A configuration design method of non-magnetic electric heating film based on region division

Abstract

The application discloses a non-magnetic electric heating film configuration design method based on region division and belongs to the technical field of electric heating magnetic field suppression. The method comprises the following steps: region division is performed on a heating film plane according to the size of contribution values; a base function is established in the region to represent a flow function of current distribution; the magnetic field distribution and the temperature distribution of an alkali metal gas chamber are calculated based on the flow function; constraint conditions about each coefficient in the base function are established according to the magnetic noise uniformity and the temperature uniformity; a cost function is established according to the principle of minimum magnetic noise mode of the gas chamber, and the optimal solution of each coefficient in the base function is calculated to obtain a flow function expression of the current distribution; and the heating film configuration is designed according to the current contour distribution. The method can effectively reduce the magnetic noise of the heating film and take into account the heating uniformity, and is favorable for improving the magnetic resonance signal quality in a quantum sensor.

Description

Technical Field

[0001] This invention relates to the field of electric heating magnetic field suppression technology, and in particular to a method for designing a non-magnetic electric heating film configuration based on region division. Background Technology

[0002] With the in-depth development of theories such as quantum manipulation, physical optics, and electromagnetic compatibility, quantum sensors have become increasingly popular among researchers due to their high sensitivity, chip-based design, and low cost. These sensors use an alkali metal gas cell as their core sensing element. The spatial distribution characteristics of the magnetic and temperature fields significantly influence the manipulation of the quantum state, thereby affecting the sensitivity and measurement accuracy of the magnetometer. However, while the electrically heated film provides heat to the gas cell, it inevitably introduces magnetic field interference. This magnetic noise adversely affects the preset magnetic field required for the gas cell.

[0003] To address the magnetic noise generated by heating films, existing technologies typically employ specific heating wire routing configurations to suppress it. However, this approach fails to adequately consider the issue of temperature field uniformity, especially in quantum state manipulation where a highly uniform temperature field is required. Therefore, current electric heating technologies struggle to achieve the dual goals of magnetic field suppression and uniform heating, indicating a significant deficiency in the heating wire layout of electric heating films. Summary of the Invention

[0004] The purpose of this invention is to provide a design method for a non-magnetic electric heating film configuration based on region division, which enables effective control of the temperature field and magnetic field, and is beneficial to improving the magnetic resonance signal quality of atomic magnetometers.

[0005] To achieve the above objectives, this invention provides a method for designing a non-magnetic electric heating film configuration based on region division, comprising the following steps:

[0006] S1. Analyze the contribution of the current element on the heating film to the magnetic noise at the center point of the air chamber, and divide the heating film into regions according to the magnitude of the contribution.

[0007] S2. Establish the current distribution stream function within the region, and calculate the magnetic field distribution and temperature distribution of the alkali metal gas chamber based on the stream function;

[0008] S3. Establish constraints on the coefficients in the stream function based on the uniformity of magnetic noise and temperature.

[0009] S4. Based on the principle of minimizing the magnetic noise mode of the air chamber, establish the cost function and calculate the optimal solution of each coefficient in the stream function to obtain the stream function expression of the current distribution;

[0010] S5. Design the heating film configuration based on the current contour distribution.

[0011] Preferably, in step S1, the contribution of the location of the current element on the heating film to the magnetic noise at the center point of the gas chamber is analyzed, and the heating film is divided into regions according to the magnitude of the contribution value, including:

[0012]

[0013] In the formula, B(r) represents the contribution of a current element at a certain point to the magnetic field at the center of the gas chamber, μ0 represents the vacuum permeability, and I represents the heating wire current. This represents the current element vector, where l represents the length of the current element. denoted by r, which represents the position vector from the current element to the center point of the gas chamber; denoted by r, which represents the distance from the current element to the center point of the gas chamber; and denoted by d, which represents the distance from the center point of the gas chamber to the heating film.

[0014] The heating film is divided into regions based on the change in |B(r)|. Let P be the point on the perpendicular line passing through the center point of the air chamber and perpendicular to the heating film. According to the magnetic noise equation at the center point of the air chamber, the contribution value at point P is the largest, denoted as |B(r)|. max , with |B(r)| max Based on this, the heating film is divided into regions according to the change in the magnetic noise contribution value, using the following formula:

[0015]

[0016] In the formula, Ω n ={r∈Ω∣|B(r)|∈[a n |B(r)∣ max ,a n-1 |B(r)∣ max )} indicates that on the heating film (r∈Ω), |B(r)|∈[a] n |B(r)∣ max ,a n-1 |B(r)∣ max A subset of all r, a1, a2, ..., a n This represents the weighting coefficient.

[0017] Preferably, in step S2:

[0018] The stream function of the current distribution within the region is established using Fourier series, and the formula is as follows:

[0019]

[0020] In the formula, y i (x,y) represents the i-th region Ω i The stream function, and Let represent the expansion coefficients of the Fourier series, m and n represent the mode numbers of the Fourier series, and and correspond to the wave numbers in the x and y directions, respectively. Lx L y Representing regions Ω i The lengths in the x and y directions, where (x, y) represent coordinates, and the origin of the coordinate system is the center of the heating film;

[0021] Based on the stream function y i (x,y) yields the magnetic field B(x,y,z) and temperature field T(x,y,z) of the alkali metal gas chamber.

[0022] Preferably, the constraint conditions for each coefficient in the stream function established in step S3 based on the uniformity of magnetic noise and temperature include:

[0023]

[0024] subject to:

[0025]

[0026] In the formula, ∈1 represents the maximum permissible magnetic field inhomogeneity, ∈2 represents the maximum permissible temperature field inhomogeneity, (b i,1 ,b i,2 )express The range of values ​​for α i,1 ,α i,2 )express The range of values ​​for , and These represent the mean values ​​of the magnetic field and temperature field within the air chamber, respectively.

[0027] Preferably, step S4, which involves establishing the cost function and calculating the optimal solution for each coefficient in the stream function based on the principle of minimizing the magnetic noise mode of the air chamber, includes:

[0028]

[0029] subject to:

[0030]

[0031] In the formula, f represents the stream function expression.

[0032] Therefore, the above-mentioned region-division-based non-magnetic electric heating film configuration design method of the present invention can effectively reduce the magnetic noise generated by the heating film during operation and take into account the heating uniformity, which is beneficial to improving the signal quality of quantum sensors and has a wider range of application prospects.

[0033] The technical solution of the present invention will be further described in detail below with reference to the accompanying drawings and embodiments. Attached Figure Description

[0034] Figure 1 This is a flowchart illustrating an embodiment of the non-magnetic electric heating film configuration design method based on region division according to the present invention.

[0035] Figure 2 This is a schematic diagram of the heating film region division in an embodiment of the non-magnetic electric heating film configuration design method based on region division according to the present invention. Detailed Implementation

[0036] Example

[0037] To make the objectives, technical solutions, and advantages of the embodiments of the present invention clearer, the technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are some embodiments of the present invention, but not all embodiments.

[0038] Reference Figure 1 This invention provides a method for designing a non-magnetic electric heating film configuration based on region division, which can be used in non-magnetic heating systems for quantum sensors such as atomic magnetometers and atomic gyroscopes.

[0039] The steps include:

[0040] S1. Analyze the contribution of the current element location on the heating film to the magnetic noise at the center point of the gas chamber, and divide the heating film into regions based on the magnitude of the contribution value. A schematic diagram of the region division is shown below. Figure 2 As shown, the left half is a schematic diagram of the relative spatial positions of the alkali metal gas chamber and the non-magnetic electric heating film in the quantum sensor, and the right half is the division result, with each physical region corresponding to a range of magnetic noise contribution values.

[0041] Specifically, it includes:

[0042]

[0043] In the formula, B(r) represents the contribution of a current element at a certain point to the magnetic field at the center of the gas chamber, μ0 represents the vacuum permeability, and I represents the heating wire current. This represents the current element vector, where l represents the length of the current element. Let |B(r)| represent the position vector from the current element to the center point of the air chamber, r represent the distance from the current element to the center point of the air chamber, and d represent the distance from the center point of the air chamber to the heating film. As the position of the current element changes, its contribution to the magnetic noise at the center point of the air chamber also changes; that is, as r increases, |B(r)| decreases. Therefore, based on reverse design thinking, the heating film is divided into regions according to the change in |B(r). Let the straight line passing through the center point of the air chamber be perpendicular to the heating film, with the foot of the perpendicular at point P. According to the magnetic noise equation at the center point of the air chamber, the contribution value at point P is the largest, denoted as |B(r)|. max , with |B(r)| maxBased on this, the heating film is divided into regions according to the change in the magnetic noise contribution value, using the following formula:

[0044]

[0045] In the formula, Ω n ={r∈Ω∣|B(r)|∈[a n |B(r)∣ max ,a n-1 |B(r)∣ max )} indicates that on the heating film (r∈Ω), |B(r)|∈[a] n |B(r)∣ max ,a n-1 |B(r)∣ max A subset of all r, a1, a2, ..., a n This represents the weighting coefficient.

[0046] S2. Establish basis functions within the region to characterize the current distribution using a stream function, and calculate the magnetic field and temperature distribution within the alkali metal gas chamber based on the stream function. Specifically, this includes:

[0047] First, the stream function of the current distribution in the region is established using Fourier series, as shown in the formula:

[0048]

[0049] In the formula, y i (x,y) represents the i-th region Ω i The stream function describes the current distribution within the region. and ... x L y Representing regions Ω i The lengths in the x and y directions, where (x,y) represent coordinates, and the origin of the coordinate system is the center of the heating film.

[0050] Then based on the stream function y i (x,y) yields the magnetic field B(x,y,z) and temperature field T(x,y,z) of the alkali metal gas chamber.

[0051] When creating a stream function, spherical harmonic functions can also be used for representation.

[0052] S3. Establish constraints on the coefficients of the stream function based on the uniformity of magnetic noise and temperature. Specifically, this includes:

[0053]

[0054] subject to:

[0055]

[0056] In the formula, ∈1 represents the maximum permissible magnetic field inhomogeneity, ∈2 represents the maximum permissible temperature field inhomogeneity, (b i,1 ,b i,2 )express The range of values ​​for α i,1 ,α i,2 )express The range of values ​​for , and These represent the mean values ​​of the magnetic field and temperature field within the air chamber, respectively.

[0057] S4. Based on the principle of minimizing the magnetic noise mode of the air chamber, establish the cost function and calculate the optimal solution of each coefficient in the stream function to obtain the stream function expression of the current distribution.

[0058] Based on the principle of minimizing the magnetic noise mode of the air chamber, a cost function is established, and the optimal solutions for each coefficient in the stream function are calculated, including:

[0059]

[0060] subject to:

[0061]

[0062] In the formula, f represents the stream function expression.

[0063] S5. Design the heating film configuration based on the current contour distribution.

[0064] Therefore, the above-mentioned region-division-based non-magnetic electric heating film configuration design method of the present invention can effectively reduce the magnetic noise generated by the heating film during operation and take into account the heating uniformity, which is beneficial to improving the signal quality of quantum sensors and has a wider range of application prospects.

[0065] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention and not to limit them. Although the present invention has been described in detail with reference to preferred embodiments, those skilled in the art should understand that modifications or equivalent substitutions can still be made to the technical solutions of the present invention, and these modifications or equivalent substitutions cannot cause the modified technical solutions to deviate from the spirit and scope of the technical solutions of the present invention.

Claims

1. A method for designing a non-magnetic electric heating film configuration based on region division, characterized in that the steps include... include: S1. Analyze the contribution of the current element on the heating film to the magnetic noise at the center point of the air chamber, and divide the heating film into regions according to the magnitude of the contribution. Specifically, it includes: ； In the formula, This represents the contribution of a current element at a certain point to the magnetic field at the center point of the air chamber. Represents the permeability of free space. Indicates the heating wire current. Represents the current element vector. Indicates the length of the current element. This represents the position vector from the current element to the center point of the gas chamber. This represents the distance from the current element to the center point of the gas chamber. This indicates the distance from the center point of the air chamber to the heating film; according to The change in the heating film is used to divide the region. Let the straight line passing through the center point of the air chamber be perpendicular to the heating film, with point P as the foot of the perpendicular. According to the magnetic noise equation at the center point of the air chamber, point P has the largest contribution value, denoted as […]. ,by Based on this, the heating film is divided into regions according to the change in the magnetic noise contribution value, using the following formula: ； In the formula, Indicated on the heating film ( )satisfy All The subset formed Indicates the weighting coefficient; S2. Establish the current distribution stream function within the region, and calculate the magnetic field distribution and temperature distribution of the alkali metal gas chamber based on the stream function; S3. Establish constraints on the coefficients in the stream function based on the uniformity of magnetic noise and temperature. S4. Based on the principle of minimizing the magnetic noise mode of the air chamber, establish the cost function and calculate the optimal solution of each coefficient in the stream function to obtain the stream function expression of the current distribution; S5. Design the heating film configuration based on the current contour distribution.

2. The method for designing a non-magnetic electric heating film configuration based on region division according to claim 1, characterized in that, In step S2: The stream function of the current distribution within the region is established using Fourier series, and the formula is as follows: ； In the formula, Indicates the first each region The stream function, and Let represent the expansion coefficients of the Fourier series, respectively. Let represent the number of modes in the Fourier series, and represent the wavenumbers in the x and y directions, respectively. Representing regions The length in the x and y directions, The coordinate system is denoted by , where the origin of the coordinate system is the center of the heating film. Based on stream functions The magnetic field of the alkali metal gas cell is obtained and temperature field .

3. The method for designing a non-magnetic electric heating film configuration based on region division according to claim 2, characterized in that, The constraints established in step S3 regarding the coefficients of the stream function based on the uniformity of magnetic noise and temperature include: ； In the formula, This indicates the maximum permissible magnetic field inhomogeneity. This indicates the maximum permissible temperature field inhomogeneity. express The range of values ​​for , express The range of values ​​for , and These represent the mean values ​​of the magnetic field and temperature field within the air chamber, respectively.

4. The method for designing a non-magnetic electric heating film configuration based on region division according to claim 1, characterized in that, Step S4, which establishes the cost function and calculates the optimal solution for each coefficient in the stream function based on the principle of minimizing the magnetic noise mode of the air chamber, includes: ； In the formula, This represents a stream function expression.

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