the optimization calculation is performed using a genetic algorithm.

[0015] Furthermore, a preferred embodiment is provided, in which the optimization calculation method based on the genetic algorithm in step 3 is:

[0016] Assume that the inner spherical coil U = outer spherical coil V = number of coil turns N, set the termination condition, start the optimization calculation from N = 1 and judge whether the optimization result meets the termination condition. If it meets the condition, terminate the optimization and output the result. If not, increase N to expand the solution domain and search for a better solution until the convergence condition is met.

[0017] Furthermore, a preferred embodiment is provided, in step 1, the method for calculating the magnitude of the magnetic field generated by the i-th pair of coils at the space (x, y, z) is:

[0018]

[0019] Where μ0 is the magnetic permeability of vacuum; e x ,e y ,e z are unit vectors in the x, y, and z directions respectively.

[0020] Furthermore, a preferred embodiment is provided, in step 1, the magnetic field of the double-layer spherical self-shielding uniform field coil is obtained by accumulating the magnetic fields of the coils as follows:

[0021]

[0022] Among them, B pi is the magnetic field generated by the inner primary coil, B si is the magnetic field generated by the outer layer of the secondary coil.

[0023] Furthermore, a preferred embodiment is provided, in which the method for describing the uniformity of the magnetic field by the relative error ε in step 2 is:

[0024]

[0025] Among them, B F Represents the magnetic flux density vector at a certain field point F in the uniform region, B O Represents the magnetic flux density vector at the center point O.

[0026] Furthermore, a preferred embodiment is provided, in which the method for describing the self-shielding effect of the coil by the ratio δ in step 2 is:

[0027]

[0028] Where B E Represents the magnetic flux density vector at a certain field point E in the shielding area.

[0029] Furthermore, a preferred embodiment is provided, in step 2, the uneven error ε is set max and the attenuation coefficient constant threshold δ max， The method for describing the uniformity effect and self-shielding effect of the coil is based on the ratio of the magnetic field area within the good field area that meets the corresponding threshold conditions:

[0030] ratio1=V area / V uniform ×100% (5)

[0031] ratio2=S ref_sphere / S shield ×100% (6)

[0032] Where V area is the total volume of the coil-wrapped space, V uniform is the magnetic field volume within the magnetic field region within the good field region that is smaller than the inhomogeneity error threshold; S ref_sphere is the area of ​​the reference shielding sphere, S shield is the magnetic field area within the good field region that is less than the attenuation coefficient threshold.

[0033] Furthermore, a preferred embodiment is provided, wherein the number of turns N of the coil is 1.

[0034] Furthermore, a preferred embodiment is provided, in step 3, the method of constructing a nonlinear multi-objective optimization problem with constraints and further converting it into a single-objective optimization problem by weighting is:

[0035]

[0036] The present invention is beneficial in that:

[0037] The double-layer spherical self-shielding uniform field coil and design method described in the present invention designs a new type of spherically distributed self-shielding uniform field coil and proposes a corresponding design method based on the coil. In terms of optimizing the objective function design, the areas of the uniform area and the shielding area are used as optimization targets, which can generate a uniform field inside the coil while rapidly decaying the magnetic field outside the coil to zero.

[0038] The present invention is also applicable to the fields of uniform magnetic field generating devices in shielding systems and internal modulation coils of optically pumped magnetometers (OPMs). BRIEF DESCRIPTION OF THE DRAWINGS

[0039] Figure 1 This is a geometric diagram of a double-layer spherical self-shielding uniform field coil according to the first embodiment.

[0040] Figure 2This is a flow chart of optimization calculations in a design method for a double-layer spherical self-shielding uniform field coil described in embodiment 2.

[0041] Figure 3 This is a distribution diagram of the uneven error in the center cross section of the coil according to the eleventh embodiment.

[0042] Figure 4 This is the attenuation coefficient distribution diagram of the coil center section described in embodiment eleven. DETAILED DESCRIPTION

[0043] In order to make the purpose, technical solutions and advantages of the implementation methods of this application clearer, the technical solutions in the implementation methods of this application will be clearly and completely described below in combination with the drawings in the implementation methods of this application. Obviously, the described implementation methods are only part of the implementation methods of this application, not all of the implementation methods.

[0044] Embodiment 1: This embodiment proposes a double-layer spherical self-shielding uniform field coil. The double-layer spherical self-shielding uniform field coil is implemented using a double-layer nested spherical coil structure. The double-layer nested structure includes an inner spherical coil and an outer spherical coil. The inner spherical coil is a primary coil, which is fed with a forward current to generate a uniform magnetic field in the central area. The outer spherical coil is a secondary shielding coil, which is fed with a reverse current to offset the magnetic field generated by the inner coil on the outside.

[0045] The inner spherical coils are composed of U pairs, distributed at a radius of R p On the sphere, the radius of the i-th pair of coils is r pi , the position plane is z=±d pi , ampere-turns is n pi I p , then

[0046] The outer spherical coils are composed of V pairs, distributed at a radius of R s On the sphere, the radius of the i-th pair of coils is r si , the position plane is z=±d si , ampere-turns is n si I s , then

[0047] Embodiment 2: This embodiment proposes a design method for a double-layer spherical self-shielding uniform field coil. The design method is based on the double-layer spherical self-shielding uniform field coil described in Embodiment 1 and includes the following steps:

[0048] Step 1: Based on the constructed double-layer spherical self-shielded uniform field coil, calculate the magnitude of the magnetic field generated by the i-th pair of coils at the space (x, y, z) according to the Biot-Savart law. The magnetic field of the double-layer spherical self-shielded uniform field coil is obtained by summing the magnetic fields of each coil.

[0049] Step 2: Based on the magnetic field size generated by the i-th pair of coils at the space (x, y, z) calculated in step 1, the uniformity of the magnetic field is described by the relative error ε and the self-shielding effect of the coil is described by the ratio δ, and the uneven error ε is set. max and the attenuation coefficient constant threshold δ max The ratio of the magnetic field area within the good field region that meets the corresponding threshold conditions is used to describe the uniformity and self-shielding effects of the coil;

[0050] Step 3: Based on the relative error ε described in step 2 to describe the uniformity of the magnetic field and the self-shielding effect of the coil, a constrained nonlinear multi-objective optimization problem is constructed, and it is further transformed into a single-objective optimization problem through a weighted approach, and the optimization calculation is performed using a genetic algorithm.

[0051] Implementation method 3: This implementation method further limits the design method of the double-layer spherical self-shielded uniform field coil described in implementation method 2. The optimization calculation method based on the genetic algorithm in step 3 is:

[0052] Assume that the inner spherical coil U = outer spherical coil V = number of coil turns N, set the termination condition, start the optimization calculation from N = 1 and judge whether the optimization result meets the termination condition. If it meets the condition, terminate the optimization and output the result. If not, increase N to expand the solution domain and search for a better solution until the convergence condition is met.

[0053] Embodiment 4: This embodiment further defines the design method of the double-layer spherical self-shielding uniform field coil described in Embodiment 2. The method for calculating the magnitude of the magnetic field generated by the i-th pair of coils at the space (x, y, z) in step 1 is:

[0054]

[0055] Where μ0 is the magnetic permeability of vacuum. x ,e y ,e z are unit vectors in the x, y, and z directions respectively.

[0056] Embodiment 5: This embodiment further defines the design method of the double-layer spherical self-shielded uniform field coil described in Embodiment 2. In step 1, the magnetic field of the double-layer spherical self-shielded uniform field coil is obtained by accumulating the magnetic fields of the coils as follows:

[0057]

[0058] Among them, B pi is the magnetic field generated by the inner primary coil, B si is the magnetic field generated by the outer layer of the secondary coil.

[0059] Embodiment 6: This embodiment further defines the design method of the double-layer spherical self-shielding uniform field coil described in Embodiment 2. In step 2, the method for describing the uniformity of the magnetic field by the relative error ε is:

[0060]

[0061] Among them, B F Represents the magnetic flux density vector at a certain field point F in the uniform region, B O Represents the magnetic flux density vector at the center point O.

[0062] Embodiment 7: This embodiment further defines the design method of the double-layer spherical self-shielding uniform field coil described in Embodiment 2. In step 2, the method for describing the self-shielding effect of the coil by the ratio δ is:

[0063]

[0064] Where B E Represents the magnetic flux density vector at a certain field point E in the shielding area.

[0065] Implementation 8: This implementation further defines the design method of the double-layer spherical self-shielding uniform field coil described in Implementation 2. In step 2, the non-uniform error ε is set. max and the attenuation coefficient constant threshold δ max， The method for describing the uniformity effect and self-shielding effect of the coil is based on the ratio of the magnetic field area within the good field area that meets the corresponding threshold conditions:

[0066] ratio1=V area / V uniform ×100% (5)

[0067] ratio2=S ref_sphere / S shield ×100% (6)

[0068] Where V area is the total volume of the coil-wrapped space, V uniform is the magnetic field volume within the magnetic field region within the good field region that is smaller than the inhomogeneity error threshold; S ref_sphere is the area of ​​the reference shielding sphere, S shield is the magnetic field area within the good field region that is less than the attenuation coefficient threshold.

[0069] Implementation 9: This implementation further limits the design method of the double-layer spherical self-shielding uniform field coil described in Implementation 3, and the number of coil turns N is 1.

[0070] Embodiment 10. This embodiment further limits the design method of the double-layer spherical self-shielded uniform field coil described in Embodiment 2. In step 3, the method of constructing a constrained nonlinear multi-objective optimization problem and further converting it into a single-objective optimization problem by weighting is as follows:

[0071]

[0072] See also Figure 1 and Figure 4 This embodiment describes a novel double-layer spherical self-shielding uniform field coil structure. The spherical coil described in this embodiment is composed of a group of symmetrical coaxial ring coils distributed on the same sphere. In order to achieve rapid attenuation of the external magnetic field and form a self-shielding effect on the basis of a uniform field, this embodiment adopts a double-layer nested spherical coil structure, such as Figure 1 As shown. The inner spherical coil is the primary coil, i.e. the dark winding, which is fed with a positive current and whose main function is to generate a uniform magnetic field in the central area; the outer spherical coil is the secondary shielding coil, i.e. the light-colored coil, which is fed with a reverse current and whose main function is to offset the magnetic field generated by the inner coil outside, thus forming a self-shielding effect. The inner coils are composed of U pairs, distributed at a radius of R p On the sphere, the radius of the i-th pair of coils is r pi , the position plane is z=±d pi , ampere-turns is n pi I p , then The outer coils consist of V pairs, distributed at a radius of R s On the sphere, the radius of the i-th pair of coils is r si , the position plane is z=±d si , ampere-turns is n si I s , then

[0073] In the design method of a double-layer spherical self-shielded uniform field coil described in this embodiment, in step 1, according to the Biot-Savart law, the magnitude of the magnetic field generated by the i-th pair of coils at the space (x, y, z) can be calculated according to formula (1). Furthermore, the magnetic field of the double-layer spherical self-shielded uniform field coil is obtained by summing the magnetic fields of each coil, as shown in formula (2). In the formula, μ0 is the vacuum permeability. e x ,e y ,e zare unit vectors in the x, y, and z directions respectively.

[0074]

[0075]

[0076] Step 2: Determine the objective function and construct the optimization problem. The relative error ε shown in formula (3) is usually used to quantitatively describe the uniformity of the magnetic field. F Represents the magnetic flux density vector at a certain field point F in the uniform region, B O represents the magnetic flux density vector at the center point O. In this embodiment, the variable ε is named as uneven error.

[0077] The smaller the unevenness error, the better the uniformity at that point.

[0078]

[0079] On the other hand, the self-shielding effect of the coil can be quantitatively described by the ratio δ shown in formula (4), where B S represents the magnetic flux density vector at a certain field point E in the shielding area. In this embodiment, the variable δ is named as the attenuation coefficient. The smaller the attenuation coefficient, the better the shielding performance at that point.

[0080]

[0081] Furthermore, based on (3) and (4), constant thresholds of the non-uniformity error and the attenuation coefficient can be set to describe the uniformity effect and self-shielding effect of the coil by the ratio of the magnetic field area in the good field area that meets the corresponding threshold conditions. Assume that the non-uniformity error threshold is ε max , the attenuation coefficient threshold is δ max The uniform effect can be described by formula (5), where V area is the total volume of the coil-wrapped space, V uniform is the magnetic field volume within the good field region that is less than the non-uniform error threshold; the shielding effect can be described by formula (6). Considering the effect of the coil magnetic field attenuation with distance, the radius R can be selected. ref (R ref >R s >R p ) as the critical surface of the shielding area (such as Figure 1 As shown), where S ref_sphere is the area of ​​the reference shielding sphere, S shield is the magnetic field area within the good field region that is smaller than the attenuation coefficient threshold.

[0082] ratio1=V area / V uniform×100% (5)

[0083] ratio2=S ref_sphere / S shield ×100% (6)

[0084] Using (5) and (6) as objective functions, a constrained nonlinear multi-objective optimization problem is constructed and further transformed into a single-objective optimization problem by weighting, as shown in Equation (7). In addition to the constraints of the spherical distribution of the coil and the number of coil turns being a positive integer, constraints are added to conditions such as the radius according to the coil assembly requirements. Compared with the series expansion method, (5) and (6) are both ratios, and their ranges are between 0 and 1. The order of magnitude is determined and close, and the weight parameters are easier to design. In addition, this objective function fully considers the distribution of the magnetic field in the target area, which is more helpful to expand the space of the uniform area and the shielding area.

[0085]

[0086] Step 4: Optimization calculation based on genetic algorithm (GA)

[0087] When the logarithms U and V of the primary and secondary coils are variables, the optimization problem (7) is a dynamic dimension optimization problem, which greatly increases the difficulty of the optimization calculation. On the other hand, the uniformity and self-shielding performance of the spherical coil are closely related to the number of coils. As the number of coils increases, the search domain of the optimization solution becomes larger, and a better solution may be found, but it will also increase the dimension of the optimization variables, thereby increasing the optimization calculation cost. Therefore, for the purpose of simplicity, it is assumed that U = V = N, and the optimization method is adopted. Figure 2 The process shown is optimized.

[0088] First, set the termination condition, then start the optimization calculation from N=1 and judge whether the optimization result meets the termination condition. If it does, terminate the optimization and output the result. If not, increase N to expand the solution domain and search for a better solution until the convergence condition is met.

[0089] In the optimization calculation, the integer variable number of coil turns n pi , n si The introduction of transforms the problem into a mixed-integer optimization problem, which is NP-hard, meaning it has exponential algorithmic complexity. Furthermore, due to the wire width, as the number of turns increases, the actual processed coils may not meet the spherical distribution constraint, resulting in discrepancies between the actual results and the theoretical analysis. Taking these two factors into account, this implementation sets the number of turns for all coils to 1.

[0090] The specific embodiments are:

[0091] Set R ref =1.5Rp , uneven error threshold ε max =0.01, the shielding coefficient threshold is δ max =0.1, the convergence condition is ratio1>65%, ratio2>65%. Finally, the convergence condition is met when N=7, and the coil ratio parameters shown in Table 1 are obtained.

[0092] Table 1

[0093]

[0094]

[0095] Figure 3 and Figure 4 The non-uniform error distribution diagram and shielding coefficient distribution diagram of the coil respectively show the uniform field performance and self-shielding performance of the self-shielding uniform field coil. The area ratio of the coil that meets the non-uniform error threshold is 63.69%. p The shielding coefficient of the coil is less than 10% in the area

[0096] Those skilled in the art will understand that the above description is only a preferred embodiment of the present invention, and the features described in the various embodiments and / or claims of the present disclosure may be combined or coupled in various ways, even if such a combination or coupling is not explicitly described in the present disclosure. It is not intended to limit the present invention. Although the present invention has been described in detail with reference to the aforementioned embodiments, those skilled in the art may still modify the technical solutions described in the aforementioned embodiments or make equivalent substitutions for some of the technical features therein. Any modifications, equivalent substitutions, improvements, etc. made within the spirit and principles of the present invention shall be included in the scope of protection of the present invention.

[0097] Although preferred embodiments of the present invention have been described, those skilled in the art may make additional changes and modifications to these embodiments once they are aware of the basic inventive concepts. Therefore, the appended claims are intended to be interpreted as including the preferred embodiments and all changes and modifications that fall within the scope of the present invention. Obviously, those skilled in the art may make various changes and modifications to the present invention without departing from the spirit and scope of the present invention. Thus, the present invention is intended to include such changes and modifications as fall within the scope of the claims and their equivalents.

Claims

1. A double-layer spherical self-shielding uniform field coil, characterized in that: The double-layer spherical self-shielding uniform field coil is implemented using a double-layer nested spherical coil structure. The double-layer nested structure includes an inner spherical coil and an outer spherical coil. The inner spherical coil is a primary coil, which is fed with a forward current to generate a uniform magnetic field in the central area. The outer spherical coil is a secondary shielding coil, which is fed with a reverse current to offset the magnetic field generated by the inner coil on the outside. The inner spherical coils are composed of U pairs, distributed at a radius of R p On the sphere, the radius of the i-th pair of coils is r pi , the position plane is z=±d pi , ampere-turns is n pi I p , then The outer spherical coils are composed of V pairs, distributed at a radius of R s On the sphere, the radius of the i-th pair of coils is r si , the position plane is z=±d si , ampere-turns is n si I s , then 2. A design method for a double-layer spherical self-shielding uniform field coil, characterized in that: The design method is implemented based on the double-layer spherical self-shielding uniform field coil according to claim 1, and the design method includes the following steps: Step 1: Based on the constructed double-layer spherical self-shielded uniform field coil, calculate the magnitude of the magnetic field generated by the i-th pair of coils at the space (x, y, z) according to the Biot-Savart law. The magnetic field of the double-layer spherical self-shielded uniform field coil is obtained by summing the magnetic fields of each coil. Step 2: Based on the magnetic field size generated by the i-th pair of coils at the space (x, y, z) calculated in step 1, the uniformity of the magnetic field is described by the relative error ε and the self-shielding effect of the coil is described by the ratio δ, and the uneven error ε is set. max and the attenuation coefficient constant threshold δ max The ratio of the magnetic field area within the good field region that meets the corresponding threshold conditions is used to describe the uniformity and self-shielding effects of the coil; Step 3: Based on the relative error ε described in step 2 to describe the uniformity of the magnetic field and the self-shielding effect of the coil, a constrained nonlinear multi-objective optimization problem is constructed, and it is further transformed into a single-objective optimization problem through a weighted approach, and the optimization calculation is performed using a genetic algorithm.

3. The design method of the double-layer spherical self-shielding uniform field coil according to claim 2 is characterized in that: The optimization calculation method based on genetic algorithm in step 3 is: Assume that the inner spherical coil U = outer spherical coil V = number of coil turns N, set the termination condition, start the optimization calculation from N = 1 and judge whether the optimization result meets the termination condition. If it meets the condition, terminate the optimization and output the result. If not, increase N to expand the solution domain and search for a better solution until the convergence condition is met.

4. The design method of the double-layer spherical self-shielding uniform field coil according to claim 2 is characterized in that: The method for calculating the magnitude of the magnetic field generated by the i-th pair of coils at the space (x, y, z) in step 1 is: Where μ0 is the vacuum permeability, e x ,e y ,e z are unit vectors in the x, y, and z directions respectively.

5. The design method of the double-layer spherical self-shielding uniform field coil according to claim 2, characterized in that: The magnetic field of the double-layer spherical self-shielded uniform field coil in step 1 is obtained by accumulating the magnetic fields of each coil as follows: Among them, B pi is the magnetic field generated by the inner primary coil, B si is the magnetic field generated by the outer layer of the secondary coil.

6. The design method of the double-layer spherical self-shielding uniform field coil according to claim 2, characterized in that: The method for describing the uniformity of the magnetic field by the relative error ε in step 2 is: Among them, B F Represents the magnetic flux density vector at a certain field point F in the uniform region, B O Represents the magnetic flux density vector at the center point O.

7. The design method of the double-layer spherical self-shielding uniform field coil according to claim 2, characterized in that: The method for describing the self-shielding effect of the coil by the ratio δ in step 2 is: Where B E Represents the magnetic flux density vector at a certain field point E in the shielding area.

8. The design method of a double-layer spherical self-shielding uniform field coil according to claim 2, characterized in that: In step 2, set the uneven error ε max and the attenuation coefficient constant threshold δ max， The method used to describe the uniformity effect and self-shielding effect of the coil is based on the ratio of the magnetic field area within the good field area that meets the corresponding threshold conditions: ratio1=V area / IN uniform ×100% (5) ratio2=S ref_sphere / S shield ×100% (6) Where V area is the total volume of the coil-wrapped space, V uniform is the magnetic field volume within the good field region that is smaller than the inhomogeneity error threshold; S ref_sphere is the area of ​​the reference shielding sphere, S shield is the magnetic field area within the good field region that is smaller than the attenuation coefficient threshold.

9. The design method of the double-layer spherical self-shielding uniform field coil according to claim 3, characterized in that: The number of turns N of the coil is 1.

10. The design method of a double-layer spherical self-shielding uniform field coil according to claim 2, characterized in that: In step 3, the method of constructing a nonlinear multi-objective optimization problem with constraints and further transforming it into a single-objective optimization problem by weighting is as follows:

Images