Design method of magnetic field coil with light through hole in side wall for SERF inertial measurement device

Abstract

The invention discloses a design method of a magnetic field coil with a light through hole in a side wall for a spin exchange relaxation (SERF)-free inertial measurement device. Aiming at the problem of complex boundary conditions caused by electromagnetic coupling of magnetic shielding and a coil in the SERF inertial measurement device and a light through hole in the side wall of the coil, the method comprises the following steps: firstly, establishing a physical model comprising the magnetic shielding and a magnetic field coil with the light through hole in the side wall; analyzing the electromagnetic coupling effect of magnetic shielding and magnetic coil current by using a mirror image method; introducing a Heaviside step function to construct a window function so as to analyze and describe the physical constraint that the current density of a coil side wall light through hole area is zero; constructing a double-section coil electromagnetic decoupling model, and dividing the surface of the coil into an upper section and a lower section along the axial direction; a linear equation of a coil current coefficient and a target magnetic field is constructed based on a target field method, the equation is solved through a regularization method, optimal flow function distribution is obtained, and finally a discrete flow function generates a coil winding path capable of automatically avoiding a side wall light through hole. According to the method, the magnetic shielding electromagnetic coupling effect can be accurately compensated, the magnetic field distortion caused by side wall opening can be effectively inhibited, and the method can be used for improving the magnetic field control precision of the SERF inertial measurement device.

Description

Technical Field

[0001] This invention belongs to the field of quantum precision measurement and sensing technology, specifically relating to a design method for a magnetic field generation system for a spin-free exchange relaxation (SERF) inertial measurement unit. In particular, it relates to a design method for a magnetic field coil with a light-transmitting hole in the sidewall, which addresses the contradiction between optical path coupling and magnetic field control in a SERF inertial measurement unit, while considering the electromagnetic coupling effect of a high-permeability magnetic shielding layer and the geometric constraints of the light-transmitting hole in the coil frame sidewall, to achieve high-precision magnetic field reconstruction. Background Technology

[0002] SERF inertial measurement units utilize the spin precession of alkali metal atoms in an extremely low magnetic field environment to measure angular velocity or magnetic field. To maintain the SERF state of the atoms, a highly uniform main magnetic field or a highly linear gradient compensation magnetic field must be generated in the atomic gas cell region.

[0003] However, in practical engineering applications, coil design faces two major challenges:

[0004] First, the magnetic shielding coupling effect. To isolate external geomagnetic field interference, coils are typically placed inside multiple layers of high-permeability magnetic shielding cylinders. The magnetic shielding layers generate strong electromagnetic coupling with the coil current, altering the original magnetic field distribution of the coil and causing traditional design methods based on the free-space assumption to fail.

[0005] Second, the geometric constraints of the sidewall apertures. To achieve optical pumping and detection of atoms, apertures must be created in the sidewalls of the coil frame. Traditional coil design methods typically assume that the coil surface is a complete cylinder. Directly drilling holes in the designed dense coil can easily cut off the optimal current path, leading to severe magnetic field distortion and gradient errors near the holes, which in turn shortens the transverse relaxation time of the atoms and reduces the sensitivity of the sensor.

[0006] Existing design methods, such as forward optimization based on discrete coils, have low degrees of freedom and struggle to handle complex boundaries. While the traditional target field method offers design flexibility, it is difficult to analytically describe the current density discontinuities caused by "forced hole drilling." Therefore, there is an urgent need for an analytical design method that can simultaneously handle magnetic shielding coupling and sidewall light-transmitting hole constraints. Summary of the Invention

[0007] The technical problem solved by this invention is to address the electromagnetic coupling between the high-permeability magnetic shielding layer and the coil in the SERF inertial measurement unit, as well as the complex boundary conditions and severe magnetic field distortion caused by opening light-transmitting holes in the coil sidewalls to meet optical path requirements. This invention provides a magnetic field coil design method that can accurately compensate for the shielding effect and automatically avoid the light-transmitting holes. This method can achieve high-precision magnetic field control while ensuring unobstructed optical paths, effectively extending the relaxation time of atoms.

[0008] To solve the above-mentioned technical problems, the technical solution adopted by the present invention is as follows:

[0009] A design method for a magnetic field coil with a light-transmitting hole in the sidewall of a SERF inertial measurement unit, characterized by comprising the following steps:

[0010] Step S1, System Parameter Definition: Determine the geometric parameters of the magnetic shielding and the coil system with light-transmitting holes in the sidewalls, using the atomic gas cell inside the SERF inertial measurement unit as the target field region. Specifically, set the radius of the magnetic field coil to R. c The length is 2H c The radius of the magnetic shielding layer is R s The length is 2H s The radius of the light-transmitting hole on the side wall of the coil is R. hole The target area is defined as a spherical region of atomic gas chambers with a diameter of 10 mm.

[0011] Step S2, Magnetic Shielding Coupling Analysis: The boundary conditions of the magnetic shielding layer are handled using the image method to analyze the electromagnetic coupling effect between the magnetic shielding layer and the coil current. Furthermore, this invention introduces the image reflection coefficient R. m To correct the Green's function in free space, the mirror reflection coefficient R of the magnetic shielding layer... m The expression is:

[0012]

[0013] Where M and N are the circumferential and axial Fourier expansion orders of the coil current density, respectively, μ0 is the free magnetic permeability, i is the imaginary unit, p is the order of the mirror pseudo-current reflection, z is the axial position coordinate, and μ s I is the relative permeability of the magnetic shielding layer. m and K m They are the m-th order modified Bessel functions of the first and second kind, respectively, I′ m and K′ m It is its derivative with respect to the independent variable.

[0014] Step S3: A Heaviside step function is introduced to construct a window function to analytically describe the physical constraint that the current density in the light-transmitting aperture region of the coil sidewall is zero. Further, the even-order and odd-order mirror window functions are specifically defined as follows:

[0015]

[0016]

[0017] Where H(x) is the Heaviside step function, and α and β are the geometric boundary parameters of the window function. By setting α = ±R... hole ,β=±Hc This restricts the effective distribution range of current density to outside the light-transmitting aperture.

[0018] Step S4, Two-Segment Model Establishment: A two-segment electromagnetic decoupling model is established, dividing the coil surface into upper and lower segments along the axial direction, with the center of the light-transmitting aperture as the boundary. Furthermore, the current density on the coil surface is decomposed into the upper segment component. and the next segment The superposition of the elements, combined with the window function, is used to perform a Fourier series expansion, thereby achieving the "removal" of the light-transmitting aperture region at the analytical level.

[0019]

[0020] in, and These represent the upper and lower components of the surface current density of the cylindrical coil, respectively, P. n01 P n02 P nm1 P nm2 Q nm1 and Q nm2 These are the weighting coefficients for the coil currents in the upper and lower segments. Step S5, Construction of the linear equation system: Based on the target field method and the aforementioned two-segment electromagnetic decoupling model, a linear equation system is constructed between the coil current coefficients and the magnetic field distribution in the target region:

[0021] Ax = B t

[0022] Among them B t Let x be the target magnetic field vector, x be the coil current coefficient vector to be solved, and A be the system matrix that combines the image method coefficients and the two-segment model.

[0023] Step S6, Solving for the optimal solution: The Tikhonov regularization method is used to solve the linear equation system. By adjusting the regularization parameters to balance the magnetic field accuracy and the energy or curvature constraints of the coil, the optimal coil current coefficient is obtained, and then the flow function distribution on the coil surface is reconstructed.

[0024] Step S7, Wire Path Generation: Discretize the optimal stream function distribution using contour lines to generate coil wire paths that automatically avoid the side wall light-transmitting holes.

[0025] Compared with the prior art, the present invention has the following beneficial effects:

[0026] 1. High analytical accuracy and accurate boundary description: This invention innovatively proposes a method based on...

[0027] The two-segment modeling method using the Heaviside function precisely describes the geometric constraints of the aperture at the mathematical analytical level. Compared to the traditional mesh-based aperture method, this method avoids the discretization errors caused by mesh generation and can calculate the current distribution at the aperture edge more smoothly and accurately.

[0028] 2. Electromagnetic Decoupling and Integrated Design: This invention utilizes the mirror method to incorporate the influence of the high-permeability magnetic shielding layer into the design closed loop, quantifying the reflection effect of the shielding layer. The designed coil is not only unaffected by the shielding layer but can also utilize the reflected field of the shielding layer to enhance magnetic field performance, achieving an integrated electromagnetic decoupling design between the coil and the shielding layer.

[0029] 3. Self-consistent structure and superior performance: The coil wire path generated by this method naturally avoids the light-transmitting aperture, eliminating the need for subsequent physical cutting and ensuring the continuity of the current path. While meeting the requirements of the side-pumped and detection optical paths of the SERF device, it effectively suppresses magnetic field distortion and gradient errors caused by the aperture, helping to maintain a low-gradient environment in the atomic gas chamber, thereby extending the T1 and T2 relaxation times of atoms and improving the sensitivity of the sensor.

[0030] 4. High versatility: This method is applicable to the design of coils that generate arbitrary target magnetic fields, and the size and position of the light-transmitting aperture can be flexibly adjusted, providing a universal solution for the integrated design of miniaturized atomic sensors. Attached Figure Description

[0031] Figure 1 This is a flowchart illustrating the design method of a magnetic field coil with a light-transmitting hole in the sidewall of a SERF inertial measurement device according to the present invention.

[0032] Figure 2 This is a schematic diagram of a two-dimensional winding path of a coil that automatically avoids the light-transmitting hole, generated in an embodiment of the design method of a magnetic field coil with a light-transmitting hole in the side wall of a SERF inertial measurement device according to the present invention. The dashed lines and solid lines in the figure represent different current directions, respectively.

[0033] Figure 3 This is a schematic diagram of the three-dimensional flow function distribution of the coil that automatically avoids the light-transmitting hole, generated in an embodiment of the design method of a magnetic field coil with a light-transmitting hole in the side wall of a SERF inertial measurement device according to the present invention.

[0034] Figure 4 This is a schematic diagram of the three-dimensional outline of a coil that automatically avoids the light-transmitting hole, generated in an embodiment of the design method of a magnetic field coil with a light-transmitting hole in the side wall of a SERF inertial measurement device according to the present invention. Detailed Implementation

[0035] The present invention will now be described in further detail with reference to the accompanying drawings and specific embodiments.

[0036] Example: A gradient coil design with a light-transmitting aperture on the sidewall of a SERF inertial measurement unit. Figure 1 As shown, this embodiment provides a design method for a magnetic field coil with a light-transmitting hole in the sidewall of a SERF inertial measurement unit. The method aims to design a biaxial gradient coil that operates inside a multi-layered magnetically shielded cylinder and has a light-transmitting hole in the sidewall.

[0037] The specific implementation steps are as follows:

[0038] Step S1: Set the geometric parameters of the SERF inertial measurement unit, with the coil frame radius being R. c =40mm, total axial length is 2H c =140mm. Radius R of the external magnetic shielding layer s =80mm, length 2H s =260mm, using relative permeability μ s =10 4 The material is permalloy. A light-transmitting hole with radius R is located at the center of the coil sidewall. hole =2.5mm, used for laser beam passage. The target area is a spherical region with a diameter of 10mm, corresponding to the actual working position of the atomic gas chamber.

[0039] Step S2: Since the coil is placed inside a high-permeability shielding cylinder, the reflection effect of the shielding layer must be considered. This embodiment uses the image method to represent the effect of the shielding layer as an equivalent magnetic field generated by a series of mirror currents. A Green's function incorporating the shielding effect is constructed, in which the image reflection coefficient R is introduced. m The mirror reflection coefficient R of the magnetic shielding layer m The expression is:

[0040]

[0041] Where M and N are the circumferential and axial Fourier expansion orders of the coil current density, respectively, μ0 is the free magnetic permeability, i is the imaginary unit, p is the order of the mirror pseudo-current reflection, z is the axial position coordinate, and μ s I is the relative permeability of the magnetic shielding layer. m and K m They are the m-th order modified Bessel functions of the first and second kind, respectively, I′ m and K′ m Let R be its derivative with respect to the independent variable. This coefficient characterizes the enhancement effect of the magnetic shielding layer on the reflection of different spatial frequency magnetic field components generated by the coil. By introducing R... m This achieves electromagnetic decoupling between the coil and the shielding layer.

[0042] Step S3: In order to accurately describe the aperture in the analytical model, this embodiment introduces the Heaviside step function to construct window functions of even and odd order.

[0043]

[0044] Where H(x) is the Heaviside step function, and α and β are the geometric boundary parameters of the window function. By setting α = ±R... hole ,β=±H c Mathematically, the effective distribution interval of the current density is restricted to z∈[R]. hole H c ] and z∈[-H c ,-R hole ], thus making z∈[-R hole ,R hole The current density within the interval is zero.

[0045] Step S4: Based on the window function in Step S3, establish a two-segment coil model. Decompose the total current density on the coil surface into the upper segment component. and the next segment Using Fourier series expansion of the current density, let the current weighting coefficient to be solved be x = [P] n01 ,P n02 ,P nm1 ,P nm2 Q nm1 Q nm2 ] Τ At this point, the magnetic field generated by the coil can be expressed as a linear combination of these coefficients, and this expression naturally satisfies the zero current constraint at the light-transmitting aperture.

[0046]

[0047] in, and These represent the upper and lower components of the surface current density of the cylindrical coil, respectively, P. n01 P n02 P nm1 P nm2 Q nm1 and Q nm2 The weighting coefficients for the coil currents of the upper and lower segments are denoted as .

[0048] Step S5: Using the target field method, select N within the target region. t =80 target field points. Construct a system of linear equations:

[0049] Ax = B t

[0050] Among them B t Let x be the target magnetic field vector, x be the coil current coefficient vector to be solved, and A be the system matrix that combines the image method coefficients and the two-segment model.

[0051] Step S6: Since directly solving this system of equations constitutes an ill-conditioned inverse problem, this embodiment employs the Tikhonov regularization method. The objective function is constructed as follows:

[0052]

[0053] Where λ is the regularization parameter, F curv This is the regularization matrix related to the coil curvature. By selecting an appropriate value for λ, the complexity of the coil is limited while ensuring the accuracy of the magnetic field. After obtaining the optimal coil coefficient x, it is substituted into the stream function expansion to calculate the stream function values ​​at the grid points on the coil surface.

[0054] Step S7: As Figure 2 As shown, contour lines are extracted from the stream function. With 10 turns in the coil, 10 equally spaced stream function contour lines are extracted as the conductor path.

[0055] In summary, this embodiment ultimately designs a magnetic field gradient coil with a light-transmitting hole in the sidewall of a SERF inertial measurement device. The design method proposed in this invention can effectively solve the contradiction between "light transmission" and "field homogenization" in the SERF device, and provides a reliable solution for the physical system design of high-precision atomic sensors.

[0056] 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 design method for a magnetic field coil with a light-transmitting hole in the sidewall of a spin-free exchange relaxation (SERF) inertial measurement unit, characterized in that, Includes the following steps: Step S1: Determine the geometric parameters of the magnetic shielding and the coil system with light-transmitting holes in the sidewall, and take the atomic gas cell inside the SERF inertial measurement device as the target field region; Step S2: The boundary conditions of the magnetic shielding layer are processed using the mirror method, and the electromagnetic coupling effect between the magnetic shielding layer and the coil current is analyzed. Step S3: Introduce the Heaviside step function to construct a window function to ensure the constraint that the current density is zero in the light-transmitting aperture region; Step S4: Establish a two-segment electromagnetic decoupling model by dividing the coil surface into upper and lower segments along the axial direction. Step S5: Based on the target field method and the two-segment electromagnetic decoupling model, construct a set of linear equations between the coil current coefficient and the magnetic field distribution in the target region. Step S6: Solve the linear equation system using a regularization method to obtain the optimal coil current coefficient, and then reconstruct the flow function distribution on the coil surface; Step S7: Discretize the optimal stream function distribution using contour lines to generate coil wire paths that automatically avoid the side wall light-transmitting holes.

2. The design method for a magnetic field coil with a light-transmitting hole in the sidewall of a SERF inertial measurement device according to claim 1, characterized in that, The specific parameters of the magnetic shielding and coil system in step S1 are as follows: the radius of the magnetic field coil in the SERF inertial measurement device is R. c The length is 2H c The radius of the magnetic shielding layer is R s The length is 2H s The radius of the light-transmitting hole on the side wall of the coil is R. hole The target area is defined as a spherical region of atomic gas chambers with a diameter of 10 mm.

3. The design method for a magnetic field coil with a light-transmitting hole in the sidewall of a SERF inertial measurement device according to claim 1, characterized in that, In step S2, the electromagnetic coupling effect between the magnetic shielding and the coil system is analyzed using the image method, and the image reflection coefficient R of the magnetic shielding layer is... m The expression is: Where M and N are the circumferential and axial Fourier expansion orders of the coil current density, respectively, μ0 is the free magnetic permeability, i is the imaginary unit, p is the order of the image pseudo-current reflection, z is the axial position coordinate, and μ s I is the relative permeability of the magnetic shielding layer. m and K m These are the m-th order modified Bessel functions of the first and second kind, respectively, I ′ m and K′ m It is its derivative with respect to the independent variable.

4. The design method for a magnetic field coil with a light-transmitting hole in the sidewall of a SERF inertial measurement device according to claim 1, characterized in that, The even and odd order mirror window functions constructed using the Heaviside step function in step S3 are specifically defined as follows: Where H(x) is the Heaviside step function, and α and β are the geometric boundary parameters of the window function.

5. The design method for a magnetic field coil with a light-transmitting hole in the sidewall of a SERF inertial measurement device according to claim 1, characterized in that, The two-stage electromagnetic decoupling model in step S4 is specifically as follows: With the center of the light-transmitting aperture as the boundary, the surface current density of the cylindrical coil is decomposed into the upper component. and the next segment P n01 P n02 P nm1 P nm2 Q nm1 and Q nm2 The weighting coefficients for the coil currents of the upper and lower segments are denoted as .

6. The design method for a magnetic field coil with a light-transmitting hole in the sidewall of a SERF inertial measurement device according to claim 1, characterized in that, In step S5, based on the target field method and the two-segment electromagnetic decoupling model, a set of linear equations is constructed between the coil current coefficient and the magnetic field distribution in the target region: Ax=B t Among them B t Target magnetic field vector, x = [P n01 ,P n02 ,P nm1 ,P nm2 Q nm1 Q nm2 ] Τ Let A be the coil current coefficient vector, and let A be the system matrix under the image method coefficient and the two-segment model.

7. The design method for a magnetic field coil with a light-transmitting hole in the sidewall of a SERF inertial measurement device according to claim 1, characterized in that, In step S6, the optimal coil current coefficient is solved using a regularization method to obtain the optimal flow function distribution: the linear equation system is solved using the Tikhonov regularization method, and the magnetic field accuracy and coil curvature constraint are balanced by adjusting the regularization parameter.

8. The design method for a magnetic field coil with a light-transmitting hole in the sidewall of a SERF inertial measurement device according to claim 1, characterized in that, In step S7, the discrete optimal stream function generates a coil winding path that automatically avoids the side wall light-transmitting hole: the optimal stream function distribution obtained by the solution is extracted by contour lines to generate a coil winding path that avoids the light-transmitting hole in a streamlined manner.

Images