A high uniformity saddle shim coil design method for eliminating the magnetic shielding coupling effect

Abstract

A high-uniformity saddle-shaped shim coil design method for eliminating the magnetic shielding coupling effect, including decomposing the total magnetic induction intensity expression generated by the saddle-shaped coil group under the ferromagnetic boundary into two parts of the magnetic induction intensity generated by the coil group under the free boundary and the magnetic induction intensity generated by the coupling effect, obtaining the analytical expression of the magnetic induction intensity generated by the coil due to the coupling effect; through a multi-objective optimization algorithm, taking the ratio expression of the magnetic field generated by the coil due to the coupling effect to the magnetic field generated by the coil at the center under the ferromagnetic boundary and the ratio expression of the magnetic field generated by the coil under the ferromagnetic boundary to the magnetic field generated by the coil at the center as two objective functions, taking the straight line segment height, the circular arc segment spread angle and the coil turns and current of the four pairs of saddle-shaped coils as the optimization parameters for design, obtaining a set of optimal saddle-shaped coil group parameters, and eliminating the adverse effects of the coupling effect of the high magnetic permeability material on the coil generated magnetic field on the uniformity of the coil generated magnetic field from the source.

Description

TECHNICAL FIELD

[0001] The application relates to a high-uniformity saddle-shaped shim coil design method for eliminating the coupling effect between a passive magnetic shielding device and an active magnetic compensation coil, and belongs to the technical field of magnetic field coil design. BACKGROUND

[0002] The uniform magnetic field coil is widely applied to weak magnetic measurement, quantum precision measurement and the like, and can provide an accurately controllable uniform magnetic field to perform compensation, modulation or calibration of a magnetic field. Generally, in order to avoid the interference of an external magnetic field and ensure the stability and uniformity of a magnetic field environment of a measurement system, the uniform magnetic field coil also needs to be applied in cooperation with a high-performance passive magnetic shielding system. Since the magnetic shielding structure has the characteristic of converging magnetic lines, the magnetic field distribution of the coil originally in the internal space of the measurement system will be changed, the uniformity of the magnetic field generated by the coil is affected, and the precision of the measurement instrument is adversely affected. Therefore, it is necessary to suppress the coupling effect between the magnetic shielding device and the coil.

[0003] The multi-layer cylindrical magnetic shielding barrel is the most widely used magnetic shielding system, and a cylindrical coil is commonly used to improve the utilization rate of the internal space. The cylindrical coil is composed of an axial coil and a radial coil. For the radial shim coil, a saddle-shaped structure is commonly used for design due to its compact structure and easy construction. Although the traditional saddle-shaped coil has high internal magnetic field uniformity under a free boundary, the internal uniformity can be reduced by nearly 50% when the coil is placed in the magnetic shielding barrel due to the influence of the coupling effect. In order to reduce the coupling effect between the coil and the magnetic shielding barrel and improve the measurement precision and the magnetic field uniformity, a self-shielding coil is commonly used at present. The design objectives of the traditional self-shielding coil include two parts, one is that the external magnetic field of the coil needs to be quickly attenuated, and the other is that the internal magnetic field of the coil needs to have high uniformity. However, the effect of indirectly suppressing the coupling effect by accelerating the attenuation of the external magnetic field of the coil is not complete. In order to improve the internal magnetic field uniformity of the coil, the complexity of the structure of the self-shielding coil usually needs to be increased, such as increasing the length-diameter ratio of the saddle-shaped coil, increasing the logarithm of the saddle-shaped coil group, and the like. Therefore, there is an urgent need for a saddle-shaped shim coil which can eliminate the coupling effect to the greatest extent, ensure high internal magnetic field uniformity, fast external magnetic field attenuation, and has a relatively simple structure. SUMMARY

[0004] The present application aims at the problems of the current traditional saddle coil, such as sharp reduction of uniformity under the ferromagnetic boundary, incomplete inhibition effect of self-shielded saddle coil on coupling effect, and complex structure, and provides a design method of high-uniform saddle shim coil for eliminating the coupling effect of magnetic shield.

[0005] The technical solution of the present application is as follows:

[0006] The design method of high-uniform saddle shim coil for eliminating the coupling effect of magnetic shield comprises the following steps: the total magnetic induction intensity expression of the saddle coil group under the ferromagnetic boundary is decomposed into two parts, i.e., the magnetic induction intensity generated under the free boundary and the magnetic induction intensity generated by the coupling effect, so as to obtain the analytical expression of the magnetic induction intensity generated by the coupling effect between the saddle coil group and the magnetic shield barrel; the multi-objective optimization algorithm is used to directly optimize the coil coupling rate and the magnetic field uniformity, so that the coil group can inhibit the adverse effect of the coupling effect on the magnetic field uniformity to the greatest extent; and after the optimization design, the designed saddle shim coil group can have fast external magnetic field attenuation, larger internal central uniform area and higher magnetic field uniformity under the simple structure, which is more beneficial to the engineering application of the coil in the magnetic field calibration and the like.

[0007] The design method comprises the following steps:

[0008] Step 1: determining the structure of the saddle shim coil group: the saddle shim coil group is located at the geometric center of the cylindrical magnetic shield barrel, the saddle shim coil group is composed of two pairs of main coils and two pairs of shield coils, the two pairs of main coils are located outside the two pairs of shield coils, the height of the magnetic shield barrel is 2H m , the inner radius is R b , and the outer radius is R c, the xyz three-dimensional rectangular coordinate system is established with the geometric center as the origin, the x-axis is parallel to the geometric center connecting line between the coils, the y-axis is parallel to the gap of the pair of coils, and the z-axis is parallel to the axial direction of the magnetic shielding barrel, and the structural parameters of the saddle-shaped shim coil group include: the height of the straight line segment of the first pair of main coils 2l m1 , the height of the straight line segment of the second pair of main coils 2l m2 , the height of the straight line segment of the first pair of shielding coils 2l s1 , the height of the straight line segment of the second pair of shielding coils 2l s2 , the opening angle of the arc segment of the first pair of main coils , the opening angle of the arc segment of the second pair of main coils , the opening angle of the arc segment of the first pair of shielding coils , the opening angle of the arc segment of the second pair of shielding coils , the radius of the main coil R m , the radius of the shielding coil R s , the number of turns of the main coil n m , the number of turns of the shielding coil n s , the loop current of the main coil I m , the loop current of the shielding coil I s , and the length of the side of the central cube-shaped target region 2L p ;

[0009] Step 2, by the multi-stage expansion formula of the magnetic vector potential of the saddle-shaped coil, the total magnetic moment m p of the coil group is set to 0, and the radius R s of the shielding coil is solved inversely.

[0010] Step 3, the expression of the magnetic field generated by the saddle-shaped coil in the magnetic shielding barrel is obtained, and the magnetic induction intensity B ox generated by the coil due to the coupling effect is obtained.

[0011] Step 4, a target point is selected in the target region, a first target function f1 is established to minimize the coupling rate of the coil group, and a second target function f2 is established to minimize the relative magnetic field deviation of the coil group.

[0012] Step 5, based on the Matlab platform, the MOPSO algorithm is used to optimize the structural parameters of the saddle-shaped shim coil group, and the structural parameter set of the optimal saddle-shaped shim coil group is obtained.

[0013] Step 2 includes the following formula:

[0014]

[0015] where I m and I s , one is positive and the other is negative.

[0016] Step 3 includes the following formula:

[0017]

[0018] where B x is the total x-direction magnetic field generated by the saddle coil, B ox is the x-direction magnetic field generated by the coupling effect of the saddle coil and the magnetic shield barrel, B ρ is the p-direction magnetic field generated by the saddle coil in the cylindrical coordinate system, B φ is the φ-direction magnetic field generated by the saddle coil in the cylindrical coordinate system, B oρ is the p-direction magnetic field generated by the coupling effect in the cylindrical coordinate system, B oφ is the φ-direction magnetic field generated by the coupling effect in the cylindrical coordinate system, ρ is the radial distance, and φ is the azimuth angle.

[0019] The following formula is included in step 4:

[0020]

[0021] s.t.0.15R m <l j <2R m (j=1,2,3,4)

[0022] 0.08<R s <0.95R b (j=1,2,3,4)

[0023]

[0024] l j+1 -l j ≥l min

[0025]

[0026] where f1 is the first objective function, N p is the number of target points, N p is a positive integer, B ox (x,y,z) is the x-direction magnetic field generated by the coupling effect of the saddle coil and the magnetic shield barrel at any point, B x (0,0,0) is the x-direction total magnetic field generated by the saddle coil set at the coordinate origin under the ferromagnetic boundary, ε is the magnetic field uniformity, B x (x,y,z) is the x-direction total magnetic field generated by the saddle coil set at any point under the ferromagnetic boundary, l j is the set of half-heights of the straight segments of the saddle coil set, is the set of half-opening angles of the circular arc segments of the saddle coil set, l min is a preset value, is a preset value.

[0027]

[0028] The technical effects of the present application are as follows: the design method of the high-uniformity saddle-shaped shim coil for eliminating the coupling effect of magnetic shielding, which includes two pairs of main coils and two pairs of shielding coils, decomposes the total magnetic induction intensity expression of the saddle-shaped coil group under the ferromagnetic boundary into two parts, i.e., the magnetic induction intensity generated by the coil group under the free boundary and the magnetic induction intensity generated by the coupling effect, to obtain the analytical expression of the magnetic induction intensity generated by the coil due to the coupling effect. Through the multi-objective optimization algorithm, the expression of the ratio of the magnetic field generated by the coil due to the coupling effect to the magnetic field generated by the coil at the center under the ferromagnetic boundary and the expression of the ratio of the magnetic field generated by the coil to the magnetic field generated by the coil at the center are taken as two objective functions, the height of the straight line segment, the size of the circular arc segment, the number of turns of the coil, the size and direction of the current of the four pairs of saddle-shaped coils are taken as the parameters to be optimized for design, and a set of optimal saddle-shaped coil group parameters are obtained. The saddle-shaped uniform magnetic field coil group optimized by the present application can maximize the elimination of the adverse effects of the coupling effect of the high magnetic permeability material on the uniformity of the magnetic field generated by the coil from the source, and ensure higher magnetic field uniformity inside the coil, faster magnetic field decay outside the coil, and a larger magnetic field uniform area under a relatively simple structure.

[0029] The present application has the following advantages compared with the prior art:

[0030] 1) Compared with the traditional saddle-shaped coil under the same radius, when the same current is passed, the internal magnetic field uniformity of both under the free boundary is similar, but the magnetic field decay outside the designed coil group is faster, and the aspect ratio of the coil is smaller. When placed in the ferromagnetic boundary, the traditional saddle-shaped coil is greatly affected by the coupling effect, and the internal magnetic field uniformity is significantly reduced. The coupling rate of the designed coil group can be reduced to less than 5% of the traditional saddle-shaped coil, and the coupling effect is almost eliminated, so that the magnetic field distribution under the ferromagnetic boundary is basically the same as that under the free boundary, and the internal magnetic field uniformity can still be maintained.

[0031] 2) Compared with the self-shielded saddle-shaped coil under the same radius, when a unit current is passed, the magnetic field decay outside both under the free boundary is similar, but the internal central magnetic field uniform area of the self-shielded saddle-shaped coil is smaller. When placed in the ferromagnetic boundary, the designed coil group is less affected by the coupling effect, and the coupling rate can be reduced to less than 10% of the self-shielded saddle-shaped coil, and the central shim area is still larger. Under a simple configuration, similar external magnetic field decay and higher internal magnetic field uniformity are achieved. BRIEF DESCRIPTION OF DRAWINGS

[0032] Figure 1is a high-uniformity saddle-shaped shim coil structure diagram involved in a high-uniformity saddle-shaped shim coil design method for eliminating the magnetic shielding coupling effect. The outermost cylindrical shell in the diagram is a magnetic shielding barrel, the geometric center of which is concentric with the designed saddle-shaped shim coil group, and the height of the magnetic shielding barrel is 2H m . The designed saddle-shaped shim coil group includes two pairs of main coils and two pairs of shielding coils, the outer side being the main coils (including the first pair of main coils and the second pair of main coils) and the inner side being the shielding coils (including the first pair of shielding coils and the second pair of shielding coils). A xyz three-dimensional rectangular coordinate system is established with the geometric center point of the overall structure as the origin, the x-axis is parallel to the geometric center line of each saddle-shaped coil, the y-axis is parallel to the coinciding gap of the saddle-shaped coil, and the z-axis is parallel to the axial direction of the magnetic shielding structure.

[0033] Figure 2 is Figure 1 a schematic diagram of the xy plane projection of the medium-high uniformity saddle-shaped shim coil. Figure 2 medium R m is the main coil radius, R s is the shielding coil radius, R b is the inner radius of the magnetic shielding structure, R c is the outer radius of the magnetic shielding structure. The central square is the projection of the target area, and the square side length is

[0034] Figure 3 is a saddle-shaped shim coil group structure diagram designed by the high-uniformity saddle-shaped shim coil design method of the present application for eliminating the coupling effect. Figure 3 The straight line segment height of the two pairs of main coils is 2l m1 , 2l m2 , respectively, and the circular segment spread angle is The loop current is I m , and the coil turns are n m ; the straight line segment height of the two pairs of shielding coils is 2l s1 , 2l s2 , respectively, and the circular segment spread angle is The loop current is I s , and the coil turns are n s . The current direction of the main coil and the shielding coil is opposite, but there is no fixed direction, and the current sign indicates its direction.

[0035] Figure 4 is a flow chart of the high-uniformity saddle-shaped shim coil design method for eliminating the magnetic shielding coupling effect. Figure 4 includes step 1, determining the structure of the saddle-shaped shim coil group: composed of two pairs of main coils and two pairs of shielding coils; step 2, through the multi-level expansion formula of the saddle-shaped coil magnetic potential, the total magnetic moment m p= 0, inverse solution of shield coil radius R s ; step 3, disassembling the saddle coil to generate a magnetic field expression in the magnetic shield barrel, and obtaining a mathematical model of the coupling effect to make the coil generate an additional magnetic induction intensity B ox ; step 4, determining a target region volume and selecting a suitable target point; step 5, establishing a target function f1: minimum coupling rate of the coil set, and f2: minimum relative magnetic field deviation of the coil set; step 6, optimizing the structure parameter of the saddle shim coil set based on the MOPSO algorithm on the Matlab platform (Matlab is a development tool software platform; MOPSO is Multiple Objective Particle Swarm Optimization); step 7, respectively establishing a finite element numerical model for calculating the magnetic field generated by the coil in the vacuum and the magnetic field generated by the magnetic shield barrel based on the COMSOL platform (COMSOL is a multi-physics simulation software platform); step 8, comparing, analyzing and evaluating the decoupling and uniformity of the magnetic field generated by the coil set to determine the optimal parameters of the structure; and step 9, forming the optimized design of the structure parameters of the saddle shim coil for eliminating the interference of the magnetic shield coupling effect.

[0036] Figure 5 is the optimization flowchart of the optimized algorithm of the saddle shim coil set for eliminating the coupling effect designed in the application. Figure 5 The method comprises the following steps: step 1, randomly initializing particles, one particle has 8 position parameters, including a saddle coil set linear segment height set 2l j (j = m1, m2, s1, s2), and a saddle coil set circular segment spread angle set ; step 2, calculating the total magnetic moment m p = 0, inverse solution of shield coil radius R s ; step 3, generating 8 parameters (2l j and ) through initialization / update, and determining R m of the saddle shim coil set, and substituting R s calculated into two optimization target functions for solving; step 4, obtaining a local optimal and global optimal particle; step 5, judging whether a termination condition is met, if not, updating the speed and position of the particle to recalculate the shield coil radius R s , and returning to step 3, if yes, entering step 6; step 6, obtaining a global optimal particle as the structure parameter set of the designed saddle shim coil set.

[0037] Figure 6a is a coupling rate schematic diagram of the saddle shim coil set for eliminating the coupling effect designed in the application. Figure 6aThe scale coordinates of x(mm), y(mm) and z(mm) are all -40 to 40, 10*|B ox / B o | indicates that the coupling ratio is amplified 10 times, B ox is the x-direction magnetic induction intensity generated by the coupling effect at the target point, B o The saddle-shaped shim coil group designed by the present invention to eliminate the coupling effect is different from the traditional saddle-shaped coil of the same size (expansion angle The ratio of the half height l of the straight line segment to the radius R (l / R = 4) is taken as an average of 5 in the target area under the same magnetic shielding environment. 3 The coupling rate of each point (the ratio of the x-direction magnetic induction intensity generated by the coupling effect at the target point to the x-direction magnetic induction intensity generated by the coil at the origin) is obtained by Figure 6a and Figure 6b The size of the ball indicates the coupling rate. The larger the volume of the ball, the greater the coupling rate and the worse the decoupling. In order to more clearly see the effect of the designed coil group on the suppression of the coupling effect, Figure 6a The coupling ratio of the present invention is magnified 10 times for plotting, and Figure 6b The coupling ratio of the traditional saddle coil drawn in the figure is not magnified and is 1 times.

[0038] Figure 6b Is used with Figure 6a Schematic diagram of the coupling ratio of a traditional saddle coil for comparison. Figure 6b The suppression effect of the coupling effect is far less than Figure 6a . |B ox / B o | represents the coupling ratio (the proportion of magnetic field generated by coupling effect), B ox is the x-direction magnetic induction intensity generated by the coupling effect at the target point, B o is the x-direction magnetic induction intensity generated by the coil at the origin.

[0039] Figure 7a This is a schematic diagram of the magnetic field uniformity of the saddle-shaped shim coil group designed by the present invention to eliminate the coupling effect. x is the x-direction magnetic induction intensity generated by the coil, nT is the magnetic induction intensity unit nanometer, ε is B x The x-direction magnetic field distribution and magnetic field uniformity generated by the saddle-shaped shim coil group designed by the present invention to eliminate the coupling effect and the traditional saddle-shaped coil of the same size in the target area under the same magnetic shielding environment are compared. Figure 7a and Figure 7b Make a comparison. Figure 7a The first column in the legend on the right side is the x-direction magnetic induction intensity B generated by the coil x , the unit is nT, the second column is the x-direction magnetic induction intensity B generated by the coilx The uniformity ε.

[0040] Figure 7b Is used with Figure 7a Schematic diagram of the magnetic field uniformity of a traditional saddle coil for comparison. Figure 7b The magnetic field uniformity is far less than Figure 7a .

[0041] Figure 8 The saddle-shaped shim coil designed by the present invention to eliminate coupling effects and the traditional saddle-shaped coil of the same size generate an x-direction magnetic field distribution diagram on the x-axis. Figure 8 The vertical coordinate is B x (nT), the scale is -100 to 100. Figure 8 The horizontal axis is the x-axis (mm), and the scale value is -300 to 300. Figure 8 The dashed curve in the figure belongs to the traditional saddle coil. Figure 8 The solid line curve in FIG. 1 belongs to the saddle-shaped shim coil designed by the present invention to eliminate the coupling effect. Figure 8 The saddle-shaped shim coil of the present invention has a relatively high internal magnetic field uniformity and a relatively fast external magnetic field attenuation, and has a sufficiently large magnetic field uniform area. Figure 8 The saddle-shaped shim coil designed by the present invention to eliminate coupling effect and the traditional saddle-shaped coil of the same size generate the distribution of the x-direction magnetic field at each point in the range from -300 mm to 300 mm on the x-axis. DETAILED DESCRIPTION

[0042] Below is the attached figure ( Figures 1-8 ) and Examples illustrate the present invention.

[0043] Figure 1 The present invention is a schematic structural diagram of a high-uniform saddle-shaped shim coil design method for eliminating magnetic shielding coupling effects. Figure 2 yes Figure 1 Schematic diagram of the xy plane projection of the medium-high uniform saddle-shaped shim coil. Figure 3 The present invention is a schematic structural diagram of a saddle-shaped shim coil group for eliminating coupling effects, designed by a method for designing a highly uniform saddle-shaped shim coil for eliminating magnetic shielding coupling effects. Figure 4 The present invention is a flow chart of a method for designing a highly uniform saddle-shaped shim coil for eliminating magnetic shielding coupling effects. Figure 5 This is an optimization flow chart of the optimization algorithm of the saddle-shaped shim coil group designed by the present invention for eliminating coupling effects. Figure 6a It is a schematic diagram of the coupling rate of the saddle-shaped shim coil group designed by the present invention to eliminate the coupling effect. Figure 6b Is used with Figure 6a Schematic diagram of the coupling ratio of a traditional saddle coil for comparison.Figure 7a is a schematic diagram of the magnetic field homogeneity of the saddle-shaped shim coil group designed by the present application to eliminate the coupling effect. Figure 7b is a schematic diagram of the magnetic field homogeneity of the traditional saddle-shaped coil for comparison. Figure 7a is a schematic diagram of the magnetic field homogeneity of the traditional saddle-shaped coil for comparison. Figure 8 is a schematic diagram of the x-direction magnetic field distribution generated by the saddle-shaped shim coil designed by the present application to eliminate the coupling effect and the same size traditional saddle-shaped coil in the x-axis. As shown in Figures 1 to 8 , a high-uniformity saddle-shaped shim coil design method for eliminating the coupling effect of magnetic shielding, characterized in that it comprises: decomposing the total magnetic induction intensity expression generated by the saddle-shaped coil group under the ferromagnetic boundary into two parts, the magnetic induction intensity generated by the coil group under the free boundary and the magnetic induction intensity generated by the coupling effect, to obtain an analytical expression of the additional magnetic induction intensity generated by the coil due to the coupling effect; taking the ratio expression of the magnetic field generated by the coil due to the coupling effect to the magnetic field generated by the coil at the center under the ferromagnetic boundary and the ratio expression of the magnetic field generated by the coil under the ferromagnetic boundary to the magnetic field generated by the coil at the center as two objective functions through a multi-objective optimization algorithm, and taking the straight line segment height, the circular arc segment spread angle, the coil turn number, and the current of the four pairs of saddle-shaped coils as the optimization parameters to design a set of optimal saddle-shaped coil group parameters, thereby eliminating the adverse effects of the coupling effect of the high magnetic permeability material on the uniformity of the magnetic field generated by the coil from the source.

[0044] comprises the following steps: step 1, determining the structure of the saddle-shaped shim coil group: the saddle-shaped shim coil group is located at the geometric center of a cylindrical magnetic shielding barrel, the saddle-shaped shim coil group is composed of two pairs of main coils and two pairs of shielding coils, the two pairs of main coils are located outside the two pairs of shielding coils, the height of the magnetic shielding barrel is 2H m , the inner radius is R b , and the outer radius is R c , an xyz three-dimensional rectangular coordinate system is established with the geometric center as the origin, the x-axis is parallel to the geometric center connecting line between the coils, the y-axis is parallel to the coincident gap of each pair of coils, and the z-axis is parallel to the axial direction of the magnetic shielding barrel, the structure parameters of the saddle-shaped shim coil group include: the straight line segment height of the first pair of main coils 2l m1 , the straight line segment height of the second pair of main coils 2l m2 , the straight line segment height of the first pair of shielding coils 2l s1 , the straight line segment height of the second pair of shielding coils 2l s2 , the circular arc segment spread angle of the first pair of main coils , the circular arc segment spread angle of the second pair of main coils , the circular arc segment spread angle of the first pair of shielding coils , the circular arc segment spread angle of the second pair of shielding coils , the main coil radius R m , the shielding coil radius R s , and the main coil turn number nm , the number of turns of the shield coil n s , the main coil loop current I m , the shield coil loop current I s , the length of the center cube target area 2L p ; Step 2, by the multi-stage expansion formula of the magnetic vector potential of the saddle coil, the total magnetic moment m generated by the coil set p = 0, the shield coil radius R is solved inversely s ; Step 3, the expression of the magnetic field generated by the saddle coil in the magnetic shielding barrel is disassembled, and the magnetic induction intensity B generated by the coil due to the coupling effect is obtained ox ; Step 4, a target point is selected in the target area, a first target function f1 is established to minimize the coupling rate of the coil set, and a second target function f2 is established to minimize the relative magnetic field deviation of the coil set; Step 5, based on the Matlab platform, the MOPSO algorithm is used to optimize the structure parameters of the saddle shim coil set, and the structure parameter set of the optimal saddle shim coil set is obtained.

[0045] In step 2, the following formula is included:

[0046]

[0047] Where I m and I s , one is positive and the other is negative.

[0048] In step 3, the following formula is included:

[0049]

[0050] Where B x is the total magnetic field in the x direction generated by the saddle coil, B ox is the x direction magnetic field generated by the coupling effect of the saddle coil and the magnetic shielding barrel, B ρ is the ρ direction magnetic field generated by the saddle coil in the cylindrical coordinate system, B φ is the φ direction magnetic field generated by the saddle coil in the cylindrical coordinate system, B oρ is the ρ direction magnetic field generated by the coupling effect in the cylindrical coordinate system, B oφ is the φ direction magnetic field generated by the coupling effect in the cylindrical coordinate system, ρ is the radial distance, and φ is the azimuth angle.

[0051] In step 4, the following formula is included:

[0052]

[0053] s.t.0.15R m <l j <2R m (j = 1, 2, 3, 4)

[0054] 0.08 < R s <0.95R b (j = 1, 2, 3, 4)

[0055]

[0056] l j+1 -l j ≥l min

[0057]

[0058] wherein f1 is the first objective function, N p is the number of target points, N p is a positive integer, B ox (x, y, z) is the x-direction magnetic field generated by the coupling effect of the saddle coil and the magnetic shielding barrel at any point, B x (0, 0, 0) is the total x-direction magnetic field generated by the saddle coil set at the coordinate origin under the ferromagnetic boundary, ε is the magnetic field uniformity, B x (x, y, z) is the total x-direction magnetic field generated by the saddle coil set at any point under the ferromagnetic boundary, l j is the set of half-heights of the straight segments of the saddle coil set, is the set of half-opening angles of the circular arc segments of the saddle coil set, l min is a preset value, is a preset value.

[0059] A high-uniformity saddle shim coil design method for eliminating the magnetic shielding coupling effect, comprising two pairs of main coils and two pairs of shielding coils, decomposes the total magnetic induction intensity expression generated by the saddle coil set under the ferromagnetic boundary into two parts of the magnetic induction intensity generated by the coil set under the free boundary and the magnetic induction intensity generated by the coupling effect, and obtains an analytical expression of the magnetic induction intensity additionally generated by the coil due to the coupling effect. Through a multi-objective optimization algorithm, the expression of the ratio of the magnetic field generated by the coil due to the coupling effect to the magnetic field generated by the coil at the center under the ferromagnetic boundary and the expression of the ratio of the magnetic field generated by the coil to the magnetic field generated by the coil at the center are taken as two objective functions, the height of the straight segments of the four pairs of saddle coils, the opening angle of the circular arc segments, and the number of turns, the size and direction of the current of the coil are taken as the optimization parameters for design, and a set of optimal saddle coil set parameters are obtained. The saddle uniform magnetic field coil set optimized by the method can eliminate the adverse effects of the coupling effect of the high magnetic permeability material on the uniformity of the magnetic field generated by the coil from the source, ensure higher magnetic field uniformity inside the coil, faster magnetic field attenuation outside the coil, and have a larger magnetic field uniformity area under a relatively simple structure.

[0060] A high uniformity saddle-shaped shim coil design method for eliminating the magnetic shielding coupling effect, the coil group has a relatively simple configuration, including two pairs of main coils and two pairs of shielding coils, the magnetic field generated by the saddle-shaped coil group under the ferromagnetic boundary is decomposed into two parts, the magnetic field generated by the coil under the free boundary and the magnetic field generated by the coupling effect between the coil and the magnetic shielding device, and the analytical expression of the magnetic induction intensity generated by the coupling effect is obtained. Using the optimization algorithm, the ratio of the magnetic field generated by the coupling effect between the magnetic shielding structure and the saddle-shaped coil to the center magnetic field of the coil under the ferromagnetic boundary and the ratio of the magnetic induction intensity of the coil to the center magnetic induction intensity of the coil are used as two optimization functions, and the circular segment spread angle of the saddle-shaped coil group is optimized The height 2l of the straight line segment of the saddle-shaped coil and the number of turns n, the direction and size of the current I are used as the optimization parameters, and the two objective functions are minimized. This method is different from the common self-shielding coil design idea, which does not indirectly suppress the coupling effect by improving the attenuation of the coil outside, so it is not necessary to select target points in the inside and outside of the coil to calculate the internal magnetic field uniformity and the external magnetic field attenuation, respectively. Only by selecting target points in the inside of the coil can the same effect be achieved, reducing the calculation amount by 50%. After optimization by this method, the magnetic field generated by the coupling effect in the target area of the coil group is extremely small, basically achieving the effect of eliminating the coupling effect. The magnetic field uniformity in the target area and the attenuation of the coil outside are better than those of the traditional saddle-shaped coil, and in a relatively simple configuration, the center shim area of the coil is still large, realizing the similar external magnetic field attenuation and higher internal magnetic field uniformity as the self-shielding saddle-shaped coil.

[0061] The method comprises the following steps:

[0062] Step 1, selecting a suitable main coil radius R according to the structural parameters of a known cylindrical magnetic shielding barrel m . The saddle-shaped shim coil group is designed to consist of two pairs of outer main coils and two pairs of inner shielding coils, and the current directions of the two pairs of coils are opposite. A three-dimensional rectangular coordinate system is established with the geometric center of the cylindrical magnetic shielding barrel as the origin, and each pair of coils is symmetrically distributed in space.

[0063] Step 2, in order to make the magnetic field outside the coil decay as quickly as possible, combining the properties of the magnetic dipole in the multi-stage expansion of the magnetic vector potential generated by the saddle-shaped coil, setting the total magnetic moment generated by the coil group to 0, and establishing a functional relationship according to the three groups of parameters of the radius, straight line segment height and circular segment spread angle of the saddle-shaped coil, the radius R s of the shielding coil is inversely solved.

[0064] Step 3, combining the conditions of different magnetic permeabilities of the ferromagnetic boundary material and the mirror method, calculating the magnetic induction intensity generated by the reflection of the magnetic current of the saddle-shaped coil by the magnetic shielding end cover, and deriving the x-direction magnetic induction intensity expression B xThe analytical expression of the magnetic induction intensity generated by the coupling effect of the coil set is given by decomposing the magnetic induction intensity generated by the coupling effect from the total magnetic field generated by the coil set in the magnetic shielding barrel ox .

[0065] Step 4, determining the target region volume, selecting a suitable target point N p In order to make the coil have a wider and consistent working magnetic field region, the target region should be relatively large, and the target region selected by the application is a cube with a half side length of The number of target points is 10, which are the 8 vertices and 2 central face points of the first quadrant cube of the target region.

[0066] Step 5, establishing two optimization design objectives (both taking the minimum value of the sum of absolute values): ① the ratio of the magnetic induction intensity generated by the coupling effect between the coil and the magnetic shielding barrel in the cylindrical magnetic shielding barrel to the central magnetic induction intensity of the coil; and ② the ratio of the total magnetic field generated by all coils to the central magnetic field under the ferromagnetic boundary.

[0067] Step 6, converting the two design objectives into a double-objective optimization problem with the coil structure parameters as the constraint conditions, and using the Multiple Objective Particle Swarm Optimization (MOPSO) optimization algorithm to solve, thereby obtaining the parameter set of the optimal saddle-shaped shimming coil set.

[0068] Step 7, using COMSOL to establish a finite element simulation model, and substituting the optimal coil set parameter set obtained by the algorithm for verification. The magnetic induction intensity and the magnetic field uniformity in the uniform region inside the free boundary and the ferromagnetic boundary, the magnetic induction intensity generated by the coupling effect, and the coupling rate of the coil are calculated respectively. The effect of suppressing the coupling effect and the size of the magnetic field uniformity generated by the coil set under the ferromagnetic boundary are verified by the calculation results of the finite element simulation.

[0069] The expression of the magnetic induction intensity generated by the saddle-shaped coil set at any point (ρ, φ, z) in the target region in the cylindrical magnetic shielding barrel in step 3 is:

[0070]

[0071] wherein G m , α b , β b , γ b , α c , β c , γ c are intermediate quantities defined for simplifying the expression, and the specific expressions are as follows:

[0072]

[0073] α b = μ0(μ r -1)I m ′(kR j )K m (kR b )

[0074] β b = μ0(μ r I m ′(kR b )K m (kR b )-I m ′(kR b )K m (kR b ))

[0075] γ b = μ0(μ r -1)I m ′(kR b )K m (kR c )

[0076] α c = μ0(μ r -1)I m ′(kR j )K m (kR c )

[0077] β c = μ0(μ r -1)I m ′(kR b )K m (kR c )

[0078] γ c = μ0(μ r I m ′(kR c )K m (kR c )-I m (kR c )K m ′(kR c ))

[0079] Among them, ρ, φ, and z are the three coordinate parameters of the target point in cylindrical coordinates. ρ represents the distance from the projection on the plane to the coordinate origin, parameter φ represents the azimuth of the projection point, and parameter z represents the distance from the point to the plane where the origin is located. j is the number of items in the parameter set, j = 1 is the first item in the parameter set, M is the logarithm of the saddle coil, which is taken as 4; μ0 is the vacuum permeability, μ r is the relative magnetic permeability of the magnetic shielding material, R j is the radius set of the saddle coil group, R j =[R m ,R m ,R s ,R s ], R m The radius of the main coil, R s is the radius of the shielding coil, I j is the current set of the closed loop of the saddle coil group, I j =[I m ,I m ,I s ,I s ], I m The current of the main coil, I s is the current of the shielding coil, n j is the number of turns of the saddle coil group, n j =[n m ,n m ,n s ,n s ],n m The number of turns of the main coil, n s is the number of turns of the shielding coil. When j=2, R2 represents R j The second item R of the set m ; When j = 3, 2l3 means 2l j The third item of the set 2l s1 .

[0080] m is the summation upper limit term in the formula, k is the integral variable, R b and R c are the inner radius and outer radius of the magnetic shielding structure, I m and I m ′ represents the first kind of modified Bessel function and its derivative, K m and K m ′ represents the first kind of modified Bessel function and its derivative respectively; i is the imaginary unit; H m is the half length of the magnetic shielding barrel. p is the number of current reflections. When the coil height is close to the height of the magnetic shielding device, the reflection effect of the end cover on the coil current seriously affects the coil magnetic field. represents the Fourier transform corresponding to the total current density.

[0081]

[0082] where 2l j is the set of the straight line segment height of the saddle coil set, 2l j = [2l m1 , 2l m2 , 2l s1 , 2l s2 ], 2l m1 and 2l m2 are the straight line segment height of the two main coils, 2l s1 and 2l s2 are the straight line segment height of the two shield coils, respectively, is the set of the circular segment spread angle of the saddle coil set, and are the straight line segment height of the two main coils, respectively, and are the straight line segment height of the two shield coils, respectively; e is the natural exponent; δ m,odd is the Dirac function, which means δ m,odd = 1 when m is odd.

[0083] The expression of the magnetic induction intensity generated by the coupling effect of the saddle coil set in the cylindrical magnetic shielding barrel in step 3 is:

[0084]

[0085] The expression of the first optimization objective function in step 4 is:

[0086]

[0087] s.t. 0.15R m < l j < 2R m (j = 1, 2, 3, 4)

[0088]

[0089] l j+1 < l j ≥ l min

[0090]

[0091] where N p is the number of target points in the uniform area inside the coil, 2l min is the minimum height of the straight line segment of the saddle coil, The minimum value of the arc segment of the saddle coil is the minimum value of the arc segment. Since the magnetic field components in y and z directions are very small, they can be ignored. Therefore, the x-direction main magnetic field generated by the coil can be approximated as the total magnetic field. B ox (x, y, z) is the x-direction magnetic induction intensity generated by the coupling effect at any target point (x, y, z), B x (0, 0, 0) is the x-direction magnetic induction intensity generated by the coil at the origin (0, 0, 0) under the ferromagnetic boundary. Since the direction of the magnetic field is determined, the direction of the vector does not need to be considered. The conversion relationship between the x-direction magnetic induction intensity generated by the coupling effect in the cylindrical coordinate system and the rectangular coordinate system is as follows:

[0092]

[0093] Compared with the decoupling of the coil set generated by only the coupling effect, the comparison of the coupling rate improves the reliability of the decoupling of the coil set, and to some extent, increases the coil constant. In order to avoid the generated magnetic induction intensity in opposite directions from canceling each other out, the sum of their absolute values is taken to ensure the reliability of the final result.

[0094] The second optimization objective function described in step 4 is the sum of the absolute values of the ratio of the total magnetic field to the central magnetic field of the coil at all target points under the ferromagnetic boundary, and its expression is as follows:

[0095]

[0096] Since the direction of the magnetic field is determined, the direction of the vector does not need to be considered. The conversion relationship between the magnetic induction intensity generated by the coil under the ferromagnetic boundary in the cylindrical coordinate system and the rectangular coordinate system is as follows:

[0097]

[0098] wherein the constraint conditions of the saddle coil structure parameters are the same as the objective function f1. In order to avoid the generated magnetic induction intensity in opposite directions from canceling each other out, the sum of their absolute values is taken to ensure the reliability of the final result.

[0099] The designed saddle shim coil set includes two pairs of main coils on the outside and two pairs of shield coils on the inside. A three-dimensional rectangular coordinate system is established with the center of the target uniform area as the origin, and the four pairs of saddle shim coils are symmetrically distributed. Wherein j is the number of items in the parameter set, j = 1 is the first item in the parameter set, R j is the radius set of the saddle coil set, R j = [R m , R m , R s , R s ], R m is the radius of the main coil, R s is the radius of the shield coil, Ij is the current set of the closed loop of the saddle coil group, I j =[I m ,I m ,I s ,I s ], I m The current of the main coil, I s is the current of the shielding coil, n j is the number of turns of the saddle coil group, n j =[n m ,n m ,n s ,n s ],n m The number of turns of the main coil, n s is the number of turns of the shielding coil, 2l j is the set of straight line heights of the saddle coil group, 2l j =[2l m1 ,2l m2 ,2l s1 ,2l s2 ],2l m1 and 2l m2 are the heights of the straight sections of the two main coils, 2l s1 and 2l s2 are the straight line heights of the two shielding coils, is the set of arc segment angles of the saddle coil group, and are the straight line heights of the two main coils, and are the heights of the straight segments of the two shielding coils respectively. When j = 2, R2 represents R j The second item R of the set m ; When j = 3, 2l3 means 2l j The third item of the set 2l s1 .

[0100] In order to make the external magnetic field of the saddle-shaped shim coil group decay most rapidly, the multipole expansion of the magnetic vector potential is used to make its magnetic dipole moment 0, thereby inversely solving the radius R of the shielding coil. s When there is a current loop, the magnetic moment m of the coil of any shape p Can be expressed as:

[0101]

[0102] Where, r' is the position vector of the current distribution source point, J is the current density of the coil, V' is the volume of the current density, n is the number of turns of any coil, I is the current of any loop, L denotes the closed loop boundary composed of the coil, S' is the projection area of the current-carrying coil in the r' x dr' direction. By substituting the structural parameters of the saddle-shaped shim coil set, and letting the magnetic dipole moment m generated by the saddle-shaped shim coil set be 0, the radius R of the shield coil can be solved p . s

[0103]

[0104] Where, the current direction of the main coil and the shield coil is opposite, without fixed direction, and the symbol represents the current direction of each.

[0105] The magnetic induction intensity expression generated by the coupling effect between the coil and the magnetic shielding barrel is derived. The magnetic induction intensity generated by the saddle-shaped coil set under the ferromagnetic boundary is the sum of the magnetic induction intensity generated by the saddle-shaped coil set under the free boundary and the magnetic induction intensity generated by the coupling effect between the coil and the magnetic shielding barrel. By separating the magnetic induction intensity generated by the coupling effect from the total magnetic field generated by the saddle-shaped coil set under the ferromagnetic boundary, an accurate analytical expression of the magnetic induction intensity generated by the coupling effect is given. Since the y-direction and z-direction magnetic field components generated by the saddle-shaped coil are very small and can be ignored, the generated x-direction main magnetic field can be approximated as the total magnetic field. Therefore, the cylindrical coordinate system needs to be converted to the rectangular coordinate system, and the z-direction magnetic induction intensity does not need to be calculated. The parameter p in the cylindrical coordinate system represents the distance from the projection point to the coordinate origin on the plane, the parameter φ represents the azimuth angle of the projection point, and the parameter z represents the distance from the point to the plane where the origin is located. The conversion relationship between the specific cylindrical coordinate system expression and the rectangular coordinate system is as follows:

[0106]

[0107]

[0108] Where, B oρ (ρ,φ,z) is the ρ-direction magnetic induction intensity generated by the coupling effect at any point (ρ,φ,z) in the cylindrical coordinate system, ρ is the radial distance, φ is the azimuth angle, and z is the height. B oφ (ρ,φ,z) is the φ-direction magnetic induction intensity generated by the coupling effect at any point (ρ,φ,z), B ox (x,y,z) is the x-direction magnetic induction intensity generated by the coupling effect at any point (x,y,z) in the rectangular coordinate system; μ0 is the vacuum permeability, p is the current reflection number, m is the upper limit term of the summation, k is the integral variable, H m is the half length of the magnetic shielding barrel, I m is the first type of modified Bessel function, I​m K is its derivative, K m K is its derivative, K m K is its derivative, min[R j ] represents the minimum value of R j in the set.

[0109] Determine the target region volume, select the appropriate target point. In order to make the coil inside a wider consistent magnetic field region, the target region is relatively large, the target region cube half length selected by the application Select the spatial position point in the target region for calculating the target function, called the target point, the number of target points is a positive integer N p Unlike the traditional self-shielded coil, which needs to select target points in the coil interior and exterior respectively, and calculate the uniformity of the coil interior magnetic field and the decay of the external magnetic field respectively. The target points selected by the application are all in the target uniform region inside the coil, so 50% of the data points can achieve the same effect, simplifying the selection process of the target point, reducing the calculation amount of the optimization process, and greatly improving the optimization efficiency.

[0110] Determine two optimization function expressions. Place the designed saddle-shaped shim coil group in the known magnetic shielding environment, in order to maximize the negative impact of the coupling effect on the coil magnetic field from the root, the sum of the absolute values of the coupling rate of the coil magnetic field at all target points (the ratio of the x-direction magnetic induction intensity generated by the coupling effect between the coil and the magnetic shielding barrel to the x-direction magnetic induction intensity at the center point of the coil under the ferromagnetic boundary) as the target function f1; in order to further improve the uniformity of the magnetic field in the center target region of the coil, the sum of the absolute values of the ratio of the total x-direction magnetic field at all target points of the designed saddle-shaped shim coil group under the ferromagnetic boundary to the center magnetic field of the coil as the target function f2.

[0111]

[0112] s.t.0.15R m < l j <2R m (j=1,2,3,4)

[0113] 0.08<R s <0.95R b (j=1,2,3,4)

[0114]

[0115] l j+1 -l j ≥l min

[0116]

[0117] Where, the total magnetic field of the coil set in the x direction at any point under the ferromagnetic boundary is B x (x, y, z), the coupling effect of the coil set and the magnetic shielding structure generates a magnetic field in the x direction at any point B ox (x, y, z), the total magnetic field of the coil set in the x direction at the coordinate origin under the ferromagnetic boundary is B x (0, 0, 0); ε represents the uniformity of the coil, the inner diameter of the magnetic shielding barrel is Rb, and the minimum distance between the straight line segments of adjacent coils is 2l min , and the minimum circular segment spread angle difference is

[0118] In order to improve the credibility of the suppression effect of the coil set on the magnetic shielding effect, the coupling rate is used to represent the form (coupling magnetic induction intensity / total magnetic induction intensity), which also increases the coil constant (magnetic induction intensity at the center point of the coil) to a certain extent; and in order to avoid the mutual cancellation of the magnetic induction intensity in opposite directions, the sum of the absolute values is taken to ensure the accuracy of the final result.

[0119] Step 6, use the multiple objective particle swarm optimization algorithm (MOPSO) for optimization calculation. In order to facilitate actual processing and assembly, reduce the amount of optimization parameters, and improve the efficiency of the algorithm, let the current and the number of turns of the main coil and the shielding coil be equal, that is, I m = I s = I, n m = n s = n. A set of straight line segment heights 2l mi , circular segment spread angle widths and straight line segment heights 2l si , circular segment spread angle widths of a set of saddle-shaped main coils are obtained from a set of randomly generated particles. Through the above four groups of parameters and the radius R m of the main coil, the total magnetic moment generated by the saddle-shaped shim coil set is calculated to be 0, and the size of the radius R s of the shielding coil is inversely solved. Substitute the above parameters to solve the optimal solution (minimum value) of the objective functions f1 and f2, and obtain the parameter group with the best performance, which is the designed saddle-shaped shim coil set parameter set.

[0120] Step 7, respectively establish the finite element simulation model of the saddle-shaped shim coil set under the free boundary and the ferromagnetic boundary, put the obtained optimal coil parameter set into, respectively calculate the magnetic induction intensity distribution and the magnetic field uniformity of the coil set in the target area of the free boundary and the ferromagnetic boundary, and calculate the coupling effect generated by the magnetic induction intensity and the coupling rate of the coil. Among them, the magnetic induction intensity generated by the coupling effect is the difference between the magnetic induction intensity generated by the coil set under the ferromagnetic boundary and the magnetic induction intensity generated by the coil set under the free boundary. The effect of suppressing the coupling effect of the coil set and the size of the magnetic field uniformity generated by the coil set under the ferromagnetic boundary are verified by the simulation results of the finite element.

[0121] A high-uniformity saddle-shaped shim coil design method for eliminating the coupling effect of magnetic shielding, comprising the following specific steps:

[0122] Step 1, in order to maintain the relatively simple structure of the coil and the relatively high internal magnetic field uniformity, the designed saddle-shaped shim coil set is composed of two pairs of saddle-shaped main coils and two pairs of concentric saddle-shaped shielding coils, and the coil set is placed in the geometric center of the cylindrical magnetic shielding device. The radius of the two pairs of saddle-shaped main coils is R m , the height set of the straight line is 2l mi =[2l m1 ,2l m2 ], and the spread angle set of the circular arc segment is The number of turns of the coil is n m , and the current of the coil is I m ; the radius of the two pairs of saddle-shaped shielding coils is R s , the height set of the straight line is 2l si =[2l s1 ,2l s2 ], and the spread angle set of the circular arc segment is The number of turns of the coil is n s , and the current of the coil is I s . The specific structure is shown in Figure 1 , Figure 2 .

[0123] After determining the structure parameters (height 2H m , inner diameter R b , outer diameter R c ) and material properties (relative permeability μ r ) of the high-permeability magnetic shielding device and the radius R m of the designed main coil, a three-dimensional rectangular coordinate system is established with the geometric center point of the saddle-shaped shim coil set as the origin. Among them, the x-axis direction is consistent with the connection line of the geometric center of each saddle-shaped coil, the y-axis direction is consistent with the coincident gap of the saddle-shaped coil, and the z-axis direction is consistent with the axial direction of the cylindrical magnetic shielding barrel.

[0124] Step 2, in order to make the saddle-shaped shim coil group outside the magnetic field most rapidly decay, by the multi-stage expansion of the magnetic vector potential, the magnetic dipole moment is 0, so as to solve the shielding coil radius R s . The current distribution of the coil at any point r(ρ, φ, z) in space excites the magnetic vector potential A(r) which can be expressed as:

[0125]

[0126] Wherein, r and r' represent the position vector in the cylindrical coordinate system, the parameter ρ in the cylindrical coordinate system represents the distance from the projection to the coordinate origin on the plane, the parameter φ represents the azimuth angle of the projection point, and the parameter z represents the distance of the point from the origin plane; r(ρ, φ, z) and r'(R, φ', z') represent the position vectors of the magnetic field target point (observation point) and the current distribution source point in the cylindrical coordinate system respectively; μ0 is the magnetic permeability of vacuum, J(r ′ ) is the current density, and V' is the volume of the current density; when the observation point is much larger than the linearity of the current distribution area, Taylor series expansion at r' = 0 can be:

[0127]

[0128] Wherein, I m represents the first type of modified Bessel function, K m represents the second type of modified Bessel function, R is the radius of the saddle-shaped coil, e is the natural index, i is the imaginary unit, k is the integral variable, m is the upper limit item of the summation, and the magnetic vector potential excited by the coil current at any point r(ρ, φ, z) in space can be written as:

[0129]

[0130] The first term A (0) (r) and the second term A (1) (r) are the magnetic vector potentials generated by the magnetic monopole and the magnetic dipole respectively, and the third term A (2) (r) is the magnetic vector potential generated by the magnetic quadrupole and above. Since the divergence of the current density is 0, the magnetic vector potential A (0) (r) of the magnetic monopole is also constant 0; and since the magnetic vector potential of the high-order magnetic multipole decays faster, at a sufficiently distant observation point, the third term A (2) (r) and the following terms in the magnetic multi-stage expansion can be ignored. Therefore, in order to make the external magnetic field decay most rapidly, only the magnetic vector potential A (1) (r) of the magnetic dipole is 0. The magnetic dipole vector potential A (1) (r) and the magnetic dipole moment m p have a certain functional relationship as follows:

[0131]

[0132] where r is the modulus of the position vector r, r = |r|. Thus, it is only necessary to make the magnetic dipole moment m p generated by the saddle-shaped shim coil set equal to 0, so that the magnetic dipole vector potential A (1) (r) is also equal to 0. When the current loop exists, the magnetic moment m p of the coil of any shape can be expressed as:

[0133]

[0134] where J is the current density of the coil, I is the current size of the coil, n is the number of turns of the coil, L denotes the boundary of the closed coil loop, and S' is the projection area of the current-carrying coil in the r' x dr' direction. Substituting the structural parameters of the saddle-shaped shim coil set, making the magnetic dipole moment m p generated by the saddle-shaped shim coil set equal to 0, the radius R s of the shield coil can be solved.

[0135]

[0136] where the current direction of the main coil is opposite to that of the shield coil, and the symbol represents the direction thereof.

[0137] Step 3, decompose the total magnetic field expression generated by the saddle-shaped coil in the magnetic shielding barrel to obtain the mathematical model of the magnetic induction intensity B ox extra generated by the coil according to the coupling effect. It is divided into 5 small steps:

[0138] Step 3.1, derive the analytical expression of the total magnetic induction intensity and the current density component generated by a single saddle-shaped coil in the vacuum.

[0139] The specific form of the magnetic vector potential A(r) expansion in step 3 is as follows:

[0140]

[0141] where i is an imaginary unit, and are the Fourier transforms of the projections J φ′ (φ', z') and J z′ (φ', z') of the current density J(r') in the φ' direction and in the z' direction, respectively, and and satisfy the current continuity condition at any source point, that is:

[0142]

[0143] and the magnetic induction intensity B and the magnetic vector potential A satisfy The divergence of the magnetic induction B is always zero, so the expression of the magnetic induction B can be obtained. The mathematical model of the total magnetic induction B generated by a single saddle coil at any point (p, f, z) in vacuum is:

[0144]

[0145] The current density component J carried by the saddle coil φ′ (φ', z') and can be expressed as:

[0146]

[0147] where H is the Heaviside function and d is the Dirac function. J φ′ The Fourier transform of (φ', z') is:

[0148]

[0149] where 2H m is the length of the magnetic shielding barrel, is the opening angle of the saddle coil, 2l is the height of the straight section of the saddle coil, and d m,odd represents d m,odd = 1 when m is odd.

[0150] Step 3.2, derive the analytical expression of the magnetic induction generated by a single saddle coil in a magnetic shielding barrel without end caps.

[0151] When the coil is placed in a magnetic shielding device made of high permeability material, serious coupling effect will occur, affecting the uniformity of the magnetic field generated by the coil. The total magnetic field in the z direction generated by the coil in the magnetic shielding barrel without end caps can be calculated according to the sum of the magnetic field generated by the equivalent current on the surface of the material:

[0152]

[0153] where R b and R c are the inner and outer radii of the cylindrical magnetic shielding barrel, I m ' represents the derivative of the first kind of modified Bessel function, K' m represents the derivative of the second kind of modified Bessel function, and are the Fourier transform expressions of the equivalent surface current on the inner and outer surfaces of the hollow cylindrical magnetic shielding barrel, which can be determined by the boundary conditions of the magnetic permeability of different materials.

[0154]

[0155] where μ r is the relative magnetic permeability of the magnetic shielding material, which can be solved from the above formula:

[0156]

[0157] wherein α b , β b , γ b , α c , β c , γ c are intermediate quantities defined for simplicity of expression, whose specific expressions are as follows:

[0158] α b = μ0(μ r - 1)I m '(kR j )K m (kR b )

[0159] β b = μ0(μ r I m '(kR b )K m '(kR b )- I m '(kR b )K m (kR b ))

[0160] γ b = μ0(μ r - 1)I m '(kR b )K m '(kR c )

[0161] α c = μ0(μr- 1)I m '(kR j )K m (kR c )

[0162] β c = μ0(μ r - 1)I m '(kR b )K m (kR c )

[0163] γ c = μ0(μ r I m '(kR c )K m (kR c )- I m (kR c)K m ′(kR c ))

[0164] The mathematical model of the magnetic induction intensity generated by a single saddle coil in a hollow magnetic shielding barrel is derived as follows:

[0165]

[0166] wherein G m is an intermediate quantity defined for the purpose of simplifying the expression, and the specific expression thereof is as follows:

[0167]

[0168] Step 3.3, deriving the analytical expression of the total magnetic induction intensity generated by a single saddle coil in a magnetic shielding barrel with an end cap.

[0169] When the magnetic shielding barrel is provided with an end cap, the magnetic field generated by the coil will be changed due to the influence of the end cap reflecting current, especially when the height of the coil is close to the height of the magnetic shielding device, the reflection effect of the end cap on the coil current will seriously affect the magnetic field of the coil. The mirror method considers that the magnetic field generated by the coil due to the action of the end cap can be equivalent to the superposition of the magnetic field generated by the original current and the mirror current. The magnetic induction intensity generated by a single saddle coil in a magnetic shielding barrel with an end cap can be represented as:

[0170]

[0171] wherein p is the number of current reflection, the original current and the first reflected current have the greatest influence on the magnetic induction intensity generated by the coil; the Fourier transform of the current density component of the saddle coil in the magnetic shielding device with an end cap is as follows:

[0172]

[0173] Step 3.4, simplifying the analytical expression of the magnetic induction intensity B x generated by the saddle shim coil set in the magnetic shielding barrel with an end cap.

[0174] Since the expression of the magnetic induction intensity generated by the above single saddle coil is relatively complex, and more pairs of saddle coils will increase the difficulty of calculation, the expression is simplified by the characteristics of even function and the conversion of Euler formula to reduce the calculation amount of the subsequent optimization algorithm. Moreover, since the magnetic field components in the y direction and the z direction generated by the saddle coil are very small and can be ignored, the main magnetic field in the x direction generated can be approximately considered as the total magnetic field, so the cylindrical coordinate system needs to be converted to the rectangular coordinate system, and the magnetic induction intensity in the z direction does not need to be calculated again. The total magnetic induction intensity expression generated by the saddle shim coil set after simplification is as follows:

[0175]

[0176] Where j is the number of items in the parameter set, j = 1 is the first item in the parameter set, R j is the radius set of the saddle coil group, R j =[R m ,R m ,R s ,R s ], R m The radius of the main coil, R s is the radius of the shielding coil, I j is the current set of the closed loop of the saddle coil group, Ij=[I m ,I m ,I s ,I s ], I m The current of the main coil, I s is the current of the shielding coil, n j is the number of turns of the saddle coil group, n j =[n m ,n m ,n s ,n s ],n m The number of turns of the main coil, n s is the number of turns of the shielding coil, 2l j is the set of straight line heights of the saddle coil group, 2l m1 and 2l m2 are the heights of the straight sections of the two main coils, 2l s1 and 2l s2 are the straight line heights of the two shielding coils, is the set of arc segment angles of the saddle coil group, and are the straight line heights of the two main coils, and are the heights of the straight segments of the two shielding coils respectively. When j = 2, R2 represents R j The second item R of the set m ; When j = 3, 2l3 means 2l j The third item of the set 2l s1 .

[0177] The formula k, p, m are parameters that determine the accuracy of the model, theoretically, the greater the value, the more accurate the calculation result, but at the same time, the time cost of calculation will increase, and too large m will also cause overflow problem in the calculation process. Therefore, through finite element simulation verification, the upper limit of integral k is 1000, the reflection times p=0, ±1, ±2, ±3, the maximum value of m is 37 when B ρ and B oρ , the maximum value of m is 35 when B φ and B oφ , which not only ensures the accuracy of the calculation, but also has a faster operation speed.

[0178] Step 3.5, derive the analytical expression of the magnetic induction B ox generated by the coupling effect of the saddle coil group.

[0179] By decomposing the expression of the magnetic induction generated by the saddle coil group under the ferromagnetic boundary into two parts: the magnetic induction generated under the free boundary and the magnetic induction generated by the coupling effect between the coil and the magnetic shielding structure, the analytical expression of the magnetic induction generated by the coupling effect between the saddle coil group and the magnetic shielding barrel is obtained. The expression of the magnetic induction generated by the coupling effect is as follows:

[0180]

[0181] The conversion relationship between the total magnetic field B x generated by the saddle coil in the x direction and the x direction magnetic field B ox generated by the coupling effect between the coil and the magnetic shielding structure is as follows:

[0182]

[0183] Step 4, determine the target region volume and select appropriate target points. According to the structural parameters of the magnetic shielding device, select the appropriate main coil radius R m , in order to ensure a larger uniform region volume, select as the target region cubic edge length 2L p . According to the general magnetic field distribution generated by the saddle coil, select target points in the target cubic region, uniform, contain more edge points, extreme points, the selection will make the calculation result more authoritative and typical. Since the above mathematical models for calculating the magnetic field have axial symmetry, this study selects 10 target points, which are distributed in the first quadrant of the target region, and the coordinates of the 10 target points are as follows:

[0184] (0, 0, 0), (L p , 0, 0), (0, L p , 0), (0, 0, L p ), (L p, 0, L p ), (L p , 0 p , 0), (0, L p , L p ), (L p , L p , L p ),

[0185]

[0186] The above are 8 vertexes and 2 face center points of the first quadrant cube of the target region.

[0187] Step 5, respectively, establish a first objective function f1: the sum of the absolute values of the ratio of the magnetic induction intensity generated by the coupling effect of all target points to the central magnetic induction intensity of the coil; a second objective function f2: the sum of the absolute values of the ratio of the total magnetic field of all target points under the ferromagnetic boundary to the central magnetic field of the coil, and give the limit condition of the coil structure parameter. Take the absolute value in order to avoid the mutual offset of the magnetic induction intensity in the opposite direction, affecting the accuracy of the final result.

[0188]

[0189] s.t.0.15R m <l j <2R m (j=1, 2, 3, 4)

[0190] 0.08<R s <0.95R b (j=1, 2, 3, 4)

[0191]

[0192] l j+1 -l j ≥l min

[0193]

[0194] Wherein, N p is the number of target points, ε represents the relative magnetic field deviation of the magnetic field generated by the coil, the total magnetic field generated by the coil group in the x direction at any point (x, y, z) under the ferromagnetic boundary is B x (x, y, z), the x direction magnetic field generated by the coupling effect of the coil group and the magnetic shielding structure at any point (x, y, z) is B ox (x, y, z), the total magnetic field generated by the coil group in the x direction at the coordinate origin under the ferromagnetic boundary is B x (0, 0, 0); ε represents the uniformity of the coil, and the inner diameter of the magnetic shielding barrel is R b;2l min the minimum height difference of the straight line segment between each pair of adjacent coils, the minimum difference of the arc segment spread angle.

[0195] Step 6, the design of eliminating the magnetic shielding effect of the saddle-shaped uniform coil set is converted into a double-target optimization problem with the coil structure parameters as the constraint conditions. In order to reduce the calculation amount of the algorithm, improve the operation speed, and facilitate subsequent coil processing and assembly, the number of turns of the main coil and the shielding coil is set to be consistent with the size of the current, that is, only the straight line segment height 2l mi , the arc segment spread angle width and the straight line segment height 2l si , the arc segment spread angle width of the saddle-shaped shielding coil are set as four groups of structure parameters to be optimized. A group of particles is randomly generated using the multiple objective particle swarm optimization (MOPSO) optimization algorithm, and the total magnetic moment generated by the saddle-shaped shim coil is 0. The radius R s of the shielding coil is solved by inverse solution. The optimal solution (minimum value) of f1 and f2 is solved by substituting the above parameters, and a group of eight parameters with the best performance is obtained, that is, the optimal saddle-shaped shim coil set parameter set.

[0196] Step 7, the finite element simulation models of the saddle-shaped shim coil set under free boundary and ferromagnetic boundary are established respectively, the optimal coil parameter set obtained is substituted, the magnetic induction intensity distribution and the magnetic field uniformity of the coil set in the target region under free boundary and ferromagnetic boundary are calculated respectively, and the coupling effect of the magnetic induction intensity and the coupling rate of the coil are calculated. The value is the difference between the magnetic induction intensity generated by the coil set under the ferromagnetic boundary and the magnetic induction intensity generated by the coil set under the free boundary. The effect of suppressing the coupling effect and the size of the magnetic field uniformity generated by the coil set under the ferromagnetic boundary are verified by the calculation results of the finite element.

[0197] The contents not described in detail in the specification of the present application belong to the prior art known to those skilled in the art. It is indicated here that the above description is helpful for those skilled in the art to understand the present application, but does not limit the protection scope of the present application. Any implementation of the above description, equivalent replacement, modification, improvement and / or deletion of the above description without departing from the essential content of the present application falls within the protection scope of the present application.

Claims

1. A method for designing a highly uniform saddle-shaped shim coil for eliminating magnetic shielding coupling effect, characterized in that: The method includes decomposing the total magnetic induction intensity expression generated by the saddle coil group under the ferromagnetic boundary into two parts: the magnetic induction intensity generated by the coil group under the free boundary and the magnetic induction intensity generated by the coupling effect, thereby obtaining an analytical expression for the additional magnetic induction intensity generated by the coil due to the coupling effect; using a multi-objective optimization algorithm, the expression of the ratio of the magnetic field generated by the coil due to the coupling effect to the magnetic field generated by the coil at the center under the ferromagnetic boundary and the expression of the ratio of the magnetic field generated by the coil at the ferromagnetic boundary to the magnetic field generated by the coil at the center are used as two objective functions, and the straight segment heights, arc segment angles, number of coil turns, and current of the four pairs of saddle coils are designed as parameters to be optimized, thereby obtaining a set of optimal saddle coil group parameters, thereby eliminating the adverse effect of the coupling effect of high magnetic permeability materials on the magnetic field generated by the coil on the uniformity of the magnetic field generated by the coil from the source to the greatest extent; The following steps are involved: Step 1: Determine the structure of the saddle-shaped shim coil group: the saddle-shaped shim coil group is located at the geometric center of the cylindrical magnetic shielding barrel. The saddle-shaped shim coil group consists of two pairs of main coils and two pairs of shielding coils. The two pairs of main coils are located outside the two pairs of shielding coils. The height of the magnetic shielding barrel is 2H. m , the inner radius is R b , the outer radius is R c , establish an xyz three-dimensional rectangular coordinate system with the geometric center as the origin, the x-axis is parallel to the line connecting the geometric centers of each coil, the y-axis is parallel to the gap between each pair of coils, and the z-axis is parallel to the axial direction of the magnetic shielding barrel. The structural parameters of the saddle-shaped shim coil group include: the height of the straight segment of the first pair of main coils is 2l m1 , the height of the straight section of the second pair of main coils is 2l m2 , the height of the straight section of the first pair of shielding coils is 2l s1 , the height of the straight section of the second pair of shielding coils is 2l s2 , the arc segment angle of the first pair of main coils The arc segment angle of the second pair of main coils The arc segment angle of the first pair of shielding coils The arc segment angle of the second pair of shielding coils Main coil radius R m , shielding coil radius R s , the number of turns of the main coil n m , shielding coil turns n s , main coil circuit current I m , shielding coil loop current I s , the side length of the central cube target area is 2L p ; Step 2: Through the multi-level expansion of the saddle coil magnetic vector potential, the total magnetic moment m generated by the coil group is p = 0, reverse solve the shielding coil radius R s ; Step 3: Disassemble the expression of the magnetic field generated by the saddle coil in the magnetic shielding barrel to obtain the additional magnetic induction intensity B generated by the coil due to the coupling effect. ox ; Step 4: Select a target point in the target area, establish a first objective function f1 to minimize the coupling rate of the coil group, and establish a second objective function f2 to minimize the relative magnetic field deviation of the coil group; Step 5: Based on the Matlab platform, the MOPSO algorithm is used to optimize the structural parameters of the saddle-shaped shim coil group to obtain the optimal structural parameter set of the saddle-shaped shim coil group.

2. The method for designing a highly uniform saddle-shaped shim coil for eliminating magnetic shielding coupling effect according to claim 1, characterized in that: Step 2 includes the following formula: Among them I m and I s , one is positive and the other is negative.

3. The method for designing a high-uniform saddle-shaped shim coil for eliminating magnetic shielding coupling effect according to claim 1, characterized in that: Step 3 includes the following formula: Among them B x is the total magnetic field in the x direction generated by the saddle coil, B ox is the x-direction magnetic field generated by the coupling effect between the saddle coil and the magnetic shielding barrel, B ρ is the magnetic field in the ρ direction generated by the saddle coil in the cylindrical coordinate system, B Ф is the magnetic field in the Ф direction generated by the saddle coil in the cylindrical coordinate system, B oρ is the magnetic field in the ρ direction generated by the coupling effect in the cylindrical coordinate system, B oФ is the Ф-direction magnetic field generated by the coupling effect in the cylindrical coordinate system, ρ is the radial distance, and Ф is the azimuth angle.

4. The method for designing a highly uniform saddle-shaped shim coil for eliminating magnetic shielding coupling effect according to claim 1, characterized in that: Step 4 includes the following formula: s.t.0.15R m <l j <2R m ,j=1,2,3,4; 0.08 <R s <0.95R b l j+1 -l j ≥l min Where f1 is the first objective function, N p is the number of target points, N p is a positive integer, B ox (x, y, z) is the x-direction magnetic field generated at any point by the coupling effect of the saddle coil and the magnetic shielding barrel, B x (0,0,0) is the total x-direction magnetic field generated by the saddle coil group at the origin of the coordinate system under the ferromagnetic boundary, ε is the magnetic field uniformity, B x (x, y, z) is the total magnetic field in the x direction generated by the saddle coil group at any point under the ferromagnetic boundary, l j is the height set of the straight line segments of the saddle coil group, is the arc segment angle set of the saddle coil group, l min is the default value, is the default value.

5. The method for designing a highly uniform saddle-shaped shim coil for eliminating magnetic shielding coupling effect according to claim 1, characterized in that:

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