Cuckoo search algorithm-based magneto-optical trap gradient magnetic field coil design method

Abstract

The invention discloses a magneto-optical trap gradient magnetic field coil design method based on a cuckoo search algorithm, relates to the field of gradient magnetic field coil design in a three-dimensional magneto-optical trap, and solves the problems that according to an existing gradient magnetic field coil design method, the calculation complexity of coil parameters is increased, and a manual coil parameter design method is low in efficiency. Comprising the following steps: S1, initializing algorithm parameters; s2, setting initial parameters of the magneto-optical trap gradient magnetic field coil; s3, constructing a magnetic field intensity model and a magnetic field gradient model on the axis of the gradient magnetic field coil; s4, setting a target function needing to be optimized; s5, iteratively optimizing various parameters of the target function by adopting a cuckoo search algorithm; and step S6, outputting each optimized parameter and an optimized result. According to the method, the parameters of the magneto-optical trap gradient magnetic field lines can be conveniently and rapidly designed according to requirements, so that the magnetic field requirements of the atom gravimeter on the atom capture efficiency and the cooling quality are met.

Description

Technical Field

[0001] The invention relates to the field of gradient magnetic field coil design in a three-dimensional magneto-optical trap, and in particular to a magneto-optical trap gradient magnetic field coil design method based on a cuckoo search algorithm. Background Art

[0002] The development of atomic interferometer gravimeter began in the 1990s. With the advancement of laser cooling atom technology, this new type of gravimeter has gradually become one of the important technologies for absolute gravity measurement. Atom interferometer gravimeter achieves interference by dropping or throwing a group of cold atoms in a vacuum. Generally, magneto-optical trap technology is used to capture and cool atoms to form a cold atom group. In the atomic interferometer gravimeter, the design parameters of the gradient magnetic field coil are crucial to achieving efficient and uniform magnetic field gradients, and they directly affect the performance and application effect of the magneto-optical trap. By accurately designing these parameters, the capture and cooling process of atoms in the magneto-optical trap can be optimized, providing a basis for high-precision quantum measurement and precision metrology.

[0003] The gradient magnetic field coils in the magneto-optical trap usually use anti-Helmholtz coils to generate gradient magnetic fields. This type of coil consists of two sets of coils with opposite currents, which can generate a linearly changing magnetic field in its central area. The design of the coil needs to ensure that the magnetic field gradient is moderate in order to effectively bind atoms. In addition, in order to reduce power consumption and heat dissipation, the design of the coil usually takes into account the relationship between resistance and current to ensure that the heat generated during operation does not affect the stability of the experiment.

[0004] The design of the gradient magnetic field coil is crucial to the performance of the magneto-optical trap. Its main parameter design includes the distance between the two coils, the coil radius, the current intensity in the coil, etc. These parameters directly affect the distribution and gradient of the magnetic field. The required magnetic field gradient value needs to be determined in the design, and then the required magnetic field is achieved by adjusting the various parameters between the coils. With the improvement of system performance, the calculation complexity of the coil parameters has also increased significantly, and the method of manually designing the coil parameters is relatively inefficient. In view of this, the present invention proposes a magneto-optical trap gradient magnetic field coil design method based on a cuckoo search algorithm, which can provide a certain reference for scientific researchers when designing magneto-optical trap gradient magnetic field coils. Summary of the invention

[0005] The present invention aims to solve the problems that the calculation complexity of coil parameters in the existing design method of gradient magnetic field coil increases, the method of manually designing coil parameters is relatively inefficient, and the like. A design method of magneto-optical trap gradient magnetic field coil based on a cuckoo search algorithm is provided.

[0006] A method for designing a magneto-optical trap gradient magnetic field coil based on a cuckoo search algorithm specifically comprises the following steps:

[0007] Step 1: Initialize the cuckoo search algorithm parameters;

[0008] Step 2, setting the initial parameters of the magneto-optical trap gradient magnetic field coil;

[0009] Step 3: construct a magnetic field intensity model and a magnetic field gradient model on the axis of the gradient magnetic field coil;

[0010] Step 4: Set the objective function to be optimized;

[0011] The objective function F=P+aN is set, and the weights of the coil turns N and the coil heating power P are adjusted by setting an adjustable parameter a according to the coil turns N and the coil heating power P, so as to achieve comprehensive optimization of the coil turns N and the coil heating power P in the objective function;

[0012] Step 5: Use the cuckoo search algorithm to iteratively optimize the parameters of the objective function;

[0013] Iterate the parameters of the objective function described in step 4 of the cuckoo search algorithm, regard each bird's nest as a potential solution, and retain the solution with the highest fitness; in each iteration, update the position of the bird's nest to find a better solution, and there is a certain probability to abandon the poor solution or rebuild a new solution; perform global and local search through the Levy flight strategy to obtain the optimized global optimal solution;

[0014] Step 6: Output the optimized global optimal solution and complete the design of the magneto-optical trap gradient magnetic field coil.

[0015] Beneficial effects of the present invention: The method of the present invention sets the objective function by adjusting the weights of the number of turns and the heating power through an adjustable parameter, taking into account the number of coil turns and the heating power of the coil, and adopts the cuckoo optimization algorithm to optimize the three parameters of the distance between two identical coaxial annular coils in the magneto-optical trap gradient magnetic field coil, the coil radius, and the current intensity in the coil, thereby effectively improving the computational efficiency of the coil multi-parameter optimization. This method can provide a reference for scientific researchers in designing magneto-optical trap gradient magnetic field coils. BRIEF DESCRIPTION OF THE DRAWINGS

[0016] Figure 1 It is a flow chart of a method for designing a magneto-optical trap gradient magnetic field coil based on a cuckoo search algorithm according to the present invention;

[0017] Figure 2 Flowchart for the cuckoo search algorithm;

[0018] Figure 3 It is a schematic diagram of the structure of the magneto-optical trap gradient magnetic field coil;

[0019] Figure 4 This is a schematic diagram of the Levy flight random walk curve;

[0020] Figure 5 The fitness evolution curve for the optimization process;

[0021] Figure 6 This is the distribution diagram of magnetic field intensity after optimization;

[0022] Figure 7 This is the magnetic field gradient distribution diagram after optimization. DETAILED DESCRIPTION

[0023] Combination Figures 1 to 7 The present embodiment is described as a method for designing a magneto-optical trap gradient magnetic field coil based on a cuckoo search algorithm. The method specifically comprises the following steps:

[0024] Step S1: Initialize the cuckoo search algorithm parameters;

[0025] In this implementation, the basic parameters of the cuckoo search algorithm are initialized, including the number of solutions per iteration, the problem dimension, the total number of iterations, and the probability of discovery;

[0026] Step S2: setting the initial parameters of the magneto-optical trap gradient magnetic field coil;

[0027] In this embodiment, the magneto-optical trap gradient magnetic field coil includes a pair of anti-Helmholtz coils, such as Figure 3 As shown in Figure 1, the anti-Helmholtz coil consists of two identical coaxial toroidal coils with opposite currents flowing through them. This design enables the coil to form a magnetic quadrupole field in a small range near its symmetry center, and the magnetic induction intensity B changes linearly in this area.

[0028] Initially set the parameter range of the anti-Helmholtz coil to be optimized, that is, the search boundary of the algorithm;

[0029] X min =[d1,I1,R1],X max =[d2,I2,R2],

[0030] Among them, the distance between the two coils D = 2d, the average radius of the coil R and the current intensity I in the coil, X min , X max They represent the lower and upper bounds of the search range respectively, d1, I1, R1, d2, I2, R2 are the lower and upper bounds of the parameters d, I, R respectively;

[0031] Step S3: constructing a magnetic field intensity model and a magnetic field gradient model on the axis of the gradient magnetic field coil;

[0032] In this embodiment, the Biot-Savart law is used to calculate the magnitude of the magnetic induction intensity of each coil in space, and the magnetic field intensity generated by the pair of anti-Helmholtz coils in the Z-axis direction is:

[0033]

[0034] Where μ0 is the magnetic permeability of vacuum, N is the number of coil turns, I is the current in the coil, R is the radius of the coil, d is the distance between the center of the two coils and the center of the circle, and z is the position in the vertical (Z-axis) direction.

[0035] The magnetic field gradient generated in the Z-axis direction is:

[0036]

[0037] It can be obtained that the magnetic field gradient at z = 0 is:

[0038]

[0039] Step S4: setting the objective function to be optimized;

[0040] In this embodiment, the objective function is set to F=P+aN; wherein P is the heating power of the coil, N is the number of coil turns, and a is an adjustable parameter;

[0041] The coil turns N and the coil heating power P are comprehensively considered, and the weights of the coil turns N and the heating power P are adjusted by setting the adjustable parameter α to achieve comprehensive optimization of the coil turns N and the heating power P in the objective function.

[0042] Among them, the magnetic field gradient value at z = 0 to be designed needs to be given In this embodiment, the magnetic field gradient value required for the design is c = 0.1 T / m; according to the formula have to In addition, the anti-Helmholtz coil heating power

[0043] Among them, c is a constant, ρ is the resistivity of the material used for the coil wire, and r is the cross-sectional radius of the coil wire.

[0044] Step S5: Adopting the cuckoo search algorithm to iteratively optimize the parameters of the objective function; transforming the problem of setting the coil parameters into the problem of solving the optimal solution of the objective function, which greatly improves the computational efficiency of the coil multi-parameter optimization.

[0045] In this embodiment, the cuckoo search algorithm is used to iterate the set objective function. In the algorithm, each bird's nest is regarded as a potential solution. The quality of these solutions is evaluated by the fitness function, and the solution with the highest fitness is retained. In each iteration, the algorithm updates the position of the bird's nest to find a better solution, and there is a certain probability of abandoning a poor solution or rebuilding a new solution. The cuckoo search algorithm enhances the search capability through Levy flight, which is a random walk method. Its step size obeys the Levy distribution, so that the algorithm has both local search capabilities and strong global search capabilities during the search process. The cuckoo search algorithm can effectively balance global exploration and local development and maintain the diversity of the population. Studies have shown that the cuckoo search algorithm can converge to the global optimum and has good convergence performance.

[0046] like Figure 2 As shown in Figure 2, the specific process of iterative optimization using the cuckoo search algorithm is as follows:

[0047] Step A, initializing the bird's nest position;

[0048] Step B, determine whether the maximum number of iterations has been reached, if so, output the result (including d, I, R, N, P and F), and end; otherwise, execute step C;

[0049] Step C, generate a new bird's nest position, calculate and compare the fitness values ​​of the two generations of bird's nests, and update the bird's nest with a better fitness value;

[0050] Step D: Determine whether to abandon or keep the bird's nest based on the discovery probability Pa;

[0051] In this embodiment, the formula for abandoning and replacing the bird's nest is as follows:

[0052]

[0053] Where, X t represents the t-th generation bird nest, γ and ε are random numbers that obey uniform distribution, Pa is the discovery probability, in this implementation, Pa=0.25, Heaviside(x) is a step function, when x≥0, Heaviside(x)=1, otherwise it is 0, X i , X j are any two other bird's nests, It is a .* operation;

[0054] Step E: Update the optimal nest position and the optimal solution (objective function F), the number of iterations + 1, and return to step B.

[0055] In this embodiment, the cuckoo search algorithm enhances the search capability through Levy flight, which is a random walk method whose step size obeys Levy distribution, so that the algorithm has both local search capability and strong global search capability during the search process. The cuckoo search algorithm can effectively balance global exploration and local development and maintain the diversity of the population. Studies have shown that the cuckoo search algorithm can converge to the global optimum and has good convergence performance.

[0056] like Figure 4 As shown, in this embodiment, Figure 4 Schematic diagram of the Levy flight random walk curve.

[0057] The formula for generating random solutions using Levy flight is as follows:

[0058]

[0059] Where α is the step size scaling factor, Levy(β) is the Levy random path, is the .* operation; Levy(β) uses the Mantegna method to generate random steps that follow the Levy distribution as follows:

[0060]

[0061] Among them, μ~N(0,σ 2 ), v~N(0,1), that is, both obey normal distribution;

[0062] and,

[0063] In the formula, Γ is the gamma function. In order to make the method have better convergence ability and global search ability, α=1, β=1.5 in the formula. If the maximum number of iterations reaches 200, stop, otherwise continue iterative optimization.

[0064] Step S6: Output the optimized parameters and the optimized results; use the optimized results to provide intuitive data display.

[0065] The optimized parameters include the distance d between the center positions of the two coils and the center of the circle, the current I in the coil, the coil radius R, the number of coil turns N, the coil heating power P and the objective function F. Figure 5-Figure 7 As shown, in this embodiment, the corresponding optimization process, as well as the results of the optimized coil parameters and the objective function can be output. Figure 5 Provide intuitive data display for the fitness evolution curve of the optimization process. Figure 6 This is the distribution diagram of magnetic field intensity after optimization; Figure 7 This is the magnetic field gradient distribution diagram after optimization.

[0066] The technical features of the above-mentioned embodiments can be combined arbitrarily. In order to make the description concise, not all possible combinations of the technical features in the above-mentioned embodiments are described. However, as long as there is no contradiction in the combination of these technical features, they should be considered to be within the scope of this specification.

[0067] The above-mentioned embodiments only express several implementation methods of the present invention, and the descriptions thereof are relatively specific and detailed, but they cannot be understood as limiting the scope of the invention patent. It should be pointed out that, for ordinary technicians in this field, several variations and improvements can be made without departing from the concept of the present invention, and these all belong to the protection scope of the present invention. Therefore, the protection scope of the patent of the present invention shall be subject to the attached claims.

Claims

1. A design method for a magneto-optical trap gradient magnetic field coil based on a cuckoo search algorithm, characterized in that: The method is implemented by the following steps: Step 1: Initialize the cuckoo search algorithm parameters; Step 2, setting the initial parameters of the magneto-optical trap gradient magnetic field coil; Step 3: construct a magnetic field intensity model and a magnetic field gradient model on the axis of the gradient magnetic field coil; Step 4: Set the objective function to be optimized; The objective function F=P+aN is set, and the weights of the coil turns N and the coil heating power P are adjusted by setting an adjustable parameter a according to the coil turns N and the coil heating power P, so as to achieve comprehensive optimization of the coil turns N and the coil heating power P in the objective function; Step 5: Use the cuckoo search algorithm to iteratively optimize the parameters of the objective function; Iterate the parameters of the objective function described in step 4 of the cuckoo search algorithm, regard each bird's nest as a potential solution, and retain the solution with the highest fitness; in each iteration, update the position of the bird's nest to find a better solution, and perform global and local searches through the Levy flight strategy to obtain the optimized global optimal solution; Step 6: Output the optimized global optimal solution and complete the design of the magneto-optical trap gradient magnetic field coil.

2. The method for designing a magneto-optical trap gradient magnetic field coil based on a cuckoo search algorithm according to claim 1, characterized in that: The cuckoo search algorithm parameters described in step 1 include the number of solutions for each iteration, the problem dimension, the total number of iterations, and the discovery probability.

3. The method for designing a magneto-optical trap gradient magnetic field coil based on a cuckoo search algorithm according to claim 1, characterized in that: The magneto-optical trap gradient magnetic field coil described in step 2 includes a pair of anti-Helmholtz coils, which are composed of two identical coaxial annular coils, and opposite currents flow through the two identical coaxial annular coils.

4. The method for designing a magneto-optical trap gradient magnetic field coil based on a cuckoo search algorithm according to claim 3, characterized in that: Set the initial parameter range of the anti-Helmholtz coil to be optimized, that is, the search boundary X of the cuckoo search algorithm min =[d1,I1,R1],X max =[d2,I2,R2], where d1, I1, R1 and d2, I2, R2 are the lower and upper limits of d, I, and R respectively; the distance D between two identical coils = 2d, d is the distance between the center position of two identical coaxial annular coils and the center of the circle, R is the average radius of the coil, and I is the current intensity in the coil.

5. The method for designing a magneto-optical trap gradient magnetic field coil based on a cuckoo search algorithm according to claim 4, characterized in that: In step 3, the Biot-Savart law is used to calculate the magnetic induction intensity of each coil in space. The magnetic field intensity generated by the pair of anti-Helmholtz coils in the Z-axis direction is: The magnetic field gradient generated in the z-axis direction is: Then: The magnetic field gradient at z = 0 is: Wherein, μ0 is the magnetic permeability of vacuum, N is the number of coil turns, and z is the position in the vertical (Z-axis) direction.

6. The method for designing a magneto-optical trap gradient magnetic field coil based on a cuckoo search algorithm according to claim 5, characterized in that: According to the set objective function, determine the magnetic field gradient value at z = 0 T / m; By formula have to In addition, the total heating power of the anti-Helmholtz coil is: Among them, c is a constant, ρ is the resistivity of the material used for the coil wire, and r is the cross-sectional radius of the coil wire.

7. The method for designing a magneto-optical trap gradient magnetic field coil based on a cuckoo search algorithm according to claim 1, characterized in that: In step 5, the specific process of iterative optimization using the cuckoo search algorithm is as follows: Step A, initializing the bird's nest position; Step B: Determine whether the maximum number of iterations has been reached. If so, output the result and end; otherwise, execute step C; Step C, generate a new bird's nest position, calculate and compare the fitness values ​​of the two generations of bird's nests, and update the bird's nest with a better fitness value; Step D: Determine whether to abandon or replace the bird's nest based on the discovery probability Pa; The formula for abandoning and replacing the bird's nest is as follows: Where, X t is the t-th generation bird nest, γ and ε are random numbers that obey uniform distribution, Pa is the discovery probability, in this implementation, Pa=0.25, Heaviside(x) is a step function, when x≥0, Heaviside(x)=1, otherwise it is 0, X i , X j For any other two bird nests, It is the .* operation; Step E: Update the optimal nest position and optimal solution, increase the number of iterations by 1, and return to step B.

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