Compact ultra-low coupling shim coil design method based on quantum genetic algorithm

Abstract

The invention discloses an ultra-low coupling shimming coil design method based on a quantum genetic algorithm. Five pairs of axial cylindrical coils which have the same radius and are symmetrical about a plane with z being equal to 0 are included. The current directions and the number of turns are different and are obtained through a simplified multi-pole moment expansion formula, the coil design problem is converted into a nonlinear optimization design problem with coil structure parameters as constraint conditions and the coil uniformity and the coupling rate as optimization targets, the problem is solved by adopting a quantum genetic algorithm, and the nonlinear optimization design problem is obtained. Therefore, coil structure parameters with excellent performance can be efficiently obtained with high quality, and the designed coil can achieve the excellent performance that compared with a traditional self-shielding coil, the uniformity is improved by one order of magnitude and the coupling rate is reduced by one order of magnitude in a large target area under the same-radius configuration. The method is suitable for application scenes such as precise magnetic field metering test and biological low-intensity magnetic field detection.

Description

Technical Field

[0001] The present invention relates to the technical field of precise magnetic field control, in particular to a design method of a compact ultra-low coupling shimming coil based on a quantum genetic algorithm, which is used for occasions such as calibration, compensation, and regulation of magnetic fields in magnetic shielding. Background Art

[0002] In high-precision weak magnetic tests such as biomagnetic field detection and quantum precision measurement, a stable zero magnetic field environment is crucial. This usually requires shielding the external magnetic field through a magnetic shielding device and then compensating for the residual magnetism in the barrel by a uniform magnetic field coil. In order to obtain a larger uniform space, the size of the coil usually needs to be increased, which results in the shortening of the distance between the coil and the wall of the magnetic shielding barrel, and the inevitable coupling effect generated by the two will further increase as the distance is shortened. This coupling effect will change the original distribution of the magnetic field generated by the coil, reduce the uniformity of the coil, and thus affect the performance of the entire system. Therefore, many researchers have designed self-shielding shimming coils to suppress the adverse effects of the coupling effect.

[0003] The self-shielding coil usually consists of a set of shielding coils that suppress the external magnetic field and a set of main coils that maintain the uniformity of the internal magnetic field nested together. This nested configuration results in a significant reduction in the effective space utilization rate, and its core uniform region is further reduced. This space redundancy characteristic makes the system face severe volume constraint challenges in miniaturized application scenarios (such as precision sensors, bio-implantable devices, etc.), and the actual application volume is reduced by about 46.36% compared with the compact design. During the design process, the self-shielding coil suppresses the coupling effect by accelerating the attenuation of the external magnetic field, which is an indirect means and is difficult to completely eliminate the adverse effects of the coupling effect on the coil performance. Moreover, the internal uniformity of the self-shielding coil is insufficient and needs to be further improved. Therefore, it is necessary to solve the above problems through optimized design, and by designing a magnetic field coil with the same radius structure, capable of eliminating the coupling effect and having higher uniformity, the accuracy of ultra-weak magnetic field manipulation can be improved.

[0004] During the process of coil optimized design, there are a large number of parameters to be optimized. Such as the number of coil groups, the number of coils in each group, the distance of each group of coils from the origin plane, the number of turns of each group of coils, and the current direction, etc. For traditional intelligent optimization algorithms, such as particle swarm optimization algorithm and genetic algorithm, although they have established a benchmark methodological status in the field of engineering optimization, their inherent asymptotic convergence characteristics lead to insufficient completeness of parameter space traversal. Experimental data shows that such algorithms generally have the problem that the number of iterations exceeds 200 rounds and still cannot break through the local extreme residence tendency in the design of electromagnetic devices (the fluctuation coefficient of the convergence curve > 0.35), and the computational complexity increases superlinearly with the dimension expansion. Therefore, an advanced intelligent optimization algorithm can be replaced to reduce the probability of premature convergence and improve the quality and speed of coil structure parameter optimization. Summary of the Invention

[0005] In view of the deficiencies in the prior art, the present invention proposes a design method for a compact ultra-low coupling shimming coil based on a quantum genetic algorithm. By using the method of magnetic shielding coupling separation, the magnetic field analytical formula generated by the coil under the ferromagnetic boundary is separated from the total magnetic field analytical formula, and the magnetic field analytical formula generated by the coupling effect is separated. The proportion of this part of the magnetic field in the total magnetic field is the coupling rate. Taking the coupling rate and uniformity of the coil as two optimization objectives, the structural parameters that are jointly optimal for the two indicators of the coil are optimized through the quantum genetic algorithm under the same radius configuration. The designed coil and the traditional self-shielding coil under the same radius configuration can achieve an ultra-low coupling rate reduced by one order of magnitude while improving the internal magnetic field uniformity by one order of magnitude.

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

[0007] A design method for a compact ultra-low coupling shimming coil based on a quantum genetic algorithm, characterized by comprising a coil group composed of several pairs of axially circular coils with the same radius. Each pair of axially circular coils with the same radius is symmetrically distributed with respect to the z = 0 plane, where z is the axial coordinate axis of the coil. Each pair of axially circular coils with the same radius has its own number of turns. The sum of the number of turns of the forward current and the sum of the number of turns of the reverse current in the coil group are the same, so as to achieve the rapid attenuation of the external magnetic field and the effect of the total magnetic moment being 0. Select target points in the uniform region inside the coil, calculate the magnetic field coupling rate and the magnetic field deviation relative to the center point at each target point respectively, and sum after assigning weights to the two indicators. The optimal solution is quickly obtained through the quantum genetic algorithm, so as to obtain an axially cylindrical coil group under the same radius structure that can reduce the coupling rate by one order of magnitude while reducing the maximum relative magnetic field deviation by one order of magnitude.

[0008] It includes the following steps:

[0009] Step 1, determine the radius R of the circular coil and the maximum value d that each pair of coils can reach from the z = 0 plane according to the structural parameters of the known magnetic shielding barrel, where z is the z-axis coordinate, and the minimum value d that each pair of coils can reach from the z = 0 plane to avoid the light aperture. max , establish the expression d min =[d1, d2, …, d i , where i is the coil pair serial number and M is the number of coil pairs. d M is the distance of the i-th pair of coils from the z = 0 plane; i

[0010] Step 2, make the total magnetic moment generated by the coil group be 0, and the sum of the number of turns of the forward current is equal to the sum of the number of turns of the reverse current;

[0011] Step 3: Derive the analytical formula of the magnetic field of the coil under free boundary and ferromagnetic boundary through the Biot-Savart law, Green's function expansion, and image method. Use the method of magnetic shielding coupling separation to derive the analytical formula of the additional magnetic field generated by the coil due to the coupling effect;

[0012] Step 4: Establish expressions for two optimization objectives. The first optimization objective is the uniformity of the magnetic field generated by the coil, represented by the relative magnetic field deviation. The second optimization objective is the ability of the coil to suppress the coupling effect, represented by the coupling rate of the coil, that is, the proportion of the magnetic field generated by the coupling effect in the total magnetic field. Assign different weights to the two optimization objectives and sum them up as the final optimized objective function expression;

[0013] Step 5: Substitute the determined coil structure parameters, and use the quantum genetic algorithm to optimize the optimization objectives. After obtaining the optimization results, respectively perform finite element simulations of the traditional self-shielding coil and the designed axial circular coil group of the same size in free space and ferromagnetic boundary, and compare the uniformity and the performance of suppressing the coupling effect of the two to verify the effectiveness of the design.

[0014] The following formulas are included in Step 3:

[0015] The magnetic field B generated by the axial cylindrical coil under free boundary z1 The analytical formula is as follows:

[0016]

[0017] where (ρ, φ, z) are the cylindrical coordinates of any point inside the coil, ρ is the radial coordinate, φ is the angular coordinate, z is the z-axis coordinate, μ0 is the vacuum permeability, R is the radius of the circular coil, e is the natural constant, i is the imaginary unit, k is the integration variable, I0 and K0 respectively represent the Bessel functions of the first and second kinds, and I0' and K0' respectively represent their derivatives, is the Fourier transform of the axial coil current density, expressed as follows:

[0018]

[0019] where M is the number of turns of the coil, I is the current passing through the coil, n i =[n1, n2, …, n M , n i is the number of turns of the i-th pair of coils;

[0020]

[0021] α b =μ0(μ r -1)I0′(kR)K0(kR b ),

[0022] β b = μ0(μ r I0(kR b )K0′(kR b ) - I0′(kR b )K0(kR b )),

[0023] γ b = μ0(μ r - 1)I0(kR b )K0′(kR c ),

[0024] α c = μ0(μ r - 1)I0′(kR)K0(kR c ),

[0025] β c = μ0(μ r - 1)I0′(kR b )K0(kR c ),

[0026] γ c = μ0(μ r I0′(kR c )K0(kR c ) - I0(kR c )K0′(kR c )),

[0027]

[0028] where B z2 (ρ, φ, z) is the magnetic field generated by an axial cylindrical coil under a ferromagnetic boundary, K1 is the modified second kind of Bessel function of the first order, G(k), α c , γ b , α b , γ c , β c , β b are all intermediate quantities, μ r is the relative magnetic permeability of the magnetic shielding material, R b is the inner radius of the magnetic shielding barrel, R c is the outer radius of the magnetic shielding barrel, is the Fourier transform of the current density after being changed due to the influence of the reflected current of the shielding barrel end cap on the coil, H is the half-length of the shielding barrel, p is the number of current reflections, is the additional magnetic field generated by the axial cylindrical coil under the ferromagnetic boundary due to the coupling effect.

[0029] The expressions included in Step 4 are as follows:

[0030]

[0031] s.t.d min <d i <d max (i = 1, 2, …, M)

[0032] |d i+1 -d i |≥d s (i = 1, 2, …, M - 1)

[0033] where f is the two optimization objective functions, ω1 and ω2 are the weights of the two optimization objectives respectively, N p is the number of target points selected in the uniform region inside the coil, is the coordinate transformation amount of, B z2 (x, y, z) is the coordinate transformation amount of B z2 (ρ, φ, z), (x, y, z) are the three-axis rectangular coordinates, I i is the current of the i-th pair of coils, s.t. is the constraint condition, d s is the minimum distance between adjacent coils after considering the actual machining accuracy, and L is the symbol for omitting the middle term of the sequence.

[0034] The quantum genetic algorithm in Step 5 includes the following steps:

[0035] Step 5.1, initialize the population according to the constraint conditions;

[0036] Step 5.2, obtain the binary encoding through quantum state observation;

[0037] Step 5.3, calculate the classical solution according to the objective function for solution space mapping;

[0038] Step 5.4, record the optimal individual parameters and fitness;

[0039] Step 5.5, determine whether the maximum number of iterations is reached. If not, update the population using the quantum rotation gate and return to Step 5.2. If so, enter Step 5.6;

[0040] Step 5.6, decode the variables and output the optimal individual parameters and fitness.

[0041] Step 5 introduces the quantum genetic algorithm into the field of coil design, solving the problems of being trapped in local optimal solutions and slow convergence rate that often occur in the multi-parameter multi-dimensional optimization problems of traditional algorithms; in the quantum genetic algorithm, each individual is no longer a simple binary encoding, but is represented by quantum bits, which enables a quantum bit to represent multiple states simultaneously, that is, the superposition state of quantum bits; this characteristic greatly increases the dimension of the search space, helping to quickly find the global optimal solution; in addition, the quantum genetic algorithm also introduces the entanglement effect between quantum bits, enabling more efficient exchange and fusion of information between different individuals, further improving the convergence rate and the quality of the solution, and being very suitable for the optimal design of complex coils.

[0042] The technical effects of the present invention are as follows: The present invention provides a design method for a compact ultra-low coupling shimming coil based on a quantum genetic algorithm, which can solve the performance deficiencies of traditional self-shielding coils, such as large volume waste, insufficient uniformity, and incomplete suppression of coupling effects. It transforms the design problem of a compact ultra-low coupling and high-uniformity coil into a non-linear optimal design problem with coil structure parameters as constraints and the uniformity and coupling rate of the coil as optimization objectives. By introducing the quantum genetic algorithm, it solves the problems of slow convergence rate and easy entrapment in local optimal solutions in the complex optimization of multiple parameters of traditional algorithms, and can quickly and effectively obtain high-quality optimization results. Finally, it can achieve the excellent performance of reducing the ultra-low coupling rate by one order of magnitude and improving the internal magnetic field uniformity by one order of magnitude under the same radius configuration as the traditional self-shielding coil. Brief Description of the Drawings

[0043] Figure 1 It is a schematic structural diagram of a cylindrical compact axial ultra-low coupling and high-uniformity circular coil designed by the design method of the present invention. Figure 1 There are a total of five pairs of cylindrical axial coils, symmetrically distributed about the z = 0 plane. A cylindrical coordinate system is established with the center point of the coil as the origin, the z-axis as the axial coordinate axis of the coil, and the r-axis as the radial coordinate axis of the coil. The distance of each pair of coils from the z = 0 plane is d i =[d1, d2,..., d5], where i is the coil serial number, and the radius of each pair of circular coils is the same, all being R. The current passed through each pair of coils is I i =[I1, I2,..., I5], and the number of turns of each pair of coils is n i =[n1, n2,..., n5]. The current direction is represented by symbols.

[0044] Figure 2 It is a schematic diagram of the designed coil in the magnetic shielding barrel environment. Figure 2 The designed coil in it is located inside the magnetic shielding barrel, and R b is the inner radius of the magnetic shielding barrel, and R cis the outer radius of the magnetic shielding barrel, and 2H is the total length of the magnetic shielding barrel. The coil is concentric and coaxial with the magnetic shielding barrel. The designed coil is the coil designed by the design method of the present invention.

[0045] Figure 3 is a comparison diagram of the relative magnetic field deviation between the traditional self-shielding coil and the designed coil in the target area under the same size. Figure 3 In (a), it is the traditional self-shielding coil, with the abscissa y (mm, scale values -20, -10, 0, 10) and the ordinate z (mm, scale values -20, -15, ··· 15). Figure 3 In (b), it is the designed coil. The relative magnetic field deviation is an evaluation index of the coil uniformity. The smaller the relative magnetic field deviation, the more uniform the coil. The relative magnetic field deviation of the coil of the present invention is below the order of magnitude of 10 -4 The target uniform area of the coil is a cube with a side length of R / 2. The figure shows the uniformity of the two coils in the x-y plane of the target area when R = 80 mm.

[0046] Figure 4 is a comparison diagram of the coupling rate between the traditional self-shielding coil and the designed coil in the target area under the same size. Figure 4 In (a), it is the traditional self-shielding coil. Figure 4 In (b), it is the designed coil. The coupling rate is an evaluation index of the coil's ability to suppress the coupling effect. The smaller the coupling rate, the stronger the coil's ability to suppress the coupling effect. The average coupling rate of the coil of the present invention in the target area is less than 0.5%, which is significantly improved compared with the traditional self-shielding coil. The calculation formula of the coupling rate is the ratio of the magnetic field generated by the coupling effect to the total magnetic field generated by the coil under the ferromagnetic boundary.

[0047] Figure 5 is the flow chart of the quantum genetic algorithm optimization. Figure 5 It includes step 1, initializing the population according to the constraint conditions; step 2, obtaining the binary coding through quantum state observation; step 3, calculating the classical solution according to the objective function for solution space mapping; step 4, recording the optimal individual parameters and fitness; step 5, judging whether the maximum number of iterations is reached. If not, updating the population by using the quantum rotation gate and then returning to step 2. If so, entering step 6; step 6, decoding the variables to output the optimal individual parameters and fitness.

[0048] Figure 6 is the iteration process diagram when the quantum genetic algorithm, the classical particle swarm algorithm, and the classical genetic algorithm are simultaneously used for the optimization design of this coil. Figure 6The abscissa is the number of iterations (the scale values are 0, 20, ··· 100), and the ordinate is the fitness value (the scale values are 0.00, 0.01, ··· 0.05). The quantum genetic algorithm involved in the present invention can quickly converge to a better individual, demonstrating excellent global search ability. Detailed implementation mode

[0049] The following combines the accompanying drawings ( Figures 1-6 ) and embodiments to illustrate the present invention.

[0050] Figure 1 It is a schematic diagram of a cylindrical compact axial ultra-low coupling high-uniformity circular coil structure designed by the design method of the present invention. Figure 2 It is a schematic diagram of the designed coil in the magnetic shielding barrel environment. Figure 3 It is a comparison diagram of the relative magnetic field deviation of the target area between the traditional self-shielding coil and the designed coil under the same size. Figure 4 It is a comparison diagram of the coupling rate between the traditional self-shielding coil and the designed coil in the target area under the same size. Figure 5 It is a flow chart of the optimization of the quantum genetic algorithm. Figure 6 It is an iteration process diagram when the quantum genetic algorithm, the classical particle swarm optimization algorithm, and the classical genetic algorithm are simultaneously used for the optimization design of this coil. Refer to Figures 1 to 6 As shown, the design method of the compact ultra-low coupling field homogenizing coil based on the quantum genetic algorithm includes a coil group composed of several pairs of coaxial circular coils with the same radius. Each pair of coaxial circular coils with the same radius is symmetrically distributed about the z = 0 plane. z is the axial coordinate axis of the coil. Each pair of coaxial circular coils with the same radius has its own number of turns. The sum of the number of turns of the forward current and the sum of the number of turns of the reverse current in the coil group are the same, so as to achieve the rapid attenuation of the external magnetic field and the effect of the total magnetic moment being 0. Select target points in the uniform area inside the coil, calculate the magnetic field coupling rate and the magnetic field deviation relative to the center point at each target point respectively, and sum them after assigning weights to the two indicators. The optimal solution is quickly obtained through the quantum genetic algorithm, so as to obtain an axial cylindrical coil group under the same radius structure, which can reduce the coupling rate by one order of magnitude while reducing the maximum relative magnetic field deviation by one order of magnitude.

[0051] It includes the following steps: Step 1, determine the radius R of the circular coil and the maximum value d that each pair of coils can reach from the z = 0 plane according to the structural parameters of the known magnetic shielding barrel max , z is the z-axis coordinate, and the minimum value d that each pair of coils can reach from the z = 0 plane to avoid the light passing hole min , establish the expression d i = [d1, d2, …, d M , i is the coil pair serial number, M is the number of coil pairs, d iis the distance of the i-th pair of coils from the z = 0 plane; Step 2, make the total magnetic moment generated by the coil group equal to 0, and the sum of the number of turns of the positive-direction current is equal to the sum of the number of turns of the reverse-direction current; Step 3, derive the magnetic field analytical formula of the coil under free boundary and ferromagnetic boundary through Biot-Savart law, Green's function expansion, and image method, and use the method of magnetic shielding coupling separation to derive the magnetic field analytical formula of the coil generated additionally due to the coupling effect; Step 4, establish the expressions of two optimization objectives. The first optimization objective is the uniformity of the magnetic field generated by the coil, which is represented by the relative magnetic field deviation. The second optimization objective is the ability of the coil to suppress the coupling effect, which is represented by the coupling rate of the coil, that is, the proportion of the magnetic field generated by the coupling effect in the total magnetic field. Assign different weights to the two optimization objectives and sum them up as the expression of the final optimized objective function; Step 5, substitute the determined coil structure parameters, use the quantum genetic algorithm to optimize the optimization objective. After obtaining the optimization result, respectively perform finite element simulations of the traditional self-shielding coil and the designed axial circular coil group of the same size in free space and ferromagnetic boundary, and compare the uniformity and the performance of suppressing the coupling effect of the two to verify the effectiveness of the design.

[0052] The said Step 3 includes:

[0053]

[0054] where B z1 (ρ, φ, z) is the magnetic field generated by the axial cylindrical coil under free boundary, (ρ, φ, z) are the cylindrical coordinates of any point inside the coil, ρ is the radial coordinate, φ is the angular coordinate, z is the z-axis coordinate, μ0 is the vacuum permeability, R is the radius of the circular coil, e is the natural constant, i is the imaginary unit, k is the integration variable, I0 and K0 respectively represent the modified Bessel functions of the first kind and the second kind of order 0, and I0’ and K0’ respectively represent their derivatives, is the Fourier transform of the axial coil current density:

[0055]

[0056] where, M is the number of pairs of coils, I is the current passing through the coil, n i = [n1, n2, …, n M , n i is the number of turns of the i-th pair of coils;

[0057]

[0058] α b = μ0(μ r - 1)I0′(kR)K0(kR b ),

[0059] βb = μ0(μ r I0(kR b )K0′(kR b ) - I0′(kR b )K0(kR b )),

[0060] γ b = μ0(μ r - 1)I0(kR b )K0′(kR c ),

[0061] α c = μ0(μ r - 1)I0′(kR)K0(kR c ),

[0062] β c = μ0(μ r - 1)I0′(kR b )K0(kR c ),

[0063] γ c = μ0(μ r I0′(kR c )K0(kR c ) - I0(kR c )K0′(kR c )),

[0064]

[0065] where B z2 (ρ, φ, z) is the magnetic field generated by an axial cylindrical coil under a ferromagnetic boundary, K1 is the modified second kind of Bessel function of the first order, G(k), α c , γ b , α b , γ c , β c , β b are all intermediate quantities, μ r is the relative magnetic permeability of the magnetic shielding material, R b is the inner radius of the magnetic shielding barrel, R c is the outer radius of the magnetic shielding barrel, is the Fourier transform of the current density after being changed by the reflected current of the end cover of the shielding barrel on the coil, H is the half-length of the shielding barrel, p is the number of current reflections, is the additional magnetic field generated by the coupling effect of the axial cylindrical coil under the ferromagnetic boundary.

[0066] The expressions included in Step 4 are as follows:

[0067]

[0068] s.t.d min <d i <d max (i = 1, 2, …, M)

[0069] |d i+1 -d i |≥d s (i = 1, 2, …, M - 1)

[0070] where f are two optimization objective functions, ω1 and ω2 are the weights of the two optimization objectives respectively, N p is the number of target points selected in the uniform region inside the coil, is the coordinate transformation quantity of, B z2 (x, y, z) is the coordinate transformation quantity of B z2 (ρ, φ, z), (x, y, z) are the three-axis rectangular coordinates, I i is the current of the i-th pair of coils, s.t. is the constraint condition, d s is the minimum distance between adjacent coils considering the actual machining accuracy, L is the symbol for omitting the middle term of the sequence.

[0071] The quantum genetic algorithm in step 5 includes the following steps: Step 5.1, initialize the population according to the constraint conditions; Step 5.2, obtain the binary encoding through quantum state observation; Step 5.3, calculate the classical solution according to the objective function for solution space mapping; Step 5.4, record the optimal individual parameters and fitness; Step 5.5, judge whether the maximum number of iterations is reached. If not, update the population using the quantum rotation gate and return to Step 5.2. If so, enter Step 5.6; Step 5.6, decode the variables to output the optimal individual parameters and fitness.

[0072] Step 5 introduces the quantum genetic algorithm into the field of coil design, solving the problems of getting stuck in local optimal solutions and slow convergence speed that often occur in traditional algorithms for multi-parameter multi-dimensional optimization problems; in the quantum genetic algorithm, each individual is no longer a simple binary encoding, but is represented by qubits, which enables a qubit to represent multiple states simultaneously, that is, the superposition state of qubits; this characteristic greatly increases the dimension of the search space, helping to quickly find the global optimal solution; in addition, the quantum genetic algorithm also introduces the entanglement effect between qubits, enabling more efficient exchange and fusion of information between different individuals, further improving the convergence speed and quality of the solution, and is very suitable for the optimal design of complex coils.

[0073] A design method of a compact ultra-low coupling shimming coil based on a quantum genetic algorithm can solve the problems of large volume waste, incomplete suppression of coupling effects, and insufficient uniformity of traditional self-shielded circular coils, and belongs to the field of precision magnetic field control technology. The ultra-low coupling shimming coil design method based on the quantum genetic algorithm of the present invention includes five pairs of axial cylindrical coils with the same radius and symmetric about the z = 0 plane. Their current directions and number of turns are different and are obtained from the simplified multipole moment expansion formula. The coil design problem is transformed into a non-linear optimization design problem with the coil structure parameters as constraints and the uniformity and coupling rate of the coil as optimization objectives. The quantum genetic algorithm is used to solve this problem, so that the coil structure parameters with excellent performance can be obtained with high quality and efficiency. The designed coil can achieve excellent performance of improving the uniformity by one order of magnitude and reducing the coupling rate by one order of magnitude in a larger target area under the configuration of the same radius, and is applicable to application scenarios such as precision magnetic field measurement and biological weak magnetic field detection.

[0074] The ultra-low coupling shimming coil design method based on the quantum genetic algorithm includes cylindrical axial coils with the same radius structure and different current directions. Through the fast convergence and stronger global search ability of the quantum genetic algorithm, the structure parameters of the coil are optimized and designed to reduce the relative magnetic field deviation in the central target area and improve the coil uniformity to the ten-thousandth level, and reduce the coupling rate by one order of magnitude through the magnetic shielding coupling separation method.

[0075] The present invention provides a design method of a compact ultra-low coupling shimming coil based on a quantum genetic algorithm, which solves the problems of large volume waste, incomplete suppression of coupling effects, and insufficient uniformity of traditional self-shielded coils. Based on the quantum genetic algorithm of the present invention, by optimizing the total objective function composed of two indexes, namely the uniformity and coupling rate of the magnetic field generated by the coil, the structural parameter results with excellent performance are obtained. As Figure 1 shown, the coil designed by the present invention is an axial circular structure with the same radius, and there are five pairs in total, symmetrically distributed about the z = 0 plane. The distance of each pair of coils from the z = 0 plane is d i = [d1, d2,..., d5], the radius of each pair of circular coils is the same, all of which are R. The current passed through each pair of coils is I i = [I1, I2,..., I5], and the number of turns of each pair of coils is n i = [n1, n2,..., n5]. The symbol represents the direction of the current.

[0076] In quantum computing, a qubit is the basic unit of information. It can simultaneously be in a superposition state of 0 and 1. This property gives quantum computing significant advantages when dealing with large amounts of information. The quantum genetic algorithm draws on this feature. By introducing qubits, the individuals in the algorithm can represent and simultaneously explore multiple possible solutions, thus greatly expanding the search space. In addition, the quantum genetic algorithm also introduces the entanglement effect between qubits, enabling more efficient exchange and fusion of information between different individuals, further improving the convergence speed and the quality of the solution, and being very suitable for the optimal design of complex coils. As Figure 5 shown, it is the flowchart of the quantum genetic algorithm. Traditional intelligent optimization algorithms often suffer from problems such as getting trapped in local optimal solutions and slow convergence speed. For the multi-parameter multi-dimensional optimization problem of complex coils, these defects are further magnified. The quantum genetic algorithm is more suitable for the optimization of such problems. As Figure 6 shown, the iteration curves of the classical particle swarm algorithm, the classical genetic algorithm, and the quantum genetic algorithm in solving the same coil optimization problem in the present invention are compared. It can be seen that the quantum genetic algorithm can quickly converge to a better individual, demonstrating excellent global search ability.

[0077] A design method of a compact ultra-low coupling shim coil based on the quantum genetic algorithm includes the following steps:

[0078] Step 1, the designed axial circular coil group includes 5 pairs of coils symmetric about the z = 0 plane, and the distance of each pair of coils from the z = 0 plane is d i = [d1, d2,..., d5]. Determine the radius R of the circular coil according to the structural parameters of the known magnetic shielding barrel, and the maximum value d max that each pair of coils can reach from the z = 0 plane, and the minimum value d min。Step 2, referring to the method of self-shielding coil to attenuate the external magnetic field, in order to accelerate the attenuation rate of the external magnetic field of the coil, the total magnetic moment generated by the coil group is set to 0. Since the radius and the current passing through the coils are the same, only the different number of turns of the coils with opposite current directions can be controlled. According to the formula, the sum of the number of turns of the positive-direction current is equal to the sum of the number of turns of the reverse-direction current. Step 3, derive the magnetic field analytical formula of the coil under free boundary and ferromagnetic boundary through Biot-Savart law, Green's function expansion, and mirror method. Use the method of magnetic shielding coupling separation to derive the analytical formula of the additional magnetic field generated by the coil due to the coupling effect. Step 4, establish the expressions of two optimization objectives. The first optimization objective is the uniformity of the magnetic field generated by the coil, which is represented by the relative magnetic field deviation; the second optimization objective is the ability of the coil to suppress the coupling effect, which is represented by the coupling rate of the coil, that is, the proportion of the magnetic field generated by the coupling effect in the total magnetic field. Different weights are assigned to the two optimization objectives and summed up as the final optimization expression. Step 5, substitute the determined coil structure parameters, and use the quantum genetic algorithm to optimize the optimization objectives. After obtaining the optimization results, the traditional self-shielding coil and the designed coil of the same size are respectively simulated by finite element in free space and ferromagnetic boundary, and their uniformity and performance of suppressing the coupling effect in the two environments are compared to verify the effectiveness of the design.

[0079] The steps 3 include the following formulas:

[0080] The magnetic field B generated by the axial cylindrical coil under free boundary z1 The analytical formula is

[0081]

[0082] where (ρ, φ, z) are the cylindrical coordinates of any point inside the coil, μ0 is the vacuum permeability, which is 4×10 7 H / m, R is the radius of the circular coil. I0 and K0 respectively represent the Bessel functions of the first kind and the second kind, and I0' and K0' respectively represent their derivatives. is the Fourier transform of the axial coil current density, which can be expressed as

[0083]

[0084] where M is the number of coil pairs, I is the current passing through the coil, n i =[n1, n2, …, n M is the number of turns of each pair of coils, d i =[d1, d2, …, d M is the distance of each pair of coils from the z = 0 plane.

[0085] The magnetic field B generated by the axial cylindrical coil under ferromagnetic boundary z2 The analytical formula is

[0086]

[0087] Among them, the function G(k) is expressed as

[0088]

[0089] Among them, R b is the inner radius of the magnetic shielding barrel, and R c is the outer radius of the magnetic shielding barrel. Other coefficients involved in the function can be expressed as

[0090] α b = μ0(μ r - 1)I0'(kR)K0(kR b )

[0091] β b = μ0(μ r I0(kR b )K0'(kR b ) - I0'(kR b )K0(kR b ))

[0092] γ b = μ0(μ r - 1)I0(kR b )K0'(kR c )

[0093] α c = μ0(μ r - 1)I0'(kR)K0(kR c )

[0094] β c = μ0(μ r - 1)I0'(kR b )K0(kR c )

[0095] γ c = μ0(μ r I0'(kR c )K0(kR c ) - I0(kR c )K0'(kR c ))

[0096] Among them, μ r is the relative magnetic permeability of the magnetic shielding barrel. After the coil is affected by the reflected current of the shielding barrel end cover, the current density changes, and its Fourier transform can be expressed as

[0097]

[0098] Among them, H is the half-length of the shielding barrel, and p is the number of current reflections.

[0099] The additional magnetic field B generated by the axial cylindrical coil under the ferromagnetic boundary due to the coupling effect oz The analytical formula is

[0100]

[0101] The optimization of the said step 4 for the model is as follows:

[0102]

[0103] s.t.d min <d i <d max (i = 1, 2, L, M)

[0104] |d i+1 -d i |≥d s (i = 1, 2, L, M - 1)

[0105] Among them, N p is the number of target points selected in the uniform area inside the coil, ω1 and ω2 are the weights of the two optimization objectives respectively, d max is the maximum value that each pair of coils can reach from the z = 0 plane, d min is the minimum value that each pair of coils can reach from the z = 0 plane to avoid the light aperture, d s is the minimum distance between adjacent coils after considering the actual machining accuracy.

[0106] The content not described in detail in the specification of the present invention belongs to the prior art well-known to those skilled in the art. It is hereby pointed out that the above description helps those skilled in the art to understand the present invention, but does not limit the protection scope of the present invention. Any implementation that makes equivalent substitutions, modifications, improvements, and / or simplifies the above description without departing from the essence of the present invention falls within the protection scope of the present invention.

Claims

1. A design method of a compact ultra-low coupling shimming coil based on a quantum genetic algorithm, characterized in that It includes a coil group composed of several pairs of axially circular coils with the same radius. Each pair of axially circular coils with the same radius is symmetrically distributed with respect to the plane of z = 0, where z is the axial coordinate axis of the coil. Each pair of axially circular coils with the same radius has its own number of turns. The sum of the number of turns of the forward current and the sum of the number of turns of the reverse current in the coil group are the same, so as to achieve the rapid attenuation of the external magnetic field and the effect of the total magnetic moment being 0. Select target points in the uniform region inside the coil, calculate the magnetic field coupling rate and the magnetic field deviation relative to the center point at each target point respectively, and sum them after assigning weights to the two indicators. The optimal solution can be quickly obtained through the quantum genetic algorithm, so as to obtain an axially cylindrical coil group with the same radius structure, which can reduce the coupling rate by one order of magnitude while the maximum relative magnetic field deviation is also reduced by one order of magnitude.

2. The design method of a compact ultra-low coupling shim coil based on a quantum genetic algorithm according to claim 1, characterized in that It includes the following steps: Step 1: Determine the radius R of the circular coil and the maximum value d that each pair of coils can reach from the z = 0 plane according to the structural parameters of the known magnetic shielding barrel max , where z is the z-axis coordinate, and the minimum value d that each pair of coils can reach from the z = 0 plane to avoid the light aperture min , and establish the expression d i = [d1, d2, …, d M , where i is the coil pair serial number, M is the number of coil pairs, and d i is the distance of the i-th pair of coils from the z = 0 plane; Step 2: Let the total magnetic moment generated by the coil group be 0, and the sum of the number of turns of the forward current is equal to the sum of the number of turns of the reverse current; Step 3: Derive the magnetic field analytical formula of the coil under free boundary and ferromagnetic boundary through the Biot-Savart law, Green's function expansion, and mirror method. Use the method of magnetic shielding coupling separation to derive the magnetic field analytical formula of the coil generated additionally due to the coupling effect; Step 4: Establish expressions for two optimization objectives. The first optimization objective is the uniformity of the magnetic field generated by the coil, which is represented by the relative magnetic field deviation. The second optimization objective is the ability of the coil to suppress the coupling effect, which is represented by the coupling rate of the coil, that is, the proportion of the magnetic field generated by the coupling effect in the total magnetic field. Assign different weights to the two optimization objectives and sum them as the expression of the final optimization objective function; Step 5: Substitute the determined coil structure parameters, use the quantum genetic algorithm to optimize the optimization objectives. After obtaining the optimization results, respectively perform finite element simulations of the traditional self-shielding coil with the same size and the designed axially circular coil group in free space and ferromagnetic boundary, and compare the uniformity and the performance of suppressing the coupling effect of the two to verify the effectiveness of the design.

3. The method for designing a compact ultra-low coupling shim coil based on a quantum genetic algorithm according to claim 2, wherein Step 3 includes: where B z1 (ρ, φ, z) is the magnetic field generated by an axially cylindrical coil under free boundaries, (ρ, φ, z) are the cylindrical coordinates of any point inside the coil, ρ is the radial coordinate, φ is the angular coordinate, z is the z-axis coordinate, μ0 is the magnetic permeability of vacuum, R is the radius of the circular coil, e is the natural constant, i is the imaginary unit, k is the integration variable, I0 and K0 represent the modified Bessel functions of the first and second kind respectively, and I0’ and K0’ represent their derivatives respectively, is the Fourier transform of the axial coil current density, expressed as follows: where M is the number of pairs of coils, I is the current passing through the coils, and n i = [n1, n2, …, n M , and n i is the number of turns of the i-th pair of coils; α b = μ0(μ r - 1)I0′(kR)K0(kR b ) β b = μ0(μ r I0(kR b )K0′(kR b ) - i0′(kR b )K0(kR b )) γ b = μ0(μ r - 1)I0(kR b )K0′(kR c ), α c = μ0(μ r - 1)I0′(kR)K0(kR c ) β c = μ0(μ r - 1)I0′(kR b )K0(kR c ), γ c = μ0(μ r I0′(kR c )K0(kR c ) - I0(kR c )K0′(kR c )) where B z2 (ρ, φ, z) is the magnetic field generated by an axial cylindrical coil under a ferromagnetic boundary, K1 is the first-order Bessel function of the second kind, G(k), α c , γ b , α b , γ c , β c , β b are all intermediate quantities, μ r is the relative permeability of the magnetic shielding material, R b is the inner radius of the magnetic shielding barrel, R c is the outer radius of the magnetic shielding barrel, is the Fourier transform of the current density after being changed due to the influence of the reflected current from the end cap of the shielding barrel, H is the half-length of the shielding barrel, p is the number of times of current reflection, is the additional magnetic field generated by the axial cylindrical coil under the ferromagnetic boundary due to the coupling effect.

4. The method for designing a compact ultra-low coupling shim coil based on a quantum genetic algorithm according to claim 2, characterized in that, Step 4 includes the following expressions: s.t.d min <d i <d max (i = 1, 2, …, M) |d i+1 -d i |≥d s (i = 1, 2, …, M - 1) where f are two optimization objective functions, ω1 and ω2 are the weights of the two optimization objectives respectively, and N p is the number of target points selected in the uniform region inside the coil, is the coordinate transformation quantity of, B z2 (x, y, z) is the coordinate transformation quantity of B z2 (ρ, φ, z), (x, y, z) are the three-axis rectangular coordinates, I i is the current of the i-th pair of coils, s.t. is the constraint condition, d s is the minimum distance between adjacent coils after considering the actual machining accuracy, and L is the symbol for omitting the middle term of the sequence.

5. The compact ultra-low coupling shim coil design method based on quantum genetic algorithm according to claim 2, characterized in that The quantum genetic algorithm in Step 5 includes the following steps: Step 5.1: Initialize the population according to the constraint conditions; Step 5.2: Obtain the binary encoding through quantum state observation; Step 5.3: Calculate the classical solution according to the objective function and perform the solution space mapping; Step 5.4: Record the optimal individual parameters and fitness; Step 5.5: Judge whether the maximum number of iterations is reached. If not, update the population using the quantum rotation gate and return to Step 5.

2. If so, enter Step 5.6; Step 5.6: Decode the variable and output the optimal individual parameters and fitness.

6. The compact ultra-low coupling shim coil design method based on quantum genetic algorithm according to claim 2, characterized in that, Step 5 introduces the quantum genetic algorithm into the field of coil design, solving the problems of getting stuck in local optimal solutions and slow convergence rate that often occur in the multi-parameter multi-dimensional optimization problems of traditional algorithms; in the quantum genetic algorithm, each individual is no longer a simple binary code, but is represented by quantum bits, which enables a quantum bit to represent multiple states simultaneously, that is, the superposition state of quantum bits; this characteristic greatly increases the dimension of the search space, helping to quickly find the global optimal solution; in addition, the quantum genetic algorithm also introduces the entanglement effect between quantum bits, enabling more efficient exchange and fusion of information between different individuals, further improving the convergence rate and quality of the solution, and is very suitable for the optimal design of complex coils.

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