A method for designing a double-layer double-plane self-shielded coil

Abstract

A design method for a double-layer, double-plane self-shielded coil significantly reduces magnetic field crosstalk and shielding barrel coupling effects, improving magnetic field stability and space utilization. It is suitable for coil design and integration applications in high-precision magnetic field control systems. A target field model is established based on the target magnetic field distribution, and magnetic flux constraints ensure that the external magnetic field of the coil approaches zero, thus achieving self-shielding characteristics. Subsequently, a stream function discretization method is used to obtain the coil winding path, and a mapping relationship and current scaling factor between the inner and outer coil layers are established to ensure that the double-layer coil effectively cancels out the external magnetic field while generating the target magnetic field. To further optimize magnetic field uniformity and energy distribution, this invention introduces a tornado optimization algorithm for global optimization of the coil distribution, thereby obtaining a coil structure with high uniformity and high attenuation performance. Finally, finite element simulation is performed on the coil shape to analyze whether its uniformity and attenuation meet the design requirements.

Description

Technical Field

[0001] This invention relates to the field of planar coil design, and in particular to a design method for a double-layer, double-planar self-shielded coil, which helps to improve coil performance. Background Technology

[0002] In recent years, atomic spin devices based on alkali metal vapor have been widely studied in the fields of quantum sensing and precision metrology. These devices, by manipulating atomic spin, achieve highly sensitive measurements of physical quantities such as magnetic fields and angular velocities, and are widely used in atomic clocks, geomagnetic detection, biomagnetic signal detection, atomic gyroscopes, and the measurement of fundamental physical constants. In these devices, a near-zero magnetic field environment is a key condition for achieving high-sensitivity measurements, especially in magnetometers and common magnetometers based on the spin-exchange relaxation-free (SERF) effect. Typically, a multi-layered shielding structure made of highly permeable magnetic materials is used for passive shielding, followed by active compensation using an internal coil to generate a uniform magnetic field. The coil structure directly determines the spatial distribution characteristics and uniformity of the magnetic field, significantly affecting system performance. However, high-permeability shielding materials can lead to the concentration of magnetic induction lines, causing strong coupling between the coil and the shielding barrel, resulting in distortion of the uniform magnetic field region, thus affecting the polarization of alkali metal atoms. Existing technologies mainly employ coil designs that consider shielding coupling or self-shielded coil structures; however, the former depends on specific shielding parameters and has poor adaptability, while the latter has a complex structure and large volume. With the miniaturization and multi-channel trend of quantum devices, traditional coil designs face problems such as crosstalk and space constraints. To address these issues, researchers have proposed solutions such as increasing the spacing between sensing elements, optimizing the modulation signal, all-optical modulation, and self-shielding design. However, the former methods are bulky or complex to implement, while self-shielding coils can generate a highly uniform magnetic field internally and decay rapidly externally, effectively reducing shielding coupling and inter-channel interference. Summary of the Invention

[0003] The purpose of this invention is to overcome the problems existing in the prior art, such as strong magnetic coupling between the coil and the shielding barrel, limited uniformity of the internal magnetic field, insufficient external attenuation performance, and poor structural flexibility. It proposes a design method for a double-layer, double-plane self-shielded coil, which can achieve high uniformity of the internal magnetic field and rapid attenuation of the external magnetic field while maintaining miniaturization and structural compactness, thereby effectively reducing magnetic crosstalk and shielding coupling effects in multi-channel systems.

[0004] The technical solution of the present invention is as follows:

[0005] A design method for a double-layer, double-plane self-shielded coil, characterized by comprising the following steps:

[0006] Step 1: Based on the reverse design of the coil according to the target field method, start from the desired target magnetic field and solve in reverse the current distribution required to generate the target magnetic field. Define the surface region parameters L1, L2, D1 and D2 for placing the current to form a double-layer double-plane coil overall arrangement. L1 is half the side length of the inner square plane coil, L2 is half the side length of the outer square plane coil, D1 is half the distance between the inner upper plane coil and the inner lower plane coil, and D2 is half the distance between the outer upper plane coil and the outer lower plane coil.

[0007] Step 2: Preset a uniform target magnetic field region and establish a cubic target region to provide a zero magnetic environment for the alkali metal gas chamber. Establish an xyz rectangular coordinate system with the center of the target region as the origin. The inner upper plane coil and the inner lower plane coil are symmetrical about the y=0 plane, and the outer upper plane coil and the outer lower plane coil are symmetrical about the y=0 plane. Set discrete coordinate points.

[0008] Step 3, set the target magnetic field value B target ;

[0009] Step 4: Ensure the self-shielding effect of the coil by setting the magnetic flux to 0, and obtain the mapping relationship between the inner and outer coils accordingly;

[0010] Step 5: Set the penalty factor λ and calculate the regularization matrix elements G;

[0011] Step 6: Construct an optimized fitness function and solve it using an optimization algorithm;

[0012] Step 7: Solve for the coefficient matrix s1, and obtain the coefficient matrix s2 through mapping;

[0013] Step 8: By discretizing the flow function, the winding configuration of the coil can be obtained, and the current scaling factor of the inner and outer coils can be obtained, thus completing the design of the double-layer double-plane self-shielded coil.

[0014] Step 4 involves using the normal self-field of the shielding coil to cancel the normal field component generated by the uniform coil on the shielding surface, as expressed below:

[0015]

[0016] in It is the normal self-field of the shielding coil. It is a coefficient matrix. It is the normal field component generated by the uniform coil on the shielding surface. It is to utilize The coefficient matrix is ​​obtained through mapping.

[0017] Step 5 employs the Tikhonov regularization operator to address the ill-conditioned nature of the first type of Fredholm integral equation. The aim is to discretize the target region into T target points, where T is a positive integer, to approximate the pre-defined target magnetic field as closely as possible. The following function is introduced as a criterion.

[0018]

[0019]

[0020]

[0021] Where F is the criterion. It is the magnetic field value at the target point. It is the power dissipated by the resistor. It is the normal self-field of the shielding coil. It is the normal field component generated by the uniform coil on the shielding surface. It is the normal self-field of a uniform coil. It is the normal field component generated by the shielding coil on the shielding surface. B target To set the target magnetic field value, λ is the penalty factor, G is the element of the regularization matrix, and s1 and s2 are coefficient matrices. and Represents the system matrix.

[0022] Step 6 includes constructing an optimized fitness function, using an optimization algorithm to optimize the penalty factor coefficient in the coil design, so that the optimized result can be used in the solution of the flow function, and the outer layer flow function can be obtained through the mapping relationship between the inner and outer coils.

[0023] Step 6 includes the following steps:

[0024] Step 6.1: Preset parameters: Set the population size N, where N is a positive integer, and the maximum number of iterations K, where K is a positive integer;

[0025] Step 6.2, perform population initialization, including initializing the location and velocity of generated storms, thunderstorms and tornadoes;

[0026] Step 6.3: Calculate the fitness value for each individual based on the objective function;

[0027] Step 6.4: Update the particle's position and velocity, and handle boundary conditions;

[0028] Step 6.5: Determine if the maximum number of iterations has been reached. If yes, output the optimal solution; otherwise, return to step 6.3.

[0029] The fitness function expression is as follows:

[0030]

[0031] in It is the fitness function. It is expressed as the cumulative sum of the internal maximum non-uniformity error and the external attenuation. It is a uniform weight. It is a decaying weight. yes In a magnetic field, The coordinates of the target field point inside the coil. yes In a magnetic field, It is the origin. yes Magnetic field; These are the coordinates of the sampling point outside the coil.

[0032] Step 7 includes the following expression:

[0033]

[0034] Step 8 includes using the contour line method to extract discrete conductor loops, thereby obtaining the winding configuration of the coil.

[0035] Step 8 includes the following expression:

[0036]

[0037] in It is a piecewise linear function, where sk is the coefficient, representing the weight of vertex k, which is equal to the current circulating around that vertex in the adjacent triangle, and bk is the selected basis function. bk is 1 at vertex k and 0 at other vertices, and the middle part is interpolated.

[0038]

[0039] Where I is the current. and represents the maximum and minimum values ​​of the stream function, and n represents the number of discrete wire loops.

[0040] The technical effects of this invention are as follows: This invention provides a design method for a double-layer, double-plane self-shielded coil. By introducing a proportionally enlarged outer shielding coil into a traditional double-plane coil structure, and combining the target field method with the tornado optimization algorithm, it achieves simultaneous optimization of internal magnetic field uniformity and external magnetic field attenuation performance. This method effectively reduces magnetic coupling between the coil and the shielding barrel while maintaining a compact structure and miniaturized size, thus improving the accuracy of the magnetic field spatial distribution. Through optimized solution of the convection function, the inner and outer coils generate superimposed magnetic fields, achieving a highly uniform magnetic field within the target region, while simultaneously achieving rapid magnetic field attenuation in the external region, thereby significantly reducing magnetic crosstalk between adjacent channels.

[0041] The present invention has the following characteristics: (1) The present invention adopts a double-layer double-plane structure in the coil design. The inner coil is used to generate a highly uniform magnetic field in the target area, and the outer coil is proportionally amplified and works in the form of reverse current to achieve self-shielding and rapid attenuation of the external magnetic field. (2) The tornado optimization algorithm is introduced into the coil design process, taking into account the magnetic energy distribution, external magnetic flux constraints and current continuity, to achieve global optimization and rapid convergence of current distribution, thereby improving the coil design accuracy and stability. (3) The present invention has the advantages of high design flexibility, high optimization accuracy and high degree of integration, and is particularly suitable for multi-channel atomic magnetometers, common magnetic systems and other highly sensitive quantum measurement devices. Attached Figure Description

[0042] Figure 1 This is a flowchart illustrating the implementation of a double-layer, double-plane self-shielded coil design method according to the present invention. Figure 1The process includes step 1, defining the surface region parameters L1, L2, D1, and D2 where current can be placed; L1 is half the side length of the inner square planar coil, L2 is half the side length of the outer square planar coil, D1 is half the distance between the inner upper and lower planar coils, and D2 is half the distance between the outer upper and lower planar coils; step 2, pre-setting the target uniform region (i.e., the target area, which is cubic in shape, with the center of the target area being the center of the double-layer double-planar coil, establishing an xyz rectangular coordinate system with the center as the origin), and discretizing the coordinate points; step 3, setting... Step 4: Set the target magnetic field value Btarget; Step 5: Ensure the self-shielding effect of the coil by setting the magnetic flux to 0, and obtain the mapping relationship between the inner and outer coils; Step 6: Set the penalty factor λ and calculate the regularization matrix element G; Step 7: Construct the optimization fitness function and solve it using an optimization algorithm; Step 8: Solve the coefficient matrix S1 and obtain the coefficient matrix S2 through mapping; Step 9: Obtain the winding form of the coil by discretizing the flow function, and obtain the current scaling factor of the inner and outer coils, thus completing the design of the double-layer double-plane self-shielded coil. Step 6 includes Step 6.1: Preset parameters, set the population size N (N is a positive integer), and the maximum number of iterations K (K is a positive integer); Step 6.2: Initialize the population, including initializing the position and velocity of the generated storm, thunderstorm, and tornado; Step 6.3: Calculate the fitness value of each individual according to the objective function; Step 6.4: Update the position and velocity of the particles and handle the boundary conditions; Step 6.5: Determine whether the maximum number of iterations has been reached. If yes, output the optimal solution; otherwise, return to Step 6.3. Step 6 includes constructing an optimized fitness function, using an optimization algorithm to optimize the penalty factor coefficient in the coil design, so that the optimized result can be used in the solution of the flow function, and the outer layer flow function can be obtained through the mapping relationship between the inner and outer coils.

[0043] Figure 2 This is a schematic diagram of a double-layer, double-plane self-shielded coil designed according to the design method of this invention. Figure 2 The target region is located at the center and is a cube with a side length of 3 mm, used to provide a zero magnetic environment for the alkali metal gas chamber. The distances between the two sets of planes symmetrical about the XOZ plane are 2D1 and 2D2, and the side lengths of the planes are 2L1 and 2L2, respectively. The origin of the coordinate system is the center point of the atomic gas chamber.

[0044] Figure 3 This is a schematic diagram of the external point selection process involved in the external attenuation calculation process of a double-layer double-plane self-shielded coil design method of the present invention. Figure 3 The calculation points are uniformly taken on a sphere with radius R, and the double-layer double-plane coil is located inside the sphere.

[0045] Figure 4This is a schematic diagram of the outer square planar coil winding routing in a double-layer, double-planar self-shielded coil designed according to the design method of this invention. The circular rings in the diagram represent the coil routing shapes discretized by contour lines; when current is passed through them, the coil can operate normally.

[0046] Figure 5 This is a schematic diagram of the inner square planar coil winding routing in a double-layer, double-planar self-shielded coil designed according to the design method of this invention. The circular rings in the diagram represent the coil routing shapes discretized by contour lines; when current is passed through them, the coil can operate normally.

[0047] Figure 6 This is a uniformity result diagram of a double-layer, double-plane self-shielded coil designed according to the design method of this invention in the XOY plane within a cube of the target region. Uniformity is defined as the relative deviation of the magnetic induction value of each calculated point within the target region from the center point. Figure 6 This indicates low relative deviation and high uniformity.

[0048] Figure 7 This is a uniformity result diagram of a double-layer, double-plane self-shielded coil designed according to the design method of this invention in the XOZ plane within a target region cube. Uniformity is defined as the relative deviation of the magnetic induction value of each calculated point within the target region from the center point. Figure 7 This indicates low relative deviation and high uniformity.

[0049] Figure 8 This is a uniformity result diagram of a double-layer, double-plane self-shielded coil designed according to the design method of this invention in the YOZ plane within a target region cube. Uniformity is defined as the relative deviation of the magnetic induction value of each calculated point within the target region from the center point. Figure 8 This indicates low relative deviation and high uniformity. Detailed Implementation

[0050] The following is in conjunction with the attached diagram ( Figures 1-8 The present invention will be described in conjunction with the examples.

[0051] Figure 1 This is a flowchart illustrating the implementation of a double-layer, double-plane self-shielded coil design method according to the present invention. Figure 2 This is a schematic diagram of a double-layer, double-plane self-shielded coil designed according to the design method of this invention. Figure 3 This is a schematic diagram of the external point selection process involved in the external attenuation calculation process of a double-layer double-plane self-shielded coil design method of the present invention. Figure 4 This is a schematic diagram of the outer square planar coil winding routing in a double-layer, double-planar self-shielded coil designed according to the design method of this invention. Figure 5 This is a schematic diagram of the inner square planar coil winding routing in a double-layer, double-planar self-shielded coil designed according to the design method of this invention. Figure 6 This is a uniformity result diagram of a double-layer, double-plane self-shielded coil designed according to the design method of this invention in the XOY plane within the target region cube. Figure 7 This is a uniformity result diagram of a double-layer, double-plane self-shielded coil designed according to the design method of this invention in the XOZ plane of the target region cube. Figure 8 This is a uniformity result diagram of the YOZ plane within the target region cube of a double-layer, double-plane self-shielded coil designed according to the design method of this invention. (Reference) Figures 1 to 8 As shown, a design method for a double-layer, double-plane self-shielded coil includes the following steps: Step 1, based on the reverse design of the coil according to the target field method, starting from the desired target magnetic field, the current distribution required to generate the target magnetic field is solved in reverse, defining the surface region parameters L1, L2, D1, and D2 for placing the current, forming the overall arrangement of the double-layer, double-plane coil. L1 is half the side length of the inner square plane coil, L2 is half the side length of the outer square plane coil, D1 is half the distance between the inner upper plane coil and the inner lower plane coil, and D2 is half the distance between the outer upper plane coil and the outer lower plane coil; Step 2, a target magnetic field uniform region is preset, and a cubic target region is established to provide a zero magnetic environment for the alkali metal gas chamber. The center of the target region is used as the origin to establish an xyz right-angled coordinate system. The design of a double-layer, double-plane self-shielded coil is as follows: Step 1: The inner upper and lower plane coils are symmetrical about the y=0 plane, and the outer upper and lower plane coils are symmetrical about the y=0 plane. Discrete coordinate points are set. Step 2: Set the target magnetic field value Btarget. Step 3: Ensure the self-shielding effect of the coil by setting the magnetic flux to 0, and obtain the mapping relationship between the inner and outer plane coils. Step 4: Set the penalty factor λ and calculate the regularization matrix element G. Step 5: Construct the optimization fitness function and solve it using an optimization algorithm. Step 6: Solve for the coefficient matrix s1 and obtain the coefficient matrix s2 through mapping. Step 7: The winding form of the coil can be obtained by discretizing the flow function, and the current scaling factor of the inner and outer plane coils can be obtained, thus completing the design of the double-layer, double-plane self-shielded coil.

[0052] In step 4, the normal self-field of the shielding coil is used to cancel the normal field component generated by the uniform coil on the shielding surface, as expressed below:

[0053]

[0054] in It is the normal self-field of the shielding coil. It is the normal field component generated by the uniform coil on the shielding surface.

[0055] Step 5 employs the Tikhonov regularization operator to address the ill-conditioned nature of the first type of Fredholm integral equation. The aim is to discretize the target region into T target points, ensuring the magnetic field distribution corresponding to the solved current density parameters approximates the pre-defined target magnetic field. The following function is introduced as a criterion.

[0056]

[0057]

[0058]

[0059] Where F is the criterion. It is the magnetic field value at the target point. It is the power dissipated by the resistor. It is the normal self-field of a uniform coil. It is the normal field component generated by the shielding coil on the shielding surface. B target To set the target magnetic field value, λ is the penalty factor, G is the element of the regularization matrix, and s1 and s2 are coefficient matrices. and Represents the system matrix.

[0060] Step 6 includes constructing an optimized fitness function, using an optimization algorithm to optimize the penalty factor coefficient in the coil design, so that the optimized result can be used in the solution of the flow function, and the outer layer flow function can be obtained through the mapping relationship between the inner and outer coils.

[0061] Step 6 includes the following steps: Step 6.1, preset parameters, setting the population size N (N is a positive integer) and the maximum number of iterations K (K is a positive integer); Step 6.2, perform population initialization, including initializing the positions and velocities of generated storms, thunderstorms, and tornadoes; Step 6.3, calculate the fitness value of each individual according to the objective function; Step 6.4, update the positions and velocities of the particles and handle boundary conditions; Step 6.5, determine whether the maximum number of iterations has been reached. If yes, output the optimal solution; otherwise, return to Step 6.3.

[0062] The fitness function expression is as follows:

[0063]

[0064] in It is the fitness function. It is expressed as the cumulative sum of the internal maximum non-uniformity error and the external attenuation. It is a uniform weight. It is a decaying weight. yes In a magnetic field, The coordinates of the target field point inside the coil. yes In a magnetic field, It is the origin. yes Magnetic field; These are the coordinates of the sampling point outside the coil.

[0065] Step 7 includes the following expression:

[0066]

[0067] Step 8 includes using the contour line method to extract discrete conductor loops, thereby obtaining the winding configuration of the coil.

[0068] Step 8 includes the following expression:

[0069]

[0070] in It is a piecewise linear function, where sk is the coefficient, representing the weight of vertex k, which is equal to the current circulating around that vertex in the adjacent triangle, and bk is the selected basis function. bk is 1 at vertex k and 0 at other vertices, and the middle part is interpolated.

[0071]

[0072] Where I is the current. and represents the maximum and minimum values ​​of the stream function, and n represents the number of discrete wire loops.

[0073] This invention discloses a reverse design method for a double-layer, double-plane self-shielded coil based on the target field method, belonging to the field of magnetic field generation and control technology. The method first establishes a target field model based on the target magnetic field distribution, and ensures that the external magnetic field of the coil tends to zero through magnetic flux constraints, thereby achieving self-shielding characteristics. Subsequently, the winding path of the coil is obtained using stream function discretization, and a mapping relationship and current scaling factor are established between the inner and outer coil layers to ensure that the double-layer coil effectively cancels out the external magnetic field while generating the target magnetic field. To further optimize the magnetic field uniformity and energy distribution, this invention introduces a tornado optimization algorithm to globally optimize the coil distribution, thereby obtaining a coil structure with high uniformity and high attenuation performance. Finally, finite element simulation is performed on the coil shape to analyze whether its uniformity and attenuation meet the design requirements. This method can significantly reduce magnetic field crosstalk and shielding barrel coupling effects, improve magnetic field stability and space utilization, and is suitable for coil design and integration applications in SERF magnetometers, multi-channel common magnetometers, and other high-precision magnetic field control systems.

[0074] A design method for a double-layer, double-plane coil includes two sets of planar coil pairs, each pair being symmetrical about the y=0 plane. The inner and outer pairs of coils are proportionally related. The coil is designed using a reverse design method based on the target field approach, starting from the desired target magnetic field and working backwards to solve for the current distribution required to generate that magnetic field. By controlling the shape distribution of the inner and outer planar coils, the magnetic flux is kept to zero, thus achieving a self-shielding effect of the external magnetic field and obtaining the mapping relationship between the inner and outer coils. Subsequently, an optimized fitness function is constructed, and the tornado optimization algorithm is introduced into the design of the double-layer, double-plane self-shielded coil to optimize the penalty factor coefficient. This method yields a self-shielded coil that maintains internal uniformity and possesses good attenuation characteristics.

[0075] Includes the following steps:

[0076] Step 1: Design the coil using the target field method of coil reverse design. Starting from the desired target magnetic field, solve in reverse the current distribution required to generate the magnetic field.

[0077] Step 2: Define the planar positions of the coil conductors according to requirements, and determine the design parameters L1, L2, D1, and D2 of the double-layer planar coil. This includes the dimensions of the coil planes and their relative distances. Simultaneously, preset the target area of ​​the central cube, discretize it into coordinate points, and set the target magnetic field value Btarget.

[0078] Step 3: Ensure the self-shielding effect of the coil by setting the magnetic flux to 0, and obtain the mapping relationship between the inner and outer coil layers.

[0079] Step 4: Construct an optimized fitness function. Use an optimization algorithm to optimize the penalty factor coefficient in the coil design. Substitute the optimized result into the solution of the flow function, and obtain the outer layer flow function through the mapping relationship between the inner and outer coils.

[0080] Step 5: Discretizing the flow function will give you the winding configuration of the coil and the current scaling factor of the inner and outer coils.

[0081] Step 6: Perform simulation verification on the obtained coil design results and conduct actual experimental verification on its FPCB fabrication to prove the effectiveness of the design method.

[0082] Step 1 includes defining the surface region where current can be placed and the internal homogeneous target field region. Then, the magnetic field is generated by the continuous surface current density, which is described by a piecewise linear stream function on a triangular mesh. Finally, the objective function is used to find the optimal discrete current mode that satisfies the constraints. During the calculation, the stream function is expanded using a set of basis functions, approximating it as linear on each face of the triangular mesh. Source points on the two planes. Represented as This piecewise linear function can be expressed as

[0083]

[0084] Wherein, the coefficient sk represents the weight of vertex k, which is equal to the current circulating around that vertex in the adjacent triangle, and bk is the selected basis function, which is 1 at vertex k and 0 at other vertices, with interpolation processing performed in the middle part.

[0085] The relationship between the magnitude of the magnetic field and the current density follows the Biot-Savart law, which can be written as an integral over the surface S.

[0086]

[0087] in yes Magnetic field at that location The coordinates of the target field point inside the coil. It is the vacuum permeability. It is a stream function, which is discretized into basis functions. The sum of and sk parameterizes the stream function, with sk as weights stacked onto the vector s, where D represents the system matrix. It is the field point of each vertex in the grid. The vector of the magnetic field contribution at that location. The field point is represented by s. When s is determined, the shape of the planar coil winding is also determined.

[0088] Step 3 includes the following principle: The principle is to use the normal self-field of the shielding coil to cancel the normal field component generated by the uniform coil on the shielding surface, as shown in the following formula.

[0089]

[0090] Here, matrix M consists of mutual inductance in current modes, and can be expressed as:

[0091]

[0092]

[0093] in It is a stream function. It is about The system matrix, It is about The system matrix, due to the shielding surface The zero-flux limitation allows all variables in the outer shielding coil to be mapped to quantities in the inner coil, specifically the inductive energy of the surface current. and power dissipation by resistor It can be represented as follows:

[0094]

[0095]

[0096] Step 4 includes: The optimization algorithm used is the Tornado Optimization Algorithm, which includes the following steps:

[0097] Step 4.1: Preset relevant parameters, including setting the maximum number of iterations, population size, and limits on location and velocity.

[0098] Step 4.2: Randomly generate the location and speed of storms, thunderstorms, and tornadoes.

[0099] Step 4.3: Calculate the fitness value of each individual based on the objective function.

[0100] Step 4.4: Update the particle position and velocity, and handle boundary conditions.

[0101] Step 4.5: After reaching the maximum number of iterations, output the optimal solution.

[0102] Step 5 includes: obtaining the weight matrix of the current function of the double-layer, double-plane coil, and then obtaining its current function. The discrete conductor loops are then extracted using the contour line method to obtain the coil winding configuration. The current relationship between the two planes can be expressed as...

[0103]

[0104] in, and represents the maximum and minimum values ​​of the stream function; n represents the number of discrete wire loops.

[0105] The fitness function mentioned in step 4.3 is expressed as the cumulative sum of the internal maximum non-uniformity error and the external decay:

[0106]

[0107] in The coordinates of the target field point inside the coil; The coordinates of the sampling point outside the coil; and These represent the weights for uniformity and decay, respectively.

[0108] A design method for a double-layer, double-plane self-shielded coil can greatly improve external attenuation while ensuring internal uniformity. First, the coil is reverse-engineered using the target field point method to obtain the coil geometry of the present invention. Then, the weight coefficients of the Tikhonov matrix are optimized using the Tornado optimization algorithm. Finally, after obtaining the shapes and current ratios of the inner and outer coils, simulation is performed to verify whether the uniformity and attenuation meet expectations.

[0109] In the above description of the double-layer, double-plane design method, the coil winding structure is significantly affected by the regularization parameter λ in the Tikhonov matrix. The magnitude of λ determines the complexity of the coil winding; a larger value makes the coil structure easier to manufacture, but may sacrifice internal uniformity. Therefore, a balance must be struck between manufacturing feasibility and magnetic field performance to find the optimal regularization parameter λ. In this invention, the tornado optimization algorithm is selected to optimize the parameter λ. It is a novel natural heuristic metaheuristic algorithm. It transforms the formation, development, and dissipation of a tornado into a search process in an optimization problem by simulating the process. This method can solve global optimization and constraint engineering problems in a continuous search space.

[0110] Contents not described in detail in this specification are existing technologies 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 the present invention, but does not limit the scope of protection of the present invention. Any equivalent substitutions, modifications, improvements, and / or simplifications of the above descriptions that do not depart from the essence of the present invention fall within the scope of protection of the present invention.

Claims

1. A design method for a double-layer, double-plane self-shielded coil, characterized in that, Includes the following steps: Step 1: Based on the reverse design of the coil according to the target field method, start from the desired target magnetic field and solve in reverse the current distribution required to generate the target magnetic field. Define the surface region parameters L1, L2, D1 and D2 for placing the current to form a double-layer double-plane coil overall arrangement. L1 is half the side length of the inner square plane coil, L2 is half the side length of the outer square plane coil, D1 is half the distance between the inner upper plane coil and the inner lower plane coil, and D2 is half the distance between the outer upper plane coil and the outer lower plane coil. Step 2: Preset a uniform target magnetic field region and establish a cubic target region to provide a zero magnetic environment for the alkali metal gas chamber. Establish an xyz rectangular coordinate system with the center of the target region as the origin. The inner upper plane coil and the inner lower plane coil are symmetrical about the y=0 plane, and the outer upper plane coil and the outer lower plane coil are symmetrical about the y=0 plane. Set discrete coordinate points. Step 3, set the target magnetic field value Btarget; Step 4: Ensure the self-shielding effect of the coil by setting the magnetic flux to 0, and obtain the mapping relationship between the inner and outer coils accordingly; Step 5: Set the penalty factor λ and calculate the regularization matrix elements G; Step 6: Construct an optimized fitness function and solve it using an optimization algorithm; Step 7: Solve for the coefficient matrix s1, and obtain the coefficient matrix s2 through mapping; Step 8: By discretizing the flow function, the winding configuration of the coil can be obtained, and the current scaling factor of the inner and outer coils can be obtained, thus completing the design of the double-layer double-plane self-shielded coil.

2. The design method of the double-layer double-plane self-shielded coil according to claim 1, characterized in that, Step 6 includes constructing an optimized fitness function, using an optimization algorithm to optimize the penalty factor coefficient in the coil design, so that the optimized result can be used in the solution of the flow function, and the outer layer flow function can be obtained through the mapping relationship between the inner and outer coils.

3. The design method of the double-layer double-plane self-shielded coil according to claim 1, characterized in that, In step 4, the normal self-field of the shielding coil is used to cancel the normal field component generated by the uniform coil on the shielding surface, as expressed below: in It is the normal self-field of the shielding coil. It is a coefficient matrix. It is the normal field component generated by the uniform coil on the shielding surface. It is to utilize The coefficient matrix is ​​obtained through mapping.

4. The design method of the double-layer double-plane self-shielded coil according to claim 1, characterized in that, Step 5 employs the Tikhonov regularization operator to address the ill-conditioned nature of the first type of Fredholm integral equation. The aim is to make the magnetic field distribution corresponding to the solved current density parameters approximate the pre-defined target magnetic field as closely as possible to the target region, which is discretized into T target points (T being a positive integer). The following function is introduced as a criterion: Where F is the criterion. It is the magnetic field value at the target point, B. target Here, λ represents the target magnetic field value, and λ represents the penalty factor. It is a coefficient matrix. It is the power dissipated by the resistor. It is the first system matrix. It is to utilize The coefficient matrix obtained through mapping It is the second system matrix. It is the normal field component generated by the uniform coil on the shielding surface. It is the normal self-field of the shielding coil. It is the normal self-field of a uniform coil. It is the normal field component generated by the shielding coil on the shielding surface. These are regularized matrix elements.

5. The design method of the double-layer double-plane self-shielded coil according to claim 1, characterized in that, Step 6 includes the following steps: Step 6.1: Preset parameters: Set the population size N, where N is a positive integer, and the maximum number of iterations K, where K is a positive integer; Step 6.2, perform population initialization, including initializing the location and velocity of generated storms, thunderstorms and tornadoes; Step 6.3: Calculate the fitness value for each individual based on the objective function; Step 6.4: Update the particle's position and velocity, and handle boundary conditions; Step 6.5: Determine if the maximum number of iterations has been reached. If yes, output the optimal solution; otherwise, return to step 6.

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6. The design method of the double-layer double-plane self-shielded coil according to claim 2, characterized in that, The fitness function expression is as follows: in It is the fitness function. It is expressed as the cumulative sum of the internal maximum non-uniformity error and the external attenuation. It is a uniform weight. It is a decaying weight. yes In a magnetic field, The coordinates of the target field point inside the coil. yes In a magnetic field, It is the origin. yes Magnetic field; These are the coordinates of the sampling point outside the coil.

7. The design method of the double-layer double-plane self-shielded coil according to claim 1, characterized in that, Step 7 includes the following expression: in It is a coefficient matrix. These are regularized matrix elements. It is the transpose symbol, and λ is the penalty factor set. It is the power dissipated by the resistor. This is the set target magnetic field value. It is the normal self-field of the shielding coil. It is the normal field component generated by the uniform coil on the shielding surface. It is to utilize The coefficient matrix is ​​obtained through mapping.

8. The design method of the double-layer double-plane self-shielded coil according to claim 1, characterized in that, Step 8 includes using the contour line method to extract discrete conductor loops, thereby obtaining the winding configuration of the coil.

9. The design method of the double-layer double-plane self-shielded coil according to claim 1, characterized in that, Step 8 includes the following expression: in It is a piecewise linear function, where sk is the coefficient, representing the weight of vertex k, which is equal to the current circulating around that vertex in the adjacent triangle, and bk is the selected basis function. bk is 1 at vertex k and 0 at other vertices, and the middle part is interpolated. ， Where I is the current. and represents the maximum and minimum values ​​of the stream function, and n represents the number of discrete wire loops.

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