Design method of axial magnetic gradient compensation coil of miniature nuclear magnetic resonance gyroscope

Abstract

The invention discloses a design method for an axial magnetic gradient compensation coil of a miniature nuclear magnetic resonance gyroscope, relates to the field of miniature nuclear magnetic resonance gyroscopes, and aims to accurately design the magnetic field intensity and direction in a target area on the premise of presetting a coil structure to be circular. And meanwhile, a light through hole position is reserved for pumping light required by the gyroscope by presetting the distribution range of the coils. In order to solve ill-conditioned problems existing in the equation set solving process, a Tikhonov regularization method is adopted for processing, and therefore the stability and accuracy of a solving result are improved; in addition, a penalty coefficient introduced in the regularization process is optimized by using a particle swarm optimization algorithm, so that the normalization and smoothness of the discretized coil are ensured. Compared with the prior art, on the basis of keeping the linear change of the axial magnetic field, the length-diameter ratio of the coil can be effectively reduced, and the coil has the advantages of being regular in structure, easy to machine and install, small in occupied space of coil distribution and the like.

Description

Technical Field

[0001] The present invention relates to the technical field of micro nuclear magnetic resonance gyroscopes, and particularly relates to a design method for an axial magnetic gradient compensation coil of a micro nuclear magnetic resonance gyroscope. Background Art

[0002] Nuclear magnetic resonance gyroscopes have potential advantages of miniaturization, high precision, and low cost, and are widely concerned in the field of inertial navigation, with broad application prospects.

[0003] When a nuclear magnetic resonance gyroscope is working, the uniformity of the axial magnetic field inside the gas chamber is directly related to the working state of the nuclear magnetic resonance gyroscope. However, due to the presence of residual magnetism inside the gas chamber, device assembly errors, and magnetic fields generated by internal instruments working, etc., a gradient is generated in the axial magnetic field inside the gas chamber. The decrease in the uniformity of the axial magnetic field will reduce the transverse relaxation time of the system, resulting in a decrease in the quality of the resonance signal of the gyroscope, and further affecting the zero-bias stability of the system.

[0004] When no axial magnetic field is applied, under the shielding of the magnetic shielding thin layer against the external magnetic field, the inside of the gas chamber is approximately in a weak magnetic or zero magnetic environment. At this time, the nucleons inside the gas chamber are in a chaotic motion state. When an axial magnetic field is applied, the precession axis of the nucleons inside the gas chamber is fixed on the z-axis. After applying the pumping light, the precession direction of the nucleons is fixed in the same direction. When the axial magnetic field is non-uniform, the precession states of the nucleons become inconsistent, and after applying a transverse excitation magnetic field, the resonance effect of the nucleons will decrease. Therefore, it is necessary to design an axial magnetic gradient compensation coil to compensate for the uniformity of the magnetic field in the axial direction.

[0005] The axial magnetic gradient compensation coil directly affects the compensation effect of the axial magnetic field uniformity. Currently, the existing general design methods are the forward method and the reverse method. In the forward method, the coil wire form is first fixed, and appropriate coil parameters are found according to the generated magnetic field. The coils designed by the traditional forward method have problems such as too large a length-to-diameter ratio, low magnetic field linearity, and limited positioning accuracy. In the reverse method, the stream function and current density are deduced from the magnetic field form of the target area, and then discretized to obtain the coil parameters. The traditional reverse method has the problem that the discretization degree is limited by the coil parameters, resulting in a large difference between the generated magnetic field and the design. Summary of the Invention

[0006] The present invention provides a design method for an axial magnetic gradient compensation coil of a micro nuclear magnetic resonance gyroscope for the above technical problems. The present invention solves the problem that the performance of the nuclear magnetic resonance gyroscope decreases due to the presence of a gradient in the axial magnetic field, helps to improve the axial magnetic field uniformity, increase the relaxation time, and enhance the zero-bias stability of the system.

[0007] To achieve the above object, the technical solution adopted by the present invention is:

[0008] A design method for an axial magnetic gradient compensation coil of a micro nuclear magnetic resonance gyroscope provided by the present invention includes the following steps:

[0009] Step S1: Determine the coil distribution range and coil shape of the axial magnetic gradient compensation coil;

[0010] Step S2: Preset the form of the planar continuous current density of the axial magnetic gradient compensation coil;

[0011] Step S3: Establish a relational expression of the magnetic field generated by the planar continuous current density at different positions according to the Biot-Savart law, then substitute the planar continuous current density into the relational expression of the magnetic field, and obtain a magnetic field expression containing the unknown planar continuous current density coefficient of the axial magnetic gradient compensation coil;

[0012] Step S4: Combine the above magnetic field expression and give the magnetic field expectation value of the target field point, and solve the unknown planar continuous current density coefficient of the axial magnetic gradient compensation coil by the target field method;

[0013] Step S5: According to the relationship between the planar continuous current density and the stream function of the axial magnetic gradient compensation coil, discretize the stream function contour line to obtain the winding form of the coil.

[0014] Further, the coils of the axial magnetic gradient compensation coil are symmetric about the plane z = 0 and are distributed on the symmetric planes on both sides of the central target area. The symmetric plane is a square with a side length of 2L, and the two symmetric planes on both sides are 2a apart.

[0015] Further, the planar continuous current density J(r) of the axial magnetic gradient compensation coil is expressed as:

[0016] J(r) = J r (r',θ')e r +J θ (r',θ')e θ

[0017] where, J r and J θ are respectively the components of the planar continuous current density in the radial direction and the azimuthal direction in the polar coordinate system; e r is the unit vector in the radial direction in the polar coordinate system, e θ is the unit vector in the azimuthal direction in the polar coordinate system, r' is the radial component in the polar coordinate system at the source point, and θ' is the azimuthal component in the polar coordinate system at the source point.

[0018] Further, the coil shape of the axial magnetic gradient compensation coil is circular. Therefore, the component J ris 0; the component J of the planar continuous current density in the azimuthal direction in the polar coordinate system θ is represented by a series of trigonometric functions to generate a magnetic field in the z-axis direction:

[0019]

[0020] where P n (n = 1, 2, 3,..., N) is the coefficient of the planar continuous current density of the axial magnetic gradient compensation coil, N is the maximum order of the Fourier series, and l and L are the minimum radius and the maximum radius of the coil respectively.

[0021] Furthermore, in step S3, the magnetic field expression is:

[0022]

[0023] where [B x , B y , B z are the components of the magnetic field in the three directions of the x-axis, y-axis, and z-axis respectively; μ0 is the vacuum permeability; r and r' are the position vectors of the target field point r(r, θ) and the source point r'(r', θ') respectively, r' is the radial component in the polar coordinate system at the source point, θ' is the azimuthal component in the polar coordinate system at the source point, r is the radial component value in the polar coordinate system at the target field point, θ is the azimuthal component value in the polar coordinate system at the target field point, ||r - r'|| is the distance between the position vectors of the target field point and the source point; i is the unit vector in the x-direction in the rectangular coordinate system; j is the unit vector in the y-direction in the rectangular coordinate system; k is the unit vector in the z-direction in the rectangular coordinate system; x is the distance in the x-direction between the source point and the target field point in the rectangular coordinate system; y is the distance in the y-direction between the source point and the target field point in the rectangular coordinate system; z is the distance in the z-direction between the source point and the target field point in the rectangular coordinate system; l and L are the minimum radius and the maximum radius of the coil respectively; J(r) is the planar continuous current density of the axial magnetic gradient compensation coil;

[0024] Integrating and then accumulating the magnetic field expression, the magnetic field expression is rewritten as:

[0025]

[0026] where z = ±a is the plane where the axial magnetic gradient compensation coil is located; P n (n = 1, 2, 3,..., N) is the coefficient of the planar continuous current density of the axial magnetic gradient compensation coil, N is the maximum order of the Fourier series; B target is the target magnetic field value.

[0027] Furthermore, in step S4, an error function E of the sum of squares of the difference between the calculated magnetic field and the expected magnetic field is calculated:

[0028]

[0029] Among them, B(r) is the induced magnetic field value; B target is the target magnetic field value; P n (n = 1, 2, 3, ..., N) is the unknown continuous current density coefficient of the axial magnetic gradient compensation coil plane, and N is the maximum order of the Fourier series.

[0030] Furthermore, in step S4, the Tikhonov regularization method is used to optimize the error between the generated magnetic field and the target magnetic field, and a penalty coefficient λ is introduced to impose constraints on the error function and then solve the unknown continuous current density coefficient of the axial magnetic gradient compensation coil plane; therefore, the residual E′ is rewritten as:

[0031]

[0032] Among them, Γ is the Tikhonov matrix, is the penalty function.

[0033] Furthermore, in step S4, the particle swarm optimization algorithm is used to optimize the penalty coefficient λ, and the unknown continuous current density coefficient P of the axial magnetic gradient compensation coil plane n is obtained by minimizing the error estimation residual E′, that is, when the derivative of the error function is zero:

[0034]

[0035] Finally, the matrix form containing the parameters to be solved is obtained:

[0036] x = (A T A + λΓ T Γ) -1 A T B

[0037] Among them:

[0038] x = [P1 P2 ··· P n T

[0039]

[0040] Among them, x is the parameter to be solved in the stream function, and the distribution function of the planar continuous current can be obtained by solving x; B is the set value of the target magnetic field in the target area, and the target magnetic field in the target area changes linearly along the z-axis direction, and the magnetic field value is 0 in the z = 0 plane; A includes the relationship between the planar continuous current density and the magnetic field.

[0041] ​Further, in step S5, the relationship between the planar continuous current density and the stream function of the axial magnetic gradient compensation coil is as follows:

[0042]

[0043] The expression of the stream function is:

[0044]

[0045] where S(r', θ') represents the magnitude of the stream function at the source point r'(r', θ', a), and the change in the stream function represents the change in the planar continuous current density; J r and J θ are the components of the planar continuous current density in the radial direction and the azimuthal direction in the polar coordinate system respectively; P n (n = 1, 2, 3,..., N) are the unknown coefficients of the planar continuous current density of the axial magnetic gradient compensation coil, N is the maximum order of the Fourier series; l and L are the minimum radius and the maximum radius of the coil respectively; t' is the value of the radial component in the polar coordinate system at the source point, θ' is the value of the azimuthal component in the polar coordinate system at the source point, r is the value of the radial component in the polar coordinate system at the target field point, and θ is the value of the azimuthal component in the polar coordinate system at the target field point.

[0046] Further, in step S5, the coil distribution form obtained by discretizing the stream function according to the contour line position is:

[0047] d i = S(r', θ') min +(i + 1 / 2)I0, (i = 0, 1, 2,..., K - 1)

[0048] where d i is the coil winding, I0 = S(r', θ') max - S(r', θ') min , S(r', θ') max is the maximum value of the stream function, S(r', θ') min is the minimum value of the stream function, and K is the number of windings of a group of coils.

[0049] The beneficial effects of the present invention are:

[0050] Compared with the prior art, the advantages of the present invention are:

[0051] (1) When designing the axial magnetic gradient compensation coil, the present invention fixes the basic form of the coil, simplifies the coil parameters, and is conducive to wire routing.

[0052] (2) The present invention shortens the coil aspect ratio, ensures the axial magnetic field gradient while improving the magnetic field surface uniformity.

[0053] (3) The present invention occupies little space, and the coil distribution exists only in the defined plane, which is applicable to a micro nuclear magnetic resonance gyroscope and is more conducive to the development trend of miniaturization of the gyroscope. Description of the Drawings

[0054] In order to more clearly illustrate the technical solutions in the embodiments of the present application, the following will briefly introduce the drawings required for the description of the embodiments. Obviously, the following drawings are only some embodiments of the present application. For those of ordinary skill in the art, without creative efforts, other drawings can also be obtained based on these drawings.

[0055] Figure 1 It is a flowchart of a design method for an axial magnetic gradient compensation coil of a micro nuclear magnetic resonance gyroscope provided by the present invention.

[0056] Figure 2 It is a schematic diagram of the position of the axial magnetic gradient compensation coil designed by the present invention.

[0057] Figure 3 It is a schematic diagram of the coil distribution of the axial magnetic gradient compensation coil designed by the present invention.

[0058] Figure 4 It is a schematic diagram of the magnetic field of the axial magnetic gradient compensation coil designed by the present invention. Detailed Embodiments

[0059] The following will further elaborate on the present invention in conjunction with the drawings.

[0060] See Figure 1 As shown, a design method for an axial magnetic gradient compensation coil of a micro nuclear magnetic resonance gyroscope provided by the present invention specifically includes the following steps:

[0061] I. Determine the coil distribution range and coil shape of the axial magnetic gradient compensation coil, and preset the form of the planar continuous current density of the axial magnetic gradient compensation coil;

[0062] As Figure 2 shown, according to the limitations of the magnetic shielding layer and the light passing hole, it is determined that the coil distribution of the axial magnetic gradient compensation coil is on two symmetric planes separated by 2a. This plane is square with a side length of 2L, that is, the coils of the axial magnetic gradient compensation coil are symmetric about the plane (z = 0) and distributed on the symmetric planes on both sides of the central target area, and a light passing hole with a radius of l is reserved in the middle of the axial magnetic gradient compensation coil.

[0063] The planar continuous current density J(r) of the axial magnetic gradient compensation coil can be expressed in the following form:

[0064] J(r) = J r (r',θ')er +J θ (r',θ')e θ

[0065] Among them, J r and J θ are respectively the components of the planar continuous current density in the radial direction and the azimuthal direction in the polar coordinate system; e r is the unit vector in the radial direction in the polar coordinate system, e θ is the unit vector in the azimuthal direction in the polar coordinate system, r' is the radial component in the polar coordinate system at the source point, and θ' is the azimuthal component in the polar coordinate system at the source point.

[0066] In the present invention, the shape of the coil of the axial magnetic gradient compensation coil is circular. Therefore, the component J r of the planar continuous current density in the radial direction is 0. In order to generate a magnetic field in the z-axis direction, the component J θ in the azimuthal direction can be represented by a series of trigonometric functions, and its specific form is as follows:

[0067]

[0068] Among them, P n (n = 1, 2, 3,..., N) are the unknown coefficients of the planar continuous current density of the axial magnetic gradient compensation coil, N is the maximum order of the Fourier series, and l and L are respectively the minimum radius and the maximum radius of the coil.

[0069] Take l = 2mm, L = 9mm, a = 9mm, K = 24, λ = 14778×10 -15 , μ0 = 4π×10 -7 , and the planar distribution (z = 9mm) of the axial magnetic gradient compensation coil is obtained as Figure 3 shown. Among them, the dashed line indicates that the current direction is negative, and the solid line indicates that the current direction is positive. The distribution of the axial magnetic gradient compensation coil on the z = -9mm plane is similar to it, only the current direction is opposite to it, that is, the dashed line indicates that the current direction is positive, and the solid line indicates that the current direction is negative. From Figure 2 , it can be seen that the axial magnetic gradient compensation coil is composed of multiple current-carrying rings with radii within (2mm, 9mm), and the radius distribution rule is obtained by discretizing the stream function. This coil configuration is easy to print and process and occupies a small space.

[0070] II. According to the Biot-Savart law, establish the relational expression of the magnetic field generated by the planar continuous current density of the axial magnetic gradient compensation coil at different positions, and then substitute the planar continuous current density of the axial magnetic gradient compensation coil into this relational expression of the magnetic field. The mathematical expressions of this process are as follows:

[0071]

[0072] Among them, [B x , B y , B z are the components of the magnetic field in the three directions of the x-axis, y-axis, and z-axis respectively; μ0 is the vacuum magnetic permeability; r and r' are the position vectors of the target field point r(r,θ) and the source point r'(r',θ') respectively, r' is the radial component in the polar coordinate system at the source point, θ' is the azimuthal angle component in the polar coordinate system at the source point, r is the radial component value in the polar coordinate system at the target field point, θ is the azimuthal angle component value in the polar coordinate system at the target field point, ||r - r'|| is the distance between the position vectors of the target field point and the source point; i is the unit vector in the x direction in the rectangular coordinate system; j is the unit vector in the y direction in the rectangular coordinate system; k is the unit vector in the z direction in the rectangular coordinate system; x is the distance in the x direction between the source point and the target field point in the rectangular coordinate system; y is the distance in the y direction between the source point and the target field point in the rectangular coordinate system; z is the distance in the z direction between the source point and the target field point in the rectangular coordinate system.

[0073] According to the above expressions, the magnetic field expression in the axial direction (z-axis direction) can be further obtained as follows:

[0074]

[0075] By changing the calculation order, integrating first and then accumulating, the above magnetic field expression can be expressed in the following form:

[0076]

[0077] Among them, z = ±a are the planes where the axial magnetic gradient compensation coils are located, that is, the coil distribution of the axial magnetic gradient compensation coils is in two planes of z = ±a, which are composed of multiple current-carrying rings with radii in (l, L). The current-carrying ring distributions in the two planes are the same, only the current directions are opposite; B target is the target magnetic field value.

[0078] III. Combine the magnetic field expression obtained in Step II and give the magnetic field expectation value of the target field point, and solve the unknown continuous current density coefficient of the axial magnetic gradient compensation coil plane through the target field method;

[0079] According to the above magnetic field expression, calculate the error function E of the sum of squares of the difference between the magnetic field and the expected magnetic field. The mathematical expression of this error function E is as follows:

[0080]

[0081] The above equations are overdetermined equations. In order to avoid solving the unknown continuous current density coefficient P of the axial magnetic gradient compensation coil plane nWhen pathological problems occur, the present invention adopts the Tikhonov regularization method to optimize the error between the generated magnetic field and the target magnetic field, and introduces a penalty coefficient λ to impose constraints on the error function and then solve the unknown planar continuous current density coefficients of the axial magnetic gradient compensation coil. Therefore, the residual E′ is rewritten in the following form:

[0082]

[0083] where Γ is the Tikhonov matrix, is the penalty function.

[0084] The particle swarm optimization algorithm is used to optimize the penalty coefficient λ to ensure the normality and smoothness of the coil after discretization. The unknown planar continuous current density coefficients P of the axial magnetic gradient compensation coil n are obtained by minimizing the error estimation residual E′ (when the derivative of the error function is zero):

[0085]

[0086] Finally, a matrix equation containing the parameters to be solved is obtained:

[0087] x = (A T A + λΓ T Γ) -1 A T B

[0088] where:

[0089] x = [P1 P2 ··· P n T

[0090]

[0091] where x is the parameter to be solved in the stream function, and the distribution function of the planar continuous current can be obtained by solving x; B is the set value of the target magnetic field in the target area, and the target magnetic field in the target area changes linearly along the z-axis direction, and the magnetic field value is 0 on the z = 0 plane; A contains the relationship between the planar continuous current density and the magnetic field.

[0092] IV. Discretize the stream function contour lines to obtain the winding form of the coil;

[0093] The relationship between the planar continuous current density of the axial magnetic gradient compensation coil and the stream function is specifically as follows:

[0094]

[0095] where r is the radius component value in the polar coordinate system at the target field point, and θ is the azimuth angle component value in the polar coordinate system at the target field point.

[0096] ​The expression of the stream function is specifically as follows:

[0097]

[0098] Among them, S(r',θ') represents the magnitude of the stream function at the source point r'(r',θ',a). The change in the stream function represents the change in the planar continuous current density. The coil distribution form obtained by discretizing the stream function according to the contour line positions is as follows:

[0099] d i = S(r',θ') min +(i + 1 / 2)I0, (i = 0, 1, 2,..., K - 1)

[0100] Among them, d i is the coil winding, I0 = S(r',θ') max - S(r',θ') min , S(r',θ') max is the maximum value of the stream function, S(r',θ') min is the minimum value of the stream function, and K is the number of windings of a group of coils.

[0101] Taking l = 2mm, L = 9mm, a = 9mm, K = 24, λ = 14778×10 -15 , μ0 = 4π×10 -7 The schematic diagram of the magnetic field of the axial magnetic gradient compensation coil obtained in the target area is as shown in Figure 4 . As can be seen from Figure 4 , for the axial magnetic gradient compensation coil designed by the present invention within a cube with a side length of 4mm centered on the target area, the magnetic field linearly changes from 800nT to -800nT along the z-axis direction, and the magnetic field value at z = 0 is 0. The magnetic field in the target area realizes a gradient change along the z-axis direction.

[0102] The above are only the preferred embodiments of the present invention. It should be noted that for those of ordinary skill in the art, without departing from the principle of the present invention, several improvements and refinements can be made, and these improvements and refinements should also be regarded as the protection scope of the present invention.

Claims

1. A design method for the axial magnetic gradient compensation coil of a micro nuclear magnetic resonance gyroscope, characterized in that, It includes the following steps: Step S1: Determine the coil distribution range and coil shape of the axial magnetic gradient compensation coil; Step S2: Preset the planar continuous current density form of the axial magnetic gradient compensation coil; Step S3: Establish the relationship expression of the magnetic field generated by the planar continuous current density at different positions according to the Biot - Savart law, then substitute the planar continuous current density into the relationship expression of the magnetic field, and obtain the magnetic field expression containing the unknown planar continuous current density coefficient of the axial magnetic gradient compensation coil; Step S4: Combine the above magnetic field expression and give the magnetic field expectation value of the target field point, and solve the unknown planar continuous current density coefficient of the axial magnetic gradient compensation coil by the target field method; Step S5: According to the relationship between the planar continuous current density and the stream function of the axial magnetic gradient compensation coil, discretize the stream function contour line to obtain the winding form of the coil.

2. A design method for an axial magnetic gradient compensation coil of a micro nuclear magnetic resonance gyroscope according to claim 1, characterized in that The coils of the axial magnetic gradient compensation coil are symmetric about the plane z = 0 and are distributed on the symmetric planes on both sides of the central target area. The symmetric plane is a square with a side length of 2L, and the two symmetric planes on both sides are 2a apart.

3. A design method for an axial magnetic gradient compensation coil of a micro nuclear magnetic resonance gyroscope according to claim 1, characterized in that, The planar continuous current density J(r) of the axial magnetic gradient compensation coil is expressed as: J(r) = J r (r', θ')e r + J θ (r', θ')e θ Among them, J r and J θ are the components of the planar continuous current density in the radial direction and the azimuthal direction in the polar coordinate system respectively; e r is the unit vector in the radial direction in the polar coordinate system, e θ is the unit vector in the azimuthal direction in the polar coordinate system, r' is the radial component in the polar coordinate system at the source point, and θ' is the azimuthal component in the polar coordinate system at the source point.

4. A design method for an axial magnetic gradient compensation coil of a micro nuclear magnetic resonance gyroscope according to claim 3, characterized in that, The coil shape of the axial magnetic gradient compensation coil is circular, so the component J of the planar continuous current density in the radial direction in the polar coordinate system r is 0; the component J of the planar continuous current density in the azimuthal direction in the polar coordinate system θ is represented by a series of trigonometric functions to generate a magnetic field in the z-axis direction: where P n (n = 1, 2, 3, ..., N) is the unknown planar continuous current density coefficient of the axial magnetic gradient compensation coil, N is the maximum order of the Fourier series, and l and L are the minimum and maximum radii of the coil, respectively.

5. A design method for an axial magnetic gradient compensation coil of a micro nuclear magnetic resonance gyroscope according to claim 1, characterized in that, In step S3, the magnetic field expression is: Among them, [B x , B y , B z are the components of the magnetic field along the x-axis, y-axis, and z-axis respectively; μ0 is the vacuum magnetic permeability; r and r' are the position vectors of the target field point r(r,θ) and the source point r'(r',θ') respectively, r' is the radial component in the polar coordinate system at the source point, θ' is the azimuthal angle component in the polar coordinate system at the source point, r is the radial component value in the polar coordinate system at the target field point, θ is the azimuthal angle component value in the polar coordinate system at the target field point, ||r - r'|| is the distance between the position vectors of the target field point and the source point; i is the unit vector in the x-direction in the Cartesian coordinate system; j is the unit vector in the y-direction in the Cartesian coordinate system; k is the unit vector in the z-direction in the Cartesian coordinate system; x is the distance in the x-direction between the source point and the target field point in the Cartesian coordinate system; y is the distance in the y-direction between the source point and the target field point in the Cartesian coordinate system; z is the distance in the z-direction between the source point and the target field point in the Cartesian coordinate system; l and L are the minimum radius and the maximum radius of the coil respectively; J(r) is the planar continuous current density of the axial magnetic gradient compensation coil; Integrate the magnetic field expression first and then accumulate it, and rewrite the magnetic field expression as: where z = ±a is the plane where the axial magnetic gradient compensation coil is located; P n (n = 1, 2, 3, ..., N) is the unknown continuous current density coefficient of the axial magnetic gradient compensation coil plane, and N is the maximum order of the Fourier series; B target is the target magnetic field value.

6. A design method for an axial magnetic gradient compensation coil of a micro nuclear magnetic resonance gyroscope according to claim 5, characterized in that In step S4, calculate the error function E of the sum of squares of the difference between the magnetic field and the expected magnetic field according to the magnetic field expression: where B(r) is the value of the induced magnetic field; B target is the value of the target magnetic field; P n (n = 1, 2, 3, ..., N) are the unknown coefficients of the continuous current density of the plane of the axial magnetic gradient compensation coil, and N is the maximum order of the Fourier series.

7. A design method for an axial magnetic gradient compensation coil of a micro nuclear magnetic resonance gyroscope according to claim 6, characterized in that In step S4, use the Tikhonov regularization method to optimize the error between the generated magnetic field and the target magnetic field, and introduce a penalty coefficient λ to impose constraints on the error function to solve the unknown planar continuous current density coefficient of the axial magnetic gradient compensation coil; Therefore, rewrite the residual E′ as: where Γ is the Tikhonov matrix, is the penalty function.

8. A design method for an axial magnetic gradient compensation coil of a micro nuclear magnetic resonance gyroscope according to claim 7, characterized in that, In step S4, the particle swarm optimization algorithm is used to optimize the penalty coefficient λ, and the unknown planar continuous current density coefficient P of the axial magnetic gradient compensation coil n is obtained by minimizing the error estimation residual E′, that is, when the derivative of the error function is zero: Finally, obtain the matrix form containing the parameters to be solved: x = (A T A + λΓ T Γ) -1 A T B Where: x = [P1 P2 ··· P n T ​ Where x is the parameter to be solved in the stream function, and the distribution function of the planar continuous current can be obtained by solving x; B is the set value of the target magnetic field in the target area, and the target magnetic field in the target area changes linearly along the z - axis direction, and the magnetic field value on the plane z = 0 is 0; A includes the relationship between the planar continuous current density and the magnetic field.

9. A design method for an axial magnetic gradient compensation coil of a micro nuclear magnetic resonance gyroscope according to claim 1, characterized in that, In step S5, the relationship between the planar continuous current density and the stream function of the axial magnetic gradient compensation coil is: The expression of the stream function is: Among them, S(r',θ') represents the magnitude of the stream function at the source point r'(r',θ',a), and the change in the stream function represents the change in the planar continuous current density; J r and J θ are respectively the components of the planar continuous current density in the radial direction and the azimuthal direction in the polar coordinate system; P n (n = 1, 2, 3,..., N) are the coefficients of the planar continuous current density of the unknown axial magnetic gradient compensation coil, and N is the maximum order of the Fourier series; l and L are respectively the minimum radius and the maximum radius of the coil; r' is the value of the radial component in the polar coordinate system at the source point, θ' is the value of the azimuthal component in the polar coordinate system at the source point, r is the value of the radial component in the polar coordinate system at the target field point, and θ is the value of the azimuthal component in the polar coordinate system at the target field point.

10. A design method for an axial magnetic gradient compensation coil of a micro nuclear magnetic resonance gyroscope according to claim 9, characterized in that In step S5, the coil distribution form obtained by discretizing the stream function according to the contour line position is: d i = S min (r',θ')+(i+1 / 2)I0,(i = 0,1,2,...,K-1) Among them, d i is the coil winding, I0 = S(r', θ') max -S(r', θ') min , S(r', θ') max is the maximum value of the stream function, S(r', θ') min is the minimum value of the stream function, and K is the number of windings of a set of coils.

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