Multi-pole magnetic trap magnetic flux distribution prediction method, device and equipment

Abstract

The invention relates to the technical field of plasma energy engineering, and discloses a multi-pole magnetic trap magnetic flux distribution prediction method, device and equipment, and the method comprises the steps: constructing a neural network architecture comprising a magnetic flux neural network, a plasma current neural network and a convolution differential operator, and outputting total magnetic flux distribution through the magnetic flux neural network, the plasma current neural network is utilized to obtain the plasma current density from the total magnetic flux distribution and obtain a first constraint condition, meanwhile, a convolution differential operator is combined to obtain a second constraint condition from the total magnetic flux distribution, and a prediction result is determined by comparing convergence errors of the two constraint conditions. Physical constraints are introduced through a convolution differential operator, the problem of large deviation between magnetic flux distribution prediction and reality caused by lack of physical constraints of a common neural network is solved, and meanwhile, through feedback coupling between the magnetic flux neural network and the plasma current neural network, the convergence and stability of the model are improved, and the prediction precision is improved. And the method is closer to the actual multi-pole magnetic trap magnetic flux distribution prediction effect.

Description

Technical Field

[0001] This application relates to the field of plasma energy engineering technology, and in particular to a method, apparatus and equipment for predicting magnetic flux distribution in a multipole magnetic trap. Background Technology

[0002] Multipole magnetic traps are magnetic confinement devices that utilize the magnetic fields generated by multiple current-carrying conductors immersed in plasma to achieve confinement. Compared to devices such as tokamas and stellarators, they have advantages such as compact structure, good stability, and high specific pressure. The equilibrium restoration of multipole magnetic traps is based on magnetohydrodynamic (MHD) theory. That is, the plasma is in a state of magnetohydrodynamic equilibrium within the magnetic confinement device. The fundamental principle is that the pressure gradient force of the plasma and the Lorentz force of the magnetic field are in balance.

[0003] In the axisymmetric case, the plasma equilibrium can be described by solving the Grad-Shafranov (GS) equilibrium equations applicable to multipole magnetic traps. However, the solution process requires numerical calculation, which is computationally complex and requires multiple iterations to converge to a suitable solution, resulting in a significant increase in computation time. Summary of the Invention

[0004] The purpose of this application is to provide a method, apparatus and device for predicting magnetic flux distribution in a multi-pole magnetic trap, which aims to solve the technical problem that general neural networks rely solely on data-driven learning and lack physical constraints, resulting in a large deviation between the predicted magnetic flux distribution and the actual value.

[0005] To achieve the above objectives, this application proposes a method for predicting the magnetic flux distribution in a multipole magnetic trap, the method comprising:

[0006] A neural network architecture comprising a magnetic flux neural network, a plasma current neural network, and a convolutional differential operator is constructed, and the total magnetic flux distribution is output through the magnetic flux neural network.

[0007] The total magnetic flux distribution is input into the plasma current neural network to obtain the plasma current density, and the first constraint condition is obtained based on the plasma current density;

[0008] The second constraint condition is obtained based on the total magnetic flux distribution and the convolution differential operator;

[0009] The first constraint and the second constraint are compared to obtain the comparison result. When the convergence error corresponding to the comparison result is less than the preset error, the total magnetic flux distribution output by the magnetic flux neural network at this time is taken as the predicted magnetic flux distribution.

[0010] In one embodiment, after the step of comparing the first constraint and the second constraint to obtain a comparison result, the method further includes:

[0011] When the convergence error corresponding to the comparison result is not less than the preset error, the process returns to the step of inputting the total magnetic flux distribution into the plasma current neural network to obtain the plasma current density, and obtaining the first constraint condition based on the plasma current density.

[0012] In one embodiment, the step of analyzing the total magnetic flux distribution output by the magnetic flux neural network includes:

[0013] Obtain the coil current parameters of the hagfish coil, and calculate the magnetic flux contribution generated by the hagfish coil based on the coil current parameters and the Green function;

[0014] Obtain the magnetic flux contribution generated by the magnetic flux neural network;

[0015] The total magnetic flux distribution is obtained by superimposing the magnetic flux contribution generated by the blind eel coil and the magnetic flux neural network.

[0016] In one embodiment, the step of obtaining the magnetic flux contribution generated by the magnetic flux neural network includes:

[0017] Obtain the magnetic flux distribution of the output layer of the magnetic flux neural network;

[0018] The magnetic flux distribution of the output layer is subjected to size transformation and horizontal mirroring.

[0019] The magnetic flux distribution of the processed output layer is used as the magnetic flux contribution.

[0020] In one embodiment, the step of inputting the total magnetic flux distribution into the plasma current neural network to obtain the plasma current density, and obtaining the first constraint condition based on the plasma current density, includes:

[0021] The total magnetic flux distribution is normalized and then input into the plasma current neural network to obtain the plasma current density.

[0022] The first constraint condition is obtained by substituting the plasma current density into the poloidal magnetic flux function in the GS equilibrium equation of the multipole magnetic trap.

[0023] In one embodiment, the step of obtaining the second constraint condition based on the total magnetic flux distribution and the convolution differential operator includes:

[0024] The radial magnetic field and the axial magnetic field in the total magnetic flux distribution are calculated using the convolution differential operator.

[0025] The second constraint condition is obtained based on the difference form of the radial magnetic field and the difference form of the axial magnetic field.

[0026] In one embodiment, after the step of comparing the first constraint and the second constraint to obtain a comparison result, the method further includes:

[0027] Obtain the loss function of the magnetic flux neural network and the loss function of the plasma current neural network;

[0028] The second constraint condition is updated based on the plasma current density and the loss function of the magnetic flux neural network, using the stochastic gradient descent method.

[0029] The first constraint condition is updated based on the loss function of the plasma current neural network and the stochastic gradient descent method.

[0030] In one embodiment, the step of using the total magnetic flux distribution output by the magnetic flux neural network as the predicted magnetic flux distribution when the convergence error corresponding to the comparison result is less than a preset error further includes:

[0031] Obtain the plasma current density and total magnetic flux distribution from the comparison results;

[0032] The root mean square error is obtained based on the plasma current density, the coil current parameters of the blind eel coil, and the differential operator related to the total magnetic flux distribution.

[0033] The mean square error is used as the convergence error, and when the convergence error is less than the preset error, the total magnetic flux distribution output by the magnetic flux neural network at this time is used as the predicted magnetic flux distribution.

[0034] Furthermore, to achieve the above objectives, this application also proposes a multi-pole magnetic trap flux distribution prediction device, the device comprising:

[0035] A network construction module is used to construct a neural network architecture that includes a magnetic flux neural network, a plasma current neural network, and a convolutional differential operator, and to output the total magnetic flux distribution through the magnetic flux neural network.

[0036] The first constraint module is used to input the total magnetic flux distribution into the plasma current neural network to obtain the plasma current density, and to obtain the first constraint condition based on the plasma current density.

[0037] The second constraint module is used to obtain the second constraint conditions based on the total magnetic flux distribution and the convolution differential operator.

[0038] The magnetic flux prediction module is used to compare the first constraint and the second constraint to obtain a comparison result. When the convergence error corresponding to the comparison result is less than a preset error, the total magnetic flux distribution output by the magnetic flux neural network at this time is used as the predicted magnetic flux distribution.

[0039] In addition, to achieve the above objectives, this application also proposes a multipole magnetic trap flux distribution prediction device, the device comprising: a memory, a processor, and a computer program stored in the memory and executable on the processor, the computer program being configured to implement the steps of the multipole magnetic trap flux distribution prediction method as described above.

[0040] This application proposes a method, apparatus, and device for predicting magnetic flux distribution in a multipole magnetic trap. The method includes: constructing a neural network architecture comprising a magnetic flux neural network, a plasma current neural network, and a convolutional differential operator, and outputting a total magnetic flux distribution through the magnetic flux neural network; inputting the total magnetic flux distribution into the plasma current neural network to obtain a plasma current density, and obtaining a first constraint condition based on the plasma current density; obtaining a second constraint condition based on the total magnetic flux distribution and the convolutional differential operator; comparing the first constraint condition and the second constraint condition to obtain a comparison result; and when the convergence error corresponding to the comparison result is less than a preset error, using the total magnetic flux distribution output by the magnetic flux neural network at this time as the predicted magnetic flux distribution. This application constructs a neural network architecture comprising a magnetic flux neural network, a plasma current neural network, and a convolutional differential operator. After outputting the total magnetic flux distribution through the magnetic flux neural network, the plasma current density is obtained from the total magnetic flux distribution using the plasma current neural network to derive the first constraint condition. Simultaneously, the second constraint condition is obtained from the total magnetic flux distribution by combining the convolutional differential operator. The prediction result is then determined by comparing the convergence errors of the two constraint conditions. This architecture introduces physical constraints through the convolutional differential operator, effectively solving the problem of large deviations between the predicted magnetic flux distribution and the actual magnetic flux distribution caused by the lack of physical constraints in general neural networks. At the same time, the feedback coupling between the magnetic flux neural network and the plasma current neural network improves the convergence and stability of the model. Compared with existing technologies, it achieves a more realistic prediction effect for the magnetic flux distribution of multi-pole magnetic traps. Attached Figure Description

[0041] The accompanying drawings, which are incorporated in and form part of this specification, illustrate embodiments consistent with this application and, together with the description, serve to explain the principles of this application.

[0042] To more clearly illustrate the technical solutions in the embodiments of this application or the prior art, the drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, for those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0043] Figure 1 This is a flowchart illustrating an embodiment of the multipole magnetic trap flux distribution prediction method of this application.

[0044] Figure 2 This is a flowchart illustrating Embodiment 2 of the multipole magnetic trap flux distribution prediction method of this application.

[0045] Figure 3 This is a flowchart illustrating Embodiment 3 of the multipole magnetic trap flux distribution prediction method of this application;

[0046] Figure 4 This is a schematic diagram of the module structure of the multipole magnetic trap flux distribution prediction device according to an embodiment of this application;

[0047] Figure 5 This is a schematic diagram of the structure of the multipole magnetic trap flux distribution prediction device in the hardware operating environment of the multipole magnetic trap flux distribution prediction method in the embodiments of this application.

[0048] Figure 6 This is a configuration diagram of the multipole magnetic trap magnetic field in an embodiment of this application;

[0049] Figure 7 This is a two-dimensional toroidal configuration diagram of the multipole magnetic trap in the embodiments of this application;

[0050] Figure 8 This is a diagram showing the arrangement of the Rokowski coil and magnetic probe in an embodiment of this application;

[0051] Figure 9a A magnetic flux distribution map reconstructed from a typical neural network architecture;

[0052] Figure 9b This is a magnetic flux distribution diagram reconstructed from the neural network architecture proposed in this application.

[0053] The purpose, features, and advantages of this application will be further explained in conjunction with the embodiments and with reference to the accompanying drawings. Detailed Implementation

[0054] It should be understood that the specific embodiments described herein are merely illustrative of the technical solutions of this application and are not intended to limit this application.

[0055] To better understand the technical solution of this application, a detailed description will be provided below in conjunction with the accompanying drawings and specific implementation methods.

[0056] The main solution of this application embodiment is as follows: constructing a neural network architecture including a magnetic flux neural network, a plasma current neural network, and a convolutional differential operator, and outputting the total magnetic flux distribution through the magnetic flux neural network; inputting the total magnetic flux distribution into the plasma current neural network to obtain the plasma current density, and obtaining a first constraint condition based on the plasma current density; obtaining a second constraint condition based on the total magnetic flux distribution and the convolutional differential operator; comparing the first constraint condition and the second constraint condition to obtain a comparison result, and when the convergence error corresponding to the comparison result is less than a preset error, using the total magnetic flux distribution output by the magnetic flux neural network at this time as the predicted magnetic flux distribution.

[0057] In the axisymmetric case, the plasma equilibrium can be described by solving the Grad-Shafranov (GS) equilibrium equations applicable to multipole magnetic traps. However, the solution process requires numerical calculation, which is computationally complex and requires multiple iterations to converge to a suitable solution, resulting in a significant increase in computation time.

[0058] This application provides a solution that constructs a neural network architecture comprising a magnetic flux neural network, a plasma current neural network, and a convolutional differential operator. After outputting the total magnetic flux distribution through the magnetic flux neural network, the plasma current density is obtained from the total magnetic flux distribution using the plasma current neural network to derive the first constraint condition. Simultaneously, the second constraint condition is obtained from the total magnetic flux distribution by combining the convolutional differential operator. The prediction result is then determined by comparing the convergence errors of the two constraint conditions. This architecture introduces physical constraints through the convolutional differential operator, effectively solving the problem of large deviations between the predicted magnetic flux distribution and the actual value caused by the lack of physical constraints in general neural networks. At the same time, the feedback coupling between the magnetic flux neural network and the plasma current neural network improves the convergence and stability of the model. Compared with existing technologies, it achieves a more realistic prediction effect for the magnetic flux distribution of multi-pole magnetic traps.

[0059] It should be noted that the executing entity in this embodiment can be a computing service device with data processing, network communication, and program execution functions, such as a tablet computer, personal computer, or mobile phone, or a multi-pole magnetic well flux distribution prediction device capable of performing the above functions. The following description uses a multi-pole magnetic well flux distribution prediction device as an example to illustrate this embodiment and the subsequent embodiments.

[0060] Based on this, embodiments of this application provide a method for predicting the magnetic flux distribution of a multipole magnetic trap, referring to... Figure 1 , Figure 1 This is a flowchart illustrating an embodiment of the multipole magnetic trap flux distribution prediction method of this application.

[0061] In this embodiment, the multipole magnetic trap flux distribution prediction method includes steps S10 to S40:

[0062] Step S10: Construct a neural network architecture that includes a magnetic flux neural network, a plasma current neural network, and a convolutional differential operator, and output the total magnetic flux distribution through the magnetic flux neural network.

[0063] It should be understood that this step is the foundational building and initial output stage of the entire prediction method. The core lies in constructing a three-in-one neural network architecture: a magnetic flux neural network, a plasma current neural network, and a convolutional differential operator. The magnetic flux neural network, as the core prediction unit, is responsible for initially outputting the predicted total magnetic flux distribution based on the input multipole magnetic trap parameters (such as magnetic trap structure parameters and initial excitation parameters). The plasma current neural network is used to establish the correlation mapping between magnetic flux distribution and plasma current density. The convolutional differential operator plays a crucial role in introducing physical constraints, and its design must conform to the differential relationship between magnetic flux and current in electromagnetism. This step clarifies the functional positioning of each module through architecture construction, and the magnetic flux neural network generates the initial data for subsequent iterative optimization.

[0064] Step S20: Input the total magnetic flux distribution into the plasma current neural network to obtain the plasma current density, and obtain the first constraint condition based on the plasma current density.

[0065] It should be noted that this step aims to derive related physical quantities based on the initial magnetic flux distribution and form the first constraint. Specifically, the total magnetic flux distribution output from step S10 is used as input to the plasma current neural network. Using the network's trained mapping relationship (i.e., the correspondence between magnetic flux distribution and plasma current density), the corresponding plasma current density is calculated. Subsequently, based on the "inherent constraint relationship between plasma current density and magnetic flux" in the fundamental principles of electromagnetism (such as the derived constraints related to Ampere's circuital law), the first constraint condition is constructed based on the calculated plasma current density. This condition is essentially a physical constraint formed from the reverse derivation perspective of "magnetic flux → current," reflecting the specifications that the current characteristics derived from the current magnetic flux distribution should satisfy.

[0066] Step S30: Obtain the second constraint condition based on the total magnetic flux distribution and the convolution differential operator.

[0067] It should be understood that this step is a crucial step in introducing direct physical constraints, forming the second layer of constraints. Operationally, based on the total magnetic flux distribution output in step S10, the pre-defined convolution differential operator in the architecture is invoked to perform differential operations on the total magnetic flux distribution. Since the design of the convolution differential operator follows the physical differential equations of magnetic flux distribution in electromagnetism (such as the application of the Poisson equation or the Laplace equation in magnetism), the physical constraint requirements that it should satisfy can be directly derived from the magnetic flux distribution itself through this operation, i.e., the second constraint condition. This constraint condition is a direct constraint from the perspective of "the physical characteristics of the magnetic flux itself," complementing the constraint formed in step S20 from the perspective of "correlated current."

[0068] Step S40: Compare the first constraint and the second constraint to obtain the comparison result. When the convergence error corresponding to the comparison result is less than the preset error, the total magnetic flux distribution output by the magnetic flux neural network at this time is taken as the predicted magnetic flux distribution.

[0069] It should be noted that this step is the iterative optimization and result output stage for achieving accurate prediction. The core is to determine whether the current magnetic flux distribution meets the physical consistency requirements by comparing the first constraint condition with the second constraint condition: the difference between the two constraints is quantified as the convergence error. If the error is less than a preset threshold (this threshold is set according to the prediction accuracy requirements), it means that the total magnetic flux distribution output by the current magnetic flux neural network satisfies both the "magnetic flux-current" correlation constraint and its own physical differential constraint, and has high realism, so it can be directly used as the final predicted magnetic flux distribution. If the error does not meet the requirements, the error is fed back to the magnetic flux neural network, driving it to adjust the network parameters and re-output the total magnetic flux distribution. The process from S20 to S40 is repeated until the convergence error reaches the target, thereby achieving iterative optimization of the prediction result.

[0070] In this embodiment, the multipole magnetic trap flux distribution prediction method includes: constructing a neural network architecture comprising a magnetic flux neural network, a plasma current neural network, and a convolutional differential operator, and outputting the total magnetic flux distribution through the magnetic flux neural network; inputting the total magnetic flux distribution into the plasma current neural network to obtain the plasma current density, and obtaining a first constraint condition based on the plasma current density; obtaining a second constraint condition based on the total magnetic flux distribution and the convolutional differential operator; comparing the first constraint condition and the second constraint condition to obtain a comparison result, and when the convergence error corresponding to the comparison result is less than a preset error, using the total magnetic flux distribution output by the magnetic flux neural network at this time as the predicted magnetic flux distribution. This application constructs a neural network architecture comprising a magnetic flux neural network, a plasma current neural network, and a convolutional differential operator. After outputting the total magnetic flux distribution through the magnetic flux neural network, the plasma current density is obtained from the total magnetic flux distribution using the plasma current neural network to derive the first constraint condition. Simultaneously, the second constraint condition is obtained from the total magnetic flux distribution by combining the convolutional differential operator. The prediction result is then determined by comparing the convergence errors of the two constraint conditions. This architecture introduces physical constraints through the convolutional differential operator, effectively solving the problem of large deviations between the predicted magnetic flux distribution and the actual magnetic flux distribution caused by the lack of physical constraints in general neural networks. At the same time, the feedback coupling between the magnetic flux neural network and the plasma current neural network improves the convergence and stability of the model. Compared with existing technologies, it achieves a more realistic prediction effect for the magnetic flux distribution of multi-pole magnetic traps.

[0071] Based on the first embodiment of this application, in the second embodiment of this application, the content that is the same as or similar to that in the first embodiment described above can be referred to the above description, and will not be repeated hereafter. Based on this, please refer to... Figure 2 , Figure 2 This is a flowchart illustrating Embodiment 2 of the multipole magnetic trap flux distribution prediction method of this application. In step S10, the multipole magnetic trap flux distribution prediction method further includes:

[0072] Step S101: Obtain the coil current parameters of the blind eel coil, and calculate the magnetic flux contribution generated by the blind eel coil based on the coil current parameters and the Green function.

[0073] It should be understood that the magnetic field potential of a multipole magnetic trap is as follows: Figure 6As shown, in the central region of this magnetic field configuration, there exists a region with weak magnetic induction, i.e., a weak magnetic field region, while the surrounding region is a strong magnetic field region formed by closed magnetic field lines enclosing a magnetic shell. This magnetic field configuration shows an increasing trend in magnetic induction intensity from the inside to the outside of the plasma, and the confined plasma exhibits good magnetohydrodynamic stability. Among them, blind eel coils 1, 2, and 4 are used to generate the confinement magnetic field, compensation coil 3 is used to counteract the electromagnetic force of the blind eel coils, solenoid 5 is used to generate a vertical magnetic field to control the plasma distribution, and label 6 represents the Ohkawa interface, within which the plasma exhibits good stability.

[0074] It should be noted that, under the static equilibrium state of plasma, magnetohydrodynamic equilibrium satisfies the following conditions:

[0075] (1) All physical quantities of the equilibrium plasma are independent of time.

[0076] (2) The plasma is static (u = 0).

[0077] Combining the above conditions and Maxwell's equations, we obtain the fundamental equations that plasma static equilibrium must satisfy:

[0078]

[0079] The two-dimensional toroidal configuration of a multipole magnetic trap is as follows Figure 7 As shown in the figure. R0 is the center point of the plasma region. J1, J2, and J4 are the current densities of the inner and outer blind eel coils, respectively; J3 is the current density of the compensation coil; and Js is the current density of the solenoid. A geodetic coordinate system is established with the axis of symmetry of the magnetic trap as the z-direction. S is defined as a circular surface parallel to the equatorial plane, with height Z and radius R. The relationship between the poloidal magnetic flux Φ(r,z) through surface S and the poloidal magnetic field B satisfies the following equation:

[0080]

[0081] Combining the derivation and calculation of formulas (1) and (2), the two-dimensional plasma static equilibrium model in the multi-pole Galata magnetic trap is obtained as shown in formula (3), which is the GS equilibrium equation of the multi-pole magnetic trap.

[0082]

[0083] In the formula, Jex is the current density generated by the blind eel coil, and Jpl is the plasma current density.

[0084] Step S102: Obtain the magnetic flux contribution generated by the magnetic flux neural network;

[0085] Step S103: The magnetic flux contribution generated by the blind eel coil and the magnetic flux contribution generated by the magnetic flux neural network are superimposed to obtain the total magnetic flux distribution.

[0086] It should be noted that the magnetic flux neural network is used to predict the magnetic flux contribution Φpl ​​generated by the plasma current based on grid point coordinates, coil parameters, and measurement data. The convolutional differential operator is used to calculate the magnetic field strengths Br, Bz, and Δ*Φ based on the total magnetic flux distribution Φ. The plasma current neural network is used to predict the plasma current density distribution Jpl based on the total magnetic flux distribution Φ. Here, the total magnetic flux distribution Φ = Φe + Φpl. Φe refers to the magnetic field contribution generated by the blind eel coil, which can be calculated using the Green's function method given the parameters of the blind eel coil, based on the magnetic field constraint characteristics of the multipole magnetic trap. This fusion calculation mode can introduce the magnetic field distribution into the network training, thereby strengthening the physical constraint characteristics of the network and improving its generalization ability.

[0087] It should be noted that this application employs a dual neural network architecture, with the output of the magnetic flux neural network serving as the input to the plasma current neural network. The output of the plasma current neural network is calculated based on the right-hand side of the GS equation, and the result, in turn, serves as a constraint, compared with the Δ*Φ calculated by the magnetic flux neural network. This process autonomously learns and optimizes the parameters of the magnetic flux neural network, influencing its training until the error between the two reaches the expected level. This dual network architecture effectively alleviates the problems of data scarcity, overfitting, and poor physical interpretability caused by the reliance on large-scale training data in neural networks.

[0088] Step S102 further includes:

[0089] Obtain the magnetic flux distribution of the output layer of the magnetic flux neural network; perform size transformation and horizontal mirroring on the magnetic flux distribution of the output layer; use the processed magnetic flux distribution of the output layer as the magnetic flux contribution.

[0090] It should be noted that since the input features of the flux neural network have different dimensions, normalization is required. The normalized features are then gridded and flattened to the same size dimension. All features are then concatenated and fed into the flux neural network. The flux neural network contains three fully linearly connected hidden layers, each with 100 neurons and a bias term. The output layer is the flux distribution of all grid points, with a size of 2145×1. After size transformation and horizontal mirroring, the predicted Φpl is obtained. The predicted Φpl is then superimposed with the coil current flux Φe calculated using the Green's function to obtain the total flux distribution Φ.

[0091] It should be understood that, with reference Figure 8 , Figure 8This is a diagram showing the arrangement of the Rokowski coil and magnetic probe in an embodiment of this application. Input parameters include grid point coordinates, coil parameters, and measurement data. The entire computational domain is divided into a 65×66 grid. Considering symmetry, only the magnetic flux distribution in the upper half needs to be predicted. Therefore, the grid point coordinate input is 2145×2, where 2145 represents the total number of grid points, and 2 represents the r-coordinate and z-coordinate of the point, respectively, referred to as the coordinate feature. The coil parameter IeM (1×5) is... Figure 6 The coil current parameters shown represent the currents flowing through the external coils 1-4 and the solenoid coil, respectively, and are referred to as coil parameter characteristics. BM(1×32) refers to the data measured at a certain moment by the 16 sets of magnetic probes arranged near the plasma interface, and is referred to as measurement characteristics. Each set of magnetic probes consists of two magnetic probes, which measure the magnetic field in the r and z directions, respectively. ID refers to the data measured at a certain moment by the Rokowski coils arranged near the plasma interface, representing the total plasma current.

[0092] In step S20, the multipole magnetic trap flux distribution prediction method further includes:

[0093] Step S201: After normalizing the total magnetic flux distribution, input it into the plasma current neural network to obtain the plasma current density;

[0094] Step S202: Substitute the plasma current density into the poloidal magnetic flux function in the GS equilibrium equation of the multipole magnetic trap to obtain the first constraint condition.

[0095] It should be noted that the total magnetic flux distribution Φ output by the magnetic flux neural network is normalized and then fed into the plasma current neural network, where the output is the plasma current density J. pl J pl Substitute the result into the right side of equation (3) and use it as the first constraint.

[0096] It should be understood that the plasma in a multipole magnetic trap has a clearly defined plasma boundary (PBI), which is the magnetic surface corresponding to the point where the plasma pressure decreases to 1 / e of the maximum pressure. Within this boundary, there exists a stably confined plasma, while outside this boundary, the plasma density distribution is almost zero. That is, J pl =rdp / dΦ only has values ​​within the PBI; outside the PBI, rdp / dΦ is zero. Therefore, the plasma current neural network only predicts the current distribution at grid points within the PBI. The plasma current neural network consists of three fully linearly connected hidden layers. The first layer has 60 neurons and no bias term, while the second and third layers each have 6 neurons and no bias term. The output layer shows the current distribution at all grid points within the PBI interface.

[0097] In step S30, the multipole magnetic trap flux distribution prediction method further includes:

[0098] Step S301: Calculate the difference form of the radial magnetic field and the difference form of the axial magnetic field in the total magnetic flux distribution according to the convolution differential operator;

[0099] Step S302: Obtain the second constraint condition based on the difference form of the radial magnetic field and the difference form of the axial magnetic field.

[0100] It should be noted that the convolution differential operator is responsible for calculating the magnetic field B based on the total magnetic flux Φ. r B z B r B z The difference form is shown in Equation 4:

[0101]

[0102] Equation (4) can be improved in terms of computational efficiency through the convolution operation in equation (5):

[0103]

[0104] The second constraint is Δ * The difference form of Φ is shown in Equation 6:

[0105]

[0106] Δ * The difference calculation of Φ can also be improved by using the convolution operation of equation (7) to improve the computational efficiency.

[0107]

[0108] In this embodiment, the total magnetic flux distribution Φ output by the magnetic flux neural network is normalized and then fed into the plasma current neural network, and the output is the plasma current density J. pl J pl Substituting the result into the right side of equation (3), the calculation is performed. The result is then compared with the result calculated by the convolutional differential as the first constraint. The difference is updated in the loss function of the magnetic flux network to form error feedback, further optimizing the parameters of the magnetic flux neural network and realizing Φ. plIterative correction. This embodiment employs a dual neural network architecture, where the output of the magnetic flux neural network serves as the input to the plasma current neural network. The output of the plasma current neural network is calculated based on the right-hand side of the GS equation, and the result, in turn, acts as a constraint, comparing it with the Δ*Φ calculated by the magnetic flux neural network. This process autonomously learns and optimizes the parameters of the magnetic flux neural network, influencing its training, until the error between the two reaches the expected level. This dual network architecture effectively alleviates the problems of data scarcity, overfitting, and poor physical interpretability caused by the reliance on large-scale training data in neural networks.

[0109] Based on the first and / or second embodiments of this application, in the third embodiment of this application, the content that is the same as or similar to that in embodiments one and two above can be referred to the above description, and will not be repeated hereafter. Based on this, please refer to... Figure 3 , Figure 3 This is a flowchart illustrating Embodiment 3 of the multipole magnetic trap flux distribution prediction method of this application. After step S40, the multipole magnetic trap flux distribution prediction method further includes:

[0110] Step S401: When the convergence error corresponding to the comparison result is not less than the preset error, return to the step of inputting the total magnetic flux distribution into the plasma current neural network to obtain the plasma current density, and obtaining the first constraint condition based on the plasma current density.

[0111] It should be noted that when the convergence error corresponding to the comparison result is not less than the preset error, it means that the total magnetic flux distribution output by the current magnetic flux neural network has not yet met the physical consistency requirements and needs to be optimized through feedback loop iteration. At this time, the total magnetic flux distribution is re-inputted into the plasma current neural network, the plasma current density is recalculated, and the first constraint condition is generated accordingly, forming a closed-loop feedback mechanism.

[0112] In step S40, the multipole magnetic trap flux distribution prediction method further includes:

[0113] Step S402: Obtain the loss function of the magnetic flux neural network and the loss function of the plasma current neural network.

[0114] It should be understood that the loss function LM of the magnetic flux neural network includes three sub-loss functions: the magnetic measurement loss function LMB, the difference loss of the GS equation within the boundary (LPBI_in), and the difference loss of the GS equation outside the boundary (LPBI_ex). The magnetic measurement loss function LMB includes two components, LMBBr and LMBz, which are calculated using the predicted Φ. It represents the average absolute error between the predicted and measured values ​​of the magnetic field strength at the magnetic probe position, as shown below:

[0115]

[0116] In the formula, MB is the magnetic probe measurement of the magnetic field, and B... Mr B Mz This represents the predicted magnetic field value, where i is the magnetic probe number and m is the number of magnetic probes. LPBI_in represents the mean absolute error of the GS equations within the plasma boundary, as shown below:

[0117]

[0118] In the formula Φ i The magnetic flux value within the PBI derived from the magnetic flux neural network, J pl The values ​​are derived from the plasma current neural network prediction, where n is the number of network points within the PBI. Since the plasma current outside the PBI boundary is zero, the GS equation is determined solely by the blind eel coil current. Therefore, LPBI_ex represents the mean absolute error of the GS equation outside the plasma boundary, as shown below:

[0119]

[0120] In the formula Φ j External magnetic flux value of PBI derived from magnetic flux prediction, J pl The value is derived from the predicted plasma current, and k represents the number of points in the external network of the PBI. In summary, the loss function of the magnetic flux neural network is:

[0121] L M =w M1 L B +w M2 L PBI_in +w M3 L PBI_ex (11)

[0122] It should be noted that the loss function L of the plasma current neural network F It includes two sub-loss functions, namely the magnetic measurement loss function L. FB Plasma dimagnetic current loss L FB Including L FBr L FBz The two components are the magnetic field strength B, calculated using Biot-Savart's law at the magnetic probe placement position, based on the output plasma current density distribution, superimposed with the external coil current. Fr B Fz The mean square error between the sum and the measured value is shown below:

[0123]

[0124] In the formula, MB is the magnetic probe measurement of the magnetic field, and B... Fr B FzThis is the predicted magnetic field value, where i is the magnetic probe number. L ID It is the absolute error between the integral of all plasma currents within the PBI interface and the measurement value of the Rokowski coil.

[0125]

[0126] In summary, the loss function of the plasma current network is:

[0127]

[0128] In the formula w F1 w F2 The weights of each sub-loss function are determined separately.

[0129] Step S403: Update the second constraint condition based on the plasma current density and the loss function of the magnetic flux neural network, using the stochastic gradient descent method;

[0130] Step S404: Update the first constraint condition according to the loss function of the plasma current neural network and the stochastic gradient descent method.

[0131] It should be noted that at the beginning of training, the weight parameters of the two neural networks, magnetic flux and plasma current, need to be initialized using the Xavier initialization scheme to avoid the gradient vanishing or exploding problems that may occur with traditional random initialization. In each iteration k≥1 (k=3000 training datasets), data at a certain time point is randomly selected from the 3000 training datasets to form a batch size of 2145 with 40 feature channels. This data is then fed into the magnetic flux neural network to generate the magnetic flux distribution solution Φ at 2145 grid points. pl k , superimposed with Φ e Get Φ k Φ k 2145 sets of data were calculated using DiffNet (B r B z Δ * Φ). Combined with the output of the (k-1)th plasma current neural network, J pl k Using the loss function L given by formula (11) M The parameters for magnetic flux prediction are updated using stochastic gradient descent. The Φ parameter in the PBI is then adjusted. k After normalization, the signal is fed into the plasma current neural network, and the output Φ of all grid points in the PBI is obtained. k The parameters of the plasma current neural network are updated by using the stochastic gradient descent algorithm and training with the loss function LF formula (14).

[0132] In step S40, the multipole magnetic trap flux distribution prediction method further includes:

[0133] Step S405: Obtain the plasma current density and total magnetic flux distribution from the comparison results;

[0134] Step S406: Obtain the root mean square error based on the plasma current density, the coil current parameters of the blind eel coil, and the differential operator related to the total magnetic flux distribution;

[0135] Step S407: Use the mean square error as the convergence error, and when the convergence error is less than the preset error, use the total magnetic flux distribution output by the magnetic flux neural network at this time as the predicted magnetic flux distribution.

[0136] It should be noted that the convergence criterion for the network is the output Δ calculated according to formula (3) of the magnetic flux neural network. * Φ and J output by the plasma current network pl Calculated 2πrμ0(J pl +J ex The mean square error is less than the convergence error. This is shown in the following formula:

[0137]

[0138] In the formula, ε is the convergence error between two given iterations.

[0139] It should be noted that comparing the magnetic flux reconstruction results of a conventional neural network with those of the network proposed in this application is as follows: Figure 9a and Figure 9b As can be seen from the contour lines in the image, the magnetic flux reconstruction method proposed in this invention produces smoother and more continuous prediction results than ordinary neural networks. It avoids the "noise" or discrete phenomena that may occur in ordinary neural networks, and can better match the actual physical model with the error controlled within a small range.

[0140] It should be noted that by deploying the model using the PyTorch framework, the trained neural network model can quickly predict magnetic flux. After preprocessing and model loading, the prediction time is approximately 6 milliseconds, enabling near real-time magnetic flux distribution reconstruction and demonstrating high potential for real-time control applications.

[0141] In this embodiment, by introducing physical coupling and feedback mechanisms, the accuracy and stability of the magnetic flux distribution are significantly improved, making it more reliable and accurate in practical applications and meeting the balance requirements of multipole magnetic traps. While ordinary neural network methods can also generate magnetic flux distributions, they exhibit inaccuracies and instabilities in some details, especially in high magnetic fields or rapidly changing regions. After the model is trained, the inference process in this application no longer relies on complex iterations, requiring only forward propagation calculations, with prediction times consistently maintained at the millisecond level. This structural advantage enables the invention to achieve fast computation not only on ordinary hardware platforms but also provides excellent applicability and scalability in embedded devices or real-time control systems.

[0142] This application also provides a multi-pole magnetic trap flux distribution prediction device; please refer to... Figure 4 The multipole magnetic trap flux distribution prediction device includes:

[0143] Network construction module 10 is used to construct a neural network architecture that includes a magnetic flux neural network, a plasma current neural network and a convolutional differential operator, and output the total magnetic flux distribution through the magnetic flux neural network;

[0144] The first constraint module 20 is used to input the total magnetic flux distribution into the plasma current neural network to obtain the plasma current density, and to obtain the first constraint condition based on the plasma current density.

[0145] The second constraint module 30 is used to obtain the second constraint conditions based on the total magnetic flux distribution and the convolution differential operator.

[0146] The magnetic flux prediction module 40 is used to compare the first constraint condition and the second constraint condition to obtain a comparison result. When the convergence error corresponding to the comparison result is less than a preset error, the total magnetic flux distribution output by the magnetic flux neural network at this time is used as the predicted magnetic flux distribution.

[0147] Optionally, the network construction module 10 is further configured to obtain the coil current parameters of the blind eel coil, and calculate the magnetic flux contribution generated by the blind eel coil based on the coil current parameters and the Green function; obtain the magnetic flux contribution generated by the magnetic flux neural network; and superimpose the magnetic flux contribution generated by the blind eel coil and the magnetic flux contribution generated by the magnetic flux neural network as the total magnetic flux distribution.

[0148] Optionally, the network construction module 10 is further configured to obtain the magnetic flux distribution of the output layer of the magnetic flux neural network; perform size transformation and horizontal mirroring processing on the magnetic flux distribution of the output layer; and use the processed magnetic flux distribution of the output layer as the magnetic flux contribution.

[0149] Optionally, the first constraint module 20 is further configured to normalize the total magnetic flux distribution and input it into the plasma current neural network to obtain the plasma current density; and substitute the plasma current density into the poloidal magnetic flux function in the GS equilibrium equation of the multipole magnetic trap to obtain the first constraint condition.

[0150] Optionally, the second constraint module 30 is further configured to calculate the difference form of the radial magnetic field and the difference form of the axial magnetic field in the total magnetic flux distribution according to the convolution differential operator; and obtain the second constraint condition according to the difference form of the radial magnetic field and the difference form of the axial magnetic field.

[0151] Optionally, the magnetic flux prediction module 40 is further configured to, when the convergence error corresponding to the comparison result is not less than a preset error, return to the step of inputting the total magnetic flux distribution into the plasma current neural network to obtain the plasma current density, and obtaining the first constraint condition based on the plasma current density.

[0152] Optionally, the magnetic flux prediction module 40 is further configured to obtain the loss function of the magnetic flux neural network and the loss function of the plasma current neural network; update the second constraint condition using stochastic gradient descent based on the plasma current density and the loss function of the magnetic flux neural network; and update the first constraint condition using stochastic gradient descent based on the loss function of the plasma current neural network.

[0153] Optionally, the magnetic flux prediction module 40 is further configured to obtain the plasma current density and total magnetic flux distribution in the comparison results; obtain the mean square error based on the plasma current density, the coil current parameters of the blind eel coil and the differential operator related to the total magnetic flux distribution; use the mean square error as the convergence error, and when the convergence error is less than a preset error, use the total magnetic flux distribution output by the magnetic flux neural network at this time as the predicted magnetic flux distribution.

[0154] The multi-pole magnetic well flux distribution prediction device provided in this application employs the multi-pole magnetic well flux distribution prediction method described in the above embodiments. This addresses the technical problem that general neural networks rely solely on data-driven learning and lack physical constraints, leading to significant deviations between predicted and actual flux distribution. Compared to existing technologies, the beneficial effects of the multi-pole magnetic well flux distribution prediction device provided in this application are the same as those of the multi-pole magnetic well flux distribution prediction method described in the above embodiments. Furthermore, other technical features of the multi-pole magnetic well flux distribution prediction device are identical to those disclosed in the methods of the above embodiments, and will not be elaborated upon here.

[0155] This application provides a multipole magnetic trap flux distribution prediction device, which includes: at least one processor; and a memory communicatively connected to the at least one processor; wherein the memory stores instructions executable by the at least one processor, and the instructions are executed by the at least one processor to enable the at least one processor to perform the multipole magnetic trap flux distribution prediction method in the above embodiment 1.

[0156] The following is for reference. Figure 5 This document illustrates a structural schematic diagram of a multipole magnetic trap flux distribution prediction device suitable for implementing embodiments of this application. The multipole magnetic trap flux distribution prediction device in the embodiments of this application may include, but is not limited to, mobile terminals such as mobile phones, laptops, digital broadcast receivers, PDAs (Personal Digital Assistants), PADs (Portable Application Description), PMPs (Portable Media Players), and in-vehicle terminals (e.g., in-vehicle navigation terminals), as well as fixed terminals such as digital TVs and desktop computers. Figure 5 The multipole magnetic trap flux distribution prediction device shown is merely an example and should not impose any limitations on the functionality and scope of use of the embodiments of this application.

[0157] like Figure 5As shown, the multipole magnetic trap flux distribution prediction device may include a processing unit 1001 (e.g., a central processing unit, a graphics processing unit, etc.), which can perform various appropriate actions and processes according to a program stored in a read-only memory 1002 or a program loaded from a storage device 1003 into a random access memory 1004. The random access memory 1004 also stores various programs and data required for the operation of the multipole magnetic trap flux distribution prediction device. The processing unit 1001, the read-only memory 1002, and the random access memory 1004 are interconnected via a bus 1005. An input / output interface 1006 is also connected to the bus. Typically, the following systems can be connected to the input / output interface 1006: input devices 1007 including, for example, a touch screen, touchpad, keyboard, mouse, image sensor, microphone, accelerometer, gyroscope, etc.; output devices 1008 including, for example, a liquid crystal display (LCD), speaker, vibrator, etc.; storage devices 1003 including, for example, magnetic tape, hard disk, etc.; and communication devices 1009. The communication device 1009 allows the multipole magnetic trap flux distribution prediction device to communicate wirelessly or wiredly with other devices to exchange data. Although the figure shows multipole magnetic trap flux distribution prediction devices with various systems, it should be understood that it is not required to implement or possess all of the systems shown. More or fewer systems may be implemented alternatively.

[0158] Specifically, according to the embodiments disclosed in this application, the processes described above with reference to the flowcharts can be implemented as computer software programs. For example, embodiments disclosed in this application include a computer program product comprising a computer program carried on a computer-readable medium, the computer program containing program code for performing the methods shown in the flowcharts. In such embodiments, the computer program can be downloaded and installed from a network via a communication device, or installed from storage device 1003, or installed from read-only memory 1002. When the computer program is executed by processing device 1001, it performs the functions defined in the methods of the embodiments disclosed in this application.

[0159] The multi-pole magnetic well flux distribution prediction device provided in this application employs the multi-pole magnetic well flux distribution prediction method described in the above embodiments. This addresses the technical problem that general neural networks rely solely on data-driven learning and lack physical constraints, leading to significant deviations between predicted and actual flux distribution. Compared to existing technologies, the beneficial effects of the multi-pole magnetic well flux distribution prediction device provided in this application are the same as those of the multi-pole magnetic well flux distribution prediction method described in the above embodiments. Furthermore, other technical features of this multi-pole magnetic well flux distribution prediction device are the same as those disclosed in the previous embodiment method, and will not be elaborated upon here.

[0160] It should be understood that the various parts disclosed in this application can be implemented using hardware, software, firmware, or a combination thereof. In the description of the above embodiments, specific features, structures, materials, or characteristics can be combined in any suitable manner in one or more embodiments or examples.

[0161] The above description is merely a specific embodiment of this application, but the scope of protection of this application is not limited thereto. Any variations or substitutions that can be easily conceived by those skilled in the art within the scope of the technology disclosed in this application should be included within the scope of protection of this application. Therefore, the scope of protection of this application should be determined by the scope of the claims.

Claims

1. A method for predicting magnetic flux distribution in a multipole magnetic trap, characterized in that, The multipole magnetic trap flux distribution prediction method includes: A neural network architecture comprising a magnetic flux neural network, a plasma current neural network, and a convolutional differential operator is constructed, and the total magnetic flux distribution is output through the magnetic flux neural network. The total magnetic flux distribution is input into the plasma current neural network to obtain the plasma current density, and the first constraint condition is obtained based on the plasma current density; The second constraint condition is obtained based on the total magnetic flux distribution and the convolution differential operator; The first constraint and the second constraint are compared to obtain the comparison result. When the convergence error corresponding to the comparison result is less than the preset error, the total magnetic flux distribution output by the magnetic flux neural network at this time is taken as the predicted magnetic flux distribution.

2. The method for predicting magnetic flux distribution in a multi-pole magnetic trap as described in claim 1, characterized in that, After the step of comparing the first constraint and the second constraint to obtain the comparison result, the method further includes: When the convergence error corresponding to the comparison result is not less than the preset error, the process returns to the step of inputting the total magnetic flux distribution into the plasma current neural network to obtain the plasma current density, and obtaining the first constraint condition based on the plasma current density.

3. The method for predicting magnetic flux distribution in a multi-pole magnetic trap as described in claim 1, characterized in that, The step of outputting the total magnetic flux distribution through the magnetic flux neural network includes: Obtain the coil current parameters of the hagfish coil, and calculate the magnetic flux contribution generated by the hagfish coil based on the coil current parameters and the Green function; Obtain the magnetic flux contribution generated by the magnetic flux neural network; The total magnetic flux distribution is obtained by superimposing the magnetic flux contribution generated by the blind eel coil and the magnetic flux neural network.

4. The method for predicting magnetic flux distribution in a multi-pole magnetic trap as described in claim 3, characterized in that, The step of obtaining the magnetic flux contribution generated by the magnetic flux neural network includes: Obtain the magnetic flux distribution of the output layer of the magnetic flux neural network; The magnetic flux distribution of the output layer is subjected to size transformation and horizontal mirroring. The magnetic flux distribution of the processed output layer is used as the magnetic flux contribution.

5. The method for predicting magnetic flux distribution in a multi-pole magnetic trap as described in claim 1, characterized in that, The step of inputting the total magnetic flux distribution into the plasma current neural network to obtain the plasma current density, and obtaining the first constraint condition based on the plasma current density, includes: The total magnetic flux distribution is normalized and then input into the plasma current neural network to obtain the plasma current density. The first constraint condition is obtained by substituting the plasma current density into the poloidal magnetic flux function in the GS equilibrium equation of the multipole magnetic trap.

6. The method for predicting magnetic flux distribution in a multi-pole magnetic trap as described in claim 1, characterized in that, The step of obtaining the second constraint condition based on the total magnetic flux distribution and the convolution differential operator includes: The radial magnetic field and the axial magnetic field in the total magnetic flux distribution are calculated using the convolution differential operator. The second constraint condition is obtained based on the difference form of the radial magnetic field and the difference form of the axial magnetic field.

7. The method for predicting magnetic flux distribution in a multi-pole magnetic trap as described in claim 1, characterized in that, After the step of comparing the first constraint and the second constraint to obtain the comparison result, the method further includes: Obtain the loss function of the magnetic flux neural network and the loss function of the plasma current neural network; The second constraint condition is updated based on the plasma current density and the loss function of the magnetic flux neural network, using the stochastic gradient descent method. The first constraint condition is updated based on the loss function of the plasma current neural network and the stochastic gradient descent method.

8. The method for predicting magnetic flux distribution in a multi-pole magnetic trap as described in claim 3, characterized in that, The step of using the total magnetic flux distribution output by the magnetic flux neural network at this time as the predicted magnetic flux distribution when the convergence error corresponding to the comparison result is less than the preset error further includes: Obtain the plasma current density and total magnetic flux distribution from the comparison results; The root mean square error is obtained based on the plasma current density, the coil current parameters of the blind eel coil, and the differential operator related to the total magnetic flux distribution. The mean square error is used as the convergence error, and when the convergence error is less than the preset error, the total magnetic flux distribution output by the magnetic flux neural network at this time is used as the predicted magnetic flux distribution.

9. A multi-pole magnetic trap flux distribution prediction device, characterized in that, The device includes: A network construction module is used to construct a neural network architecture that includes a magnetic flux neural network, a plasma current neural network, and a convolutional differential operator, and to output the total magnetic flux distribution through the magnetic flux neural network. The first constraint module is used to input the total magnetic flux distribution into the plasma current neural network to obtain the plasma current density, and to obtain the first constraint condition based on the plasma current density. The second constraint module is used to obtain the second constraint conditions based on the total magnetic flux distribution and the convolution differential operator. The magnetic flux prediction module is used to compare the first constraint and the second constraint to obtain a comparison result. When the convergence error corresponding to the comparison result is less than a preset error, the total magnetic flux distribution output by the magnetic flux neural network at this time is used as the predicted magnetic flux distribution.

10. A multi-pole magnetic trap flux distribution prediction device, characterized in that, The device includes: a memory, a processor, and a computer program stored in the memory and executable on the processor, the computer program being configured to implement the steps of the multipole magnetic trap flux distribution prediction method as described in any one of claims 1 to 8.

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