Design method of high-uniformity saddle shimming coil for eliminating magnetic shielding coupling effect

Abstract

A high-uniformity saddle shimming coil design method for eliminating a magnetic shielding coupling effect comprises the following steps: decomposing a total magnetic induction intensity expression generated by a saddle coil group under a ferromagnetic boundary into two parts, namely magnetic induction intensity generated by the coil group under a free boundary and magnetic induction intensity generated by a coupling effect; obtaining an analytical expression of the magnetic induction intensity additionally generated by the coil due to the coupling effect; a ratio expression of a magnetic field generated by a coil due to a coupling effect and a magnetic field generated by the coil at the center under a ferromagnetic boundary and a ratio expression of the magnetic field generated by the coil at the ferromagnetic boundary and the magnetic field generated by the coil at the center are taken as two objective functions through a multi-objective optimization algorithm; the linear segment height, the arc segment spread angle, the coil turn number and the current of the four pairs of saddle-shaped coils are used as to-be-optimized parameters for design, a group of optimal saddle-shaped coil group parameters are obtained, and the adverse effect of the coupling effect of a high-magnetic-conductivity material on the magnetic field generated by the coils on the uniformity of the magnetic field generated by the coils is eliminated to the greatest extent from the source.

Description

Technical Field

[0001] The invention relates to a design method for a high-uniform saddle-shaped shim coil to eliminate magnetic shielding coupling effect, wherein the coupling effect is a coupling effect generated between a passive magnetic shielding device and an active magnetic compensation coil, and belongs to the technical field of magnetic field coil design. Background Art

[0002] Uniform magnetic field coils are widely used in weak magnetic measurement testing, quantum precision measurement and other fields. They can provide a precisely controllable uniform magnetic field for magnetic field compensation, modulation or calibration operations. Usually, in order to avoid interference from external magnetic fields and ensure the stability and uniformity of the magnetic field environment in which the measurement system is located, uniform magnetic field coils also need to be used in conjunction with high-performance passive magnetic shielding systems. Since the magnetic shielding structure has the characteristics of converging magnetic lines of force, the original magnetic field distribution of the coil inside the measurement system will be changed, affecting the uniformity of the magnetic field generated by the coil and adversely affecting the accuracy of the measuring instrument. Therefore, it is very necessary to suppress the coupling effect between the magnetic shielding device and the coil.

[0003] Multilayer cylindrical magnetic shielding barrel is the most widely used type of magnetic shielding system. In order to improve the utilization rate of internal space, cylindrical coils are often used in combination. The cylindrical coil consists of an axial coil and a radial coil. For radial uniform field coils, a compact and easy-to-construct saddle structure is often used for design. Although the traditional saddle coil has a high internal magnetic field uniformity under the free boundary, it is severely affected by the coupling effect after being placed in the magnetic shielding barrel, and the internal uniformity can drop by nearly 50%. In order to reduce the coupling effect between the coil and the magnetic shielding barrel and improve the measurement accuracy and magnetic field uniformity, self-shielding coils are often used. The design goals of traditional self-shielding coils include two parts: one is that the external magnetic field of the coil needs to decay quickly, and the other is that the internal magnetic field of the coil needs to have a high uniformity. However, this indirect suppression of the coupling effect by accelerating the external attenuation of the coil is not thorough in suppressing the coupling effect. In addition, in order to improve the internal magnetic field uniformity of the coil, it is usually necessary to increase the complexity of the structure of the self-shielding coil, such as increasing the aspect ratio of the saddle coil and increasing the number of saddle coil groups. Therefore, there is an urgent need for a saddle-shaped shim coil that 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 of the invention

[0004] The present invention aims at the problems of the sharp decrease of uniformity under the ferromagnetic boundary of the current traditional saddle coil, the incomplete suppression effect of the coupling effect of the self-shielded saddle coil, and the complex structure, and proposes a design method for a high-uniform saddle-shaped shim coil that eliminates the magnetic shielding coupling effect. The present invention decomposes the expression of the magnetic induction intensity generated by the saddle coil group under the ferromagnetic boundary into two parts: the magnetic induction intensity generated under the free boundary and the magnetic induction intensity generated by the coupling effect between the coil and the magnetic shielding structure, and obtains an analytical expression of the magnetic induction intensity generated by the coupling effect between the saddle coil group and the magnetic shielding barrel. Using a multi-objective optimization algorithm, by directly optimizing the coil coupling rate and magnetic field uniformity, the coil group can suppress the adverse effect of the coupling effect on its own magnetic field uniformity from the source to the greatest extent. After the optimized design, the designed saddle-shaped shim coil group can have a fast external magnetic field attenuation, a large internal central uniform area and a high magnetic field uniformity under a simple configuration, which is more conducive to the engineering application of the coil in magnetic field calibration and other aspects.

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

[0006] A method for designing a highly uniform saddle-shaped uniform field coil for eliminating magnetic shielding coupling effect is characterized in that the method comprises decomposing the total magnetic induction intensity expression generated by a saddle-shaped coil group under a ferromagnetic boundary into two parts: the magnetic induction intensity generated by the coil group under a free boundary and the magnetic induction intensity generated by the coupling effect, thereby obtaining an analytical expression for the magnetic induction intensity additionally generated by the coil due to the coupling effect; using a multi-objective optimization algorithm to take 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 at the ferromagnetic boundary to the magnetic field generated by the coil at the center as two objective functions, taking the straight segment heights, arc segment extension angles, coil turns, and current of four pairs of saddle-shaped coils as parameters to be optimized for design, thereby obtaining a set of optimal saddle-shaped 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 to the greatest extent from the source.

[0007] The following steps are involved:

[0008] Step 1, determine the structure of the saddle-shaped shimming coil group: the saddle-shaped shimming coil group is located at the geometric center of the cylindrical magnetic shielding barrel, the saddle-shaped shimming 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, and 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 geometric center line between the coils, the y-axis is parallel to the corresponding gap of 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 second pair of main coil arc segment angle The first pair of shielding coil arc segment angle The second pair of shielding coil arc segment angle Main coil radius R m , shielding coil radius R s , the number of turns of the main coil is 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 ;

[0009] 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 ;

[0010] 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 ;

[0011] Step 4, selecting a target point in the target area, establishing a first objective function f1 to minimize the coupling rate of the coil group, and establishing a second objective function f2 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 to obtain the optimal structural parameter set of the saddle-shaped shim coil group.

[0013] Step 2 includes the following formula:

[0014]

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

[0016] Step 3 includes the following formula:

[0017]

[0018] 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 of 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 φ is the φ direction magnetic field 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 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] Step 4 includes the following formula:

[0020]

[0021] st0.15R 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 at any point by the coupling effect of the saddle coil and the magnetic shielding barrel, B x (0,0,0) is the total magnetic field in the x direction generated by the saddle coil group under the ferromagnetic boundary at the origin of the coordinate system, 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 half-height set of the straight line segments of the saddle coil group, is the half-expansion angle set of the arc segment of the saddle coil group, l min is the default value. is the default value.

[0027]

[0028] The technical effects of the present invention are as follows: The present invention provides a highly uniform saddle-shaped shim coil design method for eliminating magnetic shielding coupling effects, including two pairs of main coils and two pairs of shielding coils, and decomposes 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, and obtains an analytical expression for the additional magnetic induction intensity 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 under 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 extension angles, and the number of turns of the coils, the magnitude of the current, and the direction of the four pairs of saddle coils are designed as parameters to be optimized, and a set of optimal saddle coil group parameters are obtained. The saddle-shaped uniform magnetic field coil group optimized by the present invention can eliminate 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, and ensures higher magnetic field uniformity inside the coil, faster magnetic field attenuation outside, and a larger magnetic field uniform area under a simpler structure.

[0029] The advantages of the present invention compared with the prior art are:

[0030] 1) Compared with the traditional saddle coil at the same radius, when the same current is passed, the internal magnetic field uniformity of the two under the free boundary is similar, but the magnetic field outside the designed coil group decays faster, and the aspect ratio of the coil is smaller. When placed on the ferromagnetic boundary, the traditional saddle 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 coil, and the coupling effect is almost eliminated. Therefore, its magnetic field distribution under the ferromagnetic boundary is basically the same as that under the free boundary, and it can still maintain a high internal magnetic field uniformity.

[0031] 2) Compared with the self-shielded saddle coil at the same radius, when a unit current is passed, the external magnetic field attenuation of the two is similar under the free boundary, but the internal central magnetic field uniform area of ​​the self-shielded saddle coil is smaller. When placed on the ferromagnetic boundary, the designed coil group is less affected by the coupling effect, and its coupling rate can be reduced to less than 10% of the self-shielded saddle coil, and the central uniform field area is still large, achieving similar external magnetic field attenuation and higher internal magnetic field uniformity under a simple configuration. BRIEF DESCRIPTION OF THE DRAWINGS

[0032] Figure 1This is a schematic diagram of a high uniform saddle shimming coil structure involved in a high uniform saddle shimming coil design method for eliminating magnetic shielding coupling effect of the present invention. The outermost cylindrical thin shell in the figure is a magnetic shielding barrel, whose geometric center is concentric with the designed saddle shimming coil group, and the height of the magnetic shielding barrel is 2H m The designed saddle-shaped uniform field coil group includes two pairs of main coils and two pairs of shielding coils, the outer side is the main coil (including the first pair of main coils and the second pair of main coils), and the inner side is the shielding coil (including the first pair of shielding coils and the second pair of shielding coils). The 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 line connecting the geometric centers of each saddle coil, the y-axis is parallel to the corresponding gap of the saddle coil, and the z-axis is parallel to the axial direction of the magnetic shielding structure.

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

[0034] Figure 3 The present invention is a schematic structural diagram of a saddle-shaped shim coil group for eliminating coupling effect, which is designed by a design method of a highly uniform saddle-shaped shim coil for eliminating magnetic shielding coupling effect. Figure 3 The heights of the straight sections of the two pairs of main coils are 2l m1 、2l m2 The arc segment angles are The loop current is I m , the number of coil turns is n m ; The heights of the straight sections of the two pairs of shielding coils are 2l s1 、2l s2 The arc segment angles are The loop current is I s , the number of coil turns is n s The directions of the currents in the main coil and the shielding coil are opposite, but there is no fixed direction, and the current sign indicates its direction.

[0035] 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 effect. Figure 4 The process includes step 1, determining the structure of the saddle-shaped shim coil group: consisting of two pairs of main coils and two pairs of shielding coils; step 2, using the multi-level expansion of the saddle-shaped coil magnetic vector potential, making the total magnetic moment m generated by the coil group 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 mathematical model; step 4, determine the volume of the target area and select a suitable target point; step 5, establish the objective function f1: the coupling rate of the coil group is minimized, f2: the relative magnetic field deviation of the coil group is minimized; step 6, use the MOPSO algorithm based on the Matlab platform to optimize the structural parameters of the saddle-shaped shim coil group (Matlab, development tool software platform; MOPSO, Multiple Objective Particle Swarm Optimization, multi-objective particle swarm); step 7, based on the COMSOL platform, respectively establish finite element numerical models for calculating the magnetic field generated by the coil in a vacuum and the magnetic field generated in the magnetic shielding barrel (COMSOL is a multi-physics field simulation software platform); step 8, compare, analyze and evaluate the decoupling and uniformity of the magnetic field generated by the coil group, and determine the optimal parameters of its structure; step 9, form a high uniform magnetic field saddle-shaped shim coil structural parameter optimization design that eliminates the interference of the magnetic shielding coupling effect.

[0036] Figure 5 It 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 5 The process includes step 1, randomly initializing particles, a particle has a saddle coil group straight line segment height set 2l j (j = m1, m2, s1, s2), and the arc segment angle set of the saddle coil group There are 8 position parameters in total; Step 2, calculate the total magnetic moment m of the saddle-shaped shim coil group p = 0, reverse solve the shielding coil radius R s ; Step 3, initialize / update the 8 parameters generated (2l j and ), and R determined by the saddle-shaped shim coil group m , and the calculated R s , substitute the two optimization objective functions to solve; Step 4, obtain the local optimal and global optimal particles; Step 5, determine whether the termination condition is met, if not, update the particle speed and position and recalculate the corresponding shielding coil radius R s Then return to step 3, if yes, go to step 6; in step 6, the global optimal particle is obtained, which is the structural parameter set of the designed saddle-shaped shim coil group.

[0037] 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 6aThe scale coordinates of x(mm), y(mm) and z(mm) are all -40~40, 10*|B ox / B o | indicates that the coupling rate is amplified by 10 times, 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. 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 calculated 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 rate (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 for comparison. Figure 7a The first column in the right figure is the x-direction magnetic induction intensity B generated by the coil x , in 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 effect and the traditional saddle-shaped coil of the same size generate a magnetic field distribution diagram in the x direction on the x axis. Figure 8 The vertical coordinate is B x (nT), the scale value 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 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 shimming coil of the present invention has a relatively high magnetic field uniformity inside and a relatively fast magnetic field attenuation outside, and has a sufficiently large magnetic field uniformity 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 ( Figure 1-Figure 8 ) and Examples illustrate the present invention.

[0043] Figure 1 The invention discloses a structural schematic diagram of a high-uniform saddle-shaped shim coil involved in a design method of a high-uniform saddle-shaped shim coil for eliminating magnetic shielding coupling effect. 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 effect, which is designed by a design method of a highly uniform saddle-shaped shim coil for eliminating magnetic shielding coupling effect. 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 effect. Figure 5 It 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 It 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. Figure 7b is used with Figure 7a Schematic diagram of the magnetic field uniformity of a traditional saddle coil for comparison. Figure 8 The saddle-shaped shim coil designed by the present invention to eliminate the coupling effect and the traditional saddle-shaped coil of the same size generate the x-direction magnetic field distribution diagram on the x-axis. Figures 1 to 8 As shown, a design method for a highly uniform saddle-shaped uniform field coil for eliminating magnetic shielding coupling effect is characterized in that it includes 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, and obtaining an analytical expression for the magnetic induction intensity additionally generated by the coil due to the coupling effect; using a multi-objective optimization algorithm, 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 are used as two objective functions, and the straight segment heights, arc segment extension angles, coil turns, and current of four pairs of saddle-shaped coils are designed as parameters to be optimized, and a set of optimal saddle-shaped coil group parameters are obtained, so as to eliminate the adverse effect of the coupling effect of the high magnetic permeability material on the magnetic field generated by the coil on the uniformity of the magnetic field generated by the coil to the greatest extent from the source.

[0044] The method comprises the following steps: Step 1, determining the structure of the saddle-shaped shimming coil group: the saddle-shaped shimming coil group is located at the geometric center of the cylindrical magnetic shielding barrel, the saddle-shaped shimming 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, and 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 geometric center line between the coils, the y-axis is parallel to the corresponding gap of 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 second pair of main coil arc segment angle The first pair of shielding coil arc segment angle The second pair of shielding coil arc segment angle Main coil radius R m , shielding coil radius R s , the number of turns of the main coil is nm , 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, let the total magnetic moment m generated by the coil group 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, and obtain the additional magnetic induction intensity B generated by the coil due to the coupling effect ox ; Step 4, select the target point in the target area, establish the first objective function f1 to minimize the coupling rate of the coil group, and establish the second objective function f2 to minimize the relative magnetic field deviation of the coil group; Step 5, use the MOPSO algorithm based on the Matlab platform 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.

[0045] Step 2 includes the following formula:

[0046]

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

[0048] Step 3 includes the following formula:

[0049]

[0050] 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 of 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 φ is the φ direction magnetic field 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 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] Step 4 includes the following formula:

[0052]

[0053] st0.15R 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] 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 magnetic field in the x direction generated by the saddle coil group under the ferromagnetic boundary at the origin of the coordinate system, 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 half-height set of the straight line segments of the saddle coil group, is the half-expansion angle set of the arc segment of the saddle coil group, l min is the default value. is the default value.

[0059] A design method for a high-uniform saddle-shaped shim coil for eliminating magnetic shielding coupling effect includes two pairs of main coils and two pairs of shielding coils. The total magnetic induction intensity expression generated by the saddle-shaped coil group under the ferromagnetic boundary is decomposed 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, and the analytical expression of the magnetic induction intensity additionally generated by the coil due to the coupling effect is obtained. 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 under the ferromagnetic boundary to the magnetic field generated by the coil at the center are used as two objective functions, and the straight segment height, arc segment extension angle size, coil number of turns, current size, and direction of the four pairs of saddle-shaped coils are designed as parameters to be optimized to obtain a set of optimal saddle-shaped coil group parameters. The saddle-shaped uniform magnetic field coil group optimized by the present invention can eliminate the adverse effect of the coupling effect of the high magnetic permeability material 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, and ensures a higher magnetic field uniformity inside the coil, a faster magnetic field attenuation outside, and a larger magnetic field uniformity area under a relatively simple structure.

[0060] A method for designing a highly uniform saddle-shaped shim coil that eliminates the magnetic shielding coupling effect. The coil group is designed to have a relatively simple configuration, including two pairs of main coils and two pairs of shielding coils. The analytical expression of 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. The analytical expression of the magnetic induction intensity additionally generated by the coupling effect is obtained. Using an 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 magnetic field at the center of the coil under the ferromagnetic boundary and the ratio of the magnetic induction intensity of the coil to the magnetic induction intensity at the center of the coil are used as two optimization functions, and the arc segment extension angle of the saddle-shaped coil group is calculated. The height of the straight section of the saddle coil 2l, the number of coil turns n, and the direction and magnitude of the current I are used as parameters to be optimized, so that the two objective functions reach the minimum value. This method is different from the common self-shielding coil design idea. It does not indirectly suppress the coupling effect by improving the attenuation of the outside of the coil. Therefore, it is not necessary to select target points inside and outside the coil to calculate the internal magnetic field uniformity and external magnetic field attenuation. It is only necessary to select the target point inside the coil to achieve the same effect, reducing the amount of calculation 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, which basically achieves the effect of eliminating the coupling effect. The magnetic field uniformity in the target area and the external attenuation of the coil are better than those of the traditional saddle coil. In addition, under a relatively simple configuration, the central uniform field area of ​​the coil is still large, achieving external magnetic field attenuation similar to that of the self-shielding saddle coil and higher internal magnetic field uniformity.

[0061] The following steps are involved:

[0062] Step 1: Select the appropriate radius R of the main coil according to the known structural parameters of the cylindrical magnetic shielding barrel. m The designed saddle-shaped shim coil group consists of two pairs of outer main coils and two pairs of inner shielding coils, and the current directions of the two pairs 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, the total magnetic moment generated by the coil group is set to 0 based on the properties of the magnetic dipole in the multi-level expansion of the magnetic vector potential generated by the saddle coil. A functional relationship is established based on the three sets of parameters: the radius of the saddle coil, the height of the straight segment, and the arc segment angle, and the radius R of the shielding coil is inversely solved. s .

[0064] Step 3, combining the different magnetic permeabilities of ferromagnetic boundary materials and the mirror method, calculate the magnetic induction intensity generated by the reflection of the saddle coil current by the magnetic shielding end cover, and derive the expression B of the magnetic induction intensity in the x direction generated by the coil group in the cylindrical magnetic shielding barrel by the Biot-Savart law. xBy decomposing the magnetic induction intensity generated by the coupling effect from the total magnetic field generated by the coil group in the magnetic shielding barrel, a specific and accurate analytical expression B for the additional magnetic induction intensity generated by the coil group due to the coupling effect is given. ox .

[0065] Step 4: Determine the volume of the target area and select the appropriate target point N p In order to make the coil have a wider uniform working magnetic field area, the target area should be relatively large. The half side length of the cube of the target area selected by the present invention is The number of target points is 10, which are the 8 vertices and two center surface points of the cube in the first quadrant of the target area.

[0066] Step 5, establish two optimization design goals (both take 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 magnetic induction intensity at the center of the coil; ② the ratio of the total magnetic field generated by all coils under the ferromagnetic boundary to the magnetic field at the center of the coil.

[0067] In step 6, the two design goals are converted into a dual-objective optimization problem with coil structure parameters as constraints, and the multi-objective particle swarm optimization (MOPSO) optimization algorithm is used to solve it, thereby obtaining the optimal parameter set of the saddle-shaped shim coil group.

[0068] Step 7, use COMSOL to establish a finite element simulation model, and substitute the optimal coil group parameter set obtained by the algorithm for verification. Calculate the magnetic induction intensity and magnetic field uniformity of the coil group in the uniform area of ​​the free boundary and the ferromagnetic boundary, and the magnetic induction intensity and the coupling rate of the coil generated by the coupling effect. The calculation results of the finite element simulation verify the effect of suppressing the coupling effect and the size of the magnetic field uniformity generated by the coil group under the ferromagnetic boundary.

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

[0070]

[0071] Among them, G m , α b ,β b ,γ b ,α c ,β c ,γ c They are all intermediate quantities defined by simplified expressions, and their 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 AND m (kR b )K m ′(kR b )-AND 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 AND m ′(kR c )K m (kR c )-AND m (kR c )K m ′(kR c ))

[0079] Among them, ρ, φ, z are the three coordinate parameters of the target point in the 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 of the point from 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 is 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, respectively, and I m and I m ′ represents the first kind of modified Bessel function and its derivative, K m and K m ′ respectively represent the first kind of modified Bessel function and its derivative; 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] Among them, 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 line segments of the two shielding coils respectively; e is the natural index; δ m,odd is the Dirac function, which means that when m is an odd number, δ m,odd =1.

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

[0084]

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

[0086]

[0087] st0.15R m <l j <2R m (j=1,2,3,4)

[0088]

[0089] l j+1 -l j ≥l min

[0090]

[0091] Among them, 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, is the minimum angle of the arc segment of the saddle coil. Since the magnetic field components in the y and z directions are very small and can be ignored, the main magnetic field in the x direction generated by the coil can be approximately regarded as the total magnetic field. ox (x,y,z) is the magnetic induction intensity in the x direction 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, there is no need to consider the direction of the vector. The conversion relationship between the cylindrical coordinate system and the rectangular coordinate system of the x-direction magnetic induction intensity generated by the coupling effect is as follows:

[0092]

[0093] Compared with comparing the decoupling of the coil group only by the absolute magnetic field value generated by the coupling effect, the comparison of the coupling rate improves the credibility of the decoupling of the coil group and increases the coil constant to a certain extent. In order to avoid the 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 ratios of the total magnetic field of all target points under the ferromagnetic boundary to the magnetic field at the center of the coil, and its expression is:

[0095]

[0096] Since the direction of the magnetic field is determined, there is no need to consider the direction of the vector. The conversion relationship between the cylindrical coordinate system and the rectangular coordinate system of the magnetic induction intensity generated by the coil under the ferromagnetic boundary is as follows:

[0097]

[0098] The restriction conditions of the saddle coil structure parameters are the same as the objective function f1. In order to avoid the magnetic induction intensity results 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-shaped shim coil group includes two pairs of main coils on the outside and two pairs of shielding 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-shaped shim coils are symmetrically distributed. 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 is the radius of the main coil, R s is the radius of the shielding 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 line segments of the two shielding coils. 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 set the magnetic dipole moment to 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, 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 represents the closed loop boundary formed by the coil, and S' is the projection area of ​​the current-carrying coil in the r'×dr' direction. Substituting the structural parameters of the saddle-shaped shim coil group, let the magnetic dipole moment m generated by the saddle-shaped shim coil group be p is 0, the radius R of the shielding coil can be solved s .

[0103]

[0104] Among them, the current directions of the main coil and the shielding coil are opposite and have no fixed direction, and the symbols represent their respective current directions.

[0105] The expression of magnetic induction intensity generated by the coupling effect between the coil and the magnetic shielding barrel is derived. The magnetic induction intensity generated by the saddle coil group under the ferromagnetic boundary is composed of two parts: the magnetic induction intensity generated at the free boundary and the additional magnetic induction intensity generated by the coupling effect between the coil and the magnetic shielding barrel. By decomposing the magnetic induction intensity generated by the coupling effect from the total magnetic field generated under the ferromagnetic boundary, a specific and accurate analytical expression of the additional magnetic induction intensity generated by the coil group due to the coupling effect is given. Since the magnetic field components in the y and z directions generated by the saddle coil are very small and can be ignored, the main magnetic field in the x direction can be approximated as the total magnetic field. Therefore, it is necessary to convert the cylindrical coordinate system to the rectangular coordinate system in the future, and there is no need to calculate the magnetic induction intensity in the z direction. The parameter ρ in the cylindrical coordinate system represents the distance from the projection on the plane to the origin of the coordinates, the parameter φ represents the azimuth of the projection point, and the parameter z represents the distance of the point from 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] Among them, B oρ (ρ, φ, z) is the magnetic induction intensity in the ρ direction 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, z is the height, and B oφ (ρ,φ,z) is the magnetic induction intensity in the φ direction 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 number of current reflections, m is the summation upper limit, k is the integral variable, H m is the half length of the magnetic shielding barrel, I m is the first kind of modified Bessel function, Im ' is its derivative, K m The modified Bessel function of the second kind, K m 'For its derivative, min[R j ] indicates R j The minimum value in the set.

[0109] Determine the volume of the target area and select a suitable target point. In order to make the coil have a wider consistent working magnetic field area, the target area should be relatively large. The half side length of the cube of the target area selected by the present invention is Select the spatial position points within the target area for calculating the objective function, called target points, and the number of target points is a positive integer N p . Unlike the traditional self-shielding coil, which needs to select target points inside and outside the coil respectively, and calculate the uniformity of the magnetic field inside the coil and the attenuation of the external magnetic field respectively. The target points selected by the present invention are all in the target uniformity area inside the coil, so 50% of the data points can be used to obtain the same effect, which simplifies the target point selection process, reduces the calculation amount of the optimization process, and greatly improves the optimization efficiency.

[0110] Two optimization function expressions are determined. The designed saddle-shaped shim coil group is placed in a known magnetic shielding environment. In order to eliminate the negative impact of the coupling effect on the magnetic field of the coil to the greatest extent from the source, the absolute value 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 of the coil at the center point under the ferromagnetic boundary) is taken as the objective function f1; in order to further improve the uniformity of the magnetic field in the target area at the center of the coil, the absolute value 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 magnetic field at the center of the coil is taken as the objective function f2.

[0111]

[0112] st0.15R 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] The total magnetic field in the x direction generated by the coil group at any point 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 is B ox (x, y, z), the total magnetic field in the x direction generated by the coil group at the origin of the coordinate system 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 spacing between the heights of the adjacent coil straight segments is 2l min , the minimum arc segment angle difference is

[0118] In order to enhance the credibility of the coil group's suppression of the magnetic shielding effect, the coupling rate is expressed in the form of 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 magnetic induction intensities in opposite directions from canceling each other out, the sum of their absolute values ​​is taken to ensure the accuracy of the final result.

[0119] Step 6: Use the Multiple Objective Particle Swarm Optimization (MOPSO) algorithm for optimization calculation. In order to facilitate the actual processing and assembly, reduce the number of optimized parameters, and improve the efficiency of the algorithm, the current and number of turns of the main coil and the shielding coil are made equal, that is, I m =I s =I,n m =n s = n. A group of saddle-shaped main coils with a straight line height of 2l are obtained from a group of randomly generated particles. mi 、Arc segment width And the height of the straight section of the saddle shield coil is 2l si 、Arc segment width Four sets of structural parameters. Through the above four sets of parameters and the main coil radius R m The total magnetic moment generated by the saddle-shaped shim coil group is calculated to be 0, and the radius R of the shielding coil is inversely solved. s Substituting the above parameters, the optimal solution (minimum value) of the objective functions f1 and f2 is solved, and the parameter group with the best performance is obtained, which is the parameter set of the designed saddle-shaped shim coil group.

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

[0121] A method for designing a high uniform saddle-shaped shimming coil for eliminating magnetic shielding coupling effect comprises the following specific steps:

[0122] Step 1: In order to maintain a relatively simple coil structure and high internal magnetic field uniformity, the designed saddle-shaped shim coil group consists of two pairs of saddle-shaped main coils and two pairs of concentric saddle-shaped shielding coils. The coil group is placed at 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 straight line segments is 2l mi =[2l m1 ,2l m2 ], the arc segment angle set is The number of turns of the coil is n m , the current of the coil is I m ; The radius of the two pairs of saddle shielding coils is R s , the height set of straight line segments is 2l si =[2l s1 ,2l s2 ], the arc segment angle set is The number of turns of the coil is n s , the current of the coil is I s The specific structure is as follows Figure 1 , Figure 2 shown.

[0123] In determining the structural parameters of the high magnetic permeability magnetic shielding device (height 2H m 、Inner diameter R b 、Outer diameter R c ) and material properties (relative magnetic permeability μ r ) and the radius R of the designed main coil m Then, a three-dimensional rectangular coordinate system is established with the geometric center point of the saddle-shaped shim coil group as the origin, wherein the x-axis direction is consistent with the line connecting the geometric centers of each saddle-shaped coil, the y-axis direction is consistent with the corresponding 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 external magnetic field of the saddle-shaped shim coil group decay most rapidly, the magnetic dipole moment is set to 0 through the multi-level expansion of the magnetic vector potential, thereby inversely solving the radius R of the shielding coil. 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] Among them, r and r' both represent the position vector in the cylindrical coordinate system. The parameter ρ in the cylindrical coordinate system represents the distance from the projection on the plane to the origin of the coordinate system, the parameter φ represents the azimuth of the projection point, and the parameter z represents the distance of the point from the plane where the origin is located. 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 vacuum permeability, J(r ′ ) is the current density, V' is the volume of current density; when the observation point is much larger than the linear dimension of the current distribution area, The Taylor series can be expanded at r′=0 as:

[0127]

[0128] Among them, I m represents the modified Bessel function of the first kind, K m represents the second kind of modified Bessel function, R is the radius of the saddle coil, e is the natural index, i is the imaginary unit, k is the integral variable, m is the summation upper limit, and after substituting back into the magnetic vector potential expression, the magnetic vector potential induced by the coil current at any point r(ρ,φ,z) in space can be written as:

[0129]

[0130] Item 1A (0) (r) and the second term A (1) (r) are the magnetic vector potentials generated by the magnetic monopole and dipole, respectively. The third term A (2) (r) is the magnetic vector potential generated by the magnetic quadrupole and above. Since the current density divergence is 0, the magnetic vector potential A of the expanded magnetic monopole (0) (r) is also always 0; and because the magnetic vector potential of high-order magnetic multipoles decays faster, at a sufficiently far observation point, the third term A in the magnetic multipole expansion (2) (r) and all subsequent terms can be ignored. Therefore, in order to make the external magnetic field decay most rapidly, it is only necessary to set the magnetic vector potential A of the magnetic dipole (1) (r) is 0. The magnetic dipole vector potential A (1) (r) and magnetic dipole moment m p There is a definite functional relationship as follows:

[0131]

[0132] Among them, r is the modulus of the position vector r, r = |r|. Therefore, it is only necessary to let the magnetic dipole moment m generated by the saddle-shaped shim coil group p is 0, the magnetic dipole vector potential A (1) (r) is also 0. When there is a current loop, the magnetic moment m of a coil of any shape p Can be expressed as:

[0133]

[0134] Where J is the current density of the coil, I is the current of the coil, n is the number of turns of the coil, L represents the boundary of the closed coil loop, and S' is the projection area of ​​the current-carrying coil in the r'×dr' direction. Substituting the structural parameters of the saddle-shaped shim coil group, the magnetic dipole moment m generated by the saddle-shaped shim coil group is p is 0, the radius R of the shielding coil can be solved s .

[0135]

[0136] Among them, the current directions of the main coil and the shielding coil are opposite, and the symbols indicate their directions.

[0137] Step 3, decompose the total magnetic field expression generated by the saddle coil in the magnetic shielding barrel, and obtain the coupling effect so that the additional magnetic induction intensity B generated by the coil is ox The mathematical model is divided into 5 small steps:

[0138] Step 3.1, derive the analytical expressions for the total magnetic induction intensity and current density components generated by a single saddle coil in a vacuum.

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

[0140]

[0141] Where i is the imaginary unit, and are the projection J of the current density J(r′) in the φ′ direction φ′ (φ′,z′) and its projection J in the z′ direction z′ The Fourier transform of (φ′,z′) is and The current continuity condition is satisfied at any source point, namely:

[0142]

[0143] And the magnetic induction intensity B and the magnetic vector potential A satisfy That is, the divergence of the magnetic induction intensity B is always 0, so the representation of the magnetic induction intensity can be obtained. The mathematical model of the total magnetic induction intensity B generated by a single saddle coil at any point (ρ, φ, z) in a 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 δ is the Dirac function. φ′ The Fourier transform of (φ′,z′) is:

[0148]

[0149] Among them, 2H m is the length of the magnetic shielding barrel, is the expansion angle of the saddle coil, 2l is the height of the straight line segment of the saddle coil, δ m,odd When m is odd, δ m,odd =1.

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

[0151] When the coil is placed in a magnetic shielding device made of high magnetic permeability materials, a 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 cover can be calculated based on the sum of the magnetic fields generated by the equivalent current on the surface of the material:

[0152]

[0153] Among them, R b and R c are the inner radius and outer radius of the cylindrical magnetic shielding barrel, respectively, m ′ represents the derivative of the first kind of modified Bessel function, K′ m represents the derivative of the modified Bessel function of the second kind, and They are the Fourier transform expressions of the equivalent surface currents on the inner and outer surfaces of the hollow cylindrical magnetic shielding barrel, respectively, and they can be determined by the boundary conditions of different material permeabilities.

[0154]

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

[0156]

[0157] Among them, α b ,β b ,γ b ,α c ,β c ,γ c They are all intermediate quantities defined by simplified expressions, and their 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] Among them, G m It is also an intermediate quantity defined to simplify the expression. Its specific expression is:

[0167]

[0168] Step 3.3, derive the analytical expression for the total magnetic induction intensity generated by a single saddle coil in a magnetic shielding barrel with end covers.

[0169] When the magnetic shielding barrel is equipped with an end cap, the magnetic field generated by the coil will change due to the influence of the reflected current of the end cap, especially when the coil height 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 coil magnetic field. The mirror method believes that the magnetic field generated by the coil due to the effect 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 expressed as:

[0170]

[0171] Among them, p is the number of current reflections. 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 end caps is for:

[0172]

[0173] Step 3.4, the magnetic induction intensity B generated by the simplified saddle-shaped shim coil group in the magnetic shielding barrel with end cover x The analytical expression of .

[0174] Since the expression of the magnetic induction intensity generated by the above-mentioned single saddle coil is relatively complex, and adding more pairs of saddle coils will increase the difficulty of calculation, the expression is simplified through the characteristics of the even function and the conversion of the Euler formula to reduce the amount of calculation of the subsequent optimization algorithm. And because the magnetic field components in the y and z directions generated by the saddle coil are very small and can be ignored, the main magnetic field in the x direction can be approximately regarded as the total magnetic field. Therefore, the cylindrical coordinate system needs to be converted to a rectangular coordinate system, and there is no need to calculate the magnetic induction intensity in the z direction. The simplified expression of the total magnetic induction intensity generated by the saddle shim coil group 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 is 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 line segments of the two shielding coils. 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] In the formula, k, p, and m are all parameters that determine the accuracy of the model. Theoretically, the larger the value, the more accurate the calculation result, but at the same time, the time cost of the calculation will also increase, and too large a value of m will also cause overflow problems during the calculation process. Therefore, through finite element simulation verification, the upper limit of the integral k is taken as 1000, the number of reflections p = 0, ±1, ±2, ±3, and the calculation of B ρ and B oρ The maximum value of m is 37, and B is calculated. φ and B oφ The maximum value of m is 35, which not only ensures the accuracy of the calculation, but also has a faster computing speed.

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

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

[0180]

[0181] The total magnetic field B in the x direction generated by the saddle coil x The x-direction magnetic field B generated by the coupling effect between the coil and the magnetic shielding structure ox The conversion relationships are:

[0182]

[0183] Step 4: Determine the volume of the target area and select a suitable target point. Determine the appropriate main coil radius R according to the structural parameters of the magnetic shielding device. m To ensure a larger uniform area, The cube side length of the target area is 2L p . According to the magnetic field distribution generally generated by the saddle coil, a small number of target points are selected in the target cube area. The uniform selection that includes more edge points and extreme points will make the calculation results more authoritative and typical. Since the mathematical models for calculating the magnetic field mentioned above are axially symmetric, this study selects 10 target points, which are all distributed in the first quadrant cube of the target area. 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 ,L p ,0),(0,L p ,L p ),(L p ,L p ,L p ),

[0185]

[0186] The above are the 8 vertices and 2 face center points of the cube in the first quadrant of the target area.

[0187] Step 5, respectively establish the first objective function f1: the sum of the absolute values ​​of the ratios of the magnetic induction intensity generated by the coupling effect of all target points to the central magnetic induction intensity of the coil; the second objective function f2: the sum of the absolute values ​​of the ratios of the total magnetic field of all target points under the ferromagnetic boundary to the central magnetic field of the coil, and give the restriction conditions of the coil structure parameters. The absolute value is taken to avoid the magnetic induction intensity in opposite directions from canceling each other out and affecting the accuracy of the final result.

[0188]

[0189] st0.15R 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] Among them, N p is the number of target points, ε represents the relative magnetic field deviation of the magnetic field generated by the coil, and the total magnetic field in the x direction generated by the coil group at any point (x, y, z) under the ferromagnetic boundary is B x (x, y, z), the coupling effect of the coil group and the magnetic shielding structure generates a magnetic field in the x direction at any point (x, y, z) as B ox (x, y, z), the total magnetic field in the x direction generated by the coil group at the origin of the coordinate system 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 is the minimum height difference of the straight line segment between each pair of adjacent coils, Minimum arc segment angle difference.

[0195] Step 6: Convert the design of eliminating the magnetic shielding effect of the saddle-shaped uniform coil group into a dual-objective optimization problem with the coil structure parameters as constraints. In order to reduce the amount of calculation of the algorithm, improve the operation speed, and facilitate the subsequent coil processing and assembly, the number of turns and current of the main coil and the shielding coil are set to be consistent, that is, only the straight section height of the saddle-shaped main coil is 2l mi 、Arc segment width And the height of the straight section of the saddle shield coil is 2l si 、Arc segment width Four sets of structural parameters to be optimized. Using the Multiple Objective Particle Swarm Optimization (MOPSO) optimization algorithm, the above four sets of structural parameters are obtained from a group of randomly generated particles. The total magnetic moment generated by the saddle-shaped shim coil group is 0, and the radius R of the shielding coil is inversely solved. s Substituting the above parameters, the optimal solution (minimum value) of f1 and f2 is solved, and a set of eight parameters with the best performance is obtained, which is the optimal saddle-shaped shim coil group parameter set.

[0196] Step 7, respectively establish the finite element simulation model of the saddle-shaped shim coil group under the free boundary and the ferromagnetic boundary, substitute the obtained optimal coil parameter set, respectively calculate the magnetic induction intensity distribution and magnetic field uniformity of the coil group in the free boundary and ferromagnetic boundary target area, and calculate the magnetic induction intensity generated by the coupling effect and the coupling rate of the coil. Its value is the difference between the magnetic induction intensity generated by the coil group under the ferromagnetic boundary and the magnetic induction intensity generated by the coil group under the free boundary. The effect of suppressing the coupling effect and the size of the magnetic field uniformity generated by the coil group 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 invention belong to the prior art known to the professional and technical personnel in the field. It is pointed out here that the above description helps those skilled in the art to understand the invention, but does not limit the protection scope of the invention. Any equivalent replacement, modification and / or simplification of the above description without departing from the essence of the invention falls within the protection scope of the invention.

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, so as to obtain 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 under 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 extension angles, number of coil turns and current of four pairs of saddle coils are designed as parameters to be optimized, so as to obtain a set of optimal saddle coil group parameters, so as to eliminate 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.

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: The following steps are involved: Step 1, determine the structure of the saddle-shaped shimming coil group: the saddle-shaped shimming coil group is located at the geometric center of the cylindrical magnetic shielding barrel, the saddle-shaped shimming 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, and 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 geometric center line between the coils, the y-axis is parallel to the corresponding gap of 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 second pair of main coil arc segment angle The first pair of shielding coil arc segment angle The second pair of shielding coil arc segment angle Main coil radius R m , shielding coil radius R s , the number of turns of the main coil is 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, selecting a target point in the target area, establishing a first objective function f1 to minimize the coupling rate of the coil group, and establishing 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.

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

4. The method for designing a highly uniform saddle-shaped shimming coil for eliminating magnetic shielding coupling effect according to claim 2, 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 φ is the magnetic field in the φ 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 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.

5. The method for designing a highly uniform saddle-shaped shim coil for eliminating magnetic shielding coupling effect according to claim 2, characterized in that: Step 4 includes the following formula: s.t.0.15R m <l j <2R m (j=1,2,3,4) <h2 style=";text-align:left;direction:ltr">0.08 <R <h2 style=";text-align:left;direction:ltr"> s <h2 style=";text-align:left;direction:ltr"> <0.95R<h2 style=";text-align:left;direction:ltr"> b <h2 style=";text-align:left;direction:ltr"> (j = 1, 2, 3, 4) 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 magnetic field in the x direction generated by the saddle coil group under the ferromagnetic boundary at the origin of the coordinate system, 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.

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

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