Coil design method for suppressing ferromagnetic boundary coupling based on image method and self-shielding method

Abstract

The present invention relates to a coil design method for suppressing ferromagnetic boundary coupling based on an image method and a self-shielding method. The coil includes a primary coil and a secondary coil. The method comprises: designing the primary coil using a target field method; setting the secondary coil to be obtained by scaling the primary coil proportionally, and constructing a coil without magnetic moment; taking an arbitrary value for the proportional magnification coefficient λ within the range of 0 < λ < 1, scaling the primary coil according to the arbitrary value to obtain an initial secondary coil; and optimizing the proportional magnification coefficient λ using a particle swarm optimization algorithm to obtain an optimal secondary coil. The method first uses a self-shielding method to suppress the ferromagnetic boundary coupling between the magnetic field generated by the coil and the high-permeability inner surface of the magnetic shield. Further optimization is then performed to completely suppress the coupling effect, thereby improving the uniformity of the magnetic field gradient within the magnetic shielding room and achieving an extremely weak magnetic environment.

Description

Technical Field

[0001] The present invention relates to the technical field of electromagnetic coil design, and in particular to a coil design method for suppressing ferromagnetic boundary coupling based on an image method and a self-shielding method. Background Art

[0002] Magnetocardiography (MCG) is a noninvasive functional imaging technique that detects the weak magnetic fields generated by the heart. Compared to other cardiac imaging techniques, it does not emit harmful radiation or stimulating signals and is non-invasive to the human body, thus garnering widespread attention both domestically and internationally.

[0003] Existing magnetic field measurement devices are primarily based on superconducting quantum interference devices (SQUIDs) and atomic magnetometers. Both require a zero-magnetic field device to provide a suitable weak magnetic field test environment. This device combines a shielded room with multiple layers of high-permeability materials and active magnetic compensation coils, achieving near-zero remanent magnetization in the central region. However, the shielded room structure relies on high-permeability materials and, once established, cannot be easily altered. Therefore, the design of an active magnetic compensation coil is necessary.

[0004] Currently, dual-plane coils designed using the target field method are often used to provide sufficient space for MCG subjects and are widely used in MEG studies within magnetically shielded rooms. However, the coupling effect between the magnetic field generated by the coil and the magnetically shielded room can severely reduce the uniformity and gradient of the target area, thereby affecting the performance of the active magnetic compensation system. Summary of the Invention

[0005] The technical problem to be solved by the present invention is to provide a coil design method for suppressing ferromagnetic boundary coupling based on the image method and the self-shielding method. The coil designed using this method can effectively suppress the ferromagnetic boundary coupling effect, improve the uniformity of the magnetic field gradient inside the magnetic shielding room, and achieve an extremely weak magnetic environment.

[0006] The technical solution adopted by the present invention is a coil design method for suppressing ferromagnetic boundary coupling based on an image method and a self-shielding method. The coil includes a primary coil and a secondary coil, and the primary coil and the secondary coil are placed in parallel in a magnetically shielded room. The method includes the following steps:

[0007] S1. Design the primary coil using the target field method;

[0008] S2. Assume that the secondary coil is obtained by scaling the primary coil in equal proportion, and construct the primary coil and the secondary coil into a coil without magnetic moment, and the coil without magnetic moment satisfies the relationship: Among them, S2=L2·D2=λL1·λD1=λ 2 S1; B tIndicates the magnetic field of the target area; and Represent the magnetic fields generated by the primary coil and the secondary coil in the target area respectively; M represents the total magnetic moment; M1 and M2 represent the magnetic moments of the primary coil and the secondary coil respectively; The plane stream function of the primary coil and the magnetic field matrix of the target point; represents the plane stream function of the secondary coil and the magnetic field matrix of the target point; p mn represents the stream function coefficient matrix of the coil; λ represents the proportional amplification factor; I1 represents the current through the primary coil; I2 represents the current through the secondary coil; S1 represents the plane area of ​​the primary coil; S2 represents the plane area of ​​the secondary coil; μ represents the current proportional coefficient; according to the above relationship, when λ→1, the coil with no magnetic moment achieves self-shielding;

[0009] S3. Within the range of 0<λ<1, the proportional amplification coefficient λ takes an arbitrary value, and the primary coil is scaled according to the arbitrary value to obtain an initial secondary coil, thereby completing the first suppression of the ferromagnetic boundary coupling effect;

[0010] S4. Within the range of 0<λ<1, the particle swarm optimization algorithm is used to optimize the proportional amplification coefficient λ to obtain the optimal proportional amplification coefficient λ, and the initial secondary coil is scaled according to the optimal proportional amplification coefficient λ to obtain the optimal secondary coil, thereby completing the second suppression of the ferromagnetic boundary coupling effect.

[0011] The beneficial effects of the present invention are as follows: the coil design method for suppressing ferromagnetic boundary coupling based on the above-mentioned image method and self-shielding method is adopted, the target field method is first used to design the primary coil, and the primary coil is proportionally scaled according to any value within a certain range, so that the coil without magnetic moment achieves self-shielding; the proportional amplification coefficient is then optimized by the particle swarm optimization algorithm, and finally the optimal secondary coil is obtained according to the optimal proportional amplification coefficient to complete the coil design; the method first uses the self-shielding method to suppress the ferromagnetic boundary coupling between the magnetic field generated by the coil and the high magnetic permeability inner surface of the magnetic shielding, and then further optimizes so that the coupling effect is completely suppressed, thereby improving the uniformity of the magnetic field gradient inside the magnetic shielding room and realizing an extremely weak magnetic environment.

[0012] Preferably, in step S4, the specific process of optimizing the proportional amplification factor λ using the particle swarm optimization algorithm includes the following steps:

[0013] S4.1. According to the principle of the image method, the magnetic field strength of the image coil is obtained, and the magnetic field strength of the image coil is subtracted from the magnetic field strength of the actual coil to obtain the final magnetic field strength of the target area:

[0014] in, and They represent the magnetic fields generated by the primary coil and the secondary coil in the target area by the imaging method; and P mn,im denote the coil matrix and stream function matrix respectively;

[0015] S4.2. Setting the objective function: Wherein, B(x, y, z) represents the final magnetic field strength of the target area obtained in step S4.1; B center (0, 0, 0) represents the magnetic field generated by the coil at the center point; the search area is set to: a×b×c; the search area contains KN particles;

[0016] S4.3. Set the iterative update rule as:

[0017] V i =ω·V i +rand1·c1(X i,best -X i )+rand2·c2(X g,best -X i );

[0018] X i =X i +V i ;

[0019] Among them, X i =(x i1 ,x i2 ), X i represents the position of the i-th particle in the iteration, x i1 Represents the proportional magnification factor, x i1 =λ,x i2 Represents the current proportional coefficient, x i2 =μ; V i represents the particle velocity, V i =(v i1 , v i2 ), v i1 Indicates the limit of the proportional magnification factor, v i1 =[λmax min ];v i2 Indicates the limitation of current proportional coefficient, v i2 =[μmax min ]; c1 and c2 are learning factors; rand1 and rand2 are random numbers ranging from 0 to 1; ω is the inertia factor, which is negative; X i，best represents the optimal solution for each particle, X g，best represents the global optimal solution of the entire population;

[0020] S4.4. Input the proportional amplification coefficient λ of any value obtained in step S3 and the corresponding current proportional coefficient μ into the particle swarm optimization algorithm, and iterate according to the iterative update rule defined in step S4.3, record the number of particles KN and the objective function value ME obtained in each iteration, until the maximum number of iterations is reached, and stop the iteration; find the minimum value from all the objective function values ​​ME obtained, and the proportional amplification coefficient λ corresponding to the minimum value at this time is the optimal proportional amplification coefficient λ.

[0021] Preferably, the specific process of step S4.1 includes the following steps:

[0022] S4.11. Based on the principle of the image method, each infinite high-permeability surface of the magnetic shielding room is equivalent to a mirror, reflecting the internal dual-plane coil. At the same time, the image current generated by any high-permeability surface will be reflected again by other high-permeability surfaces. Therefore, the six high-permeability surfaces of the magnetic shielding room reflect each other, forming an infinite-order coil array.

[0023] S4.12. Assume that the image current generated by the high permeability medium plane reflecting the magnetic source and the actual current of the coil are related by the following equation: Among them, I im Represents the image current, I re represents the actual current, μ1 represents the relative magnetic permeability of air, which is usually 1; μ2 represents the relative magnetic permeability of the magnetic shielding material; through the principle of the image method, the expression of the magnetic field strength of the coil array is obtained as follows:

[0024]

[0025] in, Indicates the current density of the primary coil image method; represents the current density of the secondary coil image method; a represents the order of the equivalent coil array, represents the image current density at the i, j, and kth order, δ and ε represent the directional coefficients that determine the direction of the image current;

[0026] S4.13. Set the coil order a to a = 2, and obtain the final magnetic field strength in the target area:

[0027] in, and They represent the magnetic fields generated by the primary coil and the secondary coil in the target area by the imaging method; and P mn,im denote the coil matrix and stream function matrix respectively.

[0028] During step S4.1, the coupling effect is integrated into the design of the dual-plane coil to fundamentally suppress the influence of the ferromagnetic boundary on the magnetic field of the compensation coil. BRIEF DESCRIPTION OF THE DRAWINGS

[0029] Figure 1 It is a structural diagram of the magnetic shielding room in the present invention;

[0030] Figure 2 Schematic diagram of the structure of the magnetic field coil Bx and the corresponding stream function image in the present invention; wherein, Figure 2 (a) is a schematic diagram showing the structure of the magnetic field coil Bx. Figure 2 (b) Schematic diagram of the stream function image of the magnetic field coil Bx;

[0031] Figure 3 Schematic diagram of the structure of the magnetic field coil Bz and the corresponding stream function image in the present invention; wherein, Figure 3 (a) is a schematic diagram showing the structure of the magnetic field coil Bz. Figure 3 (b) Schematic diagram of the stream function image of the magnetic field coil Bz;

[0032] As shown in the figure: 1. Magnetic shielding room; 2. Primary coil; 3. Secondary coil; 4. Target area. DETAILED DESCRIPTION

[0033] The invention will be further described below with reference to the accompanying drawings and in combination with specific implementations, so that those skilled in the art can implement the invention with reference to the description. The protection scope of the invention is not limited to the specific implementations.

[0034] The present invention relates to a coil design method for suppressing ferromagnetic boundary coupling based on an image method and a self-shielding method. The coil includes a primary coil and a secondary coil. Figure 1 As shown, the primary coil and the secondary coil are placed in parallel in a magnetic shielding room to reduce the influence of ferromagnetic boundaries and compensate for the residual magnetic field in the target area. Figure 1 In the example, the current magnitude, distance from the center, and size of the primary and secondary coils are proportionally amplified. The superposition of the magnetic moments of the two coils approaches zero, so the two coils form non-moment coils (NMC). In the target center area, the magnetic field value approaches a constant value due to the mutual cancellation of the two coils. In the shielded area, the magnetic field value approaches zero. The sum of the magnetic moments of the primary and secondary coils approaches zero, as shown in the following formula (1):

[0035]

[0036] Among them, B t Represents the magnetic field of the target area; and The magnetic fields generated by the primary coil and the secondary coil in the target area respectively; M is the total magnetic moment; M1 and M2 represent the magnetic moments of the primary coil and the secondary coil respectively.

[0037] The specific design method includes the following steps:

[0038] S1. Design the primary coil using the target field method:

[0039] Magnetic field coils Bx, By, and Bz are set in the x, y, and z directions to form the primary coil. Since the magnetic field coil By and the magnetic field coil Bx are the same size and shape, but rotated 90 degrees, only the Bx and Bz coils need to be designed. However, the designs of the Bx and Bz coils are similar, so only the design process of the magnetic field coil Bx is described here. Specifically:

[0040] First, the current distribution on the double-plane coil is considered as a two-dimensional continuous fluid. The current density satisfies the continuity equation and the streamline differential equation. Let the stream function of the plane fluid be S(x, y). Since the current distribution is perpendicular to the Z direction, the current density in the Z direction is 0. According to the plane coil design theory, it can be obtained

[58] :

[0041]

[0042] Among them, p mn is the stream function coefficient matrix of the magnetic field coil Bx, M and N are the orders of the Fourier expansion, and Lx and Ly are the dimensions of the coil plane in the X and Y directions, respectively.

[0043] Taking the magnetic field coil Bx as an example, the current density functions in the X-axis and Y-direction are J x and J y , which can be specifically expressed as:

[0044]

[0045] In the target field method, the target area is usually discretized into T equally spaced target points. By presetting the magnetic field at the target points to a constant, the residual magnetic field at all target points is minimized to solve the coefficient matrix of the stream function, thereby obtaining the current stream function of the planar coil. According to the Biot-Savart theorem, the matrix of the current density of the planar coil and the magnetic field at the target points is constructed as follows:

[0046]

[0047] Where S is the coil plane; μ0 is the magnetic permeability in vacuum; and r is the distance between the plane coil stream function and the target point. Combining Equations (5) and (6), the magnetic field in the Bx direction can be derived and simplified as follows:

[0048]

[0049] Where A mn ∈R T×MN is the system matrix; P mn ∈R MN×1 ; B x ∈R T×1 ; r = (x, y, z) is the coordinate of the target point; r i =(x i ,y i , z i ) Plane coil stream function coordinates.

[0050]

[0051] Where: A mn Plane stream function and magnetic field matrix of target point; and are the plane stream functions of the left and right coils of a set of planar coils and the magnetic field matrix of the target point; The plane stream function of the primary coil and the magnetic field matrix of the target point; The plane stream function representing the secondary coil and the magnetic field matrix of the target point;

[0052] According to equations (1) and (6), the final magnetic field matrix is ​​obtained, and the target magnetic field value is set to construct the equation to be solved:

[0053] B x =A mn ·P mn =B target (11)

[0054] Since the above equation is ill-conditioned, this paper adopts Tikhonov regularization to solve it and introduces the coil curvature G into the equation. mn is the penalty function term, forming a Tikhonov universal function, which can be expressed as:

[0055]

[0056] Where: λ is the weighting coefficient; E is the error function; coil curvature As follows:

[0057]

[0058] when Coefficient matrix P mn It can be solved by the following formula:

[0059]

[0060] When P mnWhen is determined, the planar coil stream functions of the primary coil and the secondary coil are also uniquely determined, so that the magnetic field coil Bx can be designed and further the primary coil can be obtained.

[0061] S2. Under the influence of ferromagnetic boundary coupling, the magnetic field uniformity of the magnetic field coils Bx and Bz is severely reduced and cannot meet the compensation requirements. Therefore, it is necessary to take the influence of ferromagnetic boundaries on the magnetic field into account when designing the coils, and suppress the coupling effect from the design principle itself. The magnetic moment is a physical quantity that describes the magnetic properties of the current-carrying coil. In step S1, a three-axis coil is designed. According to the characteristic that the moment-free coil has good self-shielding performance, the secondary coil is set to be obtained by scaling the primary coil in equal proportion. The primary coil and the secondary coil are constructed as moment-free coils, then the following should be satisfied:

[0062] M=M1+M2=I1·S1+I2·S2→0 (15)

[0063] L2=λL1 (16)

[0064] D2=λD1 (17)

[0065] S2=L2·D2=λL1·λD1=λ2·S1 (18)

[0066] M=M1-M2=I1·S1-I2·S2→0

[0067] =I1·S1-μ·I1·λ2·S1=I1·S1(1-μ·λ 2 ) (19)

[0068] Where L1 and L2 are the side lengths of the two coils, both of which are squares; D1 and D2 are the vertical distances from the coil plane to the center point, respectively. The secondary coil is obtained by geometrically amplifying the primary coil, with an amplification factor of λ. That is, the parameters of the two coils follow the above relationship. According to equations (16), (17), and (18), we get:

[0069]

[0070] Although the magnetic field of the planar coil will change when it is scaled up, its uniformity will not change. The uniformity of the target area will change slightly, but it still maintains a high uniformity. A coil with no magnetic moment is constructed by placing the primary coil and the secondary coil in parallel. The magnetic field is obtained by the coil with no magnetic moment, as shown below:

[0071]

[0072] in, Represents the primary coil, represents the secondary coil;

[0073] Finally, the coil without magnetic moment satisfies the relationship:

[0074]

[0075] Among them, S2=L2·D2=λL1·λD1=λ2·S1; B t Indicates the magnetic field of the target area; and Represent the magnetic fields generated by the primary coil and the secondary coil in the target area respectively; M represents the total magnetic moment; M1 and M2 represent the magnetic moments of the primary coil and the secondary coil respectively; The plane stream function of the primary coil and the magnetic field matrix of the target point; represents the plane stream function of the secondary coil and the magnetic field matrix of the target point; p mn represents the stream function coefficient matrix of the coil; λ represents the proportional amplification coefficient; I1 represents the current passing through the primary coil; I2 represents the current passing through the secondary coil; S1 represents the plane area of ​​the primary coil; S2 represents the plane area of ​​the secondary coil; μ represents the current proportional coefficient; according to the relationship, when λ→1, the coil with no magnetic moment achieves self-shielding.

[0076] S3. In the range of 0<λ<1, the proportional amplification coefficient λ takes an arbitrary value, and the primary coil is scaled according to the arbitrary value to obtain an initial secondary coil, thereby completing the first suppression of the ferromagnetic boundary coupling effect;

[0077] Affected by ferromagnetic boundary coupling, the coil assembly now has no external magnetic moment influence, and the coil magnetic field is self-shielded, suppressing the ferromagnetic boundary coupling between the magnetic field generated by the coil assembly and the high-permeability inner surface of the magnetic shield. However, some magnetic field still produces a coupling effect. Therefore, for the boundary magnetic field that cannot be completely suppressed, we use a combination of image analysis and particle swarm optimization to suppress the ferromagnetic boundary coupling a second time.

[0078] S4. Within the range of 0<λ<1, the particle swarm optimization algorithm is used to optimize the proportional amplification coefficient λ to obtain the optimal proportional amplification coefficient λ, and the initial secondary coil is scaled according to the optimal proportional amplification coefficient λ to obtain the optimal secondary coil, thereby completing the second suppression of the ferromagnetic boundary coupling effect.

[0079] The specific process of step S4 is:

[0080] S4.1. According to the principle of the image method, the magnetic field strength of the coil in the image is obtained, and the magnetic field strength of the coil in the image is superimposed with the magnetic field strength of the actual coil to obtain the final magnetic field strength of the target area:

[0081]

[0082] in, and They represent the magnetic fields generated by the primary coil and the secondary coil in the target area by the imaging method; and P mn,im are the coil matrix and stream function matrix at this time respectively.

[0083] S4.2. Setting the objective function:

[0084]

[0085] Wherein, B(x, y, z) represents the final magnetic field strength of the target area obtained in step S4.1; B center (0,0,0) represents the magnetic field generated by the coil at the center point; the search area is set to: 200mmx200mmx200mm; the search area contains KN particles;

[0086] S4.3. Set the iterative update rule as:

[0087] V i =ω·V i +rand1·c1(X i,best -X i )+rand2·c2(X g,best -X i );

[0088] X i =X i +V i ; (25)

[0089] Among them, X i =(x i1 ,x i2 ), X i represents the position of the i-th particle in the iteration, x i1 Represents the proportional magnification factor, x i1 =λ,x i2 Represents the current proportionality coefficient, V i represents the particle velocity, V i =[v i1 , v i2 ],v i1 Indicates the limit of the proportional amplification factor,

[0090] v i1 =[λmax min ];v i2 Indicates the limitation of current proportional coefficient, v i2 =[μmax min]; c1 and c2 both represent learning factors; rand1 and rand2 both represent random numbers ranging from 0 to 1; ω represents the inertia factor, which is negative; X i,best represents the optimal solution for each particle, X g,best represents the global optimal solution of the entire population;

[0091] S4.4. Input the proportional amplification coefficient λ of any value obtained in step S3 and the corresponding current proportional coefficient μ into the particle swarm optimization algorithm, and iterate according to the iterative update rule defined in step S4.3, record the number of particles KN and the objective function value ME obtained in each iteration, until the maximum number of iterations is reached, and stop the iteration; find the minimum value from all the objective function values ​​ME obtained, and the proportional amplification coefficient λ corresponding to the minimum value at this time is the optimal proportional amplification coefficient λ.

[0092] In step S4.1, the magnetic field intensity of the target area is obtained using the imaging method principle. The specific process is as follows:

[0093] According to the principle of the image method, the image current generated by the reflection of the magnetic source on the high permeability medium plane has the following relationship with the actual current:

[0094]

[0095] Among them, I im is the image current, I re is the actual current, μ1 and μ2 are the relative magnetic permeabilities of air and the magnetic shielding material, respectively. The relative magnetic permeability of air is typically 1, while the initial relative magnetic permeability of the permalloy used in magnetic shielding can reach 80,000. Therefore, the image current and the actual current are nearly equal.

[0096] Applying the image method to a magnetic shielding room, the six high-permeability ferromagnetic boundary planes of the magnetic shielding room can be regarded as mirrors to reflect the internal dual-plane coils. At the same time, the image current generated by the shielding layer will be reflected again by other planes, ultimately forming an infinite-order coil array. Through the mirror principle, Equation (6) can be replaced by the magnetic field expression of the coil array:

[0097] Represents the current density of the primary coil image method; Represents the current density of the secondary coil image method.

[0098] Where a represents the order of the equivalent coil array, represents the image current density at the i, j, and kth order, while δ and ε are the directional coefficients that determine the image current direction. Current density is a typical polar vector: the normal component perpendicular to the reflection plane reverses direction, while the component parallel to the reflection plane remains in the same direction. Taking the X-direction current density as an example, its direction remains unchanged after reflection in the Y and Z directions, but reverses direction after reflection in the X direction. Therefore, the directional coefficients δ and ε can be determined based on the current density symmetry of the dual-plane coil and the direction of the reflection plane. The calculation method is shown in Table 1.

[0099] Table 1 Directional coefficient calculation method

[0100]

[0101] With double plane coil B x As an example, substituting the current density distribution function of the corresponding coil in the above table into equations (10) and (11), we can obtain:

[0102]

[0103] Wherein, i=1, 2 represent the primary coil and the secondary coil respectively;

[0104]

[0105] Where (x0, y0, z′1) and (x0, y0, z′2) represent source points on different planes of the coil, a represents the order of the equivalent coil array, and INT() represents the rounding function. Theoretically, the coil order is infinite, but in practice, high-order image currents are very weak after multiple reflections and can be ignored in the calculation. Setting the coil order to a = 2 can meet the accuracy requirements while reducing the computational complexity. Incorporating the coupling effect into the design of the dual-plane coil fundamentally suppresses the influence of the ferromagnetic boundary on the compensation coil magnetic field. The final magnetic field strength in the target area is:

[0106]

[0107] in, and They represent the magnetic fields generated by the primary coil and the secondary coil in the target area by the imaging method; and P mn,im denote the coil matrix and stream function matrix respectively.

[0108] Based on the design method described in the present invention, a SCC (suppressed coupling coil system, consisting of the primary coil and secondary coil described in the present invention) was designed, placed in an MSR (magnetic shielding room) with an inner dimension of 600×600×600mm, and then the performance was simulated using finite element software (Comsol Multiphysics). In order to avoid the randomness of the single-axis coil design, Bx and Bz coils were designed. The main coil parameters designed by TFM (electromagnetic field simulation module in finite element software) are as follows: the Fourier order of the stream function is set to M=N=4. The target area is discretized into T=125 target points, arranged in a 5×5×5 matrix. The coil size and distance are Lx=Ly=L1=250mm and D1=220mm, respectively. Based on these parameters, we get the number of turns of the main coil, as shown in Figure 2 and Figure 3 shown.

[0109] For the optimization of λ and μ, the number of particles in PSO is set to Kn = 20 and the number of iterations is set to T = 500. The position of the particle is represented by X i =(x i1 , x i2 ), represents the proportional magnification factor (x i1 =λ=[0.5,1.50]) and current proportional coefficient (x i2 =μ∈[λ 2 (1-10%), λ 2 (1+10%)]). Particle velocity V i =(v i1 ,v i2 ), limited to v i1 =[λmax min ]=[0.5,1.5] and v i2 =[μmax min ]=[0,0.25]. Finally, we get the optimal result; the proportional amplification factor (λ) of Bx and the current proportional coefficient (μ) are λ x and μ x The value of Bz is λ z and μ z Based on these parameters, the current proportional coefficients of the secondary coil and the primary and secondary coils are obtained.

[0110] In order to demonstrate the superiority of SCC, the designed SCC was tested in finite element software (Comsol Multiphysics) to verify its performance. In the simulation, the finite element model contains two domains: an air domain with a size of 2000×2000×2000mm and an internal MSR domain with a size of 600×600×600mm and a thickness of 1mm. For the simulation model, the relative magnetic permeability of the MSR is set to 55,000. A user-controlled mesh model is used here, and a fine mesh with a maximum unit of 10mm and a minimum unit of 0.1mm is defined to ensure the accuracy of the results. The boundary of the air domain is assumed to be an infinite element domain to avoid the influence of boundary conditions on the simulation. The coil is set to an edge current module. By setting the current in the primary coil to 1A and the current in the secondary coil to μ respectively according to the simulated current proportional coefficient. x and μ z The size of the secondary coil and the distance from the center are scaled according to the geometric magnification factor after PSO optimization, where the magnification factors of Bx and Bz are λ x and λ z , and then simulation was carried out after the establishment was completed.

[0111] Due to defects such as holes, cracks in doors, and manufacturing processes in real shielded rooms, the shielded room cannot be equated to an ideal high-permeability cube. Image method coils that take coupling effects into account will distort the target field due to defect coupling, increasing the relative error. SCC coils suppress the coupling effects between the shielded room and the coil, thereby also suppressing the effects of coupling effects from shielded room defects on the target area's magnetic field. To verify this conclusion, a second-order image method coil was designed with identical parameters. Using finite element software, a simplified shielded room model with holes and cracks and an ideal high-permeability cube shielded room model were constructed. The target field magnetic field uniformity of the SCC coil, image method coil, and target field method coil (primary coil) was compared under three conditions. Simulation experiments verified the SCC coil's ability to suppress shielded room coupling and defect coupling effects. The maximum non-uniformity error change rate for the three coils in the shielded room model is shown in Table 2.

[0112] Table 2 Maximum non-uniformity error change rate of the coil in the shielded room model

[0113] Image Method (IM) Target Field Method (TFC) SCC Bx -1.42～1.67 -1.51～1.55 -1.06～1.23 Bz -1.44～1.34 -1.6～1.53 -0.58～0.42

[0114] Through the comparative analysis of the above results, it is shown that the uniformity of the SCC coil is more advantageous. It is also proved that the SCC coil can suppress the coupling effect between the magnetic shielding room and the coil, and thus can also suppress the influence of the coupling effect of the shielding room defects on the magnetic field value in the target area.

Claims

1. A coil design method for suppressing ferromagnetic boundary coupling based on an image method and a self-shielding method, characterized by: The coil includes a primary coil and a secondary coil, and the primary coil and the secondary coil are placed in parallel in a magnetic shielding room. The method includes the following steps: S1. Design the primary coil using the target field method; S2. Assume that the secondary coil is obtained by scaling the primary coil in equal proportion, and construct the primary coil and the secondary coil into a coil without magnetic moment, and the coil without magnetic moment satisfies the relationship: Among them, S2=L2·D2=λL1·λD1=λ 2 S1; B t Indicates the magnetic field of the target area; and Represent the magnetic fields generated by the primary coil and the secondary coil in the target area respectively; M represents the total magnetic moment; M1 and M2 represent the magnetic moments of the primary coil and the secondary coil respectively; The plane stream function of the primary coil and the magnetic field matrix of the target point; represents the plane stream function of the secondary coil and the magnetic field matrix of the target point; p mn represents the stream function coefficient matrix of the coil; λ represents the proportional amplification factor; I1 represents the current through the primary coil; I2 represents the current through the secondary coil; S1 represents the plane area of ​​the primary coil; S2 represents the plane area of ​​the secondary coil; μ represents the current proportional coefficient; according to the above relationship, when λ→1, the coil with no magnetic moment achieves self-shielding; S3. Within the range of 0<λ<1, the proportional amplification coefficient λ takes an arbitrary value, and the primary coil is scaled according to the arbitrary value to obtain an initial secondary coil, thereby completing the first suppression of the ferromagnetic boundary coupling effect; S4. Within the range of 0<λ<1, the particle swarm optimization algorithm is used to optimize the proportional amplification coefficient λ to obtain the optimal proportional amplification coefficient λ, and the initial secondary coil is scaled according to the optimal proportional amplification coefficient λ to obtain the optimal secondary coil, thereby completing the second suppression of the ferromagnetic boundary coupling effect.

2. The coil design method for suppressing ferromagnetic boundary coupling based on image method and self-shielding method according to claim 1, characterized in that: In step S4, the specific process of optimizing the proportional amplification factor λ using the particle swarm optimization algorithm includes the following steps: S4.

1. According to the principle of the image method, the magnetic field strength of the image coil is obtained, and the magnetic field strength of the image coil is subtracted from the magnetic field strength of the actual coil to obtain the final magnetic field strength of the target area: in, and They represent the magnetic fields generated by the primary coil and the secondary coil in the target area by the imaging method; and P mn,im denote the coil matrix and stream function matrix respectively; S4.

2. Setting the objective function: Wherein, B(x, y, z) represents the final magnetic field strength of the target area obtained in step S4.1; B center (0,0,0) represents the magnetic field generated by the coil at the center point; the search area is set to: a×b×c; the search area contains KN particles; S4.

3. Set the iterative update rule as follows: V i =ω·V i +rand1·c1(X i,best -X i )+rand2·c2(X g,best -X i ); X i =X i +V i ; Among them, X i =(x i1 ,x i2 ), X i represents the position of the i-th particle in the iteration, x i1 Represents the proportional magnification factor, x i1 =λ,x i2 Represents the current proportional coefficient, x i2 =μ; V i represents the particle velocity, V i =(v i1 , v i2 ), v i1 Indicates the limit of the proportional magnification factor, v i1 =[λmax min ];v i2 Indicates the limitation of current proportional coefficient, v i2 =[μmax min ]; c1 and c2 are learning factors; rand1 and rand2 are random numbers ranging from 0 to 1; ω is the inertia factor, which is negative; X i，best represents the optimal solution for each particle, X g，best represents the global optimal solution of the entire population; S4.

4. Input the proportional amplification coefficient λ of any value obtained in step S3 and the corresponding current proportional coefficient μ into the particle swarm optimization algorithm, and iterate according to the iterative update rule defined in step S4.3, record the number of particles KN and the objective function value ME obtained in each iteration, until the maximum number of iterations is reached, and stop the iteration; find the minimum value from all the objective function values ​​ME obtained, and the proportional amplification coefficient λ corresponding to the minimum value at this time is the optimal proportional amplification coefficient λ.

3. The coil design method for suppressing ferromagnetic boundary coupling based on image method and self-shielding method according to claim 2, characterized in that: The specific process of step S4.1 includes the following steps: S4.

11. Based on the principle of the image method, each infinite high-permeability surface of the magnetic shielding room is equivalent to a mirror, reflecting the internal dual-plane coil. At the same time, the image current generated by any high-permeability surface will be reflected again by other high-permeability surfaces. Therefore, the six high-permeability surfaces of the magnetic shielding room reflect each other, forming an infinite-order coil array. S4.

12. Assume that the image current generated by the high permeability medium plane reflecting the magnetic source and the actual current of the coil are related by the following equation: Among them, I im Represents the image current, I re represents the actual current, μ1 represents the relative magnetic permeability of air, μ1 is set to 1; μ2 represents the relative magnetic permeability of the magnetic shielding material; through the principle of the image method, the expression of the magnetic field intensity of the coil array is obtained as follows: in, Indicates the current density of the primary coil image method; represents the current density of the secondary coil image method; a represents the order of the equivalent coil array, represents the image current density at the i, j, and kth order, δ and ε represent the directional coefficients that determine the direction of the image current; S4.

13. Set the coil order a to a = 2, and obtain the final magnetic field strength in the target area: in, and They represent the magnetic fields generated by the primary coil and the secondary coil in the target area by the imaging method; and P mn,im denote the coil matrix and stream function matrix respectively.

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