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

Abstract

The invention relates to a coil design method for suppressing ferromagnetic boundary coupling based on an image method and a self-shielding method, a coil comprises a primary coil and a secondary coil, and the method comprises the following steps: designing the primary coil by adopting a target field method; setting a secondary coil to be obtained by scaling the primary coil in equal proportion, and constructing a non-magnetic moment coil; within the range of 0 < lambda < 1, taking an arbitrary numerical value of the equal-proportion amplification coefficient lambda, and scaling the primary coil according to the arbitrary numerical value to obtain an initial secondary coil; and optimizing the equal-proportion amplification coefficient lambda by using a particle swarm optimization algorithm to obtain an optimal secondary coil. According to the method, ferromagnetic boundary coupling between a magnetic field generated by a coil and a magnetic shielding high-permeability inner surface is restrained through a self-shielding method, then optimization is further carried out to completely restrain the coupling effect, the gradient uniformity of the magnetic field in a magnetic shielding room is improved, and an extremely weak magnetic environment is achieved.

Description

Technical Field

[0001] The 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 non-invasive functional imaging technique that can detect the weak magnetic field generated by the heart. Compared with other cardiac imaging techniques, it does not release harmful radiation or stimulation signals and is non-invasive to the human body, so it has received widespread attention at home and abroad.

[0003] Existing magnetic heart measurement devices are mainly based on superconducting quantum interference devices and atomic magnetometers. Both devices require the use of zero magnetic devices to provide a weak magnetic test environment that meets the requirements. The zero magnetic device is composed of a shielded room with multiple layers of high magnetic permeability materials and an active magnetic compensation coil, which can achieve near-zero residual magnetism in the middle area of ​​the interior. However, the shielded room structure depends on high magnetic permeability materials, and once the structure is determined, it cannot be changed at will. Therefore, it is necessary to design an active magnetic compensation coil.

[0004] The dual-plane coil designed by the target field method can provide enough space for MCG subjects, and this method is widely used in MEG research in magnetic shielding rooms. However, the coupling effect between the magnetic field generated by the coil and the magnetic shielding room will seriously reduce the uniformity and gradient of the target area, thus 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 image method and self-shielding method. The coil designed by this method can effectively suppress the ferromagnetic boundary coupling effect, improve the uniformity of the magnetic field gradient inside the magnetic shielding room, and realize 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, wherein the coil comprises 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 comprises 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:

[0009] Among them, S2=L2=D2=λL1·λD1=λ 2 S1; B t Indicates the magnetic field of the target area; and They 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 representing 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 magnification 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 without magnetic moment achieves self-shielding;

[0010] S3, within the range of 0<λ<1, the proportional magnification 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;

[0011] S4. In the range of 0<λ<1, the particle swarm optimization algorithm is used to optimize the proportional magnification coefficient λ to obtain the optimal proportional magnification coefficient λ, and the initial secondary coil is scaled according to the optimal proportional magnification coefficient λ to obtain the optimal secondary coil, thereby completing the second suppression of the ferromagnetic boundary coupling effect.

[0012] 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, and the target field method is firstly adopted 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 can achieve self-shielding; then the proportional magnification factor is optimized by the particle swarm optimization algorithm, and finally the optimal secondary coil is obtained according to the optimal proportional magnification factor to complete the coil design; the method first suppresses the ferromagnetic boundary coupling between the magnetic field generated by the coil and the high magnetic permeability inner surface of the magnetic shielding through the self-shielding method, 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.

[0013] Preferably, in step S4, the specific process of optimizing the proportional magnification factor λ using the particle swarm optimization algorithm comprises the following steps:

[0014] S4.1. According to the principle of the image method, the magnetic field strength of the coil of the image is obtained, and the magnetic field strength of the coil of the image is subtracted from the magnetic field strength of the real coil to obtain the final magnetic field strength of the target area:

[0015] in, and They represent the magnetic fields generated by the primary coil and the secondary coil in the target area by the imaging method respectively; and P mn，im denote the coil matrix and stream function matrix respectively;

[0016] 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;

[0017] S4.3. Set the iterative update rule as:

[0018] V i =ω·V i +rand1·c1(X i，best -X i )+rand2·c2(X g，best -X i );

[0019] X i =X i +V i ;

[0020] 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, x i2 =μ; V i represents the particle velocity, V i =(v i1 , v i2 ), v i1 Represents the limit of the proportional gain factor, v i1 =[λmax min ];v i2 Indicates the limitation of current proportionality 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;

[0021] S4.4. Input the proportional magnification 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 magnification coefficient λ corresponding to the minimum value at this time is the optimal proportional magnification coefficient λ.

[0022] Preferably, the specific process of step S4.1 includes the following steps:

[0023] S4.11. According to the principle of the image method, each infinite high-permeability medium surface of the magnetic shielding room is equivalent to a mirror to reflect the internal double-plane coil. At the same time, the image current generated by any high-permeability medium surface will be reflected again by other high-permeability medium surfaces. Therefore, the six high-permeability medium surfaces of the magnetic shielding room reflect each other to form an infinite-order coil array.

[0024] S4.12. Assume that there is a relationship between the image current generated by the high magnetic permeability medium plane reflecting the magnetic source and the actual current of the coil: 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 intensity of the coil array is obtained as follows:

[0025]

[0026]

[0027] in, Represents 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;

[0028] S4.13, the coil order a is set to a=2, and the final magnetic field strength of the target area is obtained as:

[0029] in, and They represent the magnetic fields generated by the primary coil and the secondary coil in the target area by the imaging method respectively; and P mn,imdenote the coil matrix and stream function matrix respectively.

[0030] 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

[0031] Figure 1 It is a structural schematic diagram of the magnetic shielding room in the present invention;

[0032] Figure 2 It is a schematic diagram of the structure of the magnetic field coil Bx in the present invention and a schematic diagram of the corresponding stream function image; 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;

[0033] Figure 3 It is a schematic diagram of the structure of the magnetic field coil Bz in the present invention and a schematic diagram of the corresponding stream function image; 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;

[0034] As shown in the figure: 1. Magnetic shielding room; 2. Primary coil; 3. Secondary coil; 4. Target area. DETAILED DESCRIPTION

[0035] 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.

[0036] 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 comprises 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 the ferromagnetic boundary band and compensate for the residual magnetic field in the target area. Figure 1 In the equation, the current magnitude, distance from the center, and size of the primary coil and the secondary coil are proportional to each other, and the superposition of the magnetic moments of the two coils tends to zero, so the two coils constitute 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, and in the shielding area, the magnetic field value approaches zero, and the sum of the magnetic moments of the primary and secondary tends to zero, as shown in the following formula (1):

[0037]

[0038] Among them, B tRepresents 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.

[0039] The specific design method includes the following steps:

[0040] S1. Design the primary coil using the target field method:

[0041] Magnetic field coils Bx, By and Bz are respectively arranged in the x, y and z directions to form a primary coil; because the magnetic field coil By and the magnetic field coil Bx are of the same size and shape, but are rotated 90°, 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:

[0042] First, the current distribution on the double plane coil is regarded 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] :

[0043]

[0044] 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.

[0045] 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:

[0046]

[0047] In the calculation process of the target field method, the target area is usually discretized into T equally spaced target points. The magnetic field of the target point is preset as a constant to minimize the residual magnetic field at all target points 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 of the target point is constructed as follows:

[0048]

[0049] In the formula, S is the coil plane; μ0 is the magnetic permeability in vacuum; r is the distance between the plane coil stream function and the target point. Combining formula (5) and formula (6), the magnetic field in the Bx direction can be derived and simplified as follows:

[0050]

[0051] In the formula, 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.

[0052]

[0053] Where: A mn Plane stream function and magnetic field matrix of target point; and They are respectively the plane stream functions of the coils on the left and right sides of a set of plane coils and the magnetic field matrix of the target point; The plane stream function representing 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;

[0054] 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:

[0055] B x =A mn ·P mn =B target (11)

[0056] As the equation mentioned above 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:

[0057]

[0058] Where: λ is the weighting coefficient; E is the error function; coil curvature As follows:

[0059]

[0060] when Coefficient matrix Pmn It can be solved by the following formula:

[0061]

[0062] When P mn When 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.

[0063] S2. Under the influence of ferromagnetic boundary coupling, the magnetic field uniformity of magnetic field coils Bx and Bz is severely reduced and cannot meet the compensation requirements. Therefore, it is necessary to take into account the influence of ferromagnetic boundaries on the magnetic field 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 a current-carrying coil. In step S1, a coil in three-axis direction 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 proportion, and the primary coil and the secondary coil are constructed as moment-free coils, then the following should be satisfied:

[0064] M=M1+M2=I1·S1+I2·S2→0 (15)

[0065] L2=λL1 (16)

[0066] D2=λD1 (17)

[0067] S2=L2·D2=λL1·λD1=λ 2 ·S1 (18)

[0068] M=M1-M2=I1·S1-I2·S2→0

[0069] =I1·S1-μ·I1·λ 2 ·S1=I1·S1(1-μ·λ 2 ) (19)

[0070] Among them, L1 and L2 are the side lengths of the two sets of coils, both of which are squares; D1 and D2 are the vertical distances from the coil plane to the center point, and the secondary coil is obtained by geometrically amplifying the main coil, with an amplification factor of λ, that is, the parameters of the two sets of coils follow the above relationship. According to equations (16), (17) and (18), we get:

[0071]

[0072] λ→1

[0073] Although the magnetic field of the planar coil will change by scaling it up, its uniformity will not change, and the uniformity of the target area will change slightly, but it still maintains a high uniformity. The magnetic field is obtained by constructing a magnetic moment-free coil using the primary coil and the secondary coil placed in parallel, as shown below:

[0074]

[0075] in, represents the primary coil, represents the secondary coil;

[0076] Finally, the coil without magnetic moment satisfies the relationship:

[0077]

[0078] Among them, S2=L2·D2=λL1·λD1=λ 2 S1; B t Indicates the magnetic field of the target area; and They 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 representing 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 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.

[0079] S3, within the range of 0<λ<1, the proportional magnification 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;

[0080] Affected by the ferromagnetic boundary coupling, the coil group has no magnetic moment effect on the outside at this time, and the coil magnetic field is self-shielded, so that the ferromagnetic boundary coupling between the magnetic field generated by the coil group and the inner surface of the magnetic shielding high magnetic permeability is suppressed, but a part of the magnetic field still produces a coupling effect. Therefore, for the boundary magnetic field that cannot be completely suppressed, we use the image method and particle swarm optimization algorithm to suppress the ferromagnetic boundary coupling for the second time.

[0081] S4. In the range of 0<λ<1, the particle swarm optimization algorithm is used to optimize the proportional magnification coefficient λ to obtain the optimal proportional magnification coefficient λ, and the initial secondary coil is scaled according to the optimal proportional magnification coefficient λ to obtain the optimal secondary coil, thereby completing the second suppression of the ferromagnetic boundary coupling effect.

[0082] The specific process of step S4 is:

[0083] S4.1. According to the principle of the image method, the magnetic field strength of the coil of the image is obtained, and the magnetic field strength of the coil of the image is superimposed with the magnetic field strength of the real coil to obtain the final magnetic field strength of the target area:

[0084]

[0085] in, and They represent the magnetic fields generated by the primary coil and the secondary coil in the target area by the imaging method respectively; and P mn，im are the coil matrix and stream function matrix at this time respectively.

[0086] S4.2. Setting the objective function:

[0087]

[0088] 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;

[0089] S4.3. Set the iterative update rule as:

[0090] V i =ω·V i +rand1·c1(X i，best -X i )+rand2·c2(X g，best -X i );

[0091] x i =x i +V i ; (25)

[0092] 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, xi1 =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 magnification factor,

[0093] v i1 =[λmax min ];v i2 Indicates the limitation of current proportionality 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;

[0094] S4.4. Input the proportional magnification 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 magnification coefficient λ corresponding to the minimum value at this time is the optimal proportional magnification coefficient λ.

[0095] In step S4.1, the magnetic field strength of the target area is obtained using the principle of the image method, and the specific process is as follows:

[0096] According to the principle of the image method, the image current generated by the reflection of the magnetic source by the high magnetic permeability medium plane has the following relationship with the actual current:

[0097]

[0098] Among them, I im is the image current, I re is the actual current, μ1 and μ2 are the relative magnetic permeability of air and the relative magnetic permeability of the magnetic shielding material, respectively. Usually the relative magnetic permeability of air is 1, while the initial relative magnetic permeability of the Permalloy used in magnetic shielding can reach 80,000, so the image current and the actual current are almost equal.

[0099] Applying the image method to the magnetic shielding room, the six high permeability ferromagnetic boundary planes of the magnetic shielding room can be regarded as mirrors to reflect the internal double-plane coils. At the same time, the image current generated by the shielding layer will be reflected again by other planes, and finally form an infinite order coil array. Through the mirror principle, equation (6) can be replaced by the magnetic field expression of the coil array:

[0100]

[0101] Represents the primary coil image method current density; Represents the current density of the secondary coil image method.

[0102] Where a represents the order of the equivalent coil array, J i，j，k ( represents the image current density at the i, j, and kth order, and δ and ε are the directional coefficients that determine the direction of the image current. The current density is a typical polar vector. The direction of the normal component perpendicular to the reflection plane is reversed, while the direction of the component parallel to the reflection plane remains unchanged. Taking the current density in the X direction as an example, the direction remains unchanged after reflection in the Y and Z directions, but reverses after reflection in the X direction. Therefore, the directional coefficients δ and ε can be judged by the symmetry of the current density of the dual-plane coil and the direction of the reflection plane. The calculation method is shown in Table 1.

[0103] Table 1 Directivity coefficient calculation method

[0104]

[0105] With double planar 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:

[0106]

[0107] Wherein, i=1, 2 represent the primary coil and the secondary coil respectively;

[0108]

[0109] Among them, (x0, y0, z′1) and (x0, y0, z′2) represent the 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 fact, the high-order image current is very weak after multiple reflections and can be ignored in the calculation. Taking the coil order as a=2 can meet the accuracy requirements and reduce the amount of calculation. The coupling effect is integrated into the design of the dual-plane coil, which fundamentally suppresses the influence of the ferromagnetic boundary on the magnetic field of the compensation coil. The final magnetic field strength in the target area is:

[0110]

[0111] in, and They represent the magnetic fields generated by the primary coil and the secondary coil in the target area by the imaging method respectively; and P mn，im denote the coil matrix and stream function matrix respectively.

[0112] Based on the design method described in the present invention, a SCC (suppressed coupling coil system, consisting of the primary coil and the 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 obtained the number of turns of the main coil, as shown in Figure 2 and Figure 3 shown.

[0113] 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 proportionality factor (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 gain coefficient (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 proportionality coefficient of the secondary coil and the primary coil and the secondary coil is obtained.

[0114] In order to demonstrate the superiority of SCC, the designed SCC was verified in the 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 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 setting the current in the secondary coil to μ respectively according to the simulated current proportionality factor. x and μ z The size and distance of the secondary coil 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 a simulation was performed after the establishment was completed.

[0115] Due to the defects of holes, door gaps, and processing technology in the real shielding room, the shielding room cannot be equivalent to an ideal high magnetic permeability cube. The image method coil considering the coupling effect will cause the target field to distort the magnetic field value due to the defect coupling effect, and the relative error will increase. The SCC coil can suppress the coupling effect between the magnetic shielding room and the coil, so it can also suppress the influence of the coupling effect of the shielding room defects on the magnetic field value of the target area. In order to verify the above conclusions, a second-order image method coil was designed with the same parameters. Using finite element software, we established a simplified shielding room model with holes and door gaps and an ideal high magnetic permeability cube shielding room model. The uniformity of the target field magnetic field of the SCC coil, image method coil and target field method coil (primary coil) in three cases was compared. The ability of the SCC coil to suppress the coupling effect and defect coupling effect of the shielding room was verified by simulation experiments. The maximum non-uniformity error change rate of the three coils in the shielding room model is shown in Table 2 below.

[0116] Table 2 Maximum non-uniformity error change rate of coil in shielded room model

[0117] 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

[0118] Through the comparative analysis of the above results, the uniformity of the SCC coil has a greater advantage. At the same time, it is proved that the SCC coil can suppress the coupling effect between the magnetic shielding room and the coil, and therefore 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 in that: 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 They 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 representing 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 magnification 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 without magnetic moment achieves self-shielding; S3, within the range of 0<λ<1, the proportional magnification 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. In the range of 0<λ<1, the particle swarm optimization algorithm is used to optimize the proportional magnification coefficient λ to obtain the optimal proportional magnification coefficient λ, and the initial secondary coil is scaled according to the optimal proportional magnification 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 magnification 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 coil of the image is obtained, and the magnetic field strength of the coil of the image is subtracted from the magnetic field strength of the real 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 respectively; 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: 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 proportionality coefficient, x i2 =μ; V i represents the particle velocity, V i =(v i1 , v i2 ), v i1 Indicates the limit of the proportional gain factor, v i1 =[λmax min ];v i2 Indicates the limitation of current proportionality 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; S4.

4. Input the proportional magnification 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 magnification coefficient λ corresponding to the minimum value at this time is the optimal proportional magnification 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. According to the principle of the image method, each infinite high-permeability medium surface of the magnetic shielding room is equivalent to a mirror to reflect the internal double-plane coil. At the same time, the image current generated by any high-permeability medium surface will be reflected again by other high-permeability medium surfaces. Therefore, the six high-permeability medium surfaces of the magnetic shielding room reflect each other to form an infinite-order coil array. S4.

12. Assume that there is a relationship between the image current generated by the high magnetic permeability medium plane reflecting the magnetic source and the actual current of the coil: 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 intensity of the coil array is obtained as follows: in, Represents 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, the coil order a is set to a=2, and the final magnetic field strength of the target area is obtained as: in, and They represent the magnetic fields generated by the primary coil and the secondary coil in the target area by the imaging method respectively; and P mn ,im represent the coil matrix and stream function matrix respectively.

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