A Design Method of Magneto-Optical Trap Gradient Magnetic Field Coil Based on Cuckoo Search Algorithm

Abstract

A design method of the gradient magnetic field coil for magneto-optical trap based on the cuckoo search algorithm, which relates to the field of the gradient magnetic field coil design in the three-dimensional magneto-optical trap, solves the problems that the calculation complexity of the coil parameters increases in the existing design methods of the gradient magnetic field coil and the method of manually designing the coil parameters is relatively inefficient, and includes the following steps: Step S1: Initialize the algorithm parameters; Step S2: Set the initial parameters of the gradient magnetic field coil for the magneto-optical trap; Step S3: Construct the magnetic field strength model and the magnetic field gradient model on the axis of the gradient magnetic field coil; Step S4: Set the objective function to be optimized; Step S5: Use the cuckoo search algorithm to iteratively optimize the parameters of the objective function; Step S6: Output the optimized parameters and the optimized results. According to this method, it is convenient to quickly design the parameters of the gradient magnetic field coil for the magneto-optical trap according to the requirements, so as to meet the magnetic field requirements of the atomic gravimeter for the atomic capture efficiency and the cooling quality.

Description

Technical Field

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

[0002] The development of atomic interferometric gravimeters began in the 1990s. With the progress of laser cooling atomic technology, this new type of gravimeter has gradually become one of the important technologies for absolute gravity measurement. Atomic interferometric gravimeters achieve interference by dropping or throwing up a cloud of cold atoms in a vacuum, and generally use magneto-optical trap technology to capture and cool atoms to form a cold atom cloud. In an atomic interferometric gravimeter, the design parameters of the gradient magnetic field coil are crucial for achieving an efficient and uniform magnetic field gradient, which directly affect the performance and application effect of the magneto-optical trap. By precisely designing these parameters, the capture and cooling processes 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 coil in a magneto-optical trap usually uses an anti-Helmholtz coil to generate a gradient magnetic field. This coil consists of two coils with reverse currents, which can generate a linearly varying magnetic field in its central region. The design of the coil needs to ensure that the magnetic field gradient is moderate to effectively confine 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 for the performance of the magneto-optical trap. The main parameter designs include 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. In the design, it is necessary to determine the required magnetic field gradient value, and then adjust the various parameters between the coils to achieve the required magnetic field. With the improvement of system performance, the calculation complexity of coil parameters has increased significantly, and the method of manually designing coil parameters is relatively inefficient. In view of this, the present invention proposes a method for designing a gradient magnetic field coil of a magneto-optical trap based on the cuckoo search algorithm, which can provide certain reference for scientific researchers when designing a gradient magnetic field coil of a magneto-optical trap. Summary of the Invention

[0005] In order to solve the problems that the existing design method of the gradient magnetic field coil has an increased calculation complexity of coil parameters and the method of manually designing coil parameters is relatively inefficient, the present invention provides a method for designing a gradient magnetic field coil of a magneto-optical trap based on the cuckoo search algorithm.

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

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

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

[0009] Step 3: Construct the magnetic field strength model and magnetic field gradient model on the axis of the gradient magnetic field coil;

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

[0011] Set the objective function F = P + aN. According to the number of coil turns N and the coil heating power P, adjust the weights of the number of coil turns N and the coil heating power P by setting the adjustable parameter a to achieve the comprehensive optimization of the number of 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] Use the cuckoo search algorithm to iterate the parameters of the objective function described in Step 4. Consider each nest as a potential solution, and retain the solution with the highest fitness; in each iteration, update the position of the nest, search for a better solution, and there is a certain probability of discarding the worse solution or reconstructing a new solution; perform global and local searches through the Levy flight strategy to obtain the optimized global optimal solution;

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

[0015] Advantages 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 with an adjustable parameter, taking into account both the number of coil turns and the coil heating power. The cuckoo optimization algorithm is used to optimize the design of three parameters, namely the distance between two identical coaxial toroidal coils, the coil radius, and the current intensity in the coil, in the magneto-optical trap gradient magnetic field coil, effectively improving the calculation efficiency of multi-parameter optimization of the coil. This method can provide a reference for researchers in designing the magneto-optical trap gradient magnetic field coil. Description of the Drawings

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

[0017] Figure 2 is a flowchart of the cuckoo search algorithm;

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

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

[0020] Figure 5 For the fitness evolution curve of the optimization process;

[0021] Figure 6 For the magnetic field intensity distribution map after optimization;

[0022] Figure 7 For the magnetic field gradient distribution map after optimization. Specific implementation manner

[0023] Combined with Figures 1 to 7 This implementation manner will be described. A method for designing a gradient magnetic field coil of a magneto - optical trap based on the cuckoo search algorithm specifically includes the following steps:

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

[0025] In this implementation manner, 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 discovery probability;

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

[0027] In this implementation manner, the gradient magnetic field coil of the magneto - optical trap is set to include a pair of anti - Helmholtz coils. As Figure 3 shown, the anti - Helmholtz coil is composed of two identical co - axial toroidal coils, and reverse currents flow through these two coils. 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 varies linearly in this region.

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

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

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

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

[0032] In this implementation manner, the Biot - Savart law is used to calculate the magnitude of 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:

[0033]

[0034] Wherein, μ0 is the magnetic permeability of vacuum, N is the number of turns of the coil, I is the current in the coil, R is the radius of the coil, d is the distance between the center position 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] From this, it can be obtained that the magnetic field gradient at z = 0 is:

[0038]

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

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

[0041] It comprehensively considers the number of turns N of the coil and the heating power P of the coil, and adjusts the weights of the number of turns N of the coil and the heating power P by setting the adjustable parameter α, so as to realize the comprehensive optimization of the number of turns N of the coil and the heating power P in the objective function.

[0042] Among them, the numerical value of the magnetic field gradient at z = 0 to be designed needs to be given In this embodiment, the designed numerical value of the magnetic field gradient is c = 0.1 T / m; from the formula it can be obtained In addition, the heating power of the anti-Helmholtz coil

[0043] Wherein, 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: Use the cuckoo search algorithm to iteratively optimize the parameters of the objective function; transform the problem of setting the coil parameters into the problem of solving the optimal solution of the objective function, which greatly improves the calculation efficiency of the multi-parameter optimization of the coil.

[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, and the fitness function is used to evaluate the quality of these solutions, 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 discarding the worse solution or reconstructing a new solution. The cuckoo search algorithm enhances the search ability through Levy flight, which is a random walk method, and its step size follows the Levy distribution, enabling the algorithm to have both local search ability and strong global search ability. The cuckoo search algorithm can effectively balance global exploration and local exploitation, and maintain the diversity of the population. Research shows that the cuckoo search algorithm can converge to the global optimum and has good convergence performance.

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

[0047] Step A: Initialize the position of the bird's nest;

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

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

[0050] Step D: Determine whether to discard or retain the bird's nest according to the discovery probability Pa;

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

[0052]

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

[0054] Step E: Update the optimal bird's nest position and the optimal solution (objective function F), increment the iteration count by 1, and return to Step B.

[0055] In this embodiment, the cuckoo search algorithm enhances its search ability through Levy flight, which is a random walk method. Its step size follows the Levy distribution, enabling the algorithm to have both local search ability and strong global search ability during the search process. The cuckoo search algorithm can effectively balance global exploration and local exploitation and maintain the diversity of the population. Research shows that the cuckoo search algorithm can converge to the global optimum and has good convergence performance.

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

[0057] The formula for Levy flight to generate random solutions is as follows:

[0058]

[0059] In the formula, 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 a random step size that follows the Levy distribution. The method is as follows:

[0060]

[0061] where μ~N(0,σ 2 ), v~N(0,1), that is, both follow the normal distribution;

[0062] And,

[0063] In the formula, Γ is the gamma function. To make the method have better convergence ability and global search ability, α = 1 and β = 1.5 are taken in the formula. If the maximum number of iterations reaches 200 times, the process stops; otherwise, continue iterative optimization.

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

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

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

[0067] The above-described embodiments merely represent several implementation manners of the present invention. The description is relatively specific and detailed, but it should not be construed as a limitation on the scope of the invention patent. It should be noted that for those of ordinary skill in the art, without departing from the concept of the present invention, several modifications and improvements can still be made, and these all belong to the protection scope of the present invention. Therefore, the protection scope of the present invention patent shall be subject to the appended claims.

Claims

1. A design method for the gradient magnetic field coil of a magneto-optical trap based on the cuckoo search algorithm, characterized in that: This method is implemented by the following steps: Step 1: Initialize the parameters of the cuckoo search algorithm; Step 2: Set the initial parameters of the magneto-optical trap gradient magnetic field coil; The magneto-optical trap gradient magnetic field coil includes a pair of anti-Helmholtz coils. The anti-Helmholtz coils are composed of two identical coaxial toroidal coils, and reverse currents are passed through the two identical coaxial toroidal coils; Set the initial parameter range to be optimized for the anti-Helmholtz coil, that is: the search boundary X of the cuckoo search algorithm min = [d1, I1, R1], X max = [d2, I2, R2], where d1, I1, R1, d2, I2, R2 are the lower and upper bounds of d, I, R respectively; the distance D between two identical coils = 2d, d is the distance between the center position of two identical coaxial toroidal coils and the center of the circle, R is the average radius of the coil, and I is the current intensity in the coil; Step 3: Construct a magnetic field strength model and a magnetic field gradient model on the axis of the gradient magnetic field coil; Use the Biot-Savart law to calculate the magnitude of 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: Where, μ0 is the vacuum permeability, N is the number of turns of the coil, and z is the position in the vertical direction; Determine the magnetic field gradient value at z = 0 according to the set objective function From the formula we get In addition, the coil heating power of the anti-Helmholtz coil is: Where, 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; Step 4: Set the objective function to be optimized; Set the objective function F = P + aN. According to the number of turns N of the coil and the heating power P of the coil, by setting the adjustable parameter a to adjust the weights of the number of turns N of the coil and the heating power P of the coil, the comprehensive optimization of the number of turns N of the coil and the heating power P in the objective function is realized; Step 5: Use the cuckoo search algorithm to iteratively optimize the parameters of the objective function; Use the cuckoo search algorithm to iterate the parameters of the objective function described in Step 4. 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, search for 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 to 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 the cuckoo search algorithm according to claim 1, wherein: The cuckoo search algorithm parameters described in Step 1 include the number of solutions per 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 the cuckoo search algorithm according to claim 1, wherein: In Step 5, the specific process of iterative optimization using the cuckoo search algorithm is as follows: Step A: Initialize the position of the bird's nest; 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 position of the bird's nest, calculate and compare the fitness values of two generations of bird's nests, and update the bird's nest with the better fitness value; Step D: Determine whether to discard or replace the bird's nest according to the discovery probability Pa; The formula for discarding and replacing the bird's nest is as follows: where X t is the t-th generation of bird nests, γ and ε are random numbers following a uniform distribution, Pa is the discovery probability, with Pa = 0.25, Heaviside(x) is the step function, where Heaviside(x) = 1 when x ≥ 0 and 0 otherwise, X i , X j are any other two bird nests, is the dot product operation; Step E: Update the position of the optimal bird's nest and the optimal solution, the number of iterations +1, and return to Step B.

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