A design method of double-sided electric heating sheet magnetic field suppression configuration for atomic gas cell

Abstract

A double-sided electric heating sheet magnetic field suppression configuration design method for an atomic gas chamber is used to solve the problem of the interference magnetic field and magnetic field gradient generated by the electric heating structure in the background technology. Through simultaneous optimization design of the parameters of the upper and lower heating sheets, the overall structure is formed to effectively suppress the electric heating magnetic field and improve the magnetic field uniformity. The method is characterized in that the NSGA-II algorithm based on Pareto sorting is used to simultaneously optimize the parameters of the two electric heating sheets located on the symmetric surface of the gas chamber, obtain the optimal parameter combination of the two electric heating sheets, and realize the simultaneous optimization of the wiring design of the double-sided electric heating sheets.

Description

Technical Field

[0001] This invention relates to a design method for a magnetic field suppression configuration of a double-sided electric heating element for an atomic gas chamber, belonging to the field of atomic sensor technology. Background Technology

[0002] Atomic sensors, such as miniature atomic magnetometers, are highly sensitive to magnetic fields. However, atomic sensors typically require heating the atomic chamber to achieve a specific atomic density during operation, necessitating that the heating source itself minimize magnetic field interference. Currently, most atomic sensors employ electric heating, but the presence of the heating current inevitably introduces interfering magnetic fields, requiring specially designed heating element wiring to suppress the magnetic field it generates. Conventional design methods focus on wiring for single-sided heating element configurations, but this approach suffers from the drawback of generating a gradient magnetic field along the axial direction, and its magnetic field suppression effect is relatively limited. To address this issue, the inventors have developed a magnetic field suppression configuration design method for double-sided electric heating elements in atomic chambers, which not only significantly reduces the magnetic field generated by the electric heating element itself but also improves the uniformity of the electric heating magnetic field. Summary of the Invention

[0003] The purpose of this invention is to provide a design method for a magnetic field suppression configuration of a double-sided electric heating element for an atomic gas chamber, in order to solve the problems of interference magnetic field and magnetic field gradient generated by the electric heating structure mentioned in the background art. By simultaneously optimizing the design of the parameters of the upper and lower heating elements, an integral structure is formed to effectively suppress the electric heating magnetic field and improve the magnetic field uniformity.

[0004] To achieve the above objectives, the present invention provides the following technical solution:

[0005] A method for designing a magnetic field suppression configuration for a double-sided electric heating element in an atomic gas chamber is characterized by using the NSGA-II algorithm based on Pareto sorting to simultaneously optimize the parameters of two electric heating elements located on the symmetry plane of the gas chamber, thereby obtaining the optimal parameter combination of the two electric heating elements and achieving simultaneous optimization of the wiring design of the double-sided electric heating element.

[0006] Includes the following steps:

[0007] Step 1: Establish a coordinate system and determine the plane containing the two heating substrates and the performance evaluation indicators;

[0008] Step 2, determine the parameter to be measured;

[0009] Step 3, establish the first objective function set f1;

[0010] Step 4: Establish the second objective function set f2;

[0011] Step 5: Determine the value range of each parameter to be measured and solve for the optimal value;

[0012] Step 6: Perform multiple optimization calculations to select the ideal value from multiple sets of data, thereby obtaining the specific parameters of the overall heating configuration;

[0013] Step 7: Connect the individual heating coils to form an overall heating configuration, with the heating current being synchronous and equal everywhere. When the upper and lower heating plates are connected, they are designed as a mirror-symmetrical structure.

[0014] Step 1 includes: establishing an XYZ spatial rectangular coordinate system with the geometric center of the lower heating substrate as the origin, with the x-axis and y-axis lying in the plane of the heating substrate; selecting a parallel plane at z = h as the substrate for the upper heating film, where h represents the distance between the two heating substrates, and the specific parameter of h is given by the size of the gas chamber; selecting an a×a×a square interval in the central region of the gas chamber as the target region, the size of which is also determined by the size of the gas chamber; selecting M target points P in the central region, and using the average value of multiple target points to characterize the entire target region, therefore the value of M needs to be as large as possible; using the average value of the magnetic induction intensity generated by the two heating plates in the target region, i.e., the central region of the atomic gas chamber, as the evaluation criterion for the magnetic field suppression capability of the heating configuration; and using the maximum value of the ratio of the difference in magnetic induction intensity generated by all target points and the center point in the target region to the magnetic induction intensity at the center point as the index for evaluating the uniformity of the magnetic field.

[0015] Step 2 includes: the heating configuration consists of multiple square heating coils located in the two planes z=0 and z=h where the heating base is located. The geometric center of the lower heating coil is located at the origin, and the set center of the upper heating coil is located at (0, 0, h). The set L formed by the half-side lengths of each heating coil, the set I of the current directions, and the number N of the coils are all considered. i Set as the parameter to be determined.

[0016]

[0017]

[0018] Where f1 represents the average magnetic field strength B at all target points. avg Because the target area is a spatially asymmetric region, and the magnetic field at the target point has three vector directions, the design calculates the vector superposition of the double-sided heating film at each point, and finally takes the average value of multiple points in the target area. The value of f2 is used to determine the magnetic field uniformity of the target area, representing the degree of deviation between the magnetic field at multiple points in the target area and the magnetic field at the target center. j is the target point index, and M points P are selected in the target area, denoted as P... j1≤j≤M, where M is a positive integer and i is the coil number, 1≤i≤N i N i It is a positive integer. This indicates that the i-th double-layer square coil is at the target point P. j The magnetic field generated by a point is a vector. and Let L represent the magnetic fields generated at the target point by the i-th square coil in the lower part and the i-th square coil in the upper part, respectively. i Let I be the half-side length of the i-th square coil. i Let I be the direction of the current in the i-th square coil. i The value is +1 or -1, representing the clockwise or counterclockwise current direction, respectively. L 1i L 2i Let I represent the half-side length of the i-th square coil in the lower piece and the half-side length of the i-th square coil in the upper piece, respectively. 1i I 2i Let N represent the current direction of the i-th square coil in the lower part and the current direction of the i-th square coil in the upper part, respectively. i N represents the number of square coils, with the same number of coils on both the upper and lower plates. i Indicates that μ0 is the free permeability, I is the magnitude of the line current; B j For any target point P in the target area of ​​the overall configuration of the double-sided heating film j The magnitude of the generated magnetic field, B0 represents the magnitude of the magnetic field at the center point of the target area.

[0019] Step 5 includes: determining the set L of half-side lengths of the heating coils, the set I of current directions, and the number N of coils. i The range of values ​​for d ≤ L is such that the values ​​of the elements in set L satisfy d ≤ L. i ≤L b -d, and L i+1 –L i ≥2d, where the value of an element in set I is +1 or -1, and the parameter N i The value range is set to 4≤N i ≤10, substitute the parameters to be determined into the NSGA-II algorithm based on Pareto sorting to find the minimum optimal solution for the multiple objective functions, and finally obtain a set of optimal solutions for the objective functions: the Pareto optimal set. The most suitable parameter set is manually selected from the optimal set to obtain the specific parameters of the overall heating configuration; the half-side lengths of the heating coils form a set L = [L 11 ,L 12 ,…,L 1i ,L 1(i+1) ,…,L 1N L 21 ,L 22 ,…,L 2i,L 2(i+1) ,…,L 2N The set of current directions of each heating coil, I = [I 11 ,I 12 ,…,I 1i ,I 1(i+1) ,…,I 1N I 21 ,I 22 ,…,I 2i ,I 2(i+1) ,…,I 2N And the number of coils N i As a set of parameters to be determined, each target point P j The selection of heating elements and the distance h between the two heating elements are determined by the actual application scenario of the heating elements. The heating elements are fabricated on the heating substrate to form heating plates, which are then attached to both sides of the oven that encloses the atomic gas chamber.

[0020] The Biot-Saffar law is used to solve for the magnetic induction intensity generated by the heating configuration at each target point.

[0021]

[0022] Where μ0 is the free permeability and I is the magnitude of the line current. For the infinitesimal vector element of the coil side segment, It is the vector pointing from the infinitesimal element of the coil side segment to the target point, where r is The model;

[0023] The square coil is decomposed into four single-sided straight line segments for solution. The analytical expression for the magnetic induction intensity of the straight line segments is obtained by integrating the current segments, with the upper and lower limits of integration adjusted according to the current direction in each straight line segment.

[0024]

[0025]

[0026]

[0027]

[0028]

[0029] in Let be the magnetic field generated by the i-th square coil at the j-th target point in the lower piece. This represents any point P in the target region where the corresponding sides of the square coil, from a to b. j The generated magnetic field This represents the distance from line segment M1M2 to any point P in the target region. jThe unit direction vector of the generated magnetic field, μ0 is the free permeability, I 1i L is the direction of the current in the i-th coil within the substrate. 1i Let P be the half-side length of the i-th square heating coil within the lower substrate, M1 and M2 be the start and end points of the line segment, and P be the half-side length of the i-th square heating coil within the substrate. j P is any point in the target region. j =(x j ,y j ,z j The coordinates of M1 and M2 are determined by the half-side length L of the heating coil. j Provided.

[0030] The heating configuration design method includes a multi-layer structure, and the specific parameters of the dual heating films are given by the program.

[0031] M target points are selected on the central a×a×a region of the air chamber. The average magnetic induction intensity B generated by the overall heating configuration at all target points is... avg As a criterion for evaluating the magnetic field suppression capability of the heating configuration, B avg The smaller the value, the smaller the magnetic field generated by the heating configuration and the stronger the magnetic field suppression capability. The overall uniformity is evaluated by the percentage of the relative change in magnetic induction intensity generated by the overall heating configuration at all target points and the magnetic induction intensity at the center point. The smaller the maximum value of the relative change, the better the uniformity.

[0032] Compared with the prior art, the beneficial effects of the present invention are:

[0033] (1) The double-sided electric heating element design structure can achieve rapid heating in the air chamber. Compared with the traditional single-sided electric heating structure, it has better temperature uniformity and magnetic field uniformity. Moreover, the parameters can be constrained according to the size of the heating air chamber, and the magnetic field suppression wiring configuration on the heating element can be quickly calculated and determined.

[0034] (2) The upper and lower double-sided electric heating structure is simultaneously optimized to obtain a multi-layer overall heating configuration. The traditional method generally designs a single-sided electric heating element to optimize its single-sided performance, and then installs it on one side or symmetrical sides of the air chamber. This traditional method only designs the magnetic field cancellation for the wiring within a single side and does not consider the magnetic field cancellation effect between the two sides, which will increase the average magnetic field in the target area. The present invention considers both the magnetic field cancellation within a single side and the magnetic field cancellation effect between the two sides, which can further improve the magnetic field suppression capability of the wiring;

[0035] (3) The coil size, number and current direction of the heating configuration are optimized. The parameters of the upper and lower plates are given together by the NSGA-II algorithm program based on Pareto sort. The specific wiring of the final upper and lower plate heating configuration may not be completely consistent and may not be completely identical two-sided configurations. Attached Figure Description

[0036] Figure 1 This is a schematic diagram of the magnetic field suppression configuration of the double-sided electric heating element involved in the design method of magnetic field suppression configuration for atomic gas chambers according to the present invention. Figure 1 It includes an atomic gas chamber 1, an upper heating configuration 2, and a lower heating configuration 3.

[0037] Figure 2 This is a schematic diagram of magnetic field calculation involved in the design method of magnetic field suppression configuration of double-sided electric heating plate for atomic gas chamber of the present invention. Figure 2 The diagram shows that the overall configuration is divided into several segments of straight current, and the magnetic field effect generated by each segment of straight current at the target point is superimposed. Figure 2 It includes line segments M1 and M2, where M1 is the starting point of the line segment, M2 is the ending point of the line segment, and r is... The model, Let I be the vector pointing from the infinitesimal element of the coil segment to the target point, and let Bp be the magnetic field at the target point P. Let θ be the infinitesimal vector element of the coil side segment. and The angle between the two angles is θ1, which is the starting angle, and θ2, which is the ending angle.

[0038] Figure 3 This invention relates to a schematic diagram of target area selection and magnetic field calculation. The magnetic field at each point must take into account the magnetic field cancellation effect generated by the upper and lower heating structures. The geometric bases of the upper and lower heating structures are located on two planes, z=0 and z=h, respectively. The distance h between the two planes is adjustable and determined by the actual size of the square air chamber. The selection of the target area between the two planes can also be reasonably adjusted according to the actual size of the air chamber. Figure 3 In this context, I represents the current, dl represents a small element of the coil segment, and P represents the current. j P is any point in the target region (the central cube region between the double-sided heating elements). j =(x j ,y j ,z j O2 is the center point of the upper heating element (0, 0, h), O1 is the center point of the lower heating element (0, 0, 0), the four corner points of the square upper heating element are N1 to N4, and the four corner points of the square lower heating element are M1 to M4. L 1i L 2i These represent the half-side lengths of the i-th square coil in the lower piece and the i-th square coil in the upper piece, respectively. Detailed Implementation

[0039] The following is in conjunction with the attached diagram ( Figures 1-3 The invention will be described in the following sections and examples.

[0040] Figure 1This is a schematic diagram of the magnetic field suppression configuration of the double-sided electric heating element involved in the design method of magnetic field suppression configuration for atomic gas chambers according to the present invention. Figure 2 This is a schematic diagram of magnetic field calculation involved in the design method of magnetic field suppression configuration of double-sided electric heating plate for atomic gas chamber of the present invention. Figure 3 This is a schematic diagram illustrating the target area selection and magnetic field calculation involved in the present invention. (Reference) Figures 1 to 3 As shown, a design method for a magnetic field suppression configuration of a double-sided electric heating element for an atomic gas chamber is characterized by using a multi-objective optimization algorithm to simultaneously optimize the wiring parameters on two heating films located on the symmetrical plane of the gas chamber, thereby obtaining the overall configuration of the double heating film. The heating film (2) located above the gas chamber and the heating film (3) located below the gas chamber constitute a whole located on the symmetrical plane of the gas chamber (1). The heating film is regarded as several square coils with coincident geometric centers. The average magnitude and uniformity of the magnetic induction intensity generated by the target in the central region are used as the objective function to optimize multiple parameters such as the size, number, and current direction of the coils. Finally, the multiple square coils are connected by wiring to form the heating wire inside the heating film.

[0041] The heating film is composed of conventional square coils. The size, number, and current direction of these square coils are given by the NSGA-II algorithm based on Pareto sort. Multiple objectives are optimized simultaneously, with the minimum of the objective function set as the optimization objective, and the parameters of the electric heating film are calculated.

[0042] The set of functions is as follows:

[0043]

[0044]

[0045] Where f1 and f2 are the first and second sets of objective functions, respectively, and f1 represents the average value B of the magnetic induction intensity at all target points. avg Because the target area is a spatial range without symmetry, and the magnetic field at the target point has a vector in three directions, the design calculates the vector superposition generated by the double-sided heating film at each point, and finally takes the modulus to calculate the average value of several points in the target area; the value of the objective function set f2 is used to determine the magnetic field uniformity of the target area, which represents the degree of deviation between the magnetic field at the point in the target area and the magnetic field at the target center.

[0046] In f1, j is the target point index. M points P are selected within the target area, denoted as P. j 1≤j≤M, where M is a positive integer and i is the coil number, 1≤i≤N i N i It is a positive integer. This indicates that the i-th double-layer square coil is at the target point P. j The magnetic field generated by a point is a vector. and Let L represent the magnetic fields generated at the target point by the i-th square coil in the lower part and the i-th square coil in the upper part, respectively. i Let I be the half-side length of the i-th square coil. i Let I be the direction of the current in the i-th square coil. i The value is +1 or -1, representing the clockwise or counterclockwise current direction, respectively. L 1i L 2i Let I represent the half-side length of the i-th square coil in the lower piece and the half-side length of the i-th square coil in the upper piece, respectively. 1i I 2i Let N represent the current direction of the i-th square coil in the lower part and the current direction of the i-th square coil in the upper part, respectively. i N represents the number of square coils, with the same number of coils on both the upper and lower plates. i In this context, μ0 represents the permeability of free space, and I represents the magnitude of the line current.

[0047] f2 in B j For any target point P in the target area of ​​the overall configuration of the double-sided heating film j The magnitude of the generated magnetic field, B0 represents the magnitude of the magnetic field at the center point of the target area.

[0048]

[0049]

[0050]

[0051]

[0052] in Let be the magnetic field generated by the i-th square coil at the j-th target point in the lower piece. This represents any point P in the target region where the corresponding sides of the square coil, from a to b. j The generated magnetic field is a vector. This represents the distance from line segment M1M2 to any point P in the target region. j The unit direction vector of the generated magnetic field, μ0 is the free permeability, I 1i L is the direction of the current in the i-th coil within the substrate. 1i Let be the half-side length of the i-th square heating coil within the lower substrate.

[0053] The heating configuration is defined by the set of half-side length parameters L = [L 11 ,L 12 ,…,L 1i ,L1(i+1) ,…,L 1N L 21 ,L 22 ,…,L 2i ,L 2(i+1) ,…,L 2N ], Current direction set I = [I 11 ,I 12 ,…,I 1i ,I 1(i+1) ,…,I 1N I 21 ,I 22 ,…,I 2i ,I 2(i+1) ,…,I 2N And the number of coils N i Together, we determine that the values ​​of the elements in set L satisfy d ≤ L. i ≤L b -d, and L i+1 -L i ≥2d, where d is the minimum achievable spacing between coils, which depends on the manufacturing process. The value of the element in set I is +1 or -1.

[0054] Number of heating coils N i The parameter range is 4 to 12, and is a positive integer. The number of target points M in the target area is a known value that is a positive integer and should be as large as possible.

[0055] The heating configuration design method includes a multi-layer structure, and the specific parameters of the dual heating films are given by the program.

[0056] Includes the following steps:

[0057] Step 1: Establish a coordinate system and determine the plane containing the two heating substrates and the performance evaluation indicators;

[0058] A spatial rectangular coordinate system XYZ is established with the geometric center of the lower heating substrate as the origin. The x-axis and y-axis lie in the plane of the heating substrate. A parallel plane is selected at z = h as the substrate for the upper heating film, where h is the distance between the upper and lower heating substrates. The specific parameters are given by the size of the heated atomic gas chamber. An a×a×a central region is selected in the central area of ​​the gas chamber as the target region. The size of the target region is also determined by the size of the gas chamber. M target points P are selected in the central region, and the average value of multiple target points is used to characterize the entire target region. Therefore, the value of M needs to be as large as possible. The average value of the magnetic induction intensity generated by the two heating plates in the target region (the central region of the atomic gas chamber) is used as the evaluation criterion for the magnetic field suppression capability of the heating configuration. The maximum value of the ratio of the difference between the magnetic induction intensity generated by the heating configuration at the target point and the central point to the magnetic induction intensity at the central point is used as the index for evaluating the uniformity of the magnetic field.

[0059] Step 2, determine the parameter to be measured;

[0060] The heating configuration consists of multiple square heating coils located in the z=0 and z=h planes of the heating base. The geometric center of the lower heating coil is located at the origin, and the set center of the upper heating coil is located at (0, 0, h). The set L formed by the half-side lengths of each heating coil, the set I of the current directions, and the number N of the coils are all considered. i Set as the parameter to be determined;

[0061] Step 3, establish the objective function set f1;

[0062] Based on the Biot-Safar theorem, derive the expression for each side of the square coil at any point P in the target region. j The generated magnetic field is calculated by summing the magnetic induction intensity of each coil at a single target point, and then averaging the magnitudes of the magnetic induction intensity at all target points, which is used as the objective function f1.

[0063]

[0064] Step 4: Establish the objective function set f2;

[0065] Take any point P of the overall configuration in the target region. j The difference between the magnetic induction intensity of the target area and the magnetic induction intensity B0 at the center point (0, 0, h / 2) is compared with the magnetic induction intensity at the center point. h represents the distance between the two heating areas, and h / 2 represents the middle position. The value of the objective function set f2 is used to determine the magnetic field uniformity of the target area, which represents the degree of deviation between the magnetic field at the center of the target area and the magnetic field at the center of the target area.

[0066]

[0067] Step 5: Determine the value range of each parameter to be measured and solve for the optimal value;

[0068] Determine the set L of half-side lengths of the heating coils, the set I of current directions, and the number N of coils. i The range of values ​​for d ≤ L is such that the values ​​of the elements in set L satisfy d ≤ L. i ≤L b -d, and L i+1 -L i ≥2d, where the value of an element in set I is +1 or -1, and the parameter N i The value range is set to 4≤N i≤10, take positive integers. Substitute the parameters to be determined into the NSGA-II algorithm based on Pareto sorting to find the minimum optimal solution for the multiple objective functions. Finally, a set of optimal solutions for the objective functions is obtained: the Pareto optimal set. The most suitable parameter set is manually selected from the optimal set.

[0069] Step 6: Perform multiple optimization calculations to select the ideal value from multiple sets of data, thereby obtaining the specific parameters of the overall heating configuration;

[0070] Step 7: Connect the individual heating coils to form an overall heating configuration, with the heating current being synchronous and equal everywhere. When the upper and lower heating films are connected, they are designed as a mirror-symmetrical structure.

[0071] M target points are selected on the central a×a×a region of the air chamber. The average magnetic induction intensity B generated by the overall heating configuration at all target points is... avg As a criterion for evaluating the magnetic field suppression capability of the heating configuration, B avg The smaller the value, the smaller the magnetic field generated by the heating configuration and the stronger the magnetic field suppression capability. The overall uniformity is evaluated by the percentage of the relative change in magnetic induction intensity generated by the overall heating configuration at all target points and the magnetic induction intensity at the center point. The smaller the maximum value of the relative change, the better the uniformity.

[0072] This invention provides a method for designing a magnetic field suppression configuration for a double-sided electric heating element used in an atomic gas chamber. Under the condition of a fixed distance between the two heating films, an optimal set of double-sided heating structure combination parameters is calculated by optimizing the dimensions, current direction, and number of heating coils of multiple sets of square heating structures. The heating configuration designed by this method can effectively suppress the electric heating magnetic field and improve the uniformity of the magnetic field.

[0073] The technical solution adopted in this invention is: a magnetic field suppression configuration for a double-sided electric heating element, composed of multiple square conductive coil structures of different sizes. The overall configuration is as follows. Figure 1 As shown, the heating configuration is designed symmetrically on the upper and lower sides of the air chamber (1), consisting of an upper heating film (2) and a lower heating film (3). Both the upper and lower heating films have N i The set of square heating coils has the geometric center of the lower heating structure located at the origin, and the geometric center of the upper heating structure located at (0, 0, h), where h represents the distance between the upper and lower heating films. The value of h depends on the size of the small heating chamber.

[0074] like Figure 2 The diagram shows a magnetic field calculation, which divides the actual square coil structure into the superposition of magnetic field vectors generated by several straight currents at points in space.

[0075] Figure 3The diagram illustrates the selection of the target area and the calculation of the magnetic field. A suitable space is selected in the center region of the upper and lower heating films as the target area, and M target points P are selected within the target area. j The value of M should be as large as possible. The average value of the magnetic induction intensity generated by the heating configuration at all target points (i.e., the target area) is used as the criterion for evaluating the magnetic field suppression capability of the heating configuration. The smaller the average value, the smaller the magnetic induction intensity generated by the heating configuration, and the stronger the magnetic field suppression capability. The overall uniformity is evaluated by the percentage relative change between the magnetic induction intensity generated by the overall heating configuration at all target points and the magnetic induction intensity at the center point; the smaller the maximum relative change, the better the uniformity.

[0076] like Figure 3 As shown, the desired outcome is the set of magnetic fields at any point within the target area. This is a general conclusion, lacking symmetry. It requires superimposing the magnetic field effects generated by the four sides of the square coil at any target point (considering the directionality of the magnetic fields, vector superposition is used). M1 and M2 are the starting and ending points of the line segment; for details, please refer to... Figure 2 P j P is any point in the target region. j =(x j ,y j ,z j The coordinates of M1 and M2 are determined by the half-side length L of the heating coil. j Provided.

[0077] The average value of the magnetic induction intensity generated by the heating configuration at all target points is set as the objective function f1, and the percentage change in the relative change between the magnetic induction intensity generated by the overall heating configuration at all target points and the magnetic induction intensity at the center point is set as the objective function f2. A multi-objective optimization algorithm is introduced, which is achieved by changing the half-side length L of the heating coil. i Current direction I i And the number of heating coils N i By calculating parameters such as these, the optimal combination of heating coils is obtained. This invention can quickly calculate and determine the overall heating configuration of the double-sided heating film within a specified heating chamber size, effectively suppressing the electric heating magnetic field while improving the magnetic field uniformity within the chamber.

[0078] The optimization objective is to minimize the objective function set f. The set of half-side lengths L of the heating coils, the set of current directions I, and the number of heating coils N are used as the set of parameters to be calculated and substituted into the objective function. The optimal solution is obtained by using a multi-objective optimization algorithm, and the parameters of the heating configuration are calculated.

[0079] The program is optimized to obtain multiple independent heating coils, which are then routed in the actual configuration and connected to form the complete heating configuration. To ensure the magnetic field cancellation effect between the two-sided routing configurations in the actual configuration, mirror symmetry processing is required when connecting the actual routing configurations.

[0080] 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 method for designing a magnetic field suppression configuration for a double-sided electric heating element in an atomic gas cell, characterized in that, The NSGA-II algorithm based on Pareto sorting is used to simultaneously optimize the parameters of two electric heating sheets located on the symmetric surface of the air chamber, to obtain the optimal parameter combination of the two electric heating sheets, and to realize the simultaneous optimization of the wiring design of the double-sided electric heating sheet. The method comprises the following steps: Step 1: establishing a coordinate system, determining the plane of the two heating bases and the performance evaluation index; Step 2: determining the parameters to be measured; Step 3: establishing a first objective function set f1; Step 4: establishing a second objective function set f2; Step 5: determining the value range of each parameter to be measured, and solving the optimal value; Step 6: performing multiple optimal value solving, screening out ideal values from multiple sets of data, and obtaining the specific parameters of the overall heating configuration; Step 7: connecting each independent heating coil into an overall heating configuration, synchronously equalizing the heating current everywhere, and designing the upper and lower heating sheets into a mirror-symmetric structure when connected; In step 1, the following steps are included: establishing an XYZ space rectangular coordinate system with the geometric center of the heating base as the origin, the x-axis and the y-axis being in the plane of the heating base, and selecting a parallel plane at z=h as the base of the upper heating film, h representing the distance between the two heating bases, and the specific parameter of h being given by the size of the air chamber; selecting a square interval of a×a×a as the target region in the central region of the air chamber, the size of the target region also being determined by the size of the air chamber, and selecting M target points P in the central region, the values of the multiple target points being used to represent the entire target region, so the value of M needs to be as large as possible; the average value of the magnetic induction intensity generated by the two heating sheets in the target region, i.e., the central region of the atomic air chamber, is taken as the evaluation standard of the magnetic field suppression capability of the heating configuration, and the maximum value of the ratio of the difference between the magnetic induction intensity generated by the heating configuration at the target point and the central point to the magnetic induction intensity at the central point is taken as the index for evaluating the uniformity of the magnetic field. The step 2 comprises: heating the configuration consists of a plurality of square heating coils in the planes z=0 and z=h where the heating base is located, the geometric center of the lower sheet heating coil is located at the origin, and the collective center of the upper sheet heating coil is located at (0, 0, h), the collective L of half side lengths of each heating coil, the collective I of current directions, and the number N of coils i Let be the parameter to be solved.

2. The double-sided electric heating sheet magnetic field suppression configuration design method for an atomic air chamber according to claim 1, characterized in that Wherein f1 represents the average value B of the magnetic induction intensity of all target points avg Because the target area is a spatial range without symmetry, the magnetic field in the target point has three directional vectors, so in the design, the vector superposition generated by the double-sided heating film at each point is calculated, and finally the average value of several points in the target area is taken. The value of f2 is used to determine the magnetic field uniformity of the target area, which represents the deviation degree of the magnetic field of the target point from the magnetic field of the target center; j is the target point serial number, M P points are selected in the target area, and P j , i is the coil serial number, 1≤i≤N i , N i is a positive integer, represents the magnetic field generated by the ith double-layer square coil at the target point P j , which is a vector, and respectively represent the magnetic field generated by the ith square coil on the lower sheet and the ith square coil on the upper sheet at the target point, L i is the half side length of the ith square coil, I i is the current direction of the ith square coil, I i is +1 or-1, which respectively represents the clockwise or counterclockwise current direction, , respectively represent the half side length of the ith square coil on the lower sheet and the half side length of the ith square coil on the upper sheet, , respectively represent the current direction of the ith square coil on the lower sheet and the current direction of the ith square coil on the upper sheet, N i is the number of square coils, the number of upper and lower coils is the same, represented by N i , μ0 is the vacuum permeability, I is the line current size; B j is the magnetic field size generated by the overall configuration of the double-sided heating film in the target area at any target point P j , and B0 represents the magnetic field size of the center point of the target area.

3. The design method of double-sided electrically heated sheet magnetic field suppression configuration for atomic gas cell according to claim 1, characterized in that, Step 5 includes: determining the set L of half-side lengths of the heating coils, the set I of current directions, and the number N of coils. i The range of values ​​for d ≤ L is such that the values ​​of the elements in set L satisfy d ≤ L. i ≤L b -d, and L i+1 - L i ≥2d, where the value of an element in set I is +1 or -1, and the parameter N i The value range is set to 4≤N i ≤10, take positive integers, substitute the parameters to be solved into the NSGA-II algorithm based on Pareto sorting, and solve for the minimum optimal solution of the multiple objective functions. Finally, a set of optimal solutions of the objective functions is obtained: the Pareto optimal set. The most suitable parameter set is manually selected from the optimal set to obtain the specific parameters of the overall heating configuration; the half-side lengths of the heating coils form a set L=[L 11 , L 12 , …, L 1i , L 1（i+1） ,…, L 1N， L 21 , L 22 ,…, L 2i , L 2（i+1） ,…, L 2N The set of current directions of each heating coil, I = [I 11 , I 12 , …, I 1i ,I 1（i+1） ,…, I 1N， I 21 , I 22 , …, I 2i , I 2（i+1） ,…, I 2N And the number of coils N i As the set of parameters to be determined; each target point P j The distance h between the heating configuration and the heating configuration is determined by the actual application scenario of the heating configuration. The heating configuration is made on the heating substrate to form a heating plate, and the heating plate is attached to both sides of the oven that encloses the atomic gas chamber.

4. The design method of double-sided electrically heated sheet magnetic field suppression configuration for atomic gas cell according to claim 1, characterized in that, The magnetic induction intensity generated by the heating configuration at each target point is solved by using the Biot-Savart law : where μ0is the vacuum permeability, I is the line current magnitude, is the coil segment differential vector, is the coil segment differential vector, r is the modulus of The square coil is decomposed into four single straight line segments for solving, and the analytical expression of the magnetic induction intensity of the straight line segment adopts current segment integration, and the upper and lower limits of integration are changed according to the current direction of the straight line segment: where is the magnetic field generated by the i-th square coil of the lower sheet at the j-th target point, denotes the unit directional vector of the magnetic field generated by the corresponding side of the square coil from a to b at an arbitrary point P j in the target region, denotes the unit directional vector of the magnetic field generated by the line segment M1M2 to an arbitrary point P j in the target region, and μ0 is the vacuum permeability, is the i-th coil current direction within the lower sheet substrate, L 1i is the half side length of the i-th square heating coil within the lower sheet substrate, M 1、 M2 is the starting point and the end point of the line segment, P j is an arbitrary point in the target region, P j = (x j , y j , z j ), M 1、 The coordinates of M2 are given by the half side length L j of the heating coil.

5. The design method of double-sided electrically heated sheet magnetic field suppression configuration for atomic gas cell according to claim 1, characterized in that, The heating configuration design method comprises a multi-layer structure, and the specific parameters of the double heating film are given by the program.

6. The design method of double-sided electrically heated sheet magnetic field suppression configuration for atomic gas cell according to claim 1, characterized in that, M target points are taken on the center a x a x a area of the air chamber, and the average value B of the magnetic induction intensity generated by the overall heating configuration at all target points avg As a judgment standard of the heating configuration magnetic field suppression ability, the smaller the value of B avg , the smaller the magnetic field generated by the heating configuration, the stronger the magnetic field suppression ability; the relative change percentage of the magnetic induction intensity generated by the overall heating configuration at all target points and the center point magnetic induction intensity is used to evaluate the overall uniformity, and the smaller the maximum relative change value, the better the uniformity.

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