An electromagnetic particle simulation method, system, device and medium for a vacuum confluence area

Abstract

The present invention belongs to the field of electromagnetic particle simulation, and relates to a method, system, device and medium for electromagnetic particle simulation in a vacuum confluence area, including the following processes: S1: Construct a particle simulation domain for 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 a plurality of sub-domains; S2: Obtain the charge density and current density of grid points in each sub-domain; discretize the Maxwell equations into the form of the Cx = D equation, substitute the charge density and current density of grid points in each sub-domain into the Cx = D equation, and use the GMRES algorithm to solve the Cx = D equation to obtain the electric potential and vector magnetic potential distributions in each sub-domain; S3: Solve to obtain the electric field strength and magnetic induction intensity of grid points in each sub-domain, obtain the electric field and magnetic field received by the particles, so as to determine the particle positions at the next time step in each sub-domain; S4: Update the electric field and magnetic field received by the particles in each sub-domain at the next time step.

Description

Technical Field

[0001] The present invention belongs to the field of electromagnetic particle simulation, and relates to a method, system, device and medium for electromagnetic particle simulation in a vacuum confluence area. Background Technique

[0002] With the development of pulse technology, the multi-physical field coupling effects (such as breakdown and discharge) of ultra-high power pulse transmission systems in extreme electromagnetic environments have become key issues restricting the reliability of the systems. 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 of concern to researchers. Research shows that the formation of plasma may occur during power transmission, resulting in shunting and current loss, and reducing the transmission efficiency of the system.

[0003] As a key component of high-power transmission systems, the vacuum confluence area and magnetic insulation transmission lines can converge the energy of multiple pulses, and then the inner magnetic insulation transmission line feeds the energy to the load. 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 first principles and can self-consistently obtain the particle and field distributions in space, and is one of the main methods currently used for simulation calculations. Using a two-dimensional axisymmetric structure, the electrostatic and static magnetic fields in space are solved. Traditional Jacobi iteration method, successive over-relaxation method (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 severely limits the computing speed of particle simulation. Summary of the Invention

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

[0005] To achieve the above purpose, the present invention adopts the following technical solutions:

[0006] An electromagnetic particle simulation method for a vacuum confluence area includes the following processes:

[0007] S1: Construct a particle simulation domain for the electric and magnetic fields in the vacuum confluence area, inject particles into the particle simulation domain, perform regional decomposition on the particle simulation domain to obtain a plurality of sub-domains, each sub-domain contains a plurality of grids, and each grid has four grid points;

[0008] S2: At the current time step, obtain the charge density and current density of the grid points in each sub-domain; construct the Maxwell's equations for the particle simulation domain, discretize the Maxwell's equations, substitute the charge density and current density of the grid points in each sub-domain into the discretized Maxwell's equations, and use the GMRES algorithm to solve for the electric potential and vector magnetic potential of the discretized Maxwell's equations to obtain the distributions of the electric potential and vector magnetic potential in each sub-domain;

[0009] S3: According to the distributions of the electric potential and vector magnetic potential in each sub-domain, solve to obtain the electric field intensity and magnetic induction intensity of the grid points in each sub-domain, obtain the electric and magnetic fields acting on the particles based on the electric field intensity and magnetic induction intensity, and determine the particle positions in S2 at the next time step in each sub-domain according to the electric and magnetic fields acting on the particles;

[0010] S4: According to the particle positions at the next time step, repeat S2 to S4 to update the electric and magnetic fields acting on the particles in each sub-domain at the next time step.

[0011] Preferably, the construction process of the particle simulation domain is as follows: set the physical space and grid step size of the particle simulation domain, construct the particle simulation domain according to the physical space and grid step size, and set the time step size of the particle simulation and the boundaries of the particle simulation domain.

[0012] Preferably, the process of setting the boundaries of the particle simulation domain is as follows: assume 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.

[0013] Preferably, the discretization of the Maxwell's equations, substituting the charge density and current density of the grid points in each sub-domain into the discretized Maxwell's equations, and using the GMRES algorithm to solve for the electric potential and vector magnetic potential of the discretized Maxwell's equations includes:

[0014] Write the electric potential and vector magnetic potential in the Maxwell's equations in the form of Poisson's equations;

[0015] According to the time step size of the particle simulation and the grid step size, discretize the Poisson's equations by the finite-difference time-domain method into the form of the Cx = D equation;

[0016] Use PETSc and MPI to solve the Cx = D equations at each grid point in parallel by the GMRES algorithm to obtain the electric potential and vector magnetic potential of the grid points in each sub-domain.

[0017] Preferably, the process of obtaining the current density of the grid points in each sub-domain is as follows: according to the current distribution and waveform parameters under the actual working conditions of the vacuum confluence area, set the current generating the static magnetic field at the grid points in each sub-domain, and calculate the current density based on the current of the static magnetic field.

[0018] Preferably, the process of obtaining the charge density of grid points in each subdomain is as follows: According to the particle positions, the particle charge and the current generated by the particle motion are assigned to the grid points corresponding to the particle positions based on the bilinear interpolation method, to obtain the amount of charge of the grid points in each subdomain, and then the charge density of the grid points is obtained by dividing the amount of charge by the volume corresponding to the grid points.

[0019] Preferably, the specific process of obtaining the electric and magnetic fields acting on the particles, and thus determining the particle positions at the next time step in each subdomain is as follows: The electric field intensity and magnetic induction intensity of the grid points in each subdomain are interpolated to the corresponding particle positions to obtain the electric and magnetic fields acting on the particles. Based on the electric and magnetic fields acting on the particles, the force on the particles is calculated. Based on the force on the particles, the particle velocity is obtained. Based on the particle velocity and the particle motion equation, the particle positions at the next time step in each subdomain are calculated.

[0020] An electromagnetic particle simulation system for a vacuum confluence area, comprising:

[0021] A particle simulation domain construction module: used to construct a particle simulation domain for the electric and magnetic fields in the vacuum confluence area, inject particles into the particle simulation domain, perform regional decomposition on the particle simulation domain to obtain a plurality of subdomains, each subdomain contains a plurality of grids, and each grid has four grid points;

[0022] A 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, and use the GMRES algorithm to solve the potential and vector magnetic potential of the discretized Maxwell equations to obtain the distribution of the potential and vector magnetic potential in each subdomain;

[0023] A particle motion module: used to solve and obtain the electric field intensity and magnetic induction intensity of the grid points in each subdomain according to the distribution of the potential and vector magnetic potential in each subdomain, obtain the electric and magnetic fields acting on the particles according to the electric field intensity and magnetic induction intensity, and determine the particle positions in the potential and vector magnetic potential solving module at the next time step in each subdomain according to the electric and magnetic fields acting on the particles;

[0024] An update module: used to repeat the process from the potential and vector magnetic potential solving module to the update module according to the particle positions at the next time step, and update the electric and magnetic fields acting on the particles in each subdomain at the next time step.

[0025] A computer device, comprising a memory, a processor, and a computer program stored in the memory and executable on the processor, wherein when the processor executes the computer program, the steps of the electromagnetic particle simulation method for the vacuum confluence area are implemented.

[0026] A computer-readable storage medium stores a computer program, and when the computer program is executed by a processor, the steps of the electromagnetic particle simulation method for the vacuum confluence region are implemented.

[0027] Compared with the prior art, the present invention has the following beneficial effects:

[0028] The electromagnetic particle simulation method for the vacuum confluence region according to 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. Through the domain decomposition technique, a high-performance parallel computing system for the Poisson equation and the particle motion equation is constructed, which supports various complex particle and field boundary conditions. Combining the domain decomposition strategy, high-performance numerical simulation of high-power vacuum confluence regions and related components on a large spatial scale can be realized. The finite-difference time-domain method is used to discretize the Maxwell equations, and the problems are simplified according to the characteristic working conditions of high-power confluence regions and related components. Ignoring the time-varying electromagnetic fields, the distributed parallel efficient solution of the Poisson equations for electric potential and vector magnetic potential and the particle motion equation is carried out, 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 more than 60% higher than that of the Successive Over Relaxation (SOR) method. Description of the Drawings

[0029] Figure 1 It is a flowchart of the electromagnetic particle simulation method for the vacuum confluence region in Embodiment 1 of the present invention;

[0030] Figure 2 It is a schematic diagram of the area-based z-r bilinear interpolation method in Embodiment 2 of the present invention;

[0031] Figure 3 It is a comparison chart of the calculation speeds of PETSc and SOR in Embodiment 2 of the present invention. Detailed Embodiments

[0032] Next, the technical solutions in the embodiments of the present application will be clearly and completely described in conjunction with the accompanying drawings in the embodiments of the present application.

[0033] Embodiment 1:

[0034] In this embodiment, an electromagnetic particle simulation method for the vacuum confluence region is provided, as Figure 1As shown, it includes the following processes:

[0035] S1: Construct a particle simulation domain for the electric and magnetic fields in the vacuum confluence region, inject particles into the particle simulation domain, perform domain decomposition on the particle simulation domain to obtain multiple subdomains, each subdomain contains multiple grids, and each grid has four grid points;

[0036] S2: At the current time step, obtain the charge density and current density of the grid points in each subdomain; construct the Maxwell equations for 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 for 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;

[0037] S3: According to the distribution of the electric potential and vector magnetic potential in each subdomain, solve to obtain the electric field strength and magnetic induction intensity of the grid points in each subdomain, obtain the electric and magnetic fields acting on the particles based on the electric field strength and magnetic induction intensity, and determine the particle positions in S2 at the next time step in each subdomain according to the electric and magnetic fields acting on the particles;

[0038] S4: According to the particle positions at the next time step, repeat S2 to S4 to update the electric and magnetic fields acting on the particles in each subdomain at the next time step.

[0039] Example 2:

[0040] In this example, an electromagnetic particle simulation method for the vacuum confluence region is provided, including the following processes:

[0041] Step 1: Set the physical space and grid step size of the particle simulation domain, construct a particle simulation domain for the electric and magnetic fields in the vacuum confluence region according to the physical space and grid step size. The particle simulation domain is a two-dimensional axisymmetric structure. Divide the particle simulation domain into multiple uniform grids. Assume 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.

[0042] Perform domain decomposition on the particle simulation domain to obtain multiple subdomains. Each subdomain contains multiple uniform grids, and each grid has four grid points.

[0043] Inject the particles required for simulation into the particle simulation domain. The particles include charged particles and neutral particles, and initialize the particle positions and velocity distributions.

[0044] Step 2: At the current time step, based on the particle positions, assign the particle charges and the currents generated by particle motion to the grid points corresponding to the particle positions according to the bilinear interpolation method with weights, calculate the charge amounts of the grid points in each sub-domain, and divide the charge amount by the volume corresponding to the grid point to obtain the charge density of the grid point; according to the current distribution and waveform parameters under the actual working conditions of the vacuum confluence area, set the current generating the static magnetic field at the grid points in each sub-domain, and divide the current by the area corresponding to the grid point to obtain the current density.

[0045] Specifically, as Figure 2 shown, considering both the calculation accuracy and the calculation complexity, adopt the area-based z-r bilinear interpolation method. This interpolation method divides the grid into four small rectangular regions centered on the position of the particle, and determines the weights for charge distribution by the ratio of the area of the small rectangular region to the area of the grid, so that the grid points closer to the particle can be assigned more charges. The weights of the four grid points are:

[0046]

[0047] 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 are the coordinates of the particle, z i , r j are the coordinates of the lower left grid point in a grid, z i+1 , r j are the coordinates of the lower right grid point in a grid, z i , r j+1 are the coordinates of the upper left grid point in a grid, z i+1 , r j+1 are the coordinates of the upper right grid point in a grid.

[0048] This interpolation method divides the grid into four small rectangular regions centered on the position of the particle, and determines the weights for charge distribution by the ratio of the areas of the four small rectangular regions to the area of the grid, so that the grid points closer to the particle can be assigned more charges. The charge contribution amounts of the particle to the surrounding four grid points are:

[0049]

[0050] In the formula: q p is the charge amount 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, wi+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. q 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.

[0051] The weight assignment rule for the current density is consistent with the above charge density assignment method.

[0052] Thus, the electric charge amount of the grid point can be obtained , and then the charge density is calculated :

[0053]

[0054] In the formula: V i，j is the grid volume, is the total electric charge amount of the grid point, is the charge density of the grid point.

[0055] At the same time, the current generating the static magnetic field at the grid point is obtained , and then the current density is calculated :

[0056]

[0057] In the formula: S i，j is the grid area, is the total current of the grid point, is the current density of the grid point.

[0058] Step 3: Construct the Maxwell's equations for describing the electric field and magnetic field in the particle simulation domain. According to the time step and grid step of the particle simulation, discretize the Maxwell's equations by the finite-difference time-domain method, discretize the Poisson's equation into the form of Cx = D equation, obtain the coefficient matrix C of each grid point, and initialize the coefficient matrix according to the initial boundary conditions of the particle simulation domain. Subsequently, substitute the charge density and current density of the grid points in each sub-domain into the Cx = D equation, and use the GMRES algorithm to solve the Cx = D equation for the electric potential and vector magnetic potential, so as to obtain the distributions of the electric potential and vector magnetic potential in each sub-domain.

[0059] In the solution of 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 of electric potential, and the quantity to be solved x is the electric potential at each grid point; in the solution of 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 of vector magnetic potential, and the quantity to be solved x is the vector magnetic potential at the corresponding grid point.

[0060] Specifically, without considering the variables of the electric and magnetic fields, the involved Maxwell's equations can be written as:

[0061]

[0062] In the formula, is the curl operator, B is the magnetic induction intensity, E is the electric field intensity, 0 is the vacuum permeability, J is the charge density. At the same time, according to:

[0063]

[0064] In the formula, A is the vector magnetic potential, is the curl operator, B is the magnetic induction intensity, E is the electric field intensity, is the electric potential, is the gradient operator.

[0065] The electric potential and vector magnetic potential equations in each subdomain can be written in the form of Poisson equations:

[0066]

[0067] In the formula, e is the charge density, 0 is the vacuum permittivity, is the electric potential, A is the vector magnetic potential, 0 is the vacuum permeability, J is the charge density, is the gradient operator.

[0068] Writing the electric potential and vector magnetic potential in the form of Poisson's equation helps to unify the equation format and is conducive to accelerating the solution. According to the time step and grid step of particle simulation, the Poisson equations of the electric potential and vector magnetic potential are discretized into the form of Cx = D equations by the finite-difference time-domain method. The charge density and current density of the grid points in each subdomain are substituted into the Cx = D equations, and the GMRES algorithm is used to solve the Cx = D equations at each grid point in parallel through PETSc (Portable, Extensible Toolkit for Scientific Computation) and MPI (Message Passing Interface), so as to obtain the electric potential and vector magnetic potential of the grid points in each subdomain, and then obtain the distribution of the electric potential and vector magnetic potential in each subdomain.

[0069] Step 4: According to the distribution of the electric potential and vector magnetic potential in each subdomain, solve to obtain the electric field strength and magnetic induction intensity of the grid points in each subdomain, obtain the electric and magnetic fields acting on the particles based on the electric field strength and magnetic induction intensity, and then determine the particle positions at the next time step in each subdomain according to the particle motion equation.

[0070] Specifically, according to the electric potential distribution in each subdomain, calculate the electric field strength:

[0071]

[0072] In the formula, is the electric potential, E z is the axial electric field, E r is the radial electric field, is the partial derivative symbol.

[0073] For non-boundary points, the central difference method is used to obtain the electric field:

[0074]

[0075] In the formula, i，j+1 is the electric potential of the upper grid point, i，j-1 is the electric potential of the lower grid point, 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 (i, j) of the grid point.

[0076] For the boundary points of the particle simulation domain, a certain adjacent grid point of the boundary point may be outside the computational domain. In this case, the forward or backward difference method needs to be used to obtain the electric field:

[0077]

[0078] 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 strength at the upper boundary; i，j is the electric potential at the current grid point, i-1，j is the electric potential at a grid point to the left, i-2，j is the electric potential at two grid points to the left, i，j-1 is the electric potential at a grid point below, i，j-2 is the electric potential at two grid points below, i+1，j is the electric potential at a grid point to the right, i+2，j is the electric potential at two grid points to the right, i，j+1 is the electric potential at a grid point above, i，j+2 is the electric potential at two grid points above, is the grid width in the z direction, is the grid width in the r direction, i, j represent the two-dimensional coordinates (i, j) of the grid point.

[0079] According to the vector magnetic potential distribution in each subdomain, the magnetic induction intensity B in the two-dimensional axisymmetric region is updated as follows:

[0080]

[0081] 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 symbol of partial derivative. The treatment of boundary and non-boundary points is consistent with the method for solving the electric field strength.

[0082] Interpolate the electric field strength and magnetic induction intensity of the grid points in each sub-domain to the corresponding particle positions to obtain the electric and magnetic fields acting on the particles. Calculate the particle force based on the electric and magnetic fields acting on the particles, obtain the particle velocity based on the particle force, and calculate the particle positions at the next time step in each sub-domain based on the particle velocity and the particle motion equation. At the same time, perform parallel communication on the data of the virtual grid layer outside the sub-domain boundary to facilitate the field calculation in the current sub-domain.

[0083] As Figure 3 shown, for different numbers of simulation steps, the CPU (Central Processing Unit) time consumed by the main loop and the Poisson equation using the GMRES (Generalized Minimum RESidual) algorithm through PETSc and the Successive Over Relaxation (SOR) method is presented. Here, the main loop refers to the entire outer loop composed of the electric and magnetic field solutions and the particle motion solution. For the same solution method, the fast solution of the Poisson equation is crucial for the overall acceleration of the main loop. For different solution methods, the CPU time consumed for solving the Poisson equation through PETSc is significantly less than that using the Successive Over Relaxation (SOR) method to solve the Poisson equation. The method of the present invention has a significant improvement effect on the calculation efficiency, about 60%.

[0084] Step 5:

[0085] According to the particle positions at the next time step, repeat Steps 2 to 4 to update the electric and magnetic fields acting on the particles in each sub-domain at the next time step.

[0086] Embodiment 3:

[0087] In this embodiment, an electromagnetic particle simulation system for a vacuum confluence area is provided. The electromagnetic particle simulation system for the vacuum confluence area can be used to implement the above-mentioned electromagnetic particle simulation method for the vacuum confluence area. Specifically, the electromagnetic particle simulation system for the vacuum confluence area includes a particle simulation domain construction module, an electric potential and vector magnetic potential solution module, a particle motion module, and an update module.

[0088] Among them, the particle simulation domain construction module is used to construct a particle simulation domain for the electric and magnetic fields in the vacuum confluence area, inject particles into the particle simulation domain, perform domain decomposition on the particle simulation domain to obtain a plurality of sub-domains, each sub-domain contains a plurality of grids, and each grid has four grid points.

[0089] The electric potential and vector magnetic potential solving module is used to obtain the charge density and current density of grid points in each sub-domain at the current time step; construct the Maxwell's equations of the particle simulation domain, discretize the Maxwell's equations, substitute the charge density and current density of grid points in each sub-domain into the discretized Maxwell's equations, and use the GMRES algorithm to solve the electric potential and vector magnetic potential of the discretized Maxwell's equations to obtain the distribution of the electric potential and vector magnetic potential in each sub-domain.

[0090] The particle motion module is used to solve and obtain the electric field strength and magnetic induction intensity of grid points in each sub-domain according to the distribution of the electric potential and vector magnetic potential in each sub-domain, obtain the electric and magnetic fields acting on the particles according to the electric field strength and magnetic induction intensity, and determine the particle positions in the electric potential and vector magnetic potential solving module at the next time step in each sub-domain according to the electric and magnetic fields acting on the particles.

[0091] 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 positions at the next time step, and update the electric and magnetic fields acting on the particles in each sub-domain at the next time step.

[0092] Embodiment 4:

[0093] In this embodiment, a terminal device is provided. The terminal device includes a processor and a memory. The memory is used to store a computer program, and the computer program includes program instructions. 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 may also be other general-purpose processors, Digital Signal Processors (DSPs), Application Specific Integrated Circuits (ASICs), Field-Programmable Gate Arrays (FPGAs), or other programmable logic devices, discrete gate or transistor logic devices, discrete hardware components, etc. It is the computing core and control core of the terminal, and is suitable for implementing one or more instructions. Specifically, it is suitable for loading and executing one or more instructions to implement the corresponding method flow or corresponding function. The processor described in the embodiments of the present invention can be used for the operation of the electromagnetic particle simulation method in the vacuum confluence area, including: S1: Construct a particle simulation domain for the electric and magnetic fields in the vacuum confluence area, inject particles into the particle simulation domain, perform domain decomposition on the particle simulation domain to obtain multiple sub-domains, each sub-domain 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 sub-domain; 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 sub-domain into the discretized Maxwell equations, and use the GMRES algorithm to solve the discretized Maxwell equations for the electric potential and vector magnetic potential to obtain the distribution of the electric potential and vector magnetic potential in each sub-domain; S3: According to the distribution of the electric potential and vector magnetic potential in each sub-domain, solve to obtain the electric field strength and magnetic induction intensity of the grid points in each sub-domain, obtain the electric and magnetic fields received by the particles based on the electric field strength and magnetic induction intensity, and determine the particle positions in the next time step S2 in each sub-domain based on the electric and magnetic fields received by the particles; S4: According to the particle positions in the next time step, repeat S2 to S4 to update the electric and magnetic fields received by the particles in each sub-domain at the next time step.

[0094] Embodiment 5:

[0095] In this embodiment, a computer-readable storage medium (Memory) is provided. The computer-readable storage medium is a memory device in a terminal device and is used to store 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, of course, the extended storage medium supported by the terminal device. The computer-readable storage medium provides a storage space, and this storage space stores the operating system of the terminal. Moreover, in this storage space, one or more instructions suitable for being loaded and executed by a processor are also stored. 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, such as at least one disk memory.

[0096] One or more instructions stored in the computer-readable storage medium can be loaded and executed by a processor to implement the corresponding steps of the electromagnetic particle simulation method in the vacuum confluence area in the above embodiment; one or more instructions in the computer-readable storage medium are loaded and executed by the processor to perform the following steps: S1: Construct a particle simulation domain for the electric and magnetic fields in the vacuum confluence area, inject particles into the particle simulation domain, perform domain decomposition on the particle simulation domain to obtain multiple sub-domains, each sub-domain 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 sub-domain; 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 sub-domain into the discretized Maxwell equations, and use the GMRES algorithm to solve the discretized Maxwell equations for the electric potential and vector magnetic potential to obtain the distribution of the electric potential and vector magnetic potential in each sub-domain; S3: According to the distribution of the electric potential and vector magnetic potential in each sub-domain, solve to obtain the electric field strength and magnetic induction intensity of the grid points in each sub-domain, obtain the electric and magnetic fields acting on the particles based on the electric field strength and magnetic induction intensity, and determine the particle positions in S2 at the next time step in each sub-domain based on the electric and magnetic fields acting on the particles; S4: According to the particle positions at the next time step, repeat S2 to S4 to update the electric and magnetic fields acting on the particles in each sub-domain at the next time step.

[0097] Those skilled in the art should understand that the embodiments of the present application can be provided as a method, a system, or a computer program product. Therefore, the present application can take the form of a complete hardware embodiment, a complete software embodiment, or an embodiment combining software and hardware aspects. Moreover, the present application can 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.) that contain computer-usable program code.

[0098] The present application is described with reference to the flowcharts and / or block diagrams of methods, devices (systems), and computer program products according to the embodiments of the present application. It should be understood that each flow and / or block in the flowchart and / or block diagram, as well as the combination of flows and / or blocks in the flowchart and / or block diagram, can be implemented by computer program instructions. These computer program instructions can be provided to the processor of a general-purpose computer, a special-purpose computer, an embedded processor, or other programmable data processing devices to generate a machine, such that the instructions executed by the processor of the computer or other programmable data processing devices generate means for implementing the functions specified in Figure 1 one flow or multiple flows and / or blocks Figure 1 one block or multiple blocks.

[0099] These computer program instructions can also be stored in a computer-readable memory that can direct a computer or other programmable data processing device to work in a specific manner, such that the instructions stored in the computer-readable memory generate a manufactured article including instruction means that implement the functions specified in Figure 1 one flow or multiple flows and / or blocks Figure 1 one block or multiple blocks.

[0100] These computer program instructions can also be loaded onto a computer or other programmable data processing device, such that a series of operation steps are executed on the computer or other programmable device to generate a computer-implemented process, and thus the instructions executed on the computer or other programmable device provide steps for implementing the functions specified in Figure 1 one flow or multiple flows and / or blocks Figure 1 one block or multiple blocks.

[0101] In the above embodiments of the present application, the descriptions of the respective embodiments have their own emphases. For parts not detailed in a certain embodiment, reference can be made to the relevant descriptions of other embodiments.

[0102] The above are only the preferred embodiments of the present application. It should be noted that for those of ordinary skill in the art, without departing from the principle of the present application, several improvements and refinements can be made, and these improvements and refinements should also be regarded as the protection scope of the present application.

[0103] It should be understood that the above description is for illustration purposes and not for limitation. Many embodiments and many applications other than the provided examples will be apparent to those skilled in the art upon 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.

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