Magnetic field gradient suppression method in magnetic shielding room

Abstract

The invention relates to a magnetic field gradient suppression method in a magnetic shielding chamber, and the method comprises the steps: placing five gradient coils in the magnetic shielding chamber in parallel, and dividing a target region in the magnetic shielding chamber into NUM points; acquiring a target area magnetic field distribution function in the magnetic shielding chamber; and uniformly dispersing the function into NUM coordinate points to obtain a least square error function about magnetic field distribution of the target area, and solving the least square error function by adopting Tikhonov regularization to obtain a coefficient matrix Pmn so as to design a gradient coil. According to the invention, five groups of gradient coils are simultaneously designed to inhibit the gradient magnetic field in the magnetic shielding chamber, after excitation is applied to the gradient coils, the gradients of three components of the magnetic field along three directions are obviously reduced, and the gradient magnetic fields in all directions in the magnetic shielding chamber can be effectively inhibited through the design of the gradient coils.

Description

Technical Field

[0001] The invention relates to the technical field of magnetic shielding, in particular to a method for suppressing magnetic field gradient in a magnetic shielding room. Background Art

[0002] Passive magnetic shielding technology can be used to obtain extremely low residual magnetic fields inside the magnetic shielding room, but the magnetic field shielding performance is different at different spatial locations inside the magnetic shielding room; the residual magnetic field near the magnetic shielding room is larger, while the magnetic field at the center is smaller. The change in the magnetic field causes gradient magnetic fields to appear in all directions. Gradient magnetic fields can cause large errors in many precision physical experiments, such as electron electric dipole moment measurement, heart magnetism, and brain magnetism signal measurement. Therefore, suppressing the gradient magnetic field in the magnetic shielding room can provide a more uniform zero-magnetic environment for various cutting-edge scientific experiments. Reducing the errors caused by gradient magnetic fields is the focus of magnetic shielding research. In 2014, CP Bidinostia et al. conducted a study on the static gradient magnetic field in an infinitely long cylindrical magnetic shielding structure under passive magnetic shielding. In 2018, in the brain magnetism experiment conducted by the University of Nottingham, it was necessary to process gradient magnetic fields in multiple directions.

[0003] High-performance gradient magnetic field coils are the key factor in improving the ability to suppress gradient magnetic fields in magnetic shielding rooms. Based on inverse design, the planar coils designed using the target field method have the advantages of good orthogonality, high space utilization, and small uniformity error. The gradient magnetic fields in each direction can be designed independently, so they are suitable for suppressing the gradient magnetic field in magnetic shielding rooms.

[0004] After recent years of development, the gradient coils designed using the target field method have made great progress. In 2020, Wang et al. used the particle swarm algorithm to optimize the planar coil, greatly improving its uniformity; in 2023, Shuai et al. used the funnel algorithm to design uniform magnetic field coils and gradient magnetic field coils, improving space utilization. However, existing studies are all conducted on a single direction or a single magnetic field value, and the presence of multiple magnetic field gradients in the magnetic shielding room interferes with various experiments. Therefore, how to simultaneously suppress multiple magnetic field gradients in the magnetic shielding room has become the key to the problem. Summary of the invention

[0005] The technical problem to be solved by the present invention is to provide a method for suppressing magnetic field gradient in a magnetic shielding room, which compensates all gradient magnetic fields inside the magnetic shielding room by multiple gradient coils at the same time, thereby effectively reducing the gradient magnetic field in the magnetic shielding room.

[0006] The technical solution adopted by the present invention is a method for suppressing the magnetic field gradient in a magnetic shielding room, comprising the following steps:

[0007] S1. Define the rate of change of magnetic field at a point in the magnetic shielding room as: Among them, B x+Δx represents the offset Δx magnetic field component along the x-axis in the magnetic shielding room; B x It represents the magnetic field component along the x-axis direction in the magnetic shielding room, and defines the three components Bx, By and Bz of the magnetic induction intensity of the compensation coil to be designed in the x-axis direction, y-axis direction and z-axis direction of the space as follows: According to Maxwell's equations, we can get the expression: Then, in a closed magnetic shielding room, the spatial magnetic field gradient environment is expressed as:

[0008] S2. According to the spatial magnetic field gradient environment expression, five gradient coils are designed in the magnetic shielding room to control all gradient magnetic fields. The five gradient coils are as well as The five gradient coils are placed in parallel in the magnetic shielding room, and the target area in the magnetic shielding room is divided into NUM points;

[0009] S3. Use the two-dimensional Fourier series as the basis function to represent the current flow function of any gradient coil: Among them, α n , β n , γ m , δ m represents the unknown Fourier transform coefficient, M and N represent the transform order, and L represents the coil side length;

[0010] S4, for coil According to the symmetry principle of the gradient coil, the current flow function is simplified to obtain a simplified current flow function, which is expressed as follows: Where, -L≤x, y≤L, z=+D, P mn represents the coefficient matrix; according to Biotsafar's law, the magnetic field expression in the x-axis direction is: where z and z′ represent the Z coordinates of the target field point and the dual-plane coil, respectively, and |rr′| 3 represents the distance between them; considering the preset magnetic field distribution of the target area, the magnetic field distribution function of the target area is expressed as: Where μ0 represents the vacuum magnetic permeability, B target Indicates the magnetic field value of the target area;

[0011] S5. The magnetic field distribution function of the target area is uniformly discretized into NUM coordinate points, and the least square error function of the magnetic field distribution of the target area is obtained as:

[0012] S6. Introducing the least squares error function into a penalty function, wherein the penalty function is expressed as: The Tikhonov function is obtained as: Where, Γ represents the Tychonov regular matrix, λ represents the regular coefficient, ΔS represents the arc of the coil, B(x num ,y num , z num ) represents the magnetic field strength at other points in the target field;

[0013] S7, the coefficient matrix P can be obtained by minimizing the Tikhonov functional. mn ; The coefficient matrix P obtained by solving mn Apply it to the simplified current flow function in step S4, draw an isovalue curve diagram of the flow function, and design the gradient coil according to the isovalue curve diagram Similarly, according to steps S4 to S7, the gradient coils are designed in sequence. as well as

[0014] The beneficial effect of the present invention is that the above-mentioned magnetic field gradient suppression method in a magnetic shielding room can generate a high-precision controllable compensation gradient magnetic field in a certain target area, thereby solving the problem of a large residual gradient magnetic field in the magnetic shielding room, and ultimately increasing the uniformity inside the magnetic shielding room. This paper also designs five sets of gradient coils to suppress the gradient magnetic field in the magnetic shielding room. After the gradient coils are excited, the gradients of the three components of the magnetic field in three directions are significantly reduced. The design of the gradient coils can effectively suppress the gradient magnetic field in all directions in the magnetic shielding room. This method can provide the necessary conditions for precision physical experiments, biomagnetic signal measurements, and zero-magnetic scientific research that require high gradient magnetic fields. BRIEF DESCRIPTION OF THE DRAWINGS

[0015] Figure 1 It is a schematic diagram of the structure in which the gradient coil of the present invention is placed in a magnetic shielding room;

[0016] Figure 2 This is a schematic diagram of the gradient coil structure designed according to the method of the present invention; wherein: Figure 2 (a) is a schematic diagram of the structure of the gradient coil dBx / dx; Figure 2 (b) is a schematic diagram of the structure of the gradient coil dBx / dy; Figure 2 (c) is a schematic diagram of the structure of the gradient coil dBy / dz; Figure 2 (d) is a schematic diagram of the structure of the gradient coil dBz / dz;

[0017] Figure 3 Schematic diagram of the results of testing the gradient error of the gradient coil in each working area in the present invention; wherein, Figure 3 (a) is a schematic diagram of the gradient error of the gradient coil dBx / dz on the XOY plane; Figure 3(b) is a schematic diagram of the gradient error of the gradient coil dBz / dz on the XOY plane; Figure 3 (c) is a schematic diagram of the gradient error of the gradient coil dBx / dy on the XOY plane; Figure 3 (d) is a schematic diagram of the gradient error of the gradient coil dBx / dx on the XOY plane;

[0018] Figure 4 It is a comparative schematic diagram of current excitation compensation in the present invention; wherein, Figure 4 (a) is a comparison diagram before and after the compensation current is excited to the dBx / dz coil in the x-axis direction; Figure 4 (b) is a comparison diagram before and after the compensation current is excited to the dBz / dz coil in the z-axis direction; Figure 4 (c) is a comparison diagram without compensation current excitation in the x-axis direction and the z-axis direction; Figure 4 (d) is a comparison diagram of the compensation current excitation in both the x-axis direction and the z-axis direction;

[0019] Figure 5 Schematic diagram of the gradient suppression effect of the gradient coils dBx / dz and dBz / dz on the plane XOZ in the present invention; wherein, Figure 5 (a) Schematic diagram of the gradient suppression effect of the gradient coil dBx / dz on the plane XOZ; Figure 5 (b) is a schematic diagram of the gradient suppression effect of the gradient coil dBz / dz on the plane XOZ;

[0020] As shown in the figure: 1. Gradient coil; 2. Magnetic shielding room. DETAILED DESCRIPTION

[0021] 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.

[0022] The present invention relates to a method for suppressing magnetic field gradient in a magnetic shielding room, and the specific process is as follows:

[0023] (1) Analyze the magnetic field gradient of the magnetic shielding room:

[0024] Passive magnetic shielding technology is a technology that uses the high magnetic permeability of high magnetic permeability materials such as Permalloy to make most of the magnetic flux lines of the earth's magnetic field pass through the high magnetic permeability materials to obtain an extremely weak magnetic field inside. Its shielding effect is related to the thickness of the material and the structure of the magnetic shielding room. Inside the magnetic shielding room, since the magnetic flux lines are easy to pass along the high magnetic permeability materials, the magnetic field intensity near the boundary of the magnetic shielding room is greater than the center. Therefore, a magnetic field with a certain change is generated from the boundary to the center. Then the magnetic field change rate of a certain point in the magnetic shielding is defined as:

[0025]

[0026] The change of this magnetic field can be approximated by a gradient magnetic field. The magnetic field component in the x-axis direction of the magnetic shielding room is along the x-axis. As the distance approaches the boundary, the magnetic field amplitude increases. The gradient magnetic field that can be generated by the compensation coil to be designed has a rate of change that is only related to the current. Then the three components (Bx, By, Bz) that define the magnetic induction intensity in three directions in space (x-axis, y-axis, z-axis) can be written as:

[0027]

[0028] According to Maxwell's equations, in the observation area without spatial current density, the divergence and curl of the magnetic field are both 0, so it can be obtained that the matrix in equation (2) has symmetry:

[0029]

[0030] Therefore, the above matrix (2) is expressed as:

[0031]

[0032] In a closed magnetic shielding room, the spatial magnetic field gradient environment satisfies equation (4), so only five gradient coils need to be designed. To control all gradient magnetic fields.

[0033] (2) Magnetic field gradient coil (GBC) design:

[0034] The principle of GBCs (gradient bi-planar coils) is to use continuous surface currents in space to generate the required magnetic field. The magnetic field value in the target area is determined by a predetermined shape and size, which is used as a constraint for inverting the surface current density distribution.

[0035] The magnetic field gradient coil is a double-plane coil. The model of the double-plane coil is as follows: Figure 1 As shown in the figure, the plates with a side length of 2L and a spacing of 2D are parallel to each other. The target area is divided into NUM points. The continuous current density on the plane can be regarded as a two-dimensional continuous fluid. Due to the small size and negligible thickness of the plane. A Cartesian coordinate system is established at the center of the coil, and the coordinates of the two planes are Z = ±D. The target area and the gradient are defined in the center area of ​​the origin, which is a region with a length of L. target .

[0036] Assuming that the current density J on the plane is an incompressible plane flow, it can be expressed as A series of trigonometric functions can be selected as basis functions to construct the stream function of current density based on the symmetry of the planar coil and the constraints of geometric parameters. The symmetry of the stream function is shown in Table 1.

[0037] Table 1 Symmetry of dual-plane gradient coils

[0038]

[0039] The following coil The design process of the remaining four coils is described as an example. The design process of the remaining four coils is the same.

[0040] Since the current distribution is perpendicular to the Z-axis, the current density in the Z-axis direction is 0. Using the two-dimensional Fourier series as the basis function to represent the stream function, we can get:

[0041]

[0042] Among them, α n , β n , γ m , δ m represents the unknown Fourier transform coefficient, M, N represent the transform order, and L represents the coil side length. The stream function can be simplified according to the symmetry described in Table 1. For example, the coil is antisymmetric in the x direction, antisymmetric in the y direction, and antisymmetric in the z direction, so α n =0 and δ m =0, then the simplified expression of the stream function is:

[0043]

[0044] Where -L≤x, y≤L, z=+D, the symmetry of the current density is the same as the symmetry of the stream function, as follows:

[0045]

[0046]

[0047] Where P nm is the desired Fourier series. N, M represent the finite terms of the Fourier series expansion.

[0048] According to Biotsafar's law, the relationship between current density and magnetic field, the magnetic field in the X direction is expressed as:

[0049]

[0050] where z and z′ are the Z coordinates of the target field point and the dual-plane coil, respectively, and |rr′| 3is the distance between them. Substituting the preset magnetic field distribution function of the target field into equation (9), the magnetic field distribution function of the target area is expressed as:

[0051]

[0052] Where μ0 is the vacuum permeability, B target is the magnetic field value of the target field.

[0053] The symmetry of the double-plane coil about the Z axis determines that the current direction is the same when symmetric and opposite when antisymmetric; the positive and negative signs are determined according to the current direction of the double-plane coil, with the same current direction being "+" and the opposite current direction being "-".

[0054]

[0055] Among them, (x′, y′, z1′) and (x′, y′, z2′) represent the source points on the dual-plane coil, and (x, y, z) is the field point in the target field area.

[0056] The magnetic field distribution function of the target area is uniformly discretized into NUM coordinate points, and the least squares error function of the magnetic field distribution of the target area is expressed as:

[0057]

[0058] The overdetermined equation is solved by using the Tikhonov regularization method. That is, the penalty function is introduced into equation (13), and the Tikhonov universal function is obtained as follows:

[0059]

[0060] Among them, B(x num ,y num , z num ) represents the magnetic field intensity at other points in the target field, Γ is the Tychonov regular matrix, and λ is the regular coefficient. It is difficult to determine the optimal value of the regular coefficient, which is usually determined by engineering experience. The regular matrix can be derived by the penalty function. In this paper, the coil curvature is selected as the penalty function, as shown below:

[0061]

[0062] By minimizing equation (14), we can solve the coefficient P mn That is, take the derivative of the error function and set its derivative to 0:

[0063]

[0064] Convert the solution of equation (16) into matrix form:

[0065] x=(A T A+λΓ T Γ) -1 A T B (17)

[0066] in

[0067]

[0068] Wherein, B represents the magnetic field distribution in the target area.

[0069] The unknown coefficient P in the stream function can be solved by the above method. mn , thus obtaining the current distribution function on the surface of the planar coil. The change of the value of the current function in the space where it is located corresponds to the change of the current value. Therefore, the isovalue curve of the stream function corresponds to the position of the discrete coil wire with the equivalent current passing through it. Draw the isovalue curve of the stream function, and design the following according to the isovalue curve: Figure 2 Gradient coils shown Similarly, the gradient coils are designed in sequence as well as

[0070] The present invention utilizes five gradient coils to simultaneously compensate for all the gradient magnetic fields in the magnetic shielding room, and uses finite element simulation software to verify its uniform area performance and compensation effect, and the results show that it can effectively reduce the gradient magnetic field in the magnetic shielding room.

[0071] The effectiveness of the magnetic field gradient suppression method in a magnetic shielding room of the present invention is illustrated below through specific experiments.

[0072] The magnetic shielding room is composed of a layer of Permalloy material with a thickness of 3 mm. The gradient coil is designed and placed inside it according to the design parameters (the size of the gradient coil, the shape of the winding, and the distance between the coils). The line current module is used to excite the coil with 1A. Then, the simulation results are used as input to directly calculate its gradient using the differential module. The gradient error is defined as:

[0073]

[0074] The gradient error of each working area of ​​the gradient coil is tested separately. The test results of a certain working plane are as follows: Figure 3 As shown. The maximum error of dBx / dz and dBy / dz is 2.4%, the maximum error of dBz / dz is 1.1%, and the maximum error of dBx / dy is 2.5%. Because the coil of dBx / dx is more discrete, its error is larger than other coils, with a maximum error of 6%. The gradient error test results show that the gradient coil can generate a preset gradient magnetic field in the working area.

[0075] In order to verify the compensation performance of the combined gradient coil, we selected two gradient coils to suppress the magnetic field in the MSR at the same time. Due to the different components of the geomagnetic field, gradient fields of different values ​​exist simultaneously in multiple directions in the MSR, so the gradient field needs to be suppressed simultaneously. All coils are imported into the simulation software COMSOL 6.0, and the local (Ningbo, China, longitude and latitude) magnetic field value is used as the external environmental magnetic field and imported into the approximate field module in FEM. The discrete magnetic field gradient is defined as:

[0076]

[0077] In COMSOL, 50uT magnetic field was applied in the X and Z directions to replace the geomagnetic field, and the joint gradient suppression of dBx / dz and dBz / dz was observed. The required current was calculated based on the gradient magnetic field in the magnetic shielding room and the coil constant of the gradient coil. The parameters that need to be introduced are shown in Table 2. After the above parameters are introduced into the system, although the working area becomes 1 / 4 of the original, the magnetic field gradient in the working area is greatly reduced. The magnetic field gradient before and after compensation is shown in Figure 4 shown.

[0078] Table 2 Current requirements for gradient coils

[0079] Coil Magnetic field gradient Coil constant Current dBx / dz 46.6nT / m 9537nT / A / m 4.8mA dBz / dz 48.06nT / m 41357nT / A / m 1.1mA

[0080] from Figure 4 (a)~ Figure 4 (b) It can be seen that after the separate compensation current is excited to the coil, the gradient of dBx / dz decreases from 46.6nT / m to 2.18nT / m, and the gradient of dBz / dz decreases from 48.06nT / m to 1.68nT / m. Figure 4 d shows that when the compensation current is fully turned on, the residual magnetic field is close to 0nT, and the dBx / dz and dBz / dz gradient changes are not much different from those of the single compensation. Due to the insufficient precision of the finite element mesh division, the calculated current value may not be accurate enough, resulting in Figure 4 There are some errors in Bx in d.

[0081] After the gradient is compensated, the residual magnetic field of Bx and Bz in the XOZ plane is as follows: Figure 5 As shown in Figure 2. In the z>0 region, the gradient magnetic field in the magnetic shield is significantly reduced, with the maximum difference being only 2nT. The simulation results show that GBCs can effectively reduce the magnetic field gradient in all directions within the MSR. Extending to other directions and calculating the required current can also result in better gradient suppression.

Claims

1. A method for suppressing magnetic field gradient in a magnetic shielding room, characterized in that: The following steps are involved: S1. Define the rate of change of magnetic field at a point in the magnetic shielding room as: Among them, B x+Δx represents the magnetic field component of the magnetic shielding room along the x-axis direction; B x It represents the magnetic field component along the x-axis direction in the magnetic shielding room, and defines the three components Bx, By and Bz of the magnetic induction intensity of the compensation coil to be designed in the x-axis direction, y-axis direction and z-axis direction of the space as follows: According to Maxwell's equations, we can get the expression: Then, in a closed magnetic shielding room, the spatial magnetic field gradient environment is expressed as: S2. According to the spatial magnetic field gradient environment expression, five gradient coils are designed in the magnetic shielding room to control all gradient magnetic fields. The five gradient coils are as well as The five gradient coils are placed in parallel in the magnetic shielding room, and the target area in the magnetic shielding room is divided into NUM points; S3. Use the two-dimensional Fourier series as the basis function to represent the current flow function of any gradient coil: Among them, α n , β n , γ m , δ m represents the unknown Fourier transform coefficient, M and N represent the transform order, and L represents the coil side length; S4, for coil According to the symmetry principle of the gradient coil, the current flow function is simplified to obtain a simplified current flow function, which is expressed as follows: Where, -L≤c, y≤L, z=+D, P mn represents the coefficient matrix; according to Biotsafar's law, the magnetic field expression in the x-axis direction is: where z and z′ represent the Z coordinates of the target field point and the dual-plane coil, respectively, and |rr′| 3 represents the distance between them; considering the preset magnetic field distribution of the target area, the magnetic field distribution function of the target area is expressed as: Where μ0 represents the vacuum magnetic permeability, B target Indicates the magnetic field value of the target area; S5. The magnetic field distribution function of the target area is uniformly discretized into NUM coordinate points, and the least square error function of the magnetic field distribution of the target area is obtained as: Among them, B(x num ,y num , z num ) represents the magnetic field strength at other points in the target field; S6. Introducing the least squares error function into a penalty function, wherein the penalty function is expressed as: The Tikhonov function is obtained as: Wherein, Γ represents the Tychonoff canonical matrix, λ represents the canonical coefficient, and ΔS represents the radian of the coil. S7, the coefficient matrix P can be obtained by minimizing the Tikhonov functional. mn ; The coefficient matrix P obtained by solving mn Apply it to the simplified current flow function in step S4, draw an isovalue curve diagram of the flow function, and design the gradient coil according to the isovalue curve diagram Similarly, according to steps S4 to S7, the gradient coils are designed in sequence. as well as

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