Vacuum confluence area electromagnetic particle simulation method, system, equipment and medium

Abstract

The invention belongs to the field of electromagnetic particle simulation, and relates to a vacuum confluence region electromagnetic particle simulation method, system, equipment and medium, and the method comprises the following steps: S1, constructing a particle simulation domain of an electric field and a magnetic field of a vacuum confluence region, injecting particles into the particle simulation domain, and carrying out the regional decomposition of the particle simulation domain to obtain a plurality of sub-domains; s2, acquiring charge density and current density of grid points in each sub-domain; discretizing a Maxwell equation set into a form of a Cx = D equation, substituting the charge density and the current density of the grid points in each sub-domain into the Cx = D equation, and solving the Cx = D equation by adopting a GMRES algorithm to obtain potential and vector magnetic potential distribution in each sub-domain; s3, the electric field intensity and the magnetic induction intensity of the grid points in each sub-domain are solved, the electric field and the magnetic field borne by the particles are obtained, and therefore the positions of the particles in the next time step in each sub-domain are determined; and S4, updating the electric field and the magnetic field borne by the particles in each sub-domain in the next time step.

Description

Technical Field

[0001] The invention belongs to the field of electromagnetic particle simulation, and relates to a vacuum confluence area electromagnetic particle simulation method, system, equipment and medium. Background Art

[0002] With the development of pulse technology, the multi-physics field coupling effects (such as breakdown and discharge) of ultra-high power pulse transmission systems in extreme electromagnetic environments have become a key issue restricting the reliability of the system. The performance optimization, reliability verification and improvement, and damage mechanism research of ultra-high power pulse transmission systems in extreme electromagnetic environments are currently hot topics for researchers. Studies have shown that the formation of plasma may occur during power transmission, leading to shunting and current loss, reducing the transmission efficiency of the system.

[0003] As key components of high-power transmission systems, vacuum confluence areas and magnetically insulated transmission lines can converge energy from multiple pulses, and then the energy is fed to the load by the internal magnetically insulated transmission lines. Under strong electromagnetic stress, the plasma formed by the interaction of charged particles is an important factor affecting current loss. Particle simulation is based on the first principles and can self-consistently obtain the distribution of particles and fields in space. It is one of the main methods currently used for simulation calculations. A two-dimensional axisymmetric structure is used to solve the electrostatic field and static magnetic field in space. Traditional Jacobi iteration methods, successive overrelaxation iteration methods (SOR), etc. are difficult to achieve large-scale distributed parallel computing. The single-machine single-node computing speed is slow and the memory consumption is large, which seriously limits the computing speed of particle simulation. Summary of the invention

[0004] The purpose of the present invention is to overcome the shortcomings of the above-mentioned prior art and provide a method, system, device and medium for simulating electromagnetic particles in a vacuum confluence area, which significantly improves the efficiency and accuracy of electromagnetic field solution and effectively reduces the cost of parallel communication.

[0005] In order to achieve the above object, the present invention adopts the following technical solutions: A vacuum confluence region electromagnetic particle simulation method includes the following processes: S1: construct a particle simulation domain of the electric field and magnetic field in the vacuum confluence area, inject particles into the particle simulation domain, and perform regional decomposition on the particle simulation domain to obtain multiple subdomains, each of which contains multiple grids, and each grid has four grid points; S2: At the current time step, obtain the charge density and current density of the grid points in each subdomain; construct the Maxwell equations of the particle simulation domain, discretize the Maxwell equations, substitute the charge density and current density of the grid points in each subdomain into the discretized Maxwell equations, use the GMRES algorithm to solve the electric potential and vector magnetic potential of the discretized Maxwell equations, and obtain the distribution of the electric potential and vector magnetic potential in each subdomain; S3: According to the distribution of electric potential and vector magnetic potential in each subdomain, the electric field strength and magnetic induction strength of the grid points in each subdomain are solved, and the electric field and magnetic field of the particle are obtained according to the electric field strength and magnetic induction strength. According to the electric field and magnetic field of the particle, the particle position in the next time step S2 in each subdomain is determined; S4: Repeat S2 to S4 according to the particle position in the next time step, and update the electric and magnetic fields acting on the particles in each subdomain in the next time step.

[0006] Preferably, the construction process of the particle simulation domain is: setting the physical space and grid step of the particle simulation domain, constructing the particle simulation domain according to the physical space and grid step, and setting the time step of particle simulation and the boundary of the particle simulation domain.

[0007] Preferably, the process of setting the boundary of the particle simulation domain is as follows: assuming that the upper and lower boundaries of the particle simulation domain are both ideal conductors, and the left and right boundaries of the particle simulation domain are regarded as particle absorption boundaries.

[0008] Preferably, the Maxwell equations are discretized, the charge density and current density of the grid points in each subdomain are substituted into the discretized Maxwell equations, and the electric potential and vector magnetic potential of the discretized Maxwell equations are solved using the GMRES algorithm, including: Write the electric potential and vector magnetic potential in Maxwell's equations in the form of Poisson's equations; According to the time step and grid step of particle simulation, the Poisson equation is discretized into the form of Cx=D equation by time domain difference method; PETSc and MPI are used to solve the Cx=D equation at each grid point in parallel using the GMRES algorithm to obtain the electric potential and vector magnetic potential of the grid point in each subdomain.

[0009] Preferably, the current density acquisition process of the grid points in each subdomain is as follows: according to the current distribution and waveform parameters under the actual working conditions of the vacuum confluence area, the current that generates the static magnetic field at the grid points in each subdomain is set, and the current density is obtained based on the current calculation of the static magnetic field.

[0010] Preferably, the charge density acquisition process of the grid points in each subdomain is as follows: according to the particle position, the particle charge and the current generated by the particle motion are weighted to the grid points corresponding to the particle position based on the double-line interpolation method, and the charge amount of the grid points in each subdomain is obtained, and the charge density of the grid points is obtained by dividing the charge amount by the volume corresponding to the grid points.

[0011] Preferably, the specific process of obtaining the electric field and magnetic field exerted on the particle, thereby determining the particle position in each subdomain at the next time step is as follows: interpolating the electric field strength and magnetic induction strength of the grid points in each subdomain to the corresponding particle position to obtain the electric field and magnetic field exerted on the particle, calculating the force exerted on the particle based on the electric field and magnetic field exerted on the particle, obtaining the particle velocity based on the particle force, and calculating the particle position in each subdomain at the next time step based on the particle velocity and the particle motion equation.

[0012] A vacuum confluence area electromagnetic particle simulation system, comprising: Particle simulation domain construction module: used to construct the particle simulation domain of the electric field and magnetic field in the vacuum confluence area, inject particles into the particle simulation domain, decompose the particle simulation domain into regions, and obtain multiple subdomains. Each subdomain contains multiple grids, and each grid has four grid points. Electric potential and vector magnetic potential solving module: used to obtain the charge density and current density of the grid points in each subdomain at the current time step; construct the Maxwell equations of the particle simulation domain, discretize the Maxwell equations, substitute the charge density and current density of the grid points in each subdomain into the discretized Maxwell equations, use the GMRES algorithm to solve the electric potential and vector magnetic potential of the discretized Maxwell equations, and obtain the distribution of the electric potential and vector magnetic potential in each subdomain; Particle motion module: used to solve the electric field strength and magnetic induction intensity of the grid points in each subdomain according to the distribution of electric potential and vector magnetic potential in each subdomain, obtain the electric field and magnetic field of the particle according to the electric field strength and magnetic induction intensity, and determine the particle position in the electric potential and vector magnetic potential solution module of each subdomain at the next time step according to the electric field and magnetic field of the particle; Update module: It is used to repeat the process from the electric potential and vector magnetic potential solving module to the update module according to the particle position in the next time step, and update the electric field and magnetic field exerted on the particles in each subdomain in the next time step.

[0013] A computer device comprises a memory, a processor and a computer program stored in the memory and executable on the processor. When the processor executes the computer program, the steps of the vacuum confluence region electromagnetic particle simulation method are implemented.

[0014] A computer-readable storage medium stores a computer program, and when the computer program is executed by a processor, the steps of the vacuum confluence area electromagnetic particle simulation method are implemented.

[0015] Compared with the prior art, the present invention has the following beneficial effects: The electromagnetic particle simulation method of the vacuum confluence area described in the present invention is based on the GMRES (Generalized Minimum RESidual) algorithm, adopts the PETSc (Portable, Extensible Toolkit for Scientific Computation) framework and the MPI (Message Passing Interface) parallel communication protocol architecture, and constructs a high-performance parallel computing system for the Poisson equation and the particle motion equation through the regional decomposition technology, supports a variety of complex particles and field boundary conditions, and can realize high-performance numerical simulation of high-power vacuum confluence areas and related components of large spatial scales by combining the regional decomposition strategy. The Maxwell equations are discretized by using the time-domain finite difference method, and the problem is simplified according to the characteristic working conditions of the high-power confluence area and related components, and the electromagnetic field time-varying variables are ignored. The electric potential and vector magnetic potential Poisson equations and the particle motion equations are efficiently solved in a distributed parallel manner, which significantly improves the efficiency and accuracy of electromagnetic field solution and effectively reduces the parallel communication overhead. The solution speed in the method of the present invention is increased by more than 60% compared with the calculation speed of the successive over relaxation (SOR) method. BRIEF DESCRIPTION OF THE DRAWINGS

[0016] Figure 1 This is a flow chart of the electromagnetic particle simulation method for a vacuum confluence region according to Embodiment 1 of the present invention; Figure 2 Schematic diagram of the area-based zr bilinear interpolation method according to Embodiment 2 of the present invention; Figure 3 This is a comparison chart of the calculation speeds of PETSc and SOR in Example 2 of the present invention. DETAILED DESCRIPTION

[0017] The technical solutions in the embodiments of the present application will be clearly and completely described below in conjunction with the drawings in the embodiments of the present application.

[0018] Embodiment 1: In this embodiment, a vacuum confluence region electromagnetic particle simulation method is provided, such as Figure 1 As shown, the following process is included: S1: construct a particle simulation domain of the electric field and magnetic field in the vacuum confluence area, inject particles into the particle simulation domain, and perform regional decomposition on the particle simulation domain to obtain multiple subdomains, each of which contains multiple grids, and each grid has four grid points; S2: At the current time step, obtain the charge density and current density of the grid points in each subdomain; construct the Maxwell equations of the particle simulation domain, discretize the Maxwell equations, substitute the charge density and current density of the grid points in each subdomain into the discretized Maxwell equations, use the GMRES algorithm to solve the electric potential and vector magnetic potential of the discretized Maxwell equations, and obtain the distribution of the electric potential and vector magnetic potential in each subdomain; S3: According to the distribution of electric potential and vector magnetic potential in each subdomain, the electric field strength and magnetic induction strength of the grid points in each subdomain are solved, and the electric field and magnetic field of the particle are obtained according to the electric field strength and magnetic induction strength. According to the electric field and magnetic field of the particle, the particle position in the next time step S2 in each subdomain is determined; S4: Repeat S2 to S4 according to the particle position in the next time step, and update the electric and magnetic fields acting on the particles in each subdomain in the next time step.

[0019] Embodiment 2: In this embodiment, a vacuum confluence region electromagnetic particle simulation method is provided, including the following process: Step 1: Set the physical space and grid step of the particle simulation domain. According to the physical space and grid step, construct the particle simulation domain of the electric field and magnetic field in the vacuum confluence area. The particle simulation domain is a two-dimensional axisymmetric structure. The particle simulation domain is divided into multiple uniform grids. It is assumed that the upper and lower boundaries of the particle simulation domain are ideal conductors, and the left and right boundaries of the particle simulation domain are regarded as particle absorption boundaries.

[0020] The particle simulation domain is decomposed into multiple subdomains, each of which contains multiple uniform grids, and each grid has four grid points.

[0021] Inject particles required for simulation into the particle simulation domain, including charged particles and neutral particles, and initialize particle position and velocity distribution.

[0022] Step 2: At the current time step, according to the particle position, based on the double-line interpolation method, the particle charge and the current generated by the particle motion are assigned to the grid points corresponding to the particle position according to the weights, and the charge amount of the grid points in each subdomain is calculated. The charge density of the grid points is obtained by dividing the charge amount by the volume corresponding to the grid point; according to the current distribution and waveform parameters under the actual working conditions of the vacuum confluence area, the current that generates the static magnetic field at the grid points in each subdomain is set, and the current density is obtained by dividing the current by the area corresponding to the grid point.

[0023] Specifically, Figure 2As shown in the figure, considering the calculation accuracy and complexity, the area-based ZR bilinear interpolation method is adopted. This interpolation method divides the grid into four small rectangular areas with the particle location as the center. The weight of charge distribution is determined by the ratio of the area of ​​the small rectangular area to the area of ​​the grid, so that the grid points close to the particles can be allocated more charges. The weights of the four grid points are:

[0024] In the formula, w i，j is the weight at the lower left grid point in a grid, w i+1，j is the weight at the lower right grid point in a grid, w i，j+1 is the weight at the upper left grid point in a grid, w i+1，j+1 is the weight at the upper right grid point in a grid, z p , r p is the coordinate of the particle, z i , r j is the coordinate of the lower left grid point in a grid, z i+1 , r j is the coordinate of the lower right grid point in a grid, z i , r j+1 is the coordinate of the upper left grid point in a grid, z i+1 , r j+1 is the coordinate of the upper right grid point in a grid.

[0025] This interpolation method divides the grid into four small rectangular areas with the particle location as the center. The weight of charge distribution is determined by the ratio of the area of ​​the four small rectangular areas to the area of ​​the grid, so that the grid points close to the particle can be allocated more charge. The charge contribution of the particle to the four surrounding grid points is:

[0026] Where: q p is the charge carried by the particle, w p is the particle weight, w i，j is the weight at the lower left grid point in a grid, w i+1，j is the weight at the lower right grid point in a grid, w i，j+1 is the weight at the upper left grid point in a grid, w i+1，j+1 is the weight of the upper right grid point in a grid. i，j is the charge at the lower left grid point in a grid, q i+1，j is the charge at the lower right grid point in a grid, q i，j+1 is the charge at the upper left grid point in a grid, q i+1，j+1 is the charge at the upper right grid point in a grid.

[0027] The weight distribution rule of current density is consistent with the above-mentioned charge density distribution method.

[0028] The charge at the grid point can be obtained from this , and then calculate the charge density :

[0029] Where: V i，j is the grid volume, is the total charge at the grid points, is the grid point charge density.

[0030] At the same time, the current that generates the static magnetic field at the grid point is obtained , and then calculate the current density :

[0031] Where: S i，j is the grid area, is the total current at the grid point, is the grid point current density.

[0032] Step 3: Construct the Maxwell equations for describing the electric and magnetic fields in the particle simulation domain. According to the time step and grid step of the particle simulation, the Maxwell equations are discretized by the time domain difference method, and the Poisson equation is discretized into the form of the Cx=D equation to obtain the coefficient matrix C of each grid point. The coefficient matrix is ​​initialized according to the initial boundary conditions of the particle simulation domain. Then, the charge density and current density of the grid points in each subdomain are substituted into the Cx=D equation, and the GMRES algorithm is used to solve the Cx=D equation for the electric potential and vector magnetic potential, and the distribution of the electric potential and vector magnetic potential in each subdomain is obtained.

[0033] In solving the electric potential, the source term D of the equation Cx=D is the charge density at the grid point, the coefficient matrix C is the coefficient corresponding to each grid point in the Poisson equation for the electric potential, and the quantity x is the electric potential at each grid point; in solving the vector magnetic potential, the source term D of the equation Cx=D is the current density at the corresponding grid point, the coefficient matrix C is the coefficient corresponding to each grid point in the Poisson equation for the vector magnetic potential, and the quantity x is the vector magnetic potential at the corresponding grid point.

[0034] Specifically, if the time-varying variables of the electric and magnetic fields are not considered, the Maxwell equations involved can be written as:

[0035] In the formula, is the curl calculation symbol, B is the magnetic induction intensity, E is the electric field intensity, 0 is the vacuum magnetic permeability, J is the charge density. At the same time, according to:

[0036] Where A is the vector magnetic potential, is the curl calculation symbol, B is the magnetic induction intensity, E is the electric field intensity, is the electric potential, is the gradient operator.

[0037] The electric potential and vector magnetic potential equations in each subdomain can be written in the form of Poisson's equation:

[0038] In the formula, e is the charge density, 0 is the dielectric constant of vacuum, is the electric potential, A is the vector magnetic potential, 0 is the vacuum magnetic permeability, J is the charge density, is the gradient operator.

[0039] Writing the electric potential and vector magnetic potential in the form of Poisson's equation helps unify the equation format and accelerate the solution. According to the time step and grid step of particle simulation, the Poisson's equation of electric potential and vector magnetic potential is discretized into the form of Cx=D equation by time domain difference method, and the charge density and current density of the grid point in each subdomain are substituted into the Cx=D equation. Through PETSc (Portable, Extensible Toolkit for Scientific Computation) and MPI (Message Passing Interface), the Cx=D equation at each grid point is solved in parallel using the GMRES algorithm to obtain the electric potential and vector magnetic potential of the grid point in each subdomain, thereby obtaining the distribution of the electric potential and vector magnetic potential in each subdomain.

[0040] Step 4: Based on the distribution of electric potential and vector magnetic potential in each subdomain, the electric field strength and magnetic induction intensity of the grid points in each subdomain are obtained. The electric field and magnetic field acting on the particles are obtained based on the electric field strength and magnetic induction intensity. Then, the particle position in the next time step in each subdomain is determined based on the particle motion equation.

[0041] Specifically, the electric field strength is calculated according to the potential distribution in each subdomain:

[0042] In the formula, is the electric potential, E z is the axial electric field, E r is the radial electric field, is the symbol of partial derivative.

[0043] For non-boundary points, the electric field is obtained using the central difference method:

[0044] In the formula, i，j+1 is the upper grid point potential, i，j-1 is the lower grid point potential, E z is the axial electric field, E r is the radial electric field, is the grid width in the z direction, is the grid width in the r direction, and i, j represent the two-dimensional coordinates of the grid point (i, j).

[0045] For the boundary points of the particle simulation domain, a certain adjacent grid point of the boundary point may no longer be in the computational domain. In this case, the forward or backward difference method is required to obtain the electric field:

[0046] In the formula, S sim is the computational domain, E z，i，j | i-1 Ssim is the electric field strength at the left boundary, E z，i，j | i+1 Ssim is the electric field strength at the right boundary, E z，i，j | j-1 Ssim is the electric field strength at the lower boundary, E z，i，j | j+1 Ssim is the electric field intensity at the upper boundary; i，j is the current grid point potential, i-1，j is the potential of a grid point on the left, i-2，j are the electric potentials of the two grid points on the left, i，j-1 is the potential of a grid point on the lower side, i，j-2 are the potentials of the two lower grid points, i+1，j is the potential of a grid point on the right, i+2，j are the electric potentials of the two grid points on the right, i，j+1 is the potential of a grid point on the upper side, i，j+2 are the electric potentials of the two upper grid points, is the grid width in the z direction, is the grid width in the r direction, and i, j represent the two-dimensional coordinates of the grid point (i, j).

[0047] According to the distribution of vector magnetic potential in each subdomain, the magnetic induction intensity B in the two-dimensional axisymmetric region is updated:

[0048] In the formula, B r is the radial magnetic induction intensity, B z is the axial magnetic induction intensity, B θ is the angular magnetic induction intensity, A r， is the radial vector magnetic potential, A z is the radial vector magnetic potential, A θ is the angular vector magnetic potential, is the sign of partial derivative. The treatment of boundary and non-boundary points is consistent with the solution method of electric field intensity.

[0049] The electric field strength and magnetic induction strength of the grid points in each subdomain are interpolated to the corresponding particle position to obtain the electric field and magnetic field of the particle. The particle force is calculated based on the electric field and magnetic field of the particle. The particle velocity is obtained based on the particle force. The particle position of the next time step in each subdomain is calculated based on the particle velocity and the particle motion equation. At the same time, the virtual grid layer data outside the subdomain boundary is communicated in parallel to facilitate the field calculation of the current subdomain.

[0050] like Figure 3 As shown in the figure, the CPU (Central Processing Unit) time consumed by the main loop and Poisson's equation under different simulation steps respectively by PETSc using the GMRES (Generalized Minimum RESidual) algorithm and the Successive Over Relaxation (SOR) method. Here, the main loop refers to the entire external loop consisting of the electric field and magnetic field solution and the particle motion solution. For the same solution method, the fast solution of the Poisson's equation is crucial to the overall acceleration effect of the main loop. For different solution methods, the CPU time consumed when solving the Poisson's equation by PETSc is significantly less than that of solving the Poisson's equation by the Successive Over Relaxation (SOR) method. The method of the present invention has a significant effect on improving the computational efficiency, which is about 60%.

[0051] Step 5: According to the particle position in the next time step, repeat steps 2 to 4 to update the electric and magnetic fields acting on the particles in each subdomain in the next time step.

[0052] Embodiment 3: In this embodiment, a vacuum confluence area electromagnetic particle simulation system is provided, which can be used to implement the above-mentioned vacuum confluence area electromagnetic particle simulation method. Specifically, the vacuum confluence area electromagnetic particle simulation system includes a particle simulation domain construction module, an electric potential and vector magnetic potential solution module, a particle motion module and an update module.

[0053] Among them, the particle simulation domain construction module is used to construct the particle simulation domain of the electric field and magnetic field in the vacuum confluence area, inject particles into the particle simulation domain, and decompose the particle simulation domain to obtain multiple subdomains. Each subdomain contains multiple grids, and each grid has four grid points.

[0054] The electric potential and vector magnetic potential solving module is used to obtain the charge density and current density of the grid points in each subdomain at the current time step; construct the Maxwell equations of the particle simulation domain, discretize the Maxwell equations, substitute the charge density and current density of the grid points in each subdomain into the discretized Maxwell equations, and use the GMRES algorithm to solve the electric potential and vector magnetic potential of the discretized Maxwell equations to obtain the distribution of the electric potential and vector magnetic potential in each subdomain.

[0055] The particle motion module is used to solve the electric field strength and magnetic induction intensity of the grid points in each subdomain according to the distribution of electric potential and vector magnetic potential in each subdomain, obtain the electric field and magnetic field exerted on the particles according to the electric field strength and magnetic induction intensity, and determine the particle position in the electric potential and vector magnetic potential solution module in each subdomain at the next time step according to the electric field and magnetic field exerted on the particles.

[0056] The update module is used to repeat the process from the electric potential and vector magnetic potential solving module to the update module according to the particle position in the next time step, and update the electric field and magnetic field received by the particles in each subdomain in the next time step.

[0057] Embodiment 4: In this embodiment, a terminal device is provided, which includes a processor and a memory, wherein the memory is used to store a computer program, the computer program includes program instructions, and the processor is used to execute the program instructions stored in the computer storage medium. The processor may be a central processing unit (CPU), or other general-purpose processors, digital signal processors (DSP), application-specific integrated circuits (ASIC), field-programmable gate arrays (FPGAs), or other processors. GateArray, FPGA) or other programmable logic devices, discrete gates or transistor logic devices, discrete hardware components, etc., which are the computing core and control core of the terminal, which are suitable for implementing one or more instructions, and are specifically suitable for loading and executing one or more instructions to implement corresponding method processes or corresponding functions; the processor described in the embodiment of the present invention can be used for the operation of the electromagnetic particle simulation method of the vacuum confluence area, including: S1: constructing a particle simulation domain of the electric field and magnetic field of the vacuum confluence area, injecting particles into the particle simulation domain, and performing regional decomposition on the particle simulation domain to obtain multiple subdomains, each subdomain contains multiple grids, and each grid has four grid points; S2: at the current time step, obtaining the charge density and current density of the grid points in each subdomain; constructing Maxwell equations in the particle simulation domain, discretize the Maxwell equations, substitute the charge density and current density of the grid points in each subdomain into the discretized Maxwell equations, use the GMRES algorithm to solve the electric potential and vector magnetic potential of the discretized Maxwell equations, and obtain the distribution of the electric potential and vector magnetic potential in each subdomain; S3: According to the distribution of the electric potential and vector magnetic potential in each subdomain, solve the electric field strength and magnetic induction intensity of the grid points in each subdomain, and obtain the electric field and magnetic field to which the particles are subjected based on the electric field strength and magnetic induction intensity, and determine the particle position in the next time step S2 in each subdomain based on the electric field and magnetic field to which the particles are subjected; S4: According to the particle position in the next time step, repeat S2 to S4 to update the electric field and magnetic field to which the particles are subjected in each subdomain at the next time step.

[0058] Embodiment 5: In this embodiment, a computer-readable storage medium (Memory) is provided, and the computer-readable storage medium is a memory device in a terminal device for storing programs and data. It can be understood that the computer-readable storage medium here can include both the built-in storage medium in the terminal device and the extended storage medium supported by the terminal device. The computer-readable storage medium provides a storage space, which stores the operating system of the terminal. In addition, one or more instructions suitable for being loaded and executed by the processor are also stored in the storage space, and these instructions can be one or more computer programs (including program codes). It should be noted that the computer-readable storage medium here can be a high-speed RAM memory (Random Access Memory) or a non-volatile memory (non-volatile memory), such as at least one disk storage.

[0059] The processor can load and execute one or more instructions stored in a computer-readable storage medium to implement the corresponding steps of the electromagnetic particle simulation method for a vacuum confluence area in the above-mentioned embodiment; one or more instructions in the computer-readable storage medium are loaded by the processor and the following steps are executed: S1: construct a particle simulation domain of the electric field and magnetic field in the vacuum confluence area, inject particles into the particle simulation domain, and perform regional decomposition on the particle simulation domain to obtain multiple subdomains, each of which contains multiple grids, and each grid has four grid points; S2: at the current time step, obtain the charge density and current density of the grid points in each subdomain; construct the Maxwell equations of the particle simulation domain, discretize the Maxwell equations, and convert The charge density and current density of the grid points in each subdomain are substituted into the discretized Maxwell equations, and the GMRES algorithm is used to solve the electric potential and vector magnetic potential of the discretized Maxwell equations to obtain the distribution of the electric potential and vector magnetic potential in each subdomain; S3: According to the distribution of the electric potential and vector magnetic potential in each subdomain, the electric field strength and magnetic induction intensity of the grid points in each subdomain are solved, and the electric field and magnetic field to which the particles are subjected are obtained according to the electric field strength and magnetic induction intensity, and the particle position in the next time step S2 in each subdomain is determined according to the electric field and magnetic field to which the particles are subjected; S4: According to the particle position in the next time step, S2 to S4 are repeated to update the electric field and magnetic field to which the particles are subjected in each subdomain at the next time step.

[0060] Those skilled in the art will appreciate that the embodiments of the present application may be provided as methods, systems, or computer program products. Therefore, the present application may take the form of a complete hardware embodiment, a complete software embodiment, or an embodiment combining software and hardware. Moreover, the present application may take the form of a computer program product implemented on one or more computer-usable storage media (including but not limited to disk storage, optical storage, etc.) containing computer-usable program codes.

[0061] The present application is described with reference to the flowcharts and / or block diagrams of the methods, devices (systems), and computer program products according to the embodiments of the present application. It should be understood that each process and / or box in the flowchart and / or block diagram, as well as the combination of the processes and / or boxes in the flowchart and / or block diagram, can be implemented by computer program instructions. These computer program instructions can be provided to a processor of a general-purpose computer, a special-purpose computer, an embedded processor, or other programmable data processing device to generate a machine, so that the instructions executed by the processor of the computer or other programmable data processing device generate instructions for implementing the processes in the flowchart and / or block diagram. Figure 1 A process or multiple processes and / or boxes Figure 1 A device that provides the functions specified in a block or multiple blocks.

[0062] These computer program instructions may also be stored in a computer-readable memory capable of directing a computer or other programmable data processing device to operate in a specific manner, so that the instructions stored in the computer-readable memory produce an article of manufacture comprising an instruction device, which implements the process Figure 1 A process or multiple processes and / or boxes Figure 1 A function specified in one or more boxes.

[0063] These computer program instructions can also be loaded onto a computer or other programmable data processing device so that a series of operating steps are executed on the computer or other programmable device to produce a computer-implemented process, thereby providing instructions for implementing the process. Figure 1 A process or multiple processes and / or boxes Figure 1 A step that specifies a function in one or more boxes.

[0064] In the above embodiments of the present application, the description of each embodiment has its own emphasis. For parts that are not described in detail in a certain embodiment, please refer to the relevant description of other embodiments.

[0065] The above is only a preferred implementation of the present application. It should be pointed out that for ordinary technicians in this technical field, several improvements and modifications can be made without departing from the principles of the present application. These improvements and modifications should also be regarded as the scope of protection of the present application.

[0066] It should be understood that the above description is for illustration and not for limitation. Many embodiments and many applications beyond the examples provided will be apparent to those skilled in the art by reading the above description.

Claims

1. A method for simulating electromagnetic particles in a vacuum confluence region, characterized in that: The process includes: S1: construct a particle simulation domain of the electric field and magnetic field in the vacuum confluence area, inject particles into the particle simulation domain, and perform regional decomposition on the particle simulation domain to obtain multiple subdomains, each of which contains multiple grids, and each grid has four grid points; S2: At the current time step, obtain the charge density and current density of the grid points in each subdomain; construct the Maxwell equations of the particle simulation domain, discretize the Maxwell equations, substitute the charge density and current density of the grid points in each subdomain into the discretized Maxwell equations, use the GMRES algorithm to solve the electric potential and vector magnetic potential of the discretized Maxwell equations, and obtain the distribution of the electric potential and vector magnetic potential in each subdomain; S3: According to the distribution of electric potential and vector magnetic potential in each subdomain, the electric field strength and magnetic induction strength of the grid points in each subdomain are obtained, and the electric field and magnetic field of the particle are obtained according to the electric field strength and magnetic induction strength. The position of the particle in the next time step in each subdomain is determined according to the electric field and magnetic field of the particle. S4: Repeat S2 to S4 according to the particle position in the next time step, and update the electric and magnetic fields acting on the particles in each subdomain in the next time step.

2. The vacuum confluence region electromagnetic particle simulation method according to claim 1, characterized in that: The process of constructing a particle simulation domain is as follows: setting the physical space and grid step of the particle simulation domain, constructing the particle simulation domain according to the physical space and grid step; setting the time step of particle simulation and the boundary of the particle simulation domain.

3. The vacuum confluence region electromagnetic particle simulation method according to claim 2, characterized in that: The process of setting the boundary of the particle simulation domain is as follows: assuming that the upper and lower boundaries of the particle simulation domain are ideal conductors, and the left and right boundaries of the particle simulation domain are regarded as particle absorption boundaries.

4. The vacuum confluence region electromagnetic particle simulation method according to claim 2, characterized in that: The Maxwell equations are discretized, and the charge density and current density of the grid points in each subdomain are substituted into the discretized Maxwell equations. The GMRES algorithm is used to solve the electric potential and vector magnetic potential of the discretized Maxwell equations, including: Write the electric potential and vector magnetic potential in Maxwell's equations in the form of Poisson's equations; According to the time step and grid step of particle simulation, the Poisson equation is discretized into the form of Cx=D equation by time domain difference method; In solving the electric potential, D in the Cx=D equation is the charge density at the grid point, C is the coefficient corresponding to each grid point in the electric potential Poisson equation, and x is the electric potential at each grid point; in solving the vector magnetic potential, D in the Cx=D equation is the current density at the corresponding grid point, C is the coefficient corresponding to each grid point in the vector magnetic potential Poisson equation, and x corresponds to the vector magnetic potential at the grid point; PETSc and MPI are used to solve the Cx=D equation at each grid point in parallel using the GMRES algorithm to obtain the electric potential and vector magnetic potential of the grid point in each subdomain.

5. The vacuum confluence region electromagnetic particle simulation method according to claim 1, characterized in that: The process of obtaining the current density at each grid point in each subdomain is as follows: According to the current distribution and waveform parameters under the actual working conditions of the vacuum confluence area, the current generated by the grid points in each subdomain is set to generate a static magnetic field, and the current density is obtained based on the current calculation of the static magnetic field.

6. The vacuum confluence region electromagnetic particle simulation method according to claim 1, characterized in that: The process of obtaining the charge density of the grid points in each subdomain is as follows: According to the particle position, the particle charge and the current generated by the particle motion are assigned to the grid points corresponding to the particle position according to the weights based on the double-line interpolation method. The charge amount of the grid point in each subdomain is obtained, and the charge density of the grid point is obtained by dividing the charge amount by the corresponding volume of the grid point.

7. The vacuum confluence region electromagnetic particle simulation method according to claim 1, characterized in that: The specific process of obtaining the electric and magnetic fields on the particles and determining the particle position in the next time step in each subdomain is as follows: The electric field strength and magnetic induction intensity of the grid points in each subdomain are interpolated to the corresponding particle position to obtain the electric field and magnetic field acting on the particle. The force on the particle is calculated based on the electric field and magnetic field acting on the particle. The particle velocity is obtained based on the force on the particle. The particle position in the next time step in each subdomain is calculated based on the particle velocity and the particle motion equation.

8. A vacuum confluence area electromagnetic particle simulation system, characterized in that: include: Particle simulation domain construction module: used to construct the particle simulation domain of the electric field and magnetic field in the vacuum confluence area, inject particles into the particle simulation domain, decompose the particle simulation domain into regions, and obtain multiple subdomains. Each subdomain contains multiple grids, and each grid has four grid points. Electric potential and vector magnetic potential solving module: used to obtain the charge density and current density of the grid points in each subdomain at the current time step; construct the Maxwell equations of the particle simulation domain, discretize the Maxwell equations, substitute the charge density and current density of the grid points in each subdomain into the discretized Maxwell equations, use the GMRES algorithm to solve the electric potential and vector magnetic potential of the discretized Maxwell equations, and obtain the distribution of the electric potential and vector magnetic potential in each subdomain; Particle motion module: used to solve the electric field strength and magnetic induction intensity of the grid points in each subdomain according to the distribution of electric potential and vector magnetic potential in each subdomain, obtain the electric field and magnetic field of the particle according to the electric field strength and magnetic induction intensity, and determine the particle position in the electric potential and vector magnetic potential solution module of each subdomain at the next time step according to the electric field and magnetic field of the particle; Update module: It is used to repeat the process from the electric potential and vector magnetic potential solving module to the update module according to the particle position in the next time step, and update the electric field and magnetic field exerted on the particles in each subdomain in the next time step.

9. A computer device comprising a memory, a processor, and a computer program stored in the memory and executable on the processor, characterized in that: When the processor executes the computer program, the steps of the vacuum confluence area electromagnetic particle simulation method according to any one of claims 1 to 7 are implemented.

10. A computer-readable storage medium storing a computer program, characterized in that: When the computer program is executed by a processor, the steps of the vacuum confluence area electromagnetic particle simulation method according to any one of claims 1 to 7 are implemented.

Images