Biplanar DC-RF compound field driving coil system for optical pump magnetometer

Abstract

According to the biplane DC-RF compound field driving coil system for the optical pump magnetometer, the complexity, noise and volume of the system are reduced and the measurement sensitivity and integration degree are improved by unifying the geometric configuration and differential parameters of the biplane, and particularly, the high-frequency magnetic field distortion and frequency dispersion effect in a magnetic shielding environment are optimized. Specifically, the problems of insufficient magnetic field uniformity, enhanced electromagnetic interference and RF magnetic field distortion in a large-volume area caused by non-uniform coil configuration in the traditional design are solved, so that the high uniformity of the magnetic field is realized, and the space utilization rate and the signal quality of a system are improved, and the system is characterized by comprising a standard coil unit and a radio frequency coil unit, the standard coil unit and the radio frequency coil unit both adopt a biplanar coil configuration after simulation optimization, the biplanar coil comprises a left planar coil and a right planar coil, and the left planar coil and the right planar coil are parallel, coaxially and symmetrically arranged on the two sides of a target area and used for generating and compensating a shimming magnetic field.

Description

Dual-plane DC-RF composite field drive coil system for optically pumped magnetometers Technical Field

[0001] This invention relates to the field of coil multiplexing design technology in magnetometers, and in particular to a dual-plane DC-RF composite field driving coil system for optically pumped magnetometers. Background Technology

[0002] Optically pumped magnetometers achieve highly sensitive vector or scalar geomagnetic field measurements by using laser-pumped alkali metal atoms (such as Cs and Rb). The system requires the simultaneous introduction of a static bias field and a radio frequency (RF) excitation field: a standard coil generates a quasi-static DC bias magnetic field (DC being direct current) to construct an equivalent geomagnetic field background within a shielded environment and maintain the steady-state polarization of the atomic spin ensemble; the RF coil applies a high-frequency magnetic field in the 1-100 kHz range to drive magnetic dipole transitions between Zeeman sublevels and enhance magnetic resonance signal readout.

[0003] However, in traditional magnetometer structures, the DC and RF coils are typically designed with completely independent configurations: the DC bias field is generally generated by a Helmholtz or anti-Helmholtz coil, while the RF excitation field often uses a single-planar helical coil or saddle-shaped coil structure. This separate architecture not only increases the system size and assembly complexity but also makes it difficult to optimize the spatial arrangement and magnetic field coupling between the two types of coils, increasing engineering constraints such as mutual inductance coupling, overlapping scattered fields, and coil volume occupation. Furthermore, existing technologies have not yet proposed a composite coil scheme with a unified coil topology that simultaneously meets the requirements of both DC shimming and RF excitation fields, limiting the miniaturization, integration, and configuration reuse capabilities of magnetometers, and significantly increasing design cycle and cost.

[0004] To suppress environmental magnetic noise, optically pumped magnetometers are typically housed within a magnetically shielded enclosure made of a high-permeability material. Under the influence of the bias and driving fields provided by the coil, it is essential to ensure high uniformity and low distortion of the magnetic field within the shielded enclosure. However, in the 1-100kHz radio frequency band, the biplane coil is strongly affected by distributed capacitance, skin effect, and parasitic impedance due to the increased frequency. Simultaneously, the ferromagnetic shielding layer exhibits hysteresis loss, permeability dispersion, and eddy current effects, resulting in a significant frequency dependence of the RF field distribution. Furthermore, the shielded enclosure has finite thickness, finite length, and a single-ended opening boundary condition. These factors alter the boundary conditions of the magnetic field generated by the coil, causing significant distortion within the internal space, particularly in single-ended structures where stronger axial leakage and non-uniformity are more pronounced.

[0005] Therefore, there is an urgent need for a dual-plane composite field drive coil system with a reusable coil configuration that can simultaneously meet the requirements of DC bias field and RF drive field, and can ensure magnetic field uniformity and frequency stability in a magnetically shielded environment, in order to solve the key bottlenecks of existing magnetometers in terms of magnetic field distortion, dispersion effect and structural integration. Summary of the Invention

[0006] The purpose of this invention is to provide a dual-plane DC-RF composite field driving coil system for optically pumped magnetometers. By unifying the dual-plane geometry and differentiating parameters, the system complexity, noise, and volume are reduced, while the measurement sensitivity and integration are improved. In particular, it optimizes for high-frequency magnetic field distortion and dispersion effects under magnetically shielded environments. Specifically, this invention solves the problems of insufficient magnetic field uniformity, enhanced electromagnetic interference, and RF magnetic field distortion in large areas caused by inconsistent coil configurations in traditional designs, thereby achieving high magnetic field uniformity and improving system space utilization and signal quality.

[0007] The technical solution of the present invention is as follows:

[0008] A dual-plane DC-RF composite field driving coil system is characterized by comprising a standard coil unit and a radio frequency coil unit. Both the standard coil unit and the radio frequency coil unit adopt a dual-plane coil configuration optimized by simulation. The dual-plane coil includes a left plane coil and a right plane coil, which are arranged parallel and coaxially symmetrically on both sides of the target area to generate and compensate for a uniform magnetic field.

[0009] The dual-plane coil configuration employs a reverse design method, which reverse-engineers the current distribution of the dual-plane coil based on the magnetic field requirements of the dual-plane coil multiplexing structure in the target imaging area, thereby achieving active compensation.

[0010] The target area is a square area with a side length of L, and the distance between the left plane coil and the right plane coil is H=1.5L.

[0011] The simulation optimization includes the design of a dual-plane coil through a combination of a stream function module, an equation system module, a calculation module, and a judgment module, including the following steps:

[0012] Step 1: Initialize coil parameters;

[0013] Step 2: Obtain the current function and current density function of the coil;

[0014] Step 3: Set the uniform field target field matrix and use the Biot-Savart law to calculate the magnetic field strength at the target field point; set the gradient field target field matrix and use the Biot-Savart law to calculate the magnetic field strength at the target field point.

[0015] Step 4: Solve for the undetermined coefficients using L2 or L1 regularization.

[0016] Step 5: Solve for the numerical solution of the stream function and plot the contour lines of the stream function;

[0017] Step 6: Determine whether the uniformity requirement is met. If not, optimize the regularization coefficient and weight coefficient using the two-dimensional particle swarm optimization algorithm and return to step 5. If the requirement is met, proceed to step 7.

[0018] Step 7: Export the coordinates of the coil shape and draw the coil shape graphic.

[0019] The active compensation of the dual-plane coil includes the following steps:

[0020] Step S1: Determine the size of the dual-plane coil array and obtain the stream function of the dual-plane coil using Fourier series expansion;

[0021] Step S2: Set the target magnetic field matrix of the uniform compensation field and gradient compensation field coils, calculate the magnetic field strength of the coils according to Maxwell's equations and the stream function, and establish an overdetermined compensation equation set.

[0022] Step S3: Solve the overdetermined compensation equations using the L1 regularization method or the L2 regularization method to obtain the numerical solution of the stream function, and plot the contour lines of the stream function.

[0023] Step S4: Determine the uniformity error between the target magnetic field and the actual magnetic field based on the numerical solution of the stream function. If the error meets the preset requirements, then drive the dual-plane coil array to apply a compensation current according to the stream function.

[0024] In step S5, if the error does not meet the preset requirements, a genetic algorithm is used to optimize the algorithm. After obtaining the regularization coefficient and weight coefficient, steps S3 to S4 are repeated.

[0025] Step S1 includes the following expression:

[0026]

[0027] in It is a stream function, (r,θ) is the coordinate of the current source on the two-plane coil, r is the polar radius, θ is the polar angle, K and L are both Fourier series expansions of the stream function, k and l are both index numbers, a kl b kl These are all coefficients in the current density flow function of the coil. It is the coil current density.

[0028] Step S2 includes the following expression:

[0029]

[0030] Among them B uniform It is a uniform compensation magnetic field matrix, A uniform Let ψ be the matrix relating magnetic field and current. uniform Let be the Fourier coefficient matrix of the stream function.

[0031] Step S3 includes the following expression:

[0032]

[0033] Where μ0 is the free magnetic permeability and J is the current density. Let r be the position vector, r be the position modulus, and dV be the infinitesimal volume.

[0034] Step S5 includes the following expression:

[0035]

[0036] in ω represents the velocity of the j-th individual in the genetic algorithm at the (t+1)-th iteration, where t is the current iteration number, t and j are both positive integers, and ω is the inertia weight factor. c1 is the speed of the j-th individual in the current iteration, c1 is the individual learning factor, rand is a random number between [0,1], and p best It is the best position for an individual. c is the position of the j-th individual in the current iteration, and c2 is the group learning factor. It is the individual's optimal speed. It is the position of the j-th individual in the (t+1)-th iteration.

[0037] The technical effects of this invention are as follows: Compared with existing technologies, the dual-plane DC-RF composite field driving coil system of this invention applies a genetic algorithm to the optimized design of the dual-plane multiplexed coil structure, which can significantly improve the magnetic field uniformity in large-volume regions. Compared with traditional multi-channel systems, a pair of dual-plane coils can achieve uniformity and gradient compensation, reducing the number of coils and improving the space utilization and measurement resolution of optically pumped geomagnetometers. The coils can be flexibly designed according to different device sizes, ultimately achieving high performance and low power consumption, promoting the widespread application of integrated miniaturized geomagnetometers in scientific research, especially in high-frequency operation under magnetically shielded environments, where magnetic field distortion is reduced and noise performance is improved. Attached Figure Description

[0038] Figure 1 is a schematic flowchart of the dual-plane coil design method executed by the dual-plane DC-RF composite field driven coil system for optically pumped magnetometers according to the present invention. DC stands for direct current, and RF stands for radio frequency. Figure 1 includes steps: Step 1, initializing coil parameters; Step 2, obtaining the coil's flow function and current density function; Step 3, setting the uniform field target field matrix and using the Biot-Savart law to calculate the magnetic field strength at the target field point; setting the gradient field target field matrix and using the Biot-Savart law to calculate the magnetic field strength at the target field point; Step 4, solving for the undetermined coefficients using L2 or L1 regularization; Step 5, solving for the numerical solution of the flow function and drawing the flow function contour lines; Step 6, determining whether the uniformity requirement is met. If not, the regularization coefficient and weighting coefficient are obtained through optimization using a two-dimensional particle swarm optimization algorithm, and the process returns to Step 5. If the requirement is met, the process proceeds to Step 7; Step 7, deriving the coordinates of the coil shape and drawing the coil shape graphic.

[0039] Figure 2 is a schematic flowchart of the active magnetic field compensation method for the dual-plane multiplexed structure coil in the dual-plane DC-RF composite field driven coil system for optically pumped magnetometers according to the present invention. Figure 2 includes steps S1: determining the size of the dual-plane coil array and obtaining the stream function of the dual-plane coil using Fourier series expansion; Step S2: setting the target magnetic field matrix for the uniform compensation field and gradient compensation field coils, calculating the magnetic field strength of the coils according to Maxwell's equations and the stream function, and establishing an overdetermined compensation equation set; Step S3: solving the overdetermined compensation equation set using L1 regularization or L2 regularization to obtain the numerical solution of the stream function, and plotting the contour lines of the stream function; Step S4: judging the uniformity error between the target magnetic field and the actual magnetic field based on the numerical solution of the stream function. If the error meets the preset requirements, applying a compensation current to the dual-plane coil array according to the stream function; Step S5: if the error does not meet the preset requirements, using a genetic algorithm for optimization, obtaining regularization coefficients and weighting coefficients, and repeating steps S3 to S4.

[0040] Figure 3 is a schematic diagram of the combined structure of the dual-plane coil and magnetic shielding layer involved in the dual-plane DC-RF composite field driving coil system for optically pumped magnetometers of the present invention. In Figure 3, reference numeral 1 represents the magnetic shielding layer, 2 represents the dual-plane coil, and 3 represents the target area.

[0041] Figure 4 is a schematic diagram of the shape of the dual-plane coil involved in the dual-plane DC-RF composite field driving coil system for optically pumped magnetometers of the present invention. In Figure 4(a), the shape of the dual-plane coil for axial magnetic field is shown, and in Figure 4(b), the shape of the dual-plane coil for radial magnetic field is shown.

[0042] Figure 5 is a schematic diagram of the components of the dual-plane DC-RF composite field driving coil system for optically pumped magnetometers according to the present invention. Figure 5 includes a combination of a stream function module, an equation system module, a calculation module, and a judgment module. Detailed Implementation

[0043] The present invention will now be described in conjunction with the accompanying drawings (Figures 1-5) and embodiments.

[0044] Figure 1 is a schematic flowchart of the dual-plane coil design method implemented in the dual-plane DC-RF composite field driving coil system for optically pumped magnetometers according to the present invention. Figure 2 is a schematic flowchart of the active magnetic field compensation method for the dual-plane multiplexed structure coil implemented in the dual-plane DC-RF composite field driving coil system for optically pumped magnetometers according to the present invention. Figure 3 is a schematic diagram of the combined structure of the dual-plane coil and magnetic shielding layer involved in the dual-plane DC-RF composite field driving coil system for optically pumped magnetometers according to the present invention. Figure 4 is a schematic diagram of the shape of the dual-plane coil involved in the dual-plane DC-RF composite field driving coil system for optically pumped magnetometers according to the present invention. Figure 5 is a schematic diagram of the constituent modules of the dual-plane DC-RF composite field driving coil system for optically pumped magnetometers according to the present invention. Referring to Figures 1 to 5, the dual-plane DC-RF composite field driving coil system includes a standard coil unit and an RF coil unit. Both the standard coil unit and the RF coil unit adopt a simulation-optimized dual-plane coil configuration. The dual-plane coil includes a left-plane coil and a right-plane coil, which are arranged parallel and coaxially symmetrically on both sides of the target region to generate and compensate for the uniform magnetic field. The dual-plane coil configuration adopts a reverse design method. Based on the magnetic field requirements of the dual-plane coil multiplexing structure in the target imaging region, the current distribution of the dual-plane coil is deduced to achieve active compensation. The target region is a square region with a side length of L, and the distance between the left-plane coil and the right-plane coil is H = 1.5L.

[0045] The simulation optimization includes a dual-plane coil design using a combination of a stream function module, an equation module, a calculation module, and a judgment module. The steps are as follows: Step 1, initialize coil parameters; Step 2, obtain the coil's stream function and current density function; Step 3, set the uniform field target matrix and use the Biot-Savart law to calculate the magnetic field strength at the target field point; set the gradient field target matrix and use the Biot-Savart law to calculate the magnetic field strength at the target field point; Step 4, solve for the undetermined coefficients using L2 or L1 regularization; Step 5, solve for the stream function numerical solution and draw the stream function contour lines; Step 6, determine if the uniformity requirement is met. If not, optimize using a two-dimensional particle swarm optimization algorithm to obtain the regularization coefficients and weighting coefficients, then return to Step 5. If the requirement is met, proceed to Step 7; Step 7, export the coordinates of the coil shape and draw the coil shape graphic.

[0046] The active compensation of the dual-plane coil includes the following steps: Step S1, determine the size of the dual-plane coil array, and obtain the stream function of the dual-plane coil using Fourier series expansion; Step S2, set the target magnetic field matrix of the uniform compensation field and gradient compensation field coils, calculate the magnetic field strength of the coil according to Maxwell's equations and the stream function, and establish an overdetermined compensation equation set; Step S3, calculate and solve the overdetermined compensation equation set using the L1 regularization method or the L2 regularization method, obtain the numerical solution of the stream function, and draw the contour lines of the stream function; Step S4, determine the uniformity error between the target magnetic field and the actual magnetic field according to the numerical solution of the stream function. If the error meets the preset requirements, apply a compensation current to the dual-plane coil array according to the stream function; Step S5, if the error does not meet the preset requirements, use a genetic algorithm for optimization, obtain the regularization coefficient and weight coefficient, and repeat steps S3 to S4.

[0047] Step S1 includes the following expression:

[0048]

[0049] in It is a stream function, (r,θ) is the coordinate of the current source on the two-plane coil, r is the polar radius, θ is the polar angle, K and L are both Fourier series expansions of the stream function, k and l are both index numbers, a kl b kl These are all coefficients in the current density flow function of the coil. It is the coil current density.

[0050] Step S2 includes the following expression:

[0051]

[0052] Among them B uniform It is a uniform compensation magnetic field matrix, A uniform Let ψ be the matrix relating magnetic field and current. uniform Let be the Fourier coefficient matrix of the stream function.

[0053] Step S3 includes the following expression:

[0054]

[0055] Where μ0 is the free magnetic permeability and J is the current density. Let r be the position vector, r be the position modulus, and dV be the infinitesimal volume.

[0056] Step S5 includes the following expression:

[0057]

[0058] in ω represents the velocity of the j-th individual in the genetic algorithm at the (t+1)-th iteration, where t is the current iteration number, t and j are both positive integers, and ω is the inertia weight factor. c1 is the speed of the j-th individual in the current iteration, c1 is the individual learning factor, rand is a random number between [0,1], and p best It is the best position for an individual. c is the position of the j-th individual in the current iteration, and c2 is the group learning factor. It is the individual's optimal speed. It is the position of the j-th individual in the (t+1)-th iteration.

[0059] This invention discloses a dual-plane DC-RF composite field driving coil system for optically pumped magnetometers, comprising a standard coil and a radio frequency (RF) coil multiplexing module. This structure employs a unified multiplexed dual-plane coil configuration, achieving integration of static magnetic field simulation of the geomagnetic environment and high-frequency magnetic resonance driving through subsequent size adjustments and fabrication method differentiation. The standard coil module generates a uniform DC bias field, supporting atomic spin polarization; the RF coil module applies an AC oscillating field (AC stands for alternating current), amplifying the Larmor precession signal. A coil current distribution meeting the high uniformity requirements of a large volume space is obtained through a target field inversion algorithm combined with a ferromagnetic boundary coupling model; further, L2 regularization and particle swarm optimization algorithms are combined to determine the Fourier / SVD expansion coefficients of the surface current (Fourier / SVD is Fourier / singular value decomposition). Considering the influence of a high-permeability shielding layer on the inductance, magnetic coupling, and magnetic field distribution of the dual-plane coil, an equivalent mirror coil model is constructed to compensate for magnetic field distortion caused by the ferromagnetic boundary. The reused design ensures field uniformity of <2%, making it suitable for high-performance optically pumped magnetometers.

[0060] This invention provides a dual-plane DC-RF composite field driving coil system for an optically pumped magnetometer, comprising a magnetometer body, a standard coil unit, and an RF coil unit, wherein the standard coil unit and the RF coil unit both adopt a dual-plane coil configuration optimized by simulation, and their size parameters and manufacturing methods are set differently.

[0061] The dual-plane coil configuration consists of a left-plane coil group and a right-plane coil group. The left and right plane coils are parallel and coaxially arranged, and the coil shape is square, circular, or regular polygonal. The basic parameters such as coil configuration, number of turns distribution, line width ratio, and plane spacing are determined through simulation optimization to achieve a balance between magnetic field uniformity and self-shielding characteristics. The simulation optimization adopts particle swarm optimization combined with COMSOL multiphysics simulation, with the optimization target being a magnetic field uniformity of ≥95% in the target area inside the coil.

[0062] Based on the above-mentioned dual-plane coil basic configuration, the standard coil unit is adapted to the functional requirements of simulating the geomagnetic environment. The manufacturing method adopts the traditional winding process. The coil conductor material is copper enameled wire or PCB copper-clad wire (PCB is printed circuit board). The conductor width is 0.1-0.5mm and the line spacing is 0.05-0.2mm. The standard coil unit generates a stable and uniform simulated geomagnetic magnetic field by passing in DC current or low-frequency AC current. The magnetic field strength range is 1-20μT, which is adapted to the conventional intensity range of the geomagnetic field.

[0063] Based on the above dual-plane coil basic configuration, the radio frequency coil unit is adapted to the functional requirements of periodic interference amplification. The fabrication method adopts micro-nano processing technology (such as photolithography and electroplating). The coil wire material is gold, silver or copper alloy, and the wire width is 5-50μm. The frequency of the radio frequency field is tuned to the Larmor precession frequency through a lock-in amplifier. The radio frequency coil unit is arranged around the outer surface of the vapor chamber to ensure that the high-frequency magnetic field is efficiently coupled to the atomic ensemble.

[0064] To achieve high uniformity active compensation in a large volume area of ​​dual-plane coils, this invention further provides an adaptive compensation system for a dual-plane coil array, including: a dual-plane coil array, a signal acquisition module, a compensation control module, and a feedback optimization module; and improves the system's space utilization and imaging quality.

[0065] The dual-plane radio frequency coil is used to generate and compensate for a uniform magnetic field, and includes a left plane coil and a right plane coil, which are symmetrically arranged on both sides of the target area.

[0066] The signal acquisition module is used to acquire the distribution data of the magnetic field within the target area in real time;

[0067] The compensation control module is used to calculate the compensation current based on the collected data and drive the dual-plane coil array to apply the compensation magnetic field;

[0068] The feedback optimization module is used to optimize the compensation parameters using a genetic algorithm to achieve dynamic adjustment of the magnetic field uniformity.

[0069] Preferably, the target volume corresponding to the dual-plane multiplexed coil array is square, with a side length of D and a coil plane spacing of H. The shapes of the left and right plane coils are designed using a stream function based on Fourier series expansion.

[0070] To generate a uniform magnetic field, the target volume is discretized into m sampling points at equal intervals along the three axes. The magnetic field strength at each sampling point is set as a constant for the target field, and the uniform field target matrix is ​​B. uniform ;

[0071] Preferably, the coordinates of the current source on the dual-plane coil multiplexing structure are set to (r, θ), where r is the polar radius and θ is the polar angle. The two-dimensional plane stream function is ψ, and its differential equation is ▽²ψ = 0. The stream function can be expressed using a two-dimensional Fourier series as follows:

[0072]

[0073] Where K and L are the Fourier series expansions of the stream function, H is the interplanar spacing of the coils, and a kl b kl denoted as , where is the coefficient in the current density flow function of the coil, and k and l are the orders of the Fourier series decomposition of the current density in the radial and angular directions, respectively.

[0074] Preferably, the stream function of the dual-plane coil multiplexing structure is symmetric about the x-axis, y-axis, and z-axis, resulting in the following stream function:

[0075]

[0076] The coefficients of the radial component in the stream function of the dual-plane coil multiplexing structure are solved by the least squares method.

[0077] Preferably, the compensation equations are solved using the L1 regularization method, yielding:

[0078]

[0079] Where λ is the regularization coefficient, the Gironov matrix is ​​the penalty term, and B measured To measure the magnetic field matrix, B comp To compensate for the magnetic field matrix.

[0080] Preferably, to minimize the uniformity error, the following equation is solved:

[0081]

[0082] Then, by taking the matrix derivative of the stream function, we get:

[0083]

[0084] Where ψ is the stream function coefficient vector, A is the relationship matrix between the radio frequency magnetic field and the current, and B... target Let be the target field vector.

[0085] Preferably, the magnetic field-current relationship matrix under uniform compensation is:

[0086]

[0087] Where μ0 is the vacuum permeability, J is the current density, and r is the position vector.

[0088] This application also provides a method for active magnetic field compensation of a dual-plane multiplexed coil, including the following steps:

[0089] S1. Determine the dimensions of the dual-plane coil array and obtain the flow function of the coil using Fourier series expansion;

[0090] S2. Set the target magnetic field matrix of the uniform compensation field and the gradient compensation field, calculate the magnetic field strength of the coil according to Maxwell's equations and the stream function, and establish the overdetermined compensation equation set;

[0091] S3. Solve the overdetermined system of equations using the L1 regularization method to obtain the numerical solution of the stream function, and plot the contour lines of the stream function;

[0092] S4. Determine the uniformity error between the target magnetic field and the actual magnetic field based on the numerical solution of the stream function. If the error meets the preset requirements, then drive the coil array to apply a compensation current according to the stream function.

[0093] S5. If the error does not meet the preset requirements, a genetic algorithm is used to find the optimization, and after obtaining the regularization coefficient and weight coefficient, S3-S4 are repeated.

[0094] As shown in Figures 1 and 2, this system adopts a reverse design method. Based on the magnetic field requirements of the dual-plane coil multiplexing structure in the target imaging area, the current distribution of the dual-plane coil is deduced to achieve active compensation.

[0095] In this embodiment, the following steps are included:

[0096] S1. Determine the dimensions of the dual-plane multiplexed coil array and obtain the flow function of the coil using Fourier series expansion.

[0097] A dual-plane multiplexed coil array is installed inside a shielded barrel structure, corresponding to a square region with a side length of L in the target area, with a coil plane spacing of H = 1.5L. The left and right plane coils are symmetrically arranged on both sides of the target area.

[0098] To generate a uniform magnetic field, the target volume is discretized into m=100 sampling points at equal intervals along the three axes. The magnetic field strength at each sampling point is taken as the target field and denoted as B0. The uniform field target matrix is ​​B. uniform To generate the gradient compensation field, the target volume is discretized into m sampling points.

[0099] Let the coordinates of the current source on the dual-plane coil be (r, θ), and the two-dimensional planar uniform flow function be ψ. Then its differential equation is ▽²ψ = 0. Treating the planar coil as a two-dimensional fluid, the flow function can be expressed using a two-dimensional Fourier series:

[0100]

[0101] Where K and L are the Fourier series expansions of the stream function, H is the interplanar spacing of the coils, and a kl b kl Here, K represents the coefficients in the current density flow function of the coil, and k and l represent the Fourier series decomposition orders of the current density in the radial and angular directions, respectively. Considering both the coil shape and performance, K=L=5 is chosen for this design.

[0102] S2. Set the target magnetic field matrix for the uniform compensation field and the gradient compensation field, calculate the magnetic field strength of the coil according to Maxwell's equations and the stream function, and establish the overdetermined compensation equation set.

[0103] The stream function of the uniform compensation coil is symmetric about the x-axis, y-axis, and z-axis, and the resulting stream function is:

[0104]

[0105] The coefficients of the radial component in the coil current function are solved using the least squares method. Due to the biplane arrangement, the gradient coil and the uniform coil exhibit the same symmetry about the z-axis. According to the current continuity equation, ∂J / ∂x = 0, where J is the current density. The design process for the three compensation methods is consistent; in this embodiment, B is used. 1x Taking compensation as an example. According to Maxwell's equations, only the current in the θ direction has an effect on the radio frequency field in the x direction. The current density in the θ direction is as follows:

[0106] .

[0107] According to Maxwell's equations, the relationship between current density and magnetic field can be obtained as follows:

[0108]

[0109] Where μ0 is the free permeability, B x Let dS be the magnetic field along the x-axis, and dS be the area of ​​the infinitesimal element. For uniform compensation:

[0110]

[0111] Among them B uniform It is a uniform compensation magnetic field matrix, A uniform This is the matrix relating the magnetic field and the electric current. ψ uniform Let r be the Fourier coefficient matrix of the stream function. source Let r be the source coordinates. target Let Aψ = B as the target coordinates. target This yields an overdetermined system of equations, where A is the relationship matrix between the radio frequency magnetic field and the current, ψ is the vector of stream function coefficients, and B... target The target magnetic field.

[0112] S3. Solve the overdetermined compensation equations using the L1 regularization method to obtain the numerical solution of the stream function and plot the contour lines of the stream function.

[0113] Solving the system of equations using L1 regularization yields the following Tikhonov matrices:

[0114]

[0115] Among them B measured To measure the magnetic field matrix, B comp To compensate for the magnetic field matrix, λ is the regularization coefficient, which restricts the coil shape and specific absorptivity. The Tikhonov matrix is ​​used as a penalty term. To minimize the error, matrix differentiation is performed using the convection function, yielding:

[0116]

[0117] Where ψ is the stream function coefficient vector and A is the relationship matrix between the radio frequency magnetic field and the current.

[0118] The relationship matrix between the magnetic field and the current under uniform compensation is:

[0119]

[0120] Where A uniform Let be the relationship matrix between magnetic field and current, μ0 be the permeability of free space, J be the current density, r be the position vector, and dV be the infinitesimal volume.

[0121] S4. Determine the uniformity error between the target magnetic field and the actual magnetic field based on the numerical solution of the stream function. If the error meets the preset requirements, apply a compensation current to the driving coil array according to the stream function.

[0122] Import λ ​​and weight ω into the genetic algorithm. Set up a search for the optimal value in a three-dimensional search space, with NUM=50 individuals for optimization. The position and velocity of the j-th individual are represented by x, ∠, ... j and v j Both are three-dimensional vectors; during the search process, the individual extreme value and the global extreme value are recorded as p. best and g best Each individual adjusts its position and velocity based on its individual extreme value and the global extreme value, using the following formula:

[0123]

[0124] Where ω is the inertia weight factor; t is the current iteration number; rand is a random number between [0,1]. c1 and c2 are individual and group learning factors, respectively, used to balance information exchange between individuals and the group;

[0125] The criterion is that the genetic algorithm finds the optimal set of parameters λ and ω, and the calculation error is ||BB. target || <5%, and the stream function parameter, then calculate ψ, and finally drive the coil current according to the contour line of ψ, and determine whether the maximum number of iterations has been reached. If so, output the compensation signal.

[0126] S5. If the error does not meet the preset requirements, a genetic algorithm is used to find the optimization, and after obtaining the regularization coefficient and weight coefficient, S3-S4 are repeated.

[0127] In this embodiment, if the preset requirements are not met, the genetic algorithm is returned to find the best λ and ω, and the calculation is repeated until the uniformity error is <3%.

[0128] In the following embodiments, as shown in Figures 1 to 5, the system includes: a dual-plane coil, a signal acquisition module, a compensation control module, and a feedback optimization module. The dual-plane coil is used to generate and compensate for the magnetic field, and includes a left plane coil and a right plane coil, symmetrically arranged on both sides of the target volume. The signal acquisition module is used to acquire the distribution data of the magnetic field within the target area in real time. The compensation control module is used to calculate the compensation current based on the acquired data and drive the coil array to apply the compensation magnetic field. The feedback optimization module is used to optimize the compensation parameters using a genetic algorithm to achieve dynamic adjustment of the radio frequency magnetic field uniformity.

[0129] Contents not described in detail in this specification are prior art known to those skilled in the art. It is hereby indicated that the above description is intended to help those skilled in the art understand this invention, but does not limit the scope of protection of this invention. Any equivalent substitutions, modifications, improvements, and / or simplifications of the above descriptions that do not depart from the essential content of this invention fall within the scope of protection of this invention.

Claims

1. A dual-plane DC-RF composite field driving coil system, characterized in that, It includes a standard coil unit and a radio frequency coil unit. Both the standard coil unit and the radio frequency coil unit adopt a dual-plane coil configuration optimized by simulation. The dual-plane coil includes a left plane coil and a right plane coil. The left plane coil and the right plane coil are arranged in parallel and coaxially symmetrically on both sides of the target area to generate and compensate for the uniform magnetic field.

2. The dual-plane DC-RF composite field driving coil system according to claim 1, characterized in that, The dual-plane coil configuration employs a reverse design method, which reverse-engineers the current distribution of the dual-plane coil based on the magnetic field requirements of the dual-plane coil multiplexing structure in the target imaging area, thereby achieving active compensation.

3. The dual-plane DC-RF composite field driving coil system according to claim 1, characterized in that, The target area is a square area with a side length of L, and the distance between the left plane coil and the right plane coil is H=1.5L.

4. The dual-plane DC-RF composite field driving coil system according to claim 1, characterized in that, The simulation optimization includes a dual-plane coil design using a combination of a stream function module, an equation module, a calculation module, and a judgment module. The steps are as follows: Step 1, initialize coil parameters; Step 2, obtain the coil's stream function and current density function; Step 3, set the uniform field target matrix and use the Biot-Savart law to calculate the magnetic field strength at the target field point; set the gradient field target matrix and use the Biot-Savart law to calculate the magnetic field strength at the target field point; Step 4, solve for the undetermined coefficients using L2 or L1 regularization; Step 5, solve for the stream function numerical solution and draw the stream function contour lines; Step 6, determine if the uniformity requirement is met. If not, optimize using a two-dimensional particle swarm optimization algorithm to obtain the regularization coefficients and weighting coefficients, then return to Step 5. If the requirement is met, proceed to Step 7; Step 7, export the coordinates of the coil shape and draw the coil shape graphic.

5. The dual-plane DC-RF composite field driving coil system according to claim 2, characterized in that, The active compensation of the dual-plane coil includes the following steps: Step S1, determine the size of the dual-plane coil array, and obtain the stream function of the dual-plane coil using Fourier series expansion; Step S2, set the target magnetic field matrix of the uniform compensation field and gradient compensation field coils, calculate the magnetic field strength of the coil according to Maxwell's equations and the stream function, and establish an overdetermined compensation equation set; Step S3, calculate and solve the overdetermined compensation equation set using the L1 regularization method or the L2 regularization method, obtain the numerical solution of the stream function, and draw the contour lines of the stream function; Step S4, determine the uniformity error between the target magnetic field and the actual magnetic field according to the numerical solution of the stream function. If the error meets the preset requirements, apply a compensation current to the dual-plane coil array according to the stream function; Step S5, if the error does not meet the preset requirements, use a genetic algorithm for optimization, obtain the regularization coefficient and weight coefficient, and repeat steps S3 to S4.

6. The dual-plane DC-RF composite field driving coil system according to claim 5, characterized in that, Step S1 includes the following expression: in It is a stream function, (r,θ) is the coordinate of the current source on the two-plane coil, r is the polar radius, θ is the polar angle, K and L are both Fourier series expansions of the stream function, k and l are both index numbers, a kl b kl These are all coefficients in the current density flow function of the coil. It is the coil current density.

7. The dual-plane DC-RF composite field driving coil system according to claim 5, characterized in that, Step S2 includes the following expression: Among them B uniform It is a uniform compensation magnetic field matrix, A uniform Let ψ be the matrix relating magnetic field and current. uniform Let be the Fourier coefficient matrix of the stream function.

8. The dual-plane DC-RF composite field driving coil system according to claim 5, characterized in that, Step S3 includes the following expression: Where μ0 is the free magnetic permeability and J is the current density. Let r be the position vector, r be the position modulus, and dV be the infinitesimal volume.

9. The dual-plane DC-RF composite field driving coil system according to claim 5, characterized in that, Step S5 includes the following expression: in ω represents the velocity of the j-th individual in the genetic algorithm at the (t+1)-th iteration, where t is the current iteration number, t and j are both positive integers, and ω is the inertia weight factor. c1 is the speed of the j-th individual in the current iteration, c1 is the individual learning factor, rand is a random number between [0,1], and p best It is the best position for an individual. c is the position of the j-th individual in the current iteration, and c2 is the group learning factor. It is the individual's optimal speed. It is the position of the j-th individual in the (t+1)-th iteration.

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