Radial shim coil for a hollow cylindrical working region

Abstract

The present application relates to a kind of radial field uniformity coils of hollow cylindrical working area, by decoupling the coupling of magnetic shield barrel and coil magnetic field, based on the principle of magnetic field superposition, the analytical function of the radial magnetic field component of coil at any point in space is derived, and particle swarm optimization algorithm is used to solve iteratively, so as to obtain the optimal coil design parameters satisfying the target magnetic field distribution;In the hollow cylindrical working area, the magnetic field with radial divergent shape and uniform size is formed, which is used for the magnetic compensation and probe calibration of the annular array distributed magnetometer in the muscle magnetic, leg magnetic test process, and the matching degree of the uniform field effect and sensor sensitive direction is improved.

Description

Technical Field

[0001] This invention relates to the field of biomagnetic testing equipment technology, and more specifically, to a radial shimming coil with a hollow cylindrical working area. Background Technology

[0002] In recent years, with the rapid development of biomagnetic measurement technology, detection methods based on myomagnetic signals have gradually gained attention in applications such as neurorehabilitation, neuromuscular function assessment, and electromyography (EMG) substitution. Myomagnetic signals are extremely weak magnetic field signals generated by human muscles during contraction, only on the order of pT, with very low signal strength, and are highly sensitive to external magnetic field interference. Therefore, to obtain an effective signal with a high signal-to-noise ratio, accurate measurement in a low-noise environment is required.

[0003] In existing magnetoencephalography (MEG) systems, the sensor structure is typically arranged in a ring array inside a single-ended open magnetic shielding structure, and its magnetic sensing axis (i.e., the direction in which the magnetic field response is strongest) is mostly located in the radial direction, that is, perpendicular to the longitudinal axis of the human body or the direction of limb extension. This makes the sensor more sensitive to fluctuations in the external interfering magnetic field in the radial direction, especially the inhomogeneity and gradient changes of the static magnetic field, which can easily introduce errors.

[0004] To improve system measurement accuracy, a local magnetic field shimming compensation system is typically established within the working area. Specifically, considering the radial sensitivity of the sensor, a shimming coil is designed within the hollow cylindrical region to generate a radial shimming field. This compensates for the non-ideal distribution of the external background magnetic field, improving measurement stability; it also enables static calibration of the sensor's response characteristics, establishes a magnetic response baseline, and enhances the reliability of subsequent signal processing and interpretation.

[0005] However, traditional shimming coils mainly focus on the shimming characteristics in a three-dimensional Cartesian coordinate system, which is difficult to directly adapt to biomagnetic testing applications that require radial shimming. At the same time, due to the coupling effect of the magnetic shielding structure and the human body layout, the coil needs to achieve a high radial uniformity magnetic field in a limited space, which is quite difficult to design. Summary of the Invention

[0006] The technical problem to be solved by this invention is how to design a radial shimming coil suitable for a circular cylindrical working area, so as to achieve high uniformity control of the radial magnetic field and improve the matching degree between the shimming effect and the sensor's sensitive direction.

[0007] This invention provides a radial shimming coil for a hollow cylindrical working area. The radial shimming coil is located inside a cylindrical magnetic shielding barrel with a single open end, and is used to generate a uniform radial magnetic field within the hollow cylindrical working area coaxial with the magnetic shielding barrel. The radial shimming coil is mounted on a hollow cylindrical fixture inside the magnetic shielding barrel and outside the magnetic resonance imaging (MRI) testing area. The radial shimming coil includes several pairs of inner loop coils and several outer loop coils arranged coaxially. The inner loop coils are wound around the inner circumferential surface of the fixture, and the outer loop coils are wound around the outer circumferential surface of the fixture. Each pair of inner loop coils and each pair of outer loop coils are symmetrically arranged with respect to the radial plane at the center point of the working area. The current directions between the same pair of inner loop coils are opposite, and the current directions between the same pair of outer loop coils are opposite.

[0008] Compared with the prior art, this application has the following advantages: it adopts several pairs of inner ring coils coaxially arranged on the inner circumferential surface of the fixed fixture and several pairs of outer ring coils coaxially arranged on the outer circumferential surface of the fixed fixture. Based on the radial sensitivity characteristics of the magnetometer with ring array distribution, it realizes the shimming coil that generates a radial uniform field in the hollow cylindrical working area, thereby improving the measurement stability.

[0009] In one possible implementation, the design parameters of the radial shim coil are calculated through the following steps: Step 1: Construct constraints for coil design parameters based on the structural parameters of the magnetic shielding barrel and the working area; Step 2, discretize the working area radially and axially. A set of discrete points, with a preset target value for the radial magnetic field at each discrete point; Step 3: Decouple the coupling effect between the magnetic shielding barrel and the magnetic field of the coil. Based on the principle of magnetic field superposition, construct the analytical function of the radial magnetic field component of the radial uniform field coil at any discrete point in space. Step 4: The particle swarm optimization algorithm is used to iteratively solve the analytical function of the radial magnetic field component to obtain the coil design parameters that make the magnetic field component at each discrete point satisfy the target value of the radial magnetic field.

[0010] Compared with existing technologies, the method of this application has the following advantages: by decoupling the coupling effect between the magnetic shielding barrel and the magnetic field of the coil, based on the principle of magnetic field superposition, the analytical function of the radial magnetic field component at any point in space of the radial shimming coil is derived, and the particle swarm optimization algorithm is used for iterative solution, thereby obtaining the optimal coil design parameters that satisfy the target magnetic field distribution; a magnetic field with radially divergent magnetic field lines and uniform size is formed in the hollow cylindrical working area, which is used for magnetic compensation and probe calibration of the magnetometer distributed in the ring array during muscle magnetometry and leg magnetometry testing, and improves the matching degree between the shimming effect and the sensor's sensitive direction.

[0011] In one possible implementation, the structural parameters of the magnetic shielding barrel and the working area in step 1 specifically include: the radial shimming coil is located at an inner diameter of The outer diameter is Inside the magnetic shielding barrel, the working area is a hollow cylinder, and the inner diameter of the working area is... , outer diameter ,high And the distance between the center point of the work area and the closed end of the magnetic shielding barrel. The coil design parameters include the radius of each pair of radial shim coils. The distance between each pair of radial shim coils and the center point of the working area and the turns ratio of each pair of radial shim coils ; It is a non-zero integer. ; The constraints for constructing the coil design parameters are as follows: .

[0012] In one possible implementation, step 2 specifically includes: step 201, dividing the working area radially and axially into... and Forming equidistant discrete layers The target point set consists of discrete points. , ; Step 202: Based on the magnetic field distribution characteristics of the radial shim coil, preset the target value of the radial magnetic field at each discrete point. .

[0013] In one possible implementation, step 3 specifically includes: Step 301, decoupling the coupling effect between the magnetic shielding barrel and the coil magnetic field includes: The coupling effect between the end face of the magnetic shielding barrel and the magnetic field of the coil is decoupled by the mirror method; The coupling effect of the cylindrical curved surface of the magnetic shielding barrel on the coil magnetic field is decoupled by the equivalent current density. The expression for the analytical function of the radial magnetic field component at any discrete point in space of the radial shim coil is as follows: In the formula, This represents the coordinates of any pair of radial shim coils carrying a unit current within the magnetically shielded container. The radial magnetic field component generated at that location, Indicates vacuum permeability Indicates the first For the radius of the radial shim coil, and These are the inner and outer diameters of the magnetic shielding barrel, respectively. This represents the derivative of the zeroth-order modified Bessel function of the first kind. This represents the derivative of the zeroth-order modified Bessel function of the second kind. Represents the z-axis wave number. The imaginary unit, Indicates the number of times the image is mirrored; This indicates that the coil current density can be expanded into a Fourier series form according to the angle variable. The equivalent current density on the inner surface of the magnetically shielded barrel is expanded into a Fourier series form according to the angle variable. The equivalent current density on the outer surface of the magnetically shielded barrel, expanded into a Fourier series with respect to the angle variable, is expressed as follows: ; ; ; ; ; ; ; ; ; In the formula, This indicates the relative permeability of the magnetically shielded barrel. This represents the zeroth-order modified Bessel function of the first kind. Represents the zeroth-order modified Bessel function of the second kind; Step 302: Based on the analytical function of the radial magnetic field component, construct the influence matrix between the radial magnetic field component at each discrete point and the coil design parameters. Each element in the influence matrix Represented as the first When a unit current is applied to the radial shim coil pair, at the first... discrete points The radial magnetic field component; Step 303: Based on the superposition theorem of magnetic fields, construct a system of linear equations to obtain the magnetic fields of all radial uniform coil pairs at each discrete point, expressed as: In the formula, = This represents the magnetic field components at each discrete point for all radial shim coil pairs. , Let q be the number of turns of the q-th pair of radial shim coils, which is a non-zero positive integer.

[0014] In one possible implementation, step 4 specifically includes: step 401, using the minimum magnetic field distribution non-uniformity as the optimization objective function, whereby the non-uniformity is expressed as the weighted sum of the maximum deviation of the magnetic field at each discrete point relative to the magnetic field at the center point and the mean square error, as shown in the expression: Step 402: Using the particle swarm optimization algorithm, the coil design parameters that minimize the non-uniformity of the magnetic field distribution are iteratively solved according to the optimization objective function.

[0015] In one possible implementation, the particle swarm optimization algorithm in step 402 specifically includes: The particle swarm is initialized within the constraint space of the coil design parameters, and the inertia weight and learning factor are set. The particle positions are substituted into the radial magnetic field component analytical function to calculate the radial magnetic field distribution at discrete points and obtain the fitness value. The individual optimal position and the global optimal position of the swarm are updated based on the fitness value. The particle swarm is iteratively updated according to the velocity and position update formula. When the convergence condition is met or the maximum number of iterations is reached, the global optimal particle position is output as the optimal design parameter of the radial shimming coil to achieve the preset magnetic field uniformity target. Attached Figure Description

[0016] Figure 1 This is a schematic diagram of the structure of the magnetic shielding barrel, the SERF magnetometer assembly, and the radial shimming coil of the present invention; Figure 2 This is a schematic diagram of the SERF magnetometer assembly and radial shim coil of the present invention. Figure 3 This is a schematic diagram of the radial shimming coil design of the present invention; Figure 4 This is a diagram showing the arrangement of each pair of radial shimming coils in this invention.

[0017] Explanation of reference numerals in the attached figures: 1. Magnetic shielding barrel; 2. SERF magnetometer assembly; 2.1. Fixture; 2.2. SERF magnetometer probe; 3. Radial shimming coil; 3.1. Inner loop coil; 3.2. Outer loop coil. Detailed Implementation

[0018] First, those skilled in the art should understand that these embodiments are merely used to explain the technical principles of the embodiments of this application and are not intended to limit the scope of protection of the embodiments of this application. Those skilled in the art can make adjustments as needed to adapt to specific application scenarios.

[0019] In the description of the embodiments of this application, it should be noted that, unless otherwise explicitly specified and limited, the terms "connected" and "linked" should be interpreted broadly. For example, they can refer to a fixed connection, a detachable connection, or an integral connection; they can refer to a mechanical connection or an electrical connection; they can refer to a direct connection or an indirect connection through an intermediate medium. Those skilled in the art can understand the specific meaning of the above terms in the embodiments of this application based on the specific circumstances.

[0020] In the embodiments of this application, unless otherwise expressly specified and limited, "above" or "below" the second feature can mean that the first feature is in direct contact with the second feature, or that the first feature is in indirect contact with the second feature through an intermediate medium. Furthermore, "above," "on top of," and "over" the second feature can mean that the first feature is directly above or diagonally above the second feature, or simply that the first feature is at a higher horizontal level than the second feature. "Below," "below," and "under" the second feature can mean that the first feature is directly below or diagonally below the second feature, or simply that the first feature is at a lower horizontal level than the second feature.

[0021] The present application will now be described in further detail with reference to the accompanying drawings and specific embodiments.

[0022] like Figure 1-2 As shown in the embodiment of this application, a radial shimming coil for a hollow cylindrical working area is disclosed. The radial shimming coil 3 is located inside a cylindrical magnetic shielding barrel 1 with a single open end, and is used to generate a uniform radial magnetic field within the hollow cylindrical working area coaxial with the magnetic shielding barrel 1. The radial shimming coil 3 is disposed on a hollow cylindrical fixture 2.1 inside the magnetic shielding barrel 1 and outside the magnetic resonance imaging (MRI) testing area. The radial shimming coil 3 includes several pairs of inner loop coils 3.1 and several pairs of outer loop coils 3.2 arranged coaxially. The inner loop coils 3.1 are wound around the inner circumferential surface of the fixture 2.1, and the outer loop coils 3.2 are wound around the outer circumferential surface of the fixture 2.1. Each pair of inner loop coils 3.1 and each pair of outer loop coils 3.2 are symmetrically arranged with respect to the radial plane at the center point of the working area, as shown in the figure. Figure 4 As shown; the current directions between the inner loop coils 3.1 of the same pair are opposite; the current directions between the outer loop coils 3.2 of the same pair are opposite.

[0023] See Figure 3 As shown, the design parameters of the radial shim coil 3 are calculated through the following steps: Step 1: Construct constraints for coil design parameters based on the structural parameters of the magnetic shielding barrel 1 and the working area; the structural parameters of the magnetic shielding barrel 1 and the working area include: the radial shimming coil 3 is located in an area with an inner diameter of... The outer diameter is Inside the magnetic shielding barrel 1, the working area is a hollow cylinder, and the design parameters of the working area include the inner diameter. , outer diameter ,high The distance between the center point of the working area and the closed end of the magnetic shielding barrel 1 The design parameters of the radial shim coil 3 include the radius of each pair of radial shim coils. The distance between each pair of radial shim coils and the center point of the working area and the turns ratio of each pair of radial shim coils ,and It is a non-zero integer; ;; The constraints for constructing the coil design parameters are as follows: .

[0024] Step 2, discretize the working area radially and axially. A set of discrete points, with a preset target magnetic field strength for each discrete point; specifically including: Step 201: Divide the working area radially and axially into... and Forming equidistant discrete layers The target point set consists of discrete points. , ; Step 202: Based on the magnetic field distribution characteristics of the radial shim coil, preset the target value of the radial magnetic field at each discrete point. .

[0025] Step 3: Decouple the magnetic shielding barrel 1 from the magnetic field of the coil. Based on the principle of magnetic field superposition, construct the analytical function of the radial magnetic field components of the radial shimming coil 3 at any discrete point in space; specifically including: Step 301: Expand the current density of the coil pair into a Fourier series; use the Green's function to solve for the curl of the magnetic vector potential, and separate the variables by modifying the Bessel function to obtain the radial magnetic field components at each discrete point in the unshielded state, expressed as: Next, the coupling between the magnetic shielding barrel 1 and the coil magnetic field is decoupled. This is achieved by using the image method to decouple the coupling between the end face of the closed end of the magnetic shielding barrel and the coil magnetic field, through the equivalent current density confined to the inner and outer surfaces of the magnetic shielding barrel 1. , The cylindrical curved surface of the equivalent magnetic shielding barrel 1 is used to couple the magnetic field of the coil. Based on the target magnetic field strength at each discrete point in the working area and the coil design parameters, an analytical function of the radial magnetic field component is constructed. Specifically, the expression of the analytical function of the radial magnetic field component generated at any discrete point within the magnetic shielding barrel 1 when a unit current is passed through any pair of radial shimming coils 3 with arbitrary parameters is as follows: In the formula, This represents the radial component of the magnetic field produced at any point in space when a unit current is passed through any pair of radial shim coils 3. The coordinates of this point are: , Represents the permeability of free space. Indicates the first For the radius of the radial shim coil, and These are the inner and outer diameters of the magnetic shielding barrel, respectively. This represents the derivative of the zeroth-order modified Bessel function of the first kind. Let denote the derivative of the zeroth-order modified Bessel function of the second kind, k denote the z-wave number, and i be the imaginary unit. p is the mirror image order. The coil current density is expanded into a Fourier series form according to the angle variable. The equivalent current density on the inner surface of the magnetically shielded barrel 1 is expanded into a Fourier series form according to the angle variable. The equivalent current density on the outer surface of the magnetically shielded barrel 1, expanded into a Fourier series according to the angle variable, can be specifically expressed as: ; ; ; ; ; ; ; ; ; In the formula, This indicates the relative permeability of the magnetically shielded barrel. This represents the zeroth-order modified Bessel function of the first kind. Represents the zeroth-order modified Bessel function of the second kind; Step 302: Based on the analytical function of the radial magnetic field component, construct the influence matrix between the radial magnetic field component at each discrete point and the coil design parameters. Each element in the influence matrix Represented as the first When a unit current is applied to the radial shim coil pair, at the first... discrete points The radial magnetic field component; Step 303: Based on the superposition theorem of magnetic fields, construct a system of linear equations to obtain the magnetic fields of all radial uniform coil pairs at each discrete point, expressed as: In the formula, = This represents the magnetic field components at each discrete point for all radial shim coil pairs. , Let q be the number of turns of the q-th pair of radial shim coils, which is a non-zero positive integer.

[0026] Step 4: The general expression for the radial magnetic field component is iteratively solved using a particle swarm optimization algorithm to obtain the optimal design parameters that ensure the magnetic field distribution at each discrete point meets the predefined target value; specifically including: Step 401: The objective function for optimization is to minimize the non-uniformity of the magnetic field distribution. The non-uniformity is expressed as the weighted sum of the maximum deviation of the magnetic field at each discrete point relative to the magnetic field at the center point and the mean square error, as shown in the following expression: In the formula, and As a weighting factor; The root mean square error of the magnetic field strength within the target point set reflects the overall deviation between the optimization result and the ideal magnetic field distribution; the maximum deviation term is used to limit the destruction of the overall uniform field effect by local magnetic field anomalies, as a supplement to the root mean square error.

[0027] Step 402 involves using a particle swarm optimization algorithm to iteratively solve for the coil design parameters that minimize the magnetic field non-uniformity, with the objective being to optimize the coil. Specifically, this includes: The particle swarm is initialized within the constraint space of the coil design parameters, and the inertia weight and learning factor are set. The particle positions are substituted into the radial magnetic field component analytical function to calculate the radial magnetic field distribution at discrete points and obtain the fitness value. The individual optimal position and the global optimal position of the swarm are updated based on the fitness value. The particle swarm is iteratively updated according to the velocity and position update formula. When the convergence condition is met or the maximum number of iterations is reached, the global optimal particle position is output as the optimal design parameter of the radial shimming coil to achieve the preset magnetic field uniformity target.

[0028] In the description of the embodiments of this application, it should be noted that the terms "inner" and "outer" and other terms indicating direction or positional relationship are based on the direction or positional relationship shown in the drawings. This is only for the convenience of description and does not indicate or imply that the device or component must have a specific orientation, or be constructed and operated in a specific orientation. Therefore, it should not be construed as a limitation of this application.

[0029] In the description of this application, the references to terms such as "an embodiment," "some embodiments," "in this embodiment," "specific example," or "some examples," etc., refer to specific features, structures, materials, or characteristics described in connection with that embodiment or example, which are included in at least one embodiment or example of this application. In this specification, the illustrative expressions of the above terms do not necessarily refer to the same embodiment or example. Furthermore, the specific features, structures, materials, or characteristics described may be combined in a suitable manner in any one or more embodiments or examples. Moreover, without contradiction, those skilled in the art can combine and integrate the different embodiments or examples described in this specification, as well as the features of different embodiments or examples.

[0030] The above description is merely a specific embodiment of this application, but the scope of protection of this application is not limited thereto. Any variations or substitutions that can be easily conceived by those skilled in the art within the technical scope disclosed in this application should be included within the scope of protection of this application. Therefore, the scope of protection of this application should be determined by the scope of the claims.

Claims

1. A radial shimming coil with a hollow cylindrical working region, characterized in that, The radial shim coil (3) is located inside a cylindrical magnetic shielding barrel (1) with a single-end opening, and is used to generate a uniform radial magnetic field in a hollow cylindrical working area coaxial with the magnetic shielding barrel (1). The radial shim coil (3) is set on a hollow cylindrical fixture (2.1) inside the magnetic shielding barrel (1) and outside the magnetic muscle testing area. The radial shim coil (3) includes several pairs of inner loop coils (3.1) and several outer loop coils (3.2) arranged coaxially. The inner loop coils (3.1) are wound on the inner circumferential surface of the fixture (2.1), and the outer loop coils (3.2) are wound on the outer circumferential surface of the fixture (2.1). Each pair of inner loop coils (3.1) and each pair of outer loop coils (3.2) are symmetrically arranged with the radial plane at the center point of the working area as the symmetrical plane. The current directions between the same pair of inner loop coils (3.1) are opposite, and the current directions between the same pair of outer loop coils (3.2) are opposite. The design parameters of the radial shim coil (3) are calculated through the following steps: Step 1: Construct the constraints for coil design parameters based on the structural parameters of the magnetic shielding barrel (1) and the working area; Step 2, discretize the working area radially and axially. A set of discrete points, with a preset target value for the radial magnetic field at each discrete point; Step 3: Decouple the magnetic shielding barrel (1) from the magnetic field of the coil. Based on the principle of magnetic field superposition, construct the analytical function of the radial magnetic field component of the radial uniform field coil (3) at any discrete point in space. Step 4: The particle swarm optimization algorithm is used to iteratively solve the analytical function of the radial magnetic field component to obtain the coil design parameters that make the magnetic field component at each discrete point satisfy the target value of the radial magnetic field.

2. The radial shimming coil for the hollow cylindrical working region according to claim 1, characterized in that, The structural parameters of the magnetic shielding barrel (1) and the working area in step 1 specifically include: the inner diameter of the magnetic shielding barrel (1) is... The outer diameter is The working area is a hollow cylinder, and the inner diameter of the working area is... , outer diameter ,high And the distance between the center point of the working area and the closed end of the magnetic shielding barrel (1). The coil design parameters include the radius of each pair of radial shim coils (3). The distance between each pair of radial shim coils (3) and the center point of the working area and the turns ratio of each pair of radial shim coils (3) ; It is a non-zero integer. ; The constraints for constructing the coil design parameters are as follows: 。 3. The radial shimming coil for the hollow cylindrical working region according to claim 2, characterized in that, Step 2 specifically includes: Step 201: Divide the working area radially and axially into... and Forming equidistant discrete layers The target point set consists of discrete points. , ; Step 202: Based on the magnetic field distribution characteristics of the radial shim coil, preset the target value of the radial magnetic field at each discrete point. .

4. The radial shimming coil for the hollow cylindrical working region according to claim 3, characterized in that, Step 3 specifically includes: Step 301, decoupling the coupling between the magnetic shielding barrel (1) and the coil magnetic field includes: The coupling effect between the end face of the closed end of the magnetic shielding barrel (1) and the magnetic field of the coil is decoupled by the mirror method. The coupling effect of the cylindrical curved surface of the magnetic shielding barrel (1) on the coil magnetic field is decoupled by the equivalent current density. The expression for the analytical function of the radial magnetic field component at any discrete point in space of the radial shim coil (3) is as follows: ； In the formula, This represents the coordinates of any pair of radial shim coils (3) with a unit current flowing through them, within the magnetically shielded barrel (1). The radial magnetic field component generated at that location, Indicates the permeability of vacuum Indicates the first For the radius of the radial shim coil, and These are the inner and outer diameters of the magnetic shielding barrel (1), respectively. This represents the derivative of the zeroth-order modified Bessel function of the first kind. This represents the derivative of the zeroth-order modified Bessel function of the second kind. Represents the z-axis wave number. The imaginary unit, Indicates the number of times the image is mirrored; This indicates that the coil current density can be expanded into a Fourier series form according to the angle variable. The equivalent current density on the inner surface of the magnetically shielded barrel (1) is expanded into a Fourier series form according to the angle variable. The equivalent current density on the outer surface of the magnetically shielded barrel (1) is expanded into a Fourier series form according to the angle variable, and the specific expression is as follows: ； ； ； ； ； ； ； ； ； In the formula, This indicates the relative permeability of the magnetically shielded barrel. This represents the zeroth-order modified Bessel function of the first kind. Represents the zeroth-order modified Bessel function of the second kind; Step 302: Based on the analytical function of the radial magnetic field component, construct the influence matrix between the radial magnetic field component at each discrete point and the coil design parameters. Each element in the influence matrix Represented as the first When a unit current is applied to the radial shim coil pair, at the first... discrete points The radial magnetic field component; Step 303: Based on the superposition theorem of magnetic fields, construct a system of linear equations to obtain the magnetic fields of all pairs of radial uniform coils at each discrete point, expressed as: In the formula, = This represents the magnetic field components at each discrete point for all radial shim coil pairs. , Let q be the number of turns of the q-th pair of radial shim coils, which is a non-zero positive integer.

5. The radial shimming coil for the hollow cylindrical working region according to claim 4, characterized in that, Step 4 specifically includes: Step 401: The objective function for optimization is to minimize the non-uniformity of the magnetic field distribution. The non-uniformity is expressed as the weighted sum of the maximum deviation of the magnetic field at each discrete point relative to the magnetic field at the center point and the mean square error, as shown in the following expression: ； In the formula, and As a weighting factor; Step 402: Using the particle swarm optimization algorithm, the coil design parameters that minimize the non-uniformity of the magnetic field distribution are iteratively solved according to the optimization objective function.

6. The radial shimming coil for the hollow cylindrical working region according to claim 5, characterized in that, The particle swarm optimization algorithm in step 402 specifically includes: The particle swarm is initialized within the constraint space of the coil design parameters, and the inertia weight and learning factor are set. The particle positions are substituted into the radial magnetic field component analytical function to calculate the radial magnetic field distribution at discrete points and obtain the fitness value. The individual optimal position and the global optimal position of the swarm are updated based on the fitness value. The particle swarm is iteratively updated according to the velocity and position update formula. When the convergence condition is met or the maximum number of iterations is reached, the global optimal particle position is output as the optimal design parameter of the radial shimming coil to achieve the preset magnetic field uniformity target.

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