A design method of SERF inertial measurement gradient self-shielding coil

Abstract

A design method of a SERF (Spin-Exchange-Relaxation-Free) inertial measurement gradient self-shielded coil, which generates a gradient magnetic field of a specified size in the target field region of the atomic cell inside the shielded barrel to compensate for the magnetic field gradient, while rapidly attenuating the magnetic field between the outside of the self-shielded coil to zero, thereby facilitating the reduction of the magnetic field coupling between the shielded barrel and the coil and improving the inertial measurement accuracy.

Description

TECHNICAL FIELD

[0001] The present application relates to the self-shielded coil technology, and particularly to a design method of a SERF inertial measurement gradient self-shielded coil, wherein SERF (Spin-Exchange-Relaxation-Free) is spin-exchange relaxation free, a gradient magnetic field of a specified size is generated in a target field region of an atomic cell inside a shielded barrel, i.e., an atomic cell, to compensate for a magnetic field gradient, and meanwhile, the magnetic field between the outside of the self-shielded coil is rapidly attenuated to zero, so as to be conducive to reducing the magnetic field coupling between the shielded barrel and the coil and improving the inertial measurement precision. BACKGROUND

[0002] The three-dimensional magnetic field coil not only can actively compensate the magnetic field to provide a good environment for the atom, so that the atom works in a weak magnetic environment to realize the spin-exchange relaxation free (SERF, Spin-Exchange-Relaxation-Free) state. At the same time, the combination of the ferrite shield and the coil system can shield the geomagnetic field and ensure the zero-field stability of the atom or generate a magnetic field with a specified strength. Among them, the coil can provide any waveform magnetic field excitation signal for the precession of the atom, so as to explore the response law of the atomic magnetic field. Therefore, it is an urgent problem to be solved to design a linear gradient and high-precision coil according to the special requirements of the SERF inertial sensor.

[0003] The three-axis Helmholtz coil and the saddle-shaped nested coil are commonly used to generate a three-axis uniform magnetic field in the SERF inertial measurement. In addition, a cylindrical coil composed of a Lee-Whiting coil and two saddle-shaped coils is also used to generate longitudinal and transverse magnetic fields, respectively. However, when the Helmholtz coil system is applied to a high-sensitivity sensor, there are problems of difficult miniaturization and poor magnetic field uniformity. Therefore, the practical application of the target field method proves that it has the advantages of strong adaptability and flexible control of the coil structure.

[0004] In the SERF inertial measurement, on the one hand, the coupling of the coil and the high magnetic permeability permalloy layer and the ferrite usually amplifies the coil magnetic field and affects the distribution of the magnetic field; on the other hand, the magnetic field amplification coefficient caused by the magnetic shielding varies with the magnetic permeability of the shielding material, which may increase the drift of the atomic inertial sensor. The gradient magnetic field coil compensates for the magnetic field gradient of the atomic cell, reduces the influence of the continuous coupling between the coil and the magnetic shield on the magnetization of the shielding material, thereby improving the atomic relaxation time, increasing the scale factor of the system and reducing the error. SUMMARY

[0005] The application aims at the coupling problem between the magnetic shielding material and the three-dimensional active magnetic compensation coil, meets the requirements of SERF ultra-high precision inertial measurement weak magnetic environment and gradient magnetic field, and provides a design method of the SERF inertial measurement gradient self-shielding coil.

[0006] The technical solution of the application is as follows:

[0007] A design method of a SERF inertial measurement gradient self-shielding coil, characterized in that: a spherical atom chamber is selected as a target field region of a gradient magnetic field of a main coil, and a target field of a specified cylindrical region outside the shielding coil is an external attenuation shielding region; a current density distribution on a coil surface is derived by solving a magnetic field expression of discrete target points; the current density is discretized, and a flow function is used to calculate a contour of the coil, that is, a designed flexible coil current trace, so that a gradient magnetic field of a specified size is generated in the target field region of the atom chamber, and the magnetic field between the inside of the shielding barrel and the outside of the self-shielding coil is rapidly attenuated to zero, thereby reducing the magnetic field coupling between the shielding barrel and the coil, suppressing the magnetic field gradient, and improving the inertial measurement precision.

[0008] The current density distribution includes inverse transformation of Fourier expansion of the current generated magnetic field by the target field method to obtain the current density distribution of the ideal magnetic field.

[0009] The function curvature of the current density distribution is used to constrain the penalty function of the coil, and Tikhonov regularization is used to avoid the ill-posed problem of the first type of Fredholm integral equation when solving the values of the undetermined coefficients of the current density function.

[0010] The inertial measurement gradient self-shielding coil includes a cylindrical radial self-shielding coil for generating x and y direction gradient magnetic fields and a cylindrical axial self-shielding coil for generating z direction gradient magnetic fields, and in the SERF inertial measurement, the three axes of the three-dimensional magnetic field coil generate first-order linear gradient magnetic fields in the sensitive region of the chamber, which plays a role of actively applying the gradient magnetic field. The self-shielding three-dimensional magnetic field coil suppresses the magnetic field gradient by actively applying the gradient magnetic field to the atom chamber, and rapidly attenuates the magnetic field between the magnetic shielding barrel and the shielding coil to zero, thereby reducing the atomic relaxation rate, increasing the system scale factor and reducing the error.

[0011] The cylindrical radial self-shielding coil is composed of two layers of coils, which are a gradient main coil for active gradient magnetic compensation and a shielding coil for attenuating the magnetic field between the gradient coil and the magnetic shielding barrel to zero, and the design steps are as follows:

[0012] First, the surface current density expression on the cylindrical radial self-shielded coil is determined, wherein the main coil current expression is:

[0013]

[0014] The shielded coil current expression is:

[0015]

[0016] Wherein and are the azimuthal component of the radial main coil current density expression and the axial component of the radial main coil current density expression, respectively, and are the azimuthal component of the radial shielded coil current density expression and the axial component of the radial shielded coil current density expression, respectively, R p and L p are the radius of the radial main coil and the half height of the radial main coil, respectively, R s and L s are the radius of the radial shielded coil and the half height of the radial shielded coil, respectively, θ p and z p are the polar angle of the radial main coil target region and the polar radius of the radial main coil target region, respectively, θ s and z s are the polar angle of the radial shielded coil target region and the polar radius of the radial shielded coil target region, respectively, m is the first index of the undetermined coefficients P mn and Q mn , n is the second index of the undetermined coefficients P mn and Q mn , and M is the upper limit of the index m, N is the upper limit of the index n, M and N are both the maximum order of the Fourier series expansion related to the numerical accuracy.

[0017] The cylindrical axial self-shielded coil includes an axial main coil and a shielded coil, and the design steps are as follows:

[0018] The atomic cell is selected as the target region of the main coil gradient magnetic field, the target field of the designated cylindrical region outside the shielded coil is the external attenuation shielding region, and the current density function expressions of the axial main coil and the shielded coil are respectively set as follows:

[0019]

[0020]

[0021] Wherein and are the azimuthal component of the axial main coil current density expression and the axial component of the axial main coil current density expression, respectively, and are the azimuthal component of the axial shield coil current density expression and the axial component of the axial shield coil current density expression, respectively, R p and L p are the radius of the axial main coil and the half-height of the axial main coil, respectively, R s and L s are the radius of the axial shield coil and the half-height of the axial shield coil, respectively, θ p and z p are the polar angle of the axial main coil target region and the polar radius of the main coil target region, respectively, θ s and z s are the polar angle of the axial shield coil target region and the polar radius of the axial shield coil target region, respectively, m is the index of the undetermined coefficient P m and Q m , and M is the upper limit of the index m, M is the maximum order number of the Fourier series expansion related to the numerical accuracy.

[0022] Let r p (R p ,θ p ,z p ), r s (R s ,θ s ,z s ), r DSV (R DSV ,θ DSV ,z DSV ), r OUT (R OUT ,θ OUT ,z OUT ) be the source point of the radial main coil surface, the source point of the shield coil surface, the target field point of the atomic cell gradient magnetic field, and the target field point of the shield coil outer decay magnetic field, respectively, then the atomic cell target field point and the corresponding magnetic field size of the shield coil outer are as follows:

[0023]

[0024]

[0025] Among them, the intermediate functions are respectively:

[0026]

[0027]

[0028]

[0029]

[0030] where u0 is the vacuum permeability, (r DSV -r p ) is the distance between the position vector of the field point in the target field region of the main coil and the position vector of the surface of the main coil, (r DSV -r S ) is the distance between the position vector of the field point in the target field region of the main coil and the position vector of the surface of the main coil, (r OUT -r p ) is the distance between the position vector of the field point in the target field region of the main coil and the position vector of the surface of the main coil, (r OUT -r s ) is the distance between the position vector of the field point in the target field region of the main coil and the position vector of the surface of the main coil, (r DSV ,y DSV ,z DSV ) is the field point in the target field region of the main coil, (x OUT ,y OUT ,z OUT ) is the field point in the target field region of the main coil.

[0031] The technical effects of the present application are as follows: the design method of the SERF inertial measurement gradient self-shielding coil of the present application designs the magnetic field coils in x, y and z axial directions based on the target field method, thereby reducing the coupling between the coil and the magnetic shield and the magnetization of the magnetic shield caused by the magnetic field of the coil, and finally suppressing the magnetic noise error and drift of the ultra-high precision SERF gyroscope.

[0032] Compared with the prior art, the present application has the following advantages: (1) the self-shielding three-dimensional magnetic field coil of the present application generates a gradient magnetic field of a specific size in the target field region of the atomic cell, and rapidly attenuates the magnetic field to a near-zero magnetic field outside the shielding coil. (2) The gradient magnetic field applied by the target field region of the main coil can suppress the magnetic field gradient in the atomic cell, suppress the coupling between the coil and the shielding barrel, increase the atomic relaxation time by compensating the magnetic field gradient, thereby increasing the scale factor of the SERF inertial measurement device and reducing the error, and finally improving the system performance. BRIEF DESCRIPTION OF DRAWINGS

[0033] Figure 1 is a structure schematic diagram of the SERF inertial measurement gradient self-shielding three-dimensional magnetic field coil formed by the design method of the SERF inertial measurement gradient self-shielding coil of the present application.

[0034] Figure 2 is a schematic diagram of the current trend of the cylindrical radial main coil designed by the target field method in the design method of the SERF inertial measurement gradient self-shielding coil of the present application. Figure 2 The current trend in the above is also called coil current trace, which indicates the coil contour. Figure 2The numerical points on the x-axis include -0.02, 0, 0.02 (m, meter), the numerical points on the y-axis include -0.02, -0.01, 0, 0.01, 0.02 (m), and the numerical points on the z-axis include -0.03, -0.02, -0.01, 0, 0.01, 0.02, 0.03. Figure 2 The solid line on the cylindrical surface in FIG. 1 is the current trend in the positive direction, and the dashed line is the current trend in the reverse direction.

[0035] Figure 3 FIG. 1 is a schematic diagram of the current trend of a cylindrical radial shielding coil designed by the target field method in a design method of a SERF inertial measurement gradient self-shielding coil according to the present application. Figure 3 The current trend in FIG. 1 is also called a coil current trace, which indicates the coil contour. Figure 3 The numerical points on the x-axis include -0.02, 0, 0.02 (m, meter), the numerical points on the y-axis include -0.02, -0.01, 0, 0.01, 0.02 (m), and the numerical points on the z-axis include -0.04, -0.02, 0, 0.02, 0.04. Figure 2 The solid line on the cylindrical surface in FIG. 2 is the current trend in the positive direction, and the dashed line is the current trend in the reverse direction.

[0036] Figure 4 FIG. 2 is a schematic diagram of the current trend of a cylindrical radial shielding coil designed by the target field method in a design method of a SERF inertial measurement gradient self-shielding coil according to the present application. Figure 1 FIG. 3 is a schematic diagram of the magnetic field shielding effect of a SERF inertial measurement gradient self-shielding three-dimensional magnetic field coil according to the present application. Figure 4 The numerical points on the x-axis include 0.1, 0, 0.1 (m, meter), the numerical points on the y-axis include 0.1, 0, 0.1 (m, meter), and the numerical points on the z-axis include -4, -2, 0, 2, 4*10 -8 Bz (T), Bz (T) is the magnetic field in the z-axis direction (tesla). Figure 4 In FIG. 3, the upper vertex of the gradient magnetic field decay slope is 32 nT, and the lower vertex is -32 nT.

[0037] Figure 1 In FIG. 4, 1 is a permalloy shielding cylinder, 2 is a ferrite shielding cylinder, 3 is an x-axis shielding coil, 4 is a y-axis shielding coil, 5 is a z-axis shielding coil, 6 is a shielding coil skeleton, 7 is an x-axis main coil, 8 is a y-axis main coil, 9 is a z-axis main coil, 10 is a gas chamber support, 11 is an atomic gas chamber, 12 is a precision resistor R1, 13 is a precision resistor R2, 14 is a current source, Rs is the radius of the shielding coil, Rp is the radius of the main coil, Ls is the half height of the shielding coil, Lp is the half height of the main coil, OUT is the external region, and DSV is the gas chamber region. DETAILED DESCRIPTION

[0038] The present application will be described below in conjunction with the accompanying drawings Figures 1-4 and examples.

[0039] Figure 1 is a schematic diagram of a SERF inertial measurement gradient self-shielded three-dimensional magnetic field coil structure formed by a design method of a SERF inertial measurement gradient self-shielded coil according to the present application. Figure 2 is a schematic diagram of a cylindrical radial main coil current trend designed by a target field method in a design method of a SERF inertial measurement gradient self-shielded coil according to the present application. Figure 3 is a schematic diagram of a cylindrical radial shield coil current trend designed by a target field method in a design method of a SERF inertial measurement gradient self-shielded coil according to the present application. Figure 4 is Figure 1 is a schematic diagram of a magnetic field shielding effect of a SERF inertial measurement gradient self-shielded three-dimensional magnetic field coil. Referring to Figures 1 to 4 a design method of a SERF inertial measurement gradient self-shielded coil, including selecting a spherical atomic cell as a main coil gradient magnetic field target field region, and shielding a target field of a specified cylindrical region outside the shielded coil as an external attenuation shielding region; deriving a current density distribution on the surface of the coil by solving a magnetic field expression of discrete target points; discretizing the current density, and calculating a contour of the coil by using a flow function, i.e. a designed flexible coil current trace, so that a specified size of a gradient magnetic field is generated in the target field region of the atomic cell, and the magnetic field between the inside of the shielding barrel and the outside of the self-shielded coil is rapidly attenuated to zero, thereby reducing the magnetic field coupling between the shielding barrel and the coil, suppressing the magnetic field gradient, and improving the inertial measurement precision. The current density distribution includes inverse transformation of Fourier expansion of the current generated magnetic field by using a target field method to obtain the current density distribution of the ideal magnetic field. The function curvature of the current density distribution is used to constrain the penalty function of the coil, and Tikhonov regularization is used to avoid the ill-posed problem of the first type of Fredholm integral equation when solving the value of the undetermined coefficient of the current density function. The inertial measurement gradient self-shielded coil includes a cylindrical radial self-shielded coil generating x and y direction gradient magnetic fields, and a cylindrical axial self-shielded coil generating a z direction gradient magnetic field. In the SERF inertial measurement, the three axes of the three-dimensional magnetic field coil generate a first order linear gradient magnetic field in the sensitive region of the cell, which plays a role of actively applying a magnetic field gradient. The self-shielded three-dimensional magnetic field coil suppresses the magnetic field gradient by actively applying a gradient magnetic field to the atomic cell, and rapidly attenuates the generated magnetic field to zero between the magnetic shielding barrel and the shielding coil, thereby reducing the atomic relaxation rate, increasing the system scale factor, and reducing the error.

[0040] The cylindrical radial self-shielded coil is composed of two layers of coils, i.e. a gradient main coil for active gradient magnetic compensation and a shielding coil for attenuating the magnetic field between the gradient coil and the magnetic shielding barrel to zero. The design steps are as follows: first, the surface current density expression on the cylindrical radial self-shielded coil is determined, wherein the current expression of the main coil is:

[0041]

[0042] The shielding coil current expression is:

[0043]

[0044] wherein and are the azimuthal component of the radial main coil current density expression and the axial component of the radial main coil current density expression, respectively, and are the azimuthal component of the radial shielding coil current density expression and the axial component of the radial shielding coil current density expression, respectively, R p and L p are the radius of the radial main coil and the half-height of the radial main coil, respectively, R s and L s are the radius of the radial shielding coil and the half-height of the radial shielding coil, respectively, θ p and z p are the polar angle of the radial main coil target region and the polar radius of the radial main coil target region, respectively, θ s and z s are the polar angle of the radial shielding coil target region and the polar radius of the radial shielding coil target region, respectively, m is the first index of the undetermined coefficients P mn and Q mn , n is the second index of the undetermined coefficients P mn and Q mn , and M is the upper limit of the index m, N is the upper limit of the index n, M and N are both the maximum order of the Fourier series expansion related to the numerical accuracy.

[0045] The cylindrical axial self-shielding coil includes an axial main coil and a shielding coil, and the design steps are as follows: the atomic gas chamber is selected as the target region of the main coil gradient magnetic field, the target field of the designated cylindrical region outside the shielding coil is the external attenuation shielding region, and the current density function expressions of the axial main coil and the shielding coil are respectively set as follows:

[0046]

[0047]

[0048] wherein and are the azimuthal component of the axial main coil current density expression and the axial component of the axial main coil current density expression, respectively, and are the azimuthal component of the axial shielding coil current density expression and the axial component of the axial shielding coil current density expression, respectively, R p and L prespectively the radius of the axial main coil and the half height of the axial main coil, R s and L s respectively the radius of the axial shield coil and the half height of the axial shield coil, θ p and z p respectively the polar angle of the axial main coil target region and the polar radius of the main coil target region, θ s and z s respectively the polar angle of the axial shield coil target region and the polar radius of the axial shield coil target region, m is the index of the undetermined coefficient P m and Q m , and M is the upper limit of the index m, and M is the maximum order number of the Fourier series expansion related to the numerical accuracy.

[0049] Let r p (R p , θ p , z p ), r s (R s , θ s , z s ), r DSV (R DSV , θ DSV , z DSV ), r OUT (R OUT , θ OUT , z OUT ) be the source points of the radial main coil surface, the shield coil surface source points, the target field points of the atomic cell gradient magnetic field and the target field points of the shield coil outside decay magnetic field respectively, then the atomic cell target field point and the corresponding magnetic field size of the shield coil outside are as follows:

[0050]

[0051]

[0052] Wherein, the intermediate functions are respectively:

[0053]

[0054]

[0055]

[0056]

[0057] Wherein u0 is the vacuum permeability, (r DSV -r p ) is the distance between the main coil target field region field point position vector and the main coil surface position vector, (r DSV -rS ) is the distance between the position vector of the target field point of the main coil target field region and the position vector of the surface of the shielding coil, (r OUT -r p ) is the distance between the position vector of the target field point outside the shielding coil and the position vector of the surface of the main coil, (r OUT -r s ) is the distance between the position vector of the target field point outside the shielding coil and the position vector of the surface of the shielding coil, (x DSV ,y DSV ,z DSV ) is the field point of the main coil target field region, (x OUT ,y OUT ,z OUT ) is the field point of the shielding coil target field region.

[0058] The application discloses a design method of a SERF inertial measurement gradient self-shielding coil, first, a spherical atom chamber is selected as a main coil gradient field target field region, and a target field of a specified cylindrical region outside the shielding coil is an external attenuation shielding region. Then, by solving the magnetic field expression of the discrete target point, the current density distribution of the coil surface is derived. Finally, the current density is discretized, and the profile of the coil is calculated by using the flow function, which is the designed flexible coil current trace. The method is aimed at the coupling problem between the magnetic shielding material and the three-dimensional active magnetic compensation coil, meets the special requirements of the SERF ultra-high precision inertial measurement weak magnetic environment and gradient magnetic field, and thus a gradient self-shielding three-dimensional magnetic field coil is designed. The method makes the target field region of the atom chamber generate a gradient magnetic field of a specified size, and rapidly attenuates the magnetic field between the inside of the shielding barrel and the outside of the self-shielding coil to zero. The method reduces the magnetic field coupling between the shielding barrel and the coil, suppresses the magnetic field gradient, and provides the inertial measurement precision.

[0059] The application is aimed at the coupling problem between the magnetic shielding material and the three-dimensional active magnetic compensation coil, meets the special requirements of the SERF ultra-high precision inertial measurement weak magnetic environment and gradient magnetic field, and thus a gradient self-shielding three-dimensional magnetic field coil based on a target field method is designed. The main function of the application is to generate a gradient magnetic field of a specified size in the target field region of the atom chamber inside the shielding barrel, so as to compensate the magnetic field gradient, and rapidly attenuate the magnetic field between the outside of the self-shielding coil to zero. Thus, the magnetic field coupling between the shielding barrel and the coil is reduced, and the inertial measurement precision is improved. In order to achieve the above object, the technical scheme adopted by the application is as follows:

[0060] The target field method uses the inverse transform of the Fourier expansion of the magnetic field generated by the current to obtain the current distribution of the ideal magnetic field. By solving the magnetic field expression of the discrete target points, the current density distribution on the coil surface is derived. Then the current density is discretized, and the stream function is used to calculate the profile of the coil, which is the designed flexible coil current trace. Among them, the curvature of the current density function is used to constrain the penalty function of the coil, and Tikhonov regularization is used to avoid the ill-posed problem of the first type of Fredholm integral equation when solving the values of the undetermined coefficients of the current density function.

[0061] The three-dimensional cylindrical radial self-shielded magnetic field coil is composed of a shield coil and a main coil, and the design steps are as follows:

[0062] 1) First, determine the radial current density expression used by the designed cylindrical radial self-shielded coil, and the main coil current expression is:

[0063]

[0064] The shield coil current expression is:

[0065]

[0066] Among them and are the azimuthal component of the radial main coil current density expression and the axial component of the radial main coil current density expression, and are the azimuthal component of the radial shield coil current density expression and the axial component of the radial shield coil current density expression, R p and L p are the radius of the radial main coil and the half height of the radial main coil, R s and L s are the radius of the radial shield coil and the half height of the radial shield coil, θ p and z p are the polar angle of the target area of the radial main coil and the polar radius of the target area of the radial main coil, θ s and z s are the polar angle of the target area of the radial shield coil and the polar radius of the target area of the radial shield coil, m is the first index of the undetermined coefficients P mn and Q mn , n is the second index of the undetermined coefficients P mn and Q mn , and M is the upper limit of the index m, N is the upper limit of the index n, M and N are the maximum order of the Fourier series expansion related to the numerical accuracy.

[0067] 2) According to the Biot-Savart law, the relationship between the magnetic induction vector of the field point and the current density is where u0 is the vacuum permeability, r p (R p , θ p , z p ), r s (R s , θ s , z s ), r DSV (R DSV , θ DSV , z DSV ), r OUT (R OUT , θ OUT , z OUT ) are the source points on the surface of the main coil, the source points on the surface of the shielding coil, the field points of the gradient magnetic field of the target region of the atomic cell, and the field points of the decay magnetic field of the target region outside the shielding coil, respectively. The corresponding magnetic field sizes of the atomic cell target field points and the shielding coil outside are as follows:

[0068]

[0069]

[0070] where the intermediate functions are as follows:

[0071]

[0072]

[0073]

[0074]

[0075] where u0 is the vacuum permeability, (r DSV -r p ) is the distance between the position vector of the field point of the target field region of the main coil and the position vector of the surface of the main coil, (r DSV -r S ) is the distance between the position vector of the field point of the target field region of the main coil and the position vector of the surface of the shielding coil, (r OUT -r p ) is the distance between the position vector of the field point outside the shielding coil and the position vector of the surface of the main coil, (r OUT -r s ) is the distance between the position vector of the field point outside the shielding coil and the position vector of the surface of the shielding coil, (x DSV , y DSV , z DSV ) is the field point of the target field region of the main coil, (x OUTy OUT z OUT ) is the field point of the target field region of the shielded coil.

[0076] 3) The curvature constraint is added to the current density expression, and the curvature of the stream function is used as a penalty function to optimize the coil winding mode. The stream function expression of the radial shielded coil is:

[0077]

[0078]

[0079] The axial self-shielded coil is also composed of a shielded coil and a main coil. The magnetic field of the axial coil can be derived as:

[0080]

[0081] Therefore, the design steps of the axial shielded coil are as follows:

[0082] 1) The atomic cell is selected as the target region of the main coil gradient field, and the target field of the designated region outside the shielded coil is the external decay shielded region.

[0083] 2) The current density function expressions of the axial main coil and the shielded coil are set as follows:

[0084]

[0085]

[0086] wherein and are the azimuthal component of the axial main coil current density expression and the axial component of the axial main coil current density expression, and are the azimuthal component of the axial shielded coil current density expression and the axial component of the axial shielded coil current density expression, R p and L p are the radius of the axial main coil and the half-height of the axial main coil, R s and L s are the radius of the axial shielded coil and the half-height of the axial shielded coil, θ p and z p are the polar angle of the axial main coil target region and the polar radius of the main coil target region, θ s and z s are the polar angle of the axial shielded coil target region and the polar radius of the axial shielded coil target region, and m is the undetermined coefficient P m and Q mWhere m is the index of the Fourier series, and M is the upper limit of the index m, M is the maximum order of the Fourier series expansion related to the numerical accuracy.

[0087] 3) The main coil and the shield coil are synchronously applied with the current of the specified size during operation.

[0088] By Figure 1 It can be seen that the SERF inertial measurement self-shield three-dimensional magnetic field coil in the application comprises a permalloy shielding cylinder 1, a ferrite shielding cylinder 2, an x-axis shielding coil 3, a y-axis shielding coil 4, a z-axis shielding coil 5, a coil framework 6, an x-axis main coil 7, a y-axis main coil 8, a z-axis main coil 9, an air chamber support 10, an atomic source air chamber 11, a precision resistor R1 12, a precision resistor R2 13, and a current source 14. The self-shield three-dimensional magnetic field coil in the application is divided into a cylindrical radial self-shield coil, a cylindrical axial self-shield coil and a current source. Two self-shield coils orthogonal in azimuth angle generate the magnetic field of x and y, and the cylindrical axial self-shield coil generates the magnetic field of z direction. Thus, the three-dimensional self-shield magnetic field coil is formed.

[0089] As shown in the figure, the x-axis shielding coil 3, the y-axis shielding coil 4 and the z-axis shielding coil 5 are all attached to the shielding coil framework 6, and the x-axis main coil 7, the y-axis main coil 8 and the z-axis main coil 9 are all attached to the main coil framework. The x-axis shielding coil 3 and the x-axis main coil 7 form a cylindrical radial self-shield coil to generate the magnetic field of the x-axis direction, the y-axis shielding coil 4 and the main coil 8 form another cylindrical radial self-shield coil to generate the magnetic field of the y-axis direction, and the z-axis shielding coil 5 and the z-axis main coil 9 form a cylindrical axial self-shield coil to generate the magnetic field of the z-axis direction. Figure 1 Supposing that the radius of the shielding coil is R s , the radius of the main coil is R p , the design steps are as follows: first, set the atomic air chamber and the field point of the target field region outside the shielding coil, and then determine the current density functions of the radial and axial main coils and the shielding coils:

[0090] Radial main coil:

[0091]

[0092] Radial shielding coil:

[0093]

[0094] Axial main coil:

[0095]

[0096] Axial shielding coil:

[0097]

[0098] ​

[0099] The magnetic field expression of the selected target field point is as follows by applying the Biot-Savart law to the selected target field point:

[0100]

[0101]

[0102] Then the unknown parameters in the current density are solved by using the Tikhonov regularization rule.

[0103] The stream function is obtained according to the solved parameters so as to determine the contour of the coil.

[0104] According to the design requirement, the radius of the main coil is 17 mm, the radius of the shielding coil is 19.5 mm, and the radius of the middle light hole is 1.5 mm. The main coil contour map obtained by the above method is as shown in Figure 2 The shielding coil contour map is as shown in Figure 3 The units of the x, y and z three-axis coordinate system are meters (m). The dotted line and the realization represent different current directions.

[0105] The gradient self-shielding coil main coil inhibits the magnetic field gradient and the shielding effect of the shielding coil as shown in Figure 4 It can be seen that in the space distribution range of about 15.25 mm in the x-axis range and about 15.25 mm in the y-axis range, the magnetic field presents a gradient distribution, which plays a role in inhibiting the gradient magnetic field, and the maximum and minimum magnetic fields are positive and negative 32 nT, that is, the required gradient magnetic field can be generated in the target area of the inhibited magnetic field. The linear space deviation of the gradient coil in the 0.25 times range of the main coil is better than one thousandth, and the gradient magnetic field rapidly decays outside the self-shielding coil, that is, in the range of a radius greater than 19.5 mm.

[0106] The contents not described in detail in the specification of the present application belong to the prior art known to those skilled in the art. It is indicated here that the above description is helpful for those skilled in the art to understand the present application, but does not limit the protection scope of the present application. Any implementation of equivalent replacement, modification, improvement and / or deletion of the above description without departing from the essential content of the present application falls within the protection scope of the present application.

Claims

1. A method of designing an inertial measurement gradient self-shielded coil, characterized by, The target field of a selected spherical atom chamber is taken as the main coil gradient magnetic field target field region, and the target field of a designated cylindrical region outside the shield coil is taken as an external attenuation shield region; the current density distribution on the coil surface is derived by solving the magnetic field expression of the discrete target points; the current density is discretized, and the stream function is used to calculate the profile of the coil, i.e., the designed flexible coil current trace, so that a gradient magnetic field with a specified size is generated in the target field region of the atom chamber, and the magnetic field between the shield cylinder and the coil outside the shield coil is rapidly attenuated to zero, thereby reducing the magnetic field coupling between the shield cylinder and the coil, suppressing the magnetic field gradient, and improving the inertial measurement precision; The inertial measurement gradient self-shield coil comprises a cylindrical radial self-shield coil for generating x and y direction gradient magnetic fields and a cylindrical axial self-shield coil for generating a z direction gradient magnetic field. In SERF inertial measurement, the three axes of the three-dimensional magnetic field coil generate a first-order linear gradient magnetic field in the sensitive region of the atom chamber, which plays a role in actively applying a magnetic field gradient. The self-shield three-dimensional magnetic field coil suppresses the magnetic field gradient by actively applying a gradient magnetic field to the atom chamber, and rapidly attenuates the magnetic field generated by the coil to zero between the magnetic shield cylinder and the shield coil, thereby reducing the atomic relaxation rate, increasing the system scale factor, and reducing the error. The cylindrical axial self-shield coil comprises an axial main coil and a shield coil, and the design steps are as follows: The atom chamber is selected as the main coil gradient magnetic field target field region, and the target field of a designated cylindrical region outside the shield coil is taken as an external attenuation shield region. The current density function expressions of the axial main coil and the shield coil are set as follows: wherein and are azimuthal and axial components of the axial main coil current density expression, respectively, and are azimuthal and axial components of the axial shield coil current density expression, respectively, R p and L p are the radius of the axial main coil and the half-height of the axial main coil, respectively, R s and L s are the radius of the axial shield coil and the half-height of the axial shield coil, respectively, θ p and z p are the polar angle of the axial main coil target region and the polar radius of the main coil target region, respectively, θ s and z s are the polar angle of the axial shield coil target region and the polar radius of the axial shield coil target region, respectively, m is an index of the undetermined coefficients P m and Q m , and M is the upper limit of the index m, and M is the maximum order number of the Fourier series expansion related to the numerical accuracy. Let r p (R p ,θ p ,z p ), r s (R s ,θ s ,z s ), r DSV (R DSV ,θ DSV ,z DSV ), r OUT (R OUT ,θ OUT ,z OUT ) be the source points of the radial main coil surface, the shield coil surface, the target field points of the atomic cell gradient magnetic field and the target field points of the shield coil outer decay magnetic field, respectively. The magnetic field sizes corresponding to the atomic cell target field points and the shield coil outer are as follows: The intermediate functions are as follows: where u0is the vacuum permeability, (r DSV -r p ) is the distance between the position vector of a field point in the main coil target field region and the position vector of the main coil surface, (r DSV -r S ) is the distance between the position vector of a field point in the main coil target field region and the position vector of the shield coil surface, (r OUT -r p ) is the distance between the position vector of a field point outside the shield coil target field region and the position vector of the main coil surface, (r OUT -r s ) is the distance between the position vector of a field point outside the shield coil target field region and the position vector of the shield coil surface, (x DSV ,y DSV ,z DSV ) is a field point in the main coil target field region, (x OUT ,y OUT ,z OUT ) is a field point in the shield coil target field region.

2. The method of designing an inertial measurement gradient self-shielded coil according to claim 1, wherein, The current density distribution comprises inverse transformation of the Fourier expansion of the current generated magnetic field by the target field method to obtain the current density distribution of the ideal magnetic field.

3. The method of designing an inertial measurement gradient self-shielded coil according to claim 1, wherein, The function curvature of the current density distribution is used to constrain the penalty function of the coil, and Tikhonov regularization is used to avoid the ill-posed problem of the first type of Fredholm integral equation when solving the values of the undetermined coefficients of the current density function.

4. The method of designing an inertial measurement gradient self-shielded coil according to claim 1, wherein, The cylindrical radial self-shield coil is composed of two layers of coils, i.e., a gradient main coil for active gradient magnetic compensation and a shield coil for attenuating the magnetic field between the gradient coil and the magnetic shield cylinder to zero. The design steps are as follows: First, the surface current density expression on the cylindrical radial self-shield coil is determined, wherein the main coil current expression is: The shield coil current expression is: wherein and are azimuthal and axial components of the radial main coil current density expression, respectively, and are azimuthal and axial components of the radial shield coil current density expression, respectively, R p and L p are the radius of the radial main coil and the half-height of the radial main coil, respectively, R s and L s are the radius of the radial shield coil and the half-height of the radial shield coil, respectively, θ p and z p are the polar angle of the radial main coil target region and the polar radius of the radial main coil target region, respectively, θ s and z s are the polar angle of the radial shield coil target region and the polar radius of the radial shield coil target region, respectively, m is a first index of the undetermined coefficients P mn and Q mn , n is a second index of the undetermined coefficients P mn and Q mn , and M is the upper limit of the index m and N is the upper limit of the index n, M and N are both the maximum order of the Fourier series expansion related to the numerical accuracy.

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