Method and device for determining plasma phase space control equation

Abstract

The present application provides a method and device for determining a plasma phase space control equation, which relates to the field of complex system control technology. The method comprises: simulating and sampling a plasma system to obtain particle information and phase space data of each particle in the plasma system, wherein the plasma system comprises multiple types of particles; for each time step, in a two-dimensional grid of particle velocity and position, the particle information and phase space data of each particle are counted to obtain a particle distribution function; a linear equation is constructed, and a linear combination of candidate items in the linear equation is performed to represent the plasma phase space control equation, wherein the candidate items include partial derivatives of various orders of the particle distribution function with respect to the phase space coordinates and the power of the partial derivatives; and the weight of each candidate item is calculated to determine the plasma phase space control equation. The method can solve the problem that the plasma system cannot be deduced based on data drive.

Description

Technical Field

[0001] The present application relates to the field of complex system control, and in particular, to a method and device for determining a plasma phase space control equation. Background Art

[0002] Complex nonlinear dynamic systems are widely present in nature and industry. When studying the characteristics of complex systems, it is necessary to derive the control equations of the systems. However, complex systems are composed of a large number of interacting units, and their activities are nonlinear, forming a complex organization with countless levels. Therefore, it is difficult to derive the control equations of complex systems using traditional theoretical methods.

[0003] At present, complex nonlinear dynamic systems are often modeled based on data-driven methods to obtain the basic characteristics of complex systems. Data-driven methods can be used in the field of fluid mechanics to deduce the transport equations, vorticity equations, and Navier-Stokes equations with additional terms for complex fluid systems, where the independent variable is the fluid velocity. However, in plasma systems, the independent variable is the particle distribution function, which cannot be directly obtained through experiments or simulations. Therefore, there is currently a problem that plasma systems cannot be deduced based on data-driven methods. Summary of the invention

[0004] Based on this, the purpose of the embodiments of the present application is to provide a method and device for determining the plasma phase space control equation, so as to solve the problem that the plasma system cannot be deduced based on data drive at present.

[0005] In a first aspect, an embodiment of the present application provides a method for determining a plasma phase space control equation, comprising:

[0006] Simulating and sampling a plasma system to obtain particle information and phase space data of each particle in the plasma system, wherein the plasma system includes multiple types of particles;

[0007] For each time step, in a two-dimensional grid of the velocity and position of the particle, counting the particle information and the phase space data of each particle to obtain a particle distribution function;

[0008] Constructing a linear equation, and linearly combining candidate items in the linear equation to express the plasma phase space control equation, wherein the candidate items include partial derivatives of various orders of the particle distribution function with respect to the phase space coordinates and powers of the partial derivatives;

[0009] A weight is calculated for each of the candidates to determine the plasma phase space governing equations.

[0010] In the above implementation process, based on the deduction method of three-dimensional phase space, a linear system is constructed, the phase space equation is represented by a combination of candidates of the linear equation, and the phase space control equation of the unknown plasma system is determined by preprocessing the data of the simulation or sampling of the plasma system, so as to realize the data-driven deduction of the unknown plasma system.

[0011] Optionally, counting the particle information and the phase space data of each particle in the two-dimensional grid of the velocity and position of the particle to obtain a particle distribution function comprises:

[0012] Determining the distribution of the particles in the two-dimensional grid based on the velocity and position information of the particles;

[0013] All particles are interpolated onto the grid points of the two-dimensional grid based on an area weighting method to convert the phase space data into the particle distribution function.

[0014] The interpolating all particles to the grid points of the two-dimensional grid based on the area weight method includes:

[0015] For a particle, respectively calculating the number of particles at the four grid points closest to the particle and the area of ​​the grid in the two-dimensional grid;

[0016] The particle distribution function for each time step is determined based on the number of particles at the grid points and the area of ​​the grid.

[0017] The number of particles at the four grid points is specifically: and Where i and j are the grid points, (x0, v0) are the coordinates of the particle, and N(x, v) i,j is the number of particles at the grid point (i, j), Δx and Δv are the lengths of the grid on the two-dimensional coordinate axes respectively;

[0018] The determining of the particle distribution function for each time step based on the number of particles at the grid points and the area of ​​the grid comprises:

[0019] For each time step, the particle distribution function is determined based on the number of particles at the grid point and the area of ​​the grid as f(x, v, t k ) i,j =N(x,v) i,j / (ΔxΔv), where t k is the time step.

[0020] In the above implementation process, a grid is divided on a two-dimensional coordinate system, and the independent variables of the plasma phase space control equation are obtained by determining the particle distribution on the grid points, thereby obtaining the implicit function data in the phase space through the general space data, thereby realizing the deduction of the unknown plasma phase space control equation.

[0021] Optionally, constructing a linear equation and linearly combining candidate items in the linear equation to express the plasma phase space control equation comprises:

[0022] Based on the formula f t =G(f,f x ,f v ,f xx ,f vv …) represents the plasma phase space governing equation, where f is the particle distribution function in the phase space, f t 、f x and f v are the partial derivatives of the particle distribution function with respect to the time coordinate, space coordinate and velocity coordinate respectively, G is a linear operator, f xx and f vv are the high-order partial derivatives of space coordinates and velocity coordinates respectively;

[0023] Select the values ​​of the candidate items to construct the linear equation U t =θ(U,Q)ξ, where U t is a column vector composed of the partial derivatives of the particle distribution function with respect to the time coordinate, θ(U,Q) is a q-order matrix composed of all candidate items, Q is the number of the candidate items, and ξ is a sparse column vector of q rows, representing the weight of each candidate item.

[0024] In the above implementation process, a linear equation is constructed to characterize the plasma phase space control equation in a way of calculating the weight of each candidate, which can collect the spatiotemporal information of the plasma system to obtain the control equation of the system, thereby analyzing the spatial plasma state in a larger range and at future times.

[0025] Optionally, calculating the weight of each candidate to determine the plasma phase space governing equation comprises:

[0026] Performing sparse regression on the linear equation based on the least square method with regularization to obtain a weight vector of the weights;

[0027] The plasma phase space governing equation is determined based on the weight vector.

[0028] The step of performing sparse regression on the linear equation based on the least square method with regularization to obtain the weight vector of the weights includes:

[0029] Calculate the binary norm of the sparse column vector, and when iteratively calculating the weight of each candidate item through the linear equation, set the weights less than a preset weight threshold to 0, and recursively operate on the weights greater than the preset weight threshold to perform sparse regression on the weights to obtain the weight vector.

[0030] The step of calculating the weight of each candidate to determine the plasma phase space governing equation comprises: based on the formula Calculate the weight of the candidate, where ξ is the weight of the candidate, θ is the matrix composed of all the candidate, U t is a column vector composed of the partial derivatives of the particle distribution function with respect to the time coordinate, and λ is a complexity parameter for controlling the reduction amount.

[0031] In the above implementation process, through sparse regression, the least squares method with a regularization term is used to realize feature selection of candidate items, obtain accurate weight vectors, realize the deduction of unknown plasma phase space control equations, and improve the accuracy of the obtained plasma phase space control equations.

[0032] Optionally, the sampling includes full sampling and local sampling, and before simulating and sampling the plasma system, the method may further include:

[0033] The plasma system is sampled by full sampling or partial sampling based on the size of the sampling area.

[0034] In the above implementation process, the sampling method can be determined according to the size of the sampling area in the plasma system. When the sampling area is large, the full sampling method can be used to improve the sampling efficiency. When the sampling area is small, the local sampling method can be used to improve the sampling accuracy. This improves the flexibility of sampling and can take into account both sampling efficiency and accuracy.

[0035] In a second aspect, an embodiment of the present application provides a device for determining a plasma phase space control equation, comprising:

[0036] A data acquisition module, used to simulate and sample a plasma system to obtain particle information and phase space data of each particle in the plasma system, wherein the plasma system includes multiple types of particles;

[0037] A data preprocessing module, for counting the particle information and the phase space data of each particle in a two-dimensional grid of the velocity and position of the particle for each time step, so as to obtain a particle distribution function;

[0038] A linear system building module, used for building a linear equation, performing linear combination on candidate items in the linear equation to express the plasma phase space control equation, wherein the candidate items include partial derivatives of various orders of the particle distribution function with respect to the phase space coordinates and the powers of the partial derivatives;

[0039] A sparse regression module is used to calculate the weight of each candidate to determine the plasma phase space governing equation.

[0040] In the above implementation process, based on the deduction method of three-dimensional phase space, a linear system is constructed, the phase space equation is represented by a combination of candidates of the linear equation, and the phase space control equation of the unknown plasma system is determined by preprocessing the data of the simulation or sampling of the plasma system, so as to realize the data-driven deduction of the unknown plasma system.

[0041] Optionally, the data preprocessing module may be specifically used for:

[0042] Determining the distribution of the particles in the two-dimensional grid based on the velocity and position information of the particles;

[0043] All particles are interpolated onto the grid points of the two-dimensional grid based on an area weighting method to convert the phase space data into the particle distribution function.

[0044] For a particle, respectively calculating the number of particles at the four grid points closest to the particle and the area of ​​the grid in the two-dimensional grid;

[0045] The particle distribution function for each time step is determined based on the number of particles at the grid points and the area of ​​the grid.

[0046] The number of particles at the four grid points is specifically: and Where i and j are the grid points, (x0, v0) are the coordinates of the particle, and N(x, v) i,j is the number of particles at the grid point (i, j), Δx and Δv are the lengths of the grid on the two-dimensional coordinate axes respectively;

[0047] The determining of the particle distribution function for each time step based on the number of particles at the grid points and the area of ​​the grid comprises:

[0048] For each time step, the particle distribution function is determined based on the number of particles at the grid point and the area of ​​the grid as f(x, v, t k ) i,j =N(x,v) i,j / (ΔxΔv), where tk is the time step.

[0049] In the above implementation process, a grid is divided on a two-dimensional coordinate system, and the independent variables of the plasma phase space control equation are obtained by determining the particle distribution on the grid points, thereby obtaining the implicit function data in the phase space through the general space data, thereby realizing the deduction of the unknown plasma phase space control equation.

[0050] Optionally, the linear system building block can be specifically used to:

[0051] Based on the formula f t =G(f,f x ,f v ,f xx ,f vv …) represents the plasma phase space governing equation, where f is the particle distribution function in the phase space, f t 、f x and f v are the partial derivatives of the particle distribution function with respect to the time coordinate, space coordinate and velocity coordinate respectively, G is a linear operator, f xx and f vv are the high-order partial derivatives of space coordinates and velocity coordinates respectively;

[0052] Select the values ​​of the candidate items to construct the linear equation U t =θ(U,Q)ξ, where U t is a column vector composed of the partial derivatives of the particle distribution function with respect to the time coordinate, θ(U,Q) is a q-order matrix composed of all candidate items, Q is the number of the candidate items, and ξ is a sparse column vector of q rows, representing the weight of each candidate item.

[0053] In the above implementation process, a linear equation is constructed to characterize the plasma phase space control equation in a way of calculating the weight of each candidate, which can collect the spatiotemporal information of the plasma system to obtain the control equation of the system, thereby analyzing the spatial plasma state in a larger range and at future times.

[0054] Optionally, the sparse regression module can be specifically used to:

[0055] Performing sparse regression on the linear equation based on the least square method with regularization to obtain a weight vector of the weights;

[0056] The plasma phase space governing equation is determined based on the weight vector.

[0057] Calculate the bi-norm of the sparse column vector, and when the linear equation is iteratively calculated to obtain the weight of each candidate, set the weight less than the preset weight threshold to 0, and recursively operate the weight greater than the preset weight threshold to perform sparse regression on the weight to obtain the weight vector. Wherein, based on the formula Calculate the weight of the candidate, where ξ is the weight of the candidate, θ is the matrix composed of all the candidate, U t is a column vector composed of the partial derivatives of the particle distribution function with respect to the time coordinate, and λ is a complexity parameter for controlling the reduction amount.

[0058] In the above implementation process, through sparse regression, the least squares method with a regularization term is used to realize feature selection of candidate items, obtain accurate weight vectors, realize the deduction of unknown plasma phase space control equations, and improve the accuracy of the obtained plasma phase space control equations.

[0059] Optionally, the data acquisition module may also be used to:

[0060] The sampling includes full sampling and local sampling. Before simulating and sampling the plasma system, it is determined whether to sample the plasma system in a full sampling or local sampling manner based on the size of the sampling area.

[0061] In the above implementation process, the sampling method can be determined according to the size of the sampling area in the plasma system. When the sampling area is large, the full sampling method can be used to improve the sampling efficiency. When the sampling area is small, the local sampling method can be used to improve the sampling accuracy. This improves the flexibility of sampling and can take into account both sampling efficiency and accuracy.

[0062] In a third aspect, an embodiment of the present application provides an electronic device, comprising a memory and a processor, wherein the memory stores program instructions, and when the processor reads and runs the program instructions, it executes the steps in any of the above implementation methods.

[0063] In a fourth aspect, an embodiment of the present application further provides a computer-readable storage medium, wherein the computer-readable storage medium stores computer program instructions, and when the computer program instructions are read and executed by a processor, the steps in any of the above-mentioned implementation methods are executed. BRIEF DESCRIPTION OF THE DRAWINGS

[0064] In order to more clearly illustrate the technical solutions of the embodiments of the present application, the drawings required for use in the embodiments of the present application will be briefly introduced below. It should be understood that the following drawings only show certain embodiments of the present application and therefore should not be regarded as limiting the scope. For ordinary technicians in this field, other related drawings can be obtained based on these drawings without paying creative work.

[0065] Figure 1 A schematic diagram of the steps of a method for determining a plasma phase space control equation provided in an embodiment of the present application;

[0066] Figure 2 A schematic diagram of a specific sampling principle for a plasma system provided in an embodiment of the present application;

[0067] Figure 3 A schematic diagram of the steps for calculating the particle distribution function provided in this application;

[0068] Figure 4 A schematic diagram of a plasma phase space distribution function calculation step provided in an embodiment of the present application;

[0069] Figure 5 A schematic diagram of the steps for determining a plasma phase space control equation provided in an embodiment of the present application;

[0070] Figure 6 A schematic diagram of a device for determining a plasma phase space control equation provided in an embodiment of the present application. DETAILED DESCRIPTION

[0071] The technical solutions in the embodiments of the present application will be described below in conjunction with the accompanying drawings in the embodiments of the present application. For example, the flowcharts and block diagrams in the accompanying drawings show the possible architectures, functions and operations of the systems, methods and computer program products according to multiple embodiments of the present invention. In this regard, each box in the flowchart or block diagram may represent a module, a program segment or a part of a code, and the module, a program segment or a part of a code contains one or more executable instructions for implementing the specified logical functions. It should also be noted that in some alternative implementations, the functions marked in the box may also occur in an order different from that marked in the accompanying drawings. For example, two consecutive boxes can actually be executed substantially in parallel, and they may sometimes be executed in the opposite order, depending on the functions involved. It should also be noted that each box in the block diagram and / or the flowchart, and the combination of boxes in the block diagram and / or the flowchart, can be implemented by a dedicated hardware-based system that performs a specified function or action, or can be implemented by a combination of dedicated hardware and computer instructions. In addition, the functional modules in the various embodiments of the present invention can be integrated together to form an independent part, or each module can exist separately, or two or more modules can be integrated to form an independent part.

[0072] During the research process, the applicant discovered that the plasma kinetic control equation is based on the phase space description, which has three more velocity dimensions than ordinary fluid equations. Secondly, the independent variables in the fluid control equation are mostly fluid velocities, which can be obtained directly through experiments or simulations, while the independent variables of the plasma phase space control equation are particle distribution functions, which are implicit functions of the phase space coordinates and require processing of the original data from the experiment or simulation to obtain.

[0073] Therefore, the purpose of the embodiment of the present application is to provide a method and device for determining the plasma phase space control equation, which is used to deduce the plasma phase space control equation based on data drive. Figure 1 , Figure 1 A schematic diagram of the steps of a method for determining a plasma phase space control equation provided in an embodiment of the present application, the method may include the following steps:

[0074] In step S11, a plasma system is simulated and sampled to obtain particle information and phase space data of each particle in the plasma system, wherein the plasma system includes multiple types of particles.

[0075] Among them, the plasma system can be simulated by full particle PIC (Particle in Cell) to obtain particle information, which can specifically include the position, velocity, mass, particle type, and charge density distribution, potential distribution, and electric field distribution of each particle. For example, please refer to Figure 2 , Figure 2 A schematic diagram of a specific sampling principle for a plasma system provided in an embodiment of the present application, wherein for each time step, a two-dimensional grid based on particle velocity and position is divided, and particle information at each grid is counted, thereby obtaining m×n groups of data, where m is the number of spatial grid points and n is the number of time steps.

[0076] In step S12, for each time step, in a two-dimensional grid of the velocity and position of the particle, the particle information and the phase space data of each particle are counted to obtain a particle distribution function.

[0077] Exemplarily, the space of all possible states of the plasma system can be represented by phase space, and each possible state of the plasma system corresponds to a point in the phase space. The plasma system can be locally sampled or fully sampled to obtain phase space data of the plasma based on spatial coordinates, velocity coordinates, and time coordinates.

[0078] The time step is the portion of the entire calculation that each calculation step occupies. The time occupied by each time step can be 1 second, or it can be longer or shorter than 1 second. The time occupied by each time step can be set according to the actual deduction situation.

[0079] In step S13, a linear equation is constructed, and candidate items in the linear equation are linearly combined to represent the plasma phase space control equation, wherein the candidate items include partial derivatives of various orders of the particle distribution function with respect to the phase space coordinates and the powers of the partial derivatives.

[0080] In step S14, the weight of each candidate is calculated to determine the plasma phase space governing equation.

[0081] It can be seen that the embodiment of the present application provides a deduction method based on three-dimensional phase space. By constructing a linear system, the phase space equation is represented by a combination of candidates for the linear equation. By preprocessing the data of the simulation or sampling of the plasma system, the phase space control equation of the unknown plasma system is determined, thereby realizing data-driven deduction of the unknown plasma system.

[0082] Optionally, for step S12, the present application embodiment provides an implementation step for calculating the particle distribution function, see Figure 3 , Figure 3 A schematic diagram of the steps for calculating the particle distribution function provided in this application, the steps may include the following:

[0083] In step S121, the distribution of the particles in the two-dimensional grid is determined based on the velocity and position information of the particles.

[0084] In step S122, all particles are interpolated to the grid points of the two-dimensional grid based on the area weight method to convert the phase space data into the particle distribution function.

[0085] Specifically, for a particle, the number of particles at the four grid points closest to the particle and the area of ​​the grid in the two-dimensional grid are calculated respectively. Figure 4 , Figure 4 A schematic diagram of a step for calculating the distribution function of a plasma phase space provided in an embodiment of the present application, wherein the figure shows a two-dimensional network divided by a coordinate system xv. For example, the four grid points are (i, j), (i+1, j), (i, j+1) and (i+1, j+1), and (x0, v0) are the coordinates of the particle. For a single particle, the specific interpolation process can be expressed as:

[0086]

[0087]

[0088]

[0089]

[0090] Wherein, Δx and Δv are the lengths of the grid on the xv two-dimensional coordinate axes respectively.

[0091] The particle distribution function for each time step is determined based on the number of particles at the grid points and the area of ​​the grid.

[0092] Thus, it can be determined that for each time step t k (k=0,1,2…,n), the particle distribution function is f(x,v,t k ) i,j =N(x,v) i,j / (ΔxΔv), so the governing equation of the phase space can be determined based on the particle distribution function.

[0093] It can be seen that the embodiment of the present application divides the grid on the two-dimensional coordinate system, and obtains the independent variables of the plasma phase space control equation by determining the particle distribution on the grid points, thereby achieving the implicit function data in the phase space through the general space data, thereby enabling the deduction of the unknown plasma phase space control equation.

[0094] In an optional embodiment, for step S13, the embodiment of the present application provides an implementation step of expressing the plasma phase space control equation with a linear equation, which may include:

[0095] Based on the formula f=G(f,f x,f v ,f xx ,f vv …) represents the plasma phase space governing equation, where f is the particle distribution function in the phase space, f t 、f x and f v are the partial derivatives of the particle distribution function with respect to the time coordinate, space coordinate and velocity coordinate respectively, G is a linear operator, f xx and f vv are the high-order partial derivatives of space coordinates and velocity coordinates respectively;

[0096] Select the values ​​of the candidate items to construct the linear equation U t =θ(U,Q)ξ, where U t is a column vector composed of the partial derivatives of the particle distribution function with respect to the time coordinate, θ(U,Q) is a q-order matrix composed of all candidate items, Q is the number of the candidate items, and ξ is a sparse column vector of q rows, representing the weight of each candidate item.

[0097] Specifically, the candidate items can also include nonlinear terms and additional terms. For example, when calculating electrostatic problems, the candidate items can also include the electric field intensity. Therefore, the governing equation of the phase space can be transformed into the following component form:

[0098]

[0099] The power and partial derivative order of the candidate items are set according to the actual problem. The candidate items can also be selected based on prior knowledge, thus obtaining the linear equation U t =θ(U,Q)ξ, θ(U,Q) is a (m×n)×q-order matrix composed of all candidate items.

[0100] It can be seen that the embodiment of the present application adopts the method of constructing linear equations to characterize the plasma phase space control equations by calculating the weight of each candidate, which can collect the spatiotemporal information of the plasma system to obtain the control equations of the system, thereby analyzing the spatial plasma state in a larger range and at future times.

[0101] Optionally, for step S14, the present embodiment also provides a step for determining the plasma phase space control equation, see Figure 5 , Figure 5 A schematic diagram of a step for determining a plasma phase space control equation provided in an embodiment of the present application, the step may include the following:

[0102] In step S141, sparse regression is performed on the linear equation based on the least square method with regularization to obtain a weight vector of the weights.

[0103] In step S142, the plasma phase space governing equation is determined based on the weight vector.

[0104] Specifically, the binary norm of the sparse column vector can be calculated. When the linear equation is iteratively calculated to obtain the weight of each candidate item, the weights less than a preset weight threshold are set to 0, and the weights greater than the preset weight threshold are recursively operated to perform sparse regression on the weights to obtain the weight vector.

[0105] For example, it can be based on the formula Calculate the weight of the candidate, where ξ is the weight of the candidate, θ is the matrix composed of all the candidate, U t is a column vector composed of the partial derivatives of the particle distribution function with respect to the time coordinate, and λ is a complexity parameter for controlling the reduction amount.

[0106] It can be seen that the embodiment of the present application uses a least squares method with a regularization term through sparse regression to achieve feature selection of candidate items, obtain accurate weight vectors, and realize the deduction of unknown plasma phase space control equations, which can improve the accuracy of the obtained plasma phase space control equations.

[0107] Optionally, before sampling the plasma system in step S11, it may be determined whether to sample the plasma system in a full sampling or partial sampling manner based on the size of the sampling area.

[0108] It can be seen that the embodiments of the present application can determine the sampling method according to the size of the sampling area in the plasma system. When the sampling area is large, the full sampling method can be used to improve the sampling efficiency. When the sampling area is small, the local sampling method can be used to improve the sampling accuracy. This improves the flexibility of sampling and can take into account both sampling efficiency and accuracy.

[0109] Exemplarily, the method for determining the plasma phase space control equation provided in the embodiments of the present application may also be used to perform ground testing on the electric thruster to improve the reliability of the ground testing.

[0110] In the aerospace field, the role of electric thrusters is to maintain the position of satellites, perform thrust compensation and attitude control. Electric thrusters generate thrust by ionizing electrons in a discharge chamber to form plasma.

[0111] Before flight application, the electric thruster needs to be ground tested. One of the tests is to use various probes such as Faraday probes, Langmuir probes or Mach probes to measure the physical properties of the plasma generated by the electric thruster, such as the potential, density and velocity. In actual measurements, the probe cannot be placed near the thruster outlet because the plasma environment near the outlet of the electric thruster is extremely harsh, which will damage the probe structure. The plasma density in the far field area is relatively small, which will cause large measurement errors. Therefore, the probe cannot be placed in the far field area. Therefore, in actual measurements, the probe can only be placed in some fixed positions, resulting in inaccurate probe acquisition results and poor test results.

[0112] The method for determining the plasma phase space control equation provided in the embodiment of the present application can determine the information on the plasma physical properties near the electric thruster outlet and in the far field based on the local information of the plasma measured by the probe, and can determine the plasma phase space control equation of the electric thruster to analyze the plasma properties of the electric thruster, thereby improving the reliability of ground testing.

[0113] In addition, when the electric thruster is working, the plasma ejected at high speed will expand freely in a vacuum to form a feather-like flow field, which is called an electric propulsion plume. Unlike the working fluid ejected by a chemical thruster, which is basically uncharged, the electric propulsion plume is a charged plasma, which will produce mechanical and thermal effects, sputtering contamination effects, electromagnetic effects, and potential effects on the spacecraft, affecting the working performance and service life of the spacecraft components.

[0114] Due to the high cost of space experiments, numerical simulation methods are generally used to analyze electric propulsion plume plasma, generally using the particle cloud grid method (Particle-in-cell, PIC) to numerically simulate electric propulsion plume plasma. However, the PIC method is a particle algorithm that requires a computer to track each simulated plasma particle, so the amount of calculation is huge. Generally, a numerical simulation analysis example of a medium-sized satellite plume requires a week or even a month of calculation.

[0115] By using the method for determining the plasma phase space control equation provided in the embodiment of the present application, the PIC method can be used to simulate a very small number of time steps, and then the algorithm can be used to deduce the obtained plasma data in the time domain to obtain the final plasma plume flow field result.

[0116] By using the algorithm provided in the embodiments of the present application, the numerical simulation calculation time of a medium-sized satellite plume can be reduced from one week to one month to one day or even a few hours, thereby improving analysis efficiency and saving computing resources.

[0117] Based on the same inventive concept, the present embodiment also provides a plasma phase space control equation determination device 60, see Figure 6 , Figure 6 A schematic diagram of a device for determining a plasma phase space control equation provided in an embodiment of the present application, the device may include:

[0118] A data acquisition module 61 is used to simulate and sample a plasma system to obtain particle information and phase space data of each particle in the plasma system, wherein the plasma system includes multiple types of particles;

[0119] A data preprocessing module 62 is used for counting the particle information and the phase space data of each particle in the two-dimensional grid of the velocity and position of the particle for each time step to obtain a particle distribution function;

[0120] A linear system construction module 63, used to construct a linear equation, and linearly combine candidate items in the linear equation to represent the plasma phase space control equation, wherein the candidate items include partial derivatives of various orders of the particle distribution function with respect to the phase space coordinates and the powers of the partial derivatives;

[0121] The sparse regression module 64 is used to calculate the weight of each candidate to determine the plasma phase space governing equation.

[0122] Optionally, the data preprocessing module 62 may be specifically used for:

[0123] Determining the distribution of the particles in the two-dimensional grid based on the velocity and position information of the particles;

[0124] All particles are interpolated onto the grid points of the two-dimensional grid based on an area weighting method to convert the phase space data into the particle distribution function.

[0125] Optionally, the linear system building module 63 may be specifically used for:

[0126] Based on the formula f t =G(f,f x ,f v ,f xx ,f vv …) represents the plasma phase space governing equation, where f is the particle distribution function in the phase space, f t 、f x and f v are the partial derivatives of the particle distribution function with respect to the time coordinate, space coordinate and velocity coordinate respectively, G is a linear operator, f xx and f vv are the high-order partial derivatives of space coordinates and velocity coordinates respectively;

[0127] Select the values ​​of the candidate items to construct the linear equation U t =θ(U,Q)ξ, where U t is a column vector composed of the partial derivatives of the particle distribution function with respect to the time coordinate, θ(U,Q) is a q-order matrix composed of all candidate items, Q is the number of the candidate items, and ξ is a sparse column vector of q rows, representing the weight of each candidate item.

[0128] Optionally, the sparse regression module 64 may be specifically used for:

[0129] Performing sparse regression on the linear equation based on the least square method with regularization to obtain a weight vector of the weights;

[0130] The plasma phase space governing equation is determined based on the weight vector.

[0131] Optionally, the data preprocessing module 62 may be specifically used for:

[0132] For a particle, the number of particles at the four grid points closest to the particle and the area of ​​the grid in the two-dimensional grid are calculated respectively; based on the number of particles at the grid points and the area of ​​the grid, the particle distribution function for each time step is determined.

[0133] The number of particles at the four grid points is specifically: and Where i and j are the grid points, (x0, v0) are the coordinates of the particle, and N(x, v) i,j is the number of particles at the grid point (i, j), Δx and Δv are the lengths of the grid on the two-dimensional coordinate axes respectively;

[0134] The determining of the particle distribution function for each time step based on the number of particles at the grid points and the area of ​​the grid comprises:

[0135] For each time step, the particle distribution function is determined based on the number of particles at the grid point and the area of ​​the grid as f(x, v, t k ) i,j =N(x,v) i,j / (ΔxΔv), where t k is the time step.

[0136] Optionally, the sparse regression module 64 may be specifically used for:

[0137] Calculate the bi-norm of the sparse column vector, and when the linear equation is iteratively calculated to obtain the weight of each candidate, set the weight less than the preset weight threshold to 0, and recursively operate the weight greater than the preset weight threshold to perform sparse regression on the weight to obtain the weight vector. Wherein, based on the formula Calculate the weight of the candidate, where ξ is the weight of the candidate, θ is the matrix composed of all the candidate, U t is a column vector composed of the partial derivatives of the particle distribution function with respect to the time coordinate, and λ is a complexity parameter for controlling the reduction amount.

[0138] Optionally, the data acquisition module 61 may also be used for:

[0139] The sampling includes full sampling and local sampling. Before simulating and sampling the plasma system, it is determined whether to sample the plasma system in a full sampling or local sampling manner based on the size of the sampling area.

[0140] Based on the same inventive concept, an embodiment of the present application also provides an electronic device, which includes a memory and a processor, wherein program instructions are stored in the memory, and when the processor reads and runs the program instructions, the steps in any of the above implementation methods are executed.

[0141] Based on the same inventive concept, an embodiment of the present application further provides a computer-readable storage medium, wherein the computer-readable storage medium stores computer program instructions, and when the computer program instructions are read and executed by a processor, the steps in any of the above implementation methods are executed.

[0142] The computer-readable storage medium may be a random access memory (RAM), a read-only memory (ROM), a programmable read-only memory (PROM), an erasable programmable read-only memory (EPROM), an electrically erasable programmable read-only memory (EEPROM), or any other medium that can store program codes. The storage medium is used to store the program, and the processor executes the program after receiving the execution instruction. The method executed by the electronic terminal of the process definition disclosed in any embodiment of the present invention can be applied to the processor or implemented by the processor.

[0143] In the embodiments provided in the present application, it should be understood that the disclosed devices and methods can be implemented in other ways. The device embodiments described above are merely schematic. For example, the division of the units is only a logical function division. There may be other division methods in actual implementation. For example, multiple units or components can be combined or integrated into another system, or some features can be ignored or not executed. Another point is that the mutual coupling or direct coupling or communication connection shown or discussed can be through some communication interfaces, and the indirect coupling or communication connection of the devices or units can be electrical, mechanical or other forms.

[0144] In addition, the units described as separate components may or may not be physically separated, and the components shown as units may or may not be physical units, that is, they may be located in one place or distributed on multiple network units. Some or all of the units may be selected according to actual needs to achieve the purpose of the solution of this embodiment.

[0145] Furthermore, the functional modules in the various embodiments of the present application may be integrated together to form an independent part, or each module may exist separately, or two or more modules may be integrated to form an independent part.

[0146] Alternatively, the present invention may be implemented in whole or in part by software, hardware, firmware, or any combination thereof. When implemented by software, the present invention may be implemented in whole or in part in the form of a computer program product. The computer program product includes one or more computer instructions. When the computer program instructions are loaded and executed on a computer, the process or function described in the embodiment of the present invention is generated in whole or in part.

[0147] The computer may be a general-purpose computer, a special-purpose computer, a computer network, or other programmable device. The computer instructions may be stored in a computer-readable storage medium, or transmitted from one computer-readable storage medium to another computer-readable storage medium. For example, the computer instructions may be transmitted from one website, computer, server, or data center to another website, computer, server, or data center via wired (e.g., coaxial cable, optical fiber, digital subscriber line (DSL)) or wireless (e.g., infrared, wireless, microwave, etc.) means.

[0148] In this article, the term "comprises", "comprising" or any other variation thereof is intended to cover non-exclusive inclusion, so that a process, method, article or device including a series of elements includes not only those elements, but also includes other elements not explicitly listed, or also includes elements inherent to such process, method, article or device. In the absence of more restrictions, the elements defined by the sentence "comprising..." do not exclude the presence of other identical elements in the process, method, article or device including the elements.

[0149] The above description is only an embodiment of the present application and is not intended to limit the protection scope of the present application. For those skilled in the art, the present application may have various modifications and variations. Any modification, equivalent replacement, improvement, etc. made within the spirit and principle of the present application shall be included in the protection scope of the present application.

Claims

1. A method for determining a plasma phase space control equation, characterized in that: include: Simulating and sampling a plasma system to obtain particle information and phase space data of each particle in the plasma system, wherein the plasma system includes multiple types of particles; For each time step, in a two-dimensional grid of the velocity and position of the particle, counting the particle information and the phase space data of each particle to obtain a particle distribution function; Based on the formula f t =G(f,f x ,f v ,f xx ,f vv …) represents the plasma phase space governing equation, where f is the particle distribution function in the phase space, f t 、f x and f v are the partial derivatives of the particle distribution function with respect to the time coordinate, space coordinate and velocity coordinate respectively, G is a linear operator, f xx and f vv are the high-order partial derivatives of the spatial coordinates and velocity coordinates respectively; the values ​​of the candidate items are selected to construct the linear equation U t =θ(U,Q)ξ, where U t is a column vector composed of partial derivatives of the particle distribution function with respect to the time coordinate, θ(U,Q) is a q-order matrix composed of all candidate items, Q is the number of the candidate items, ξ is a sparse column vector of q rows, representing the weight of each candidate item, and the candidate items include partial derivatives of each order of the particle distribution function with respect to the phase space coordinate and the power of the partial derivatives; A weight is calculated for each of the candidates to determine the plasma phase space governing equations.

2. The method according to claim 1, characterized in that: In the two-dimensional grid of the velocity and position of the particle, counting the particle information and the phase space data of each particle to obtain a particle distribution function comprises: Determining the distribution of the particles in the two-dimensional grid based on the velocity and position information of the particles; All particles are interpolated onto the grid points of the two-dimensional grid based on an area weighting method to convert the phase space data into the particle distribution function.

3. The method according to claim 1, characterized in that Calculating the weight of each candidate to determine the plasma phase space governing equation comprises: Performing sparse regression on the linear equation based on the least square method with regularization to obtain a weight vector of the weights; The plasma phase space governing equation is determined based on the weight vector.

4. The method according to claim 2, characterized in that: The interpolating all particles to the grid points of the two-dimensional grid based on the area weight method includes: For a particle, respectively calculating the number of particles at the four grid points closest to the particle and the area of ​​the grid in the two-dimensional grid; The particle distribution function for each time step is determined based on the number of particles at the grid points and the area of ​​the grid.

5. The method according to claim 4, characterized in that The number of particles at the four grid points is specifically: and Where i and j are the grid points, (x0, v0) are the coordinates of the particle, and N(x, v) i,j is the number of particles at the grid point (i, j), Δx and Δv are the lengths of the grid on the two-dimensional coordinate axes respectively; The determining of the particle distribution function for each time step based on the number of particles at the grid points and the area of ​​the grid comprises: For each time step, the particle distribution function is determined based on the number of particles at the grid point and the area of ​​the grid as f(x, v, t k ) i,j =N(x,v) i,j / (ΔxΔv), where t k is the time step.

6. The method according to claim 3, characterized in that: The step of performing sparse regression on the linear equation based on the least square method with regularization to obtain the weight vector of the weights includes: Calculate the binary norm of the sparse column vector, and when iteratively calculating the weight of each candidate item through the linear equation, set the weights less than a preset weight threshold to 0, and recursively operate on the weights greater than the preset weight threshold to perform sparse regression on the weights to obtain the weight vector.

7. The method according to claim 6, characterized in that The step of calculating the weight of each candidate to determine the plasma phase space governing equation comprises: based on the formula Calculate the weight of the candidate, where ξ is the weight of the candidate, θ is the matrix composed of all the candidate, U t is a column vector composed of the partial derivatives of the particle distribution function with respect to the time coordinate, and λ is a complexity parameter for controlling the reduction amount.

8. The method according to claim 1, characterized in that The sampling includes full sampling and local sampling. Before simulating and sampling the plasma system, the method further includes: The plasma system is sampled by full sampling or partial sampling based on the size of the sampling area.

9. A device for determining a plasma phase space control equation, characterized in that: include: A data acquisition module, used to simulate and sample a plasma system to obtain particle information and phase space data of each particle in the plasma system, wherein the plasma system includes multiple types of particles; A data preprocessing module, for counting the particle information and the phase space data of each particle in a two-dimensional grid of the velocity and position of the particle for each time step, so as to obtain a particle distribution function; Linear system building blocks for linear systems based on the formula f t =G(f,f x ,f v ,f xx ,f vv …) represents the plasma phase space governing equation, where f is the particle distribution function in the phase space, f t 、f x and f v are the partial derivatives of the particle distribution function with respect to the time coordinate, space coordinate and velocity coordinate respectively, G is a linear operator, f xx and f vv are the high-order partial derivatives of the spatial coordinates and velocity coordinates respectively; the values ​​of the candidate items are selected to construct the linear equation U t =θ(U,Q)ξ, where U t is a column vector composed of partial derivatives of the particle distribution function with respect to the time coordinate, θ(U,Q) is a q-order matrix composed of all candidate items, Q is the number of the candidate items, ξ is a sparse column vector of q rows, representing the weight of each candidate item, and the candidate items include partial derivatives of each order of the particle distribution function with respect to the phase space coordinate and the power of the partial derivatives; A sparse regression module is used to calculate the weight of each candidate to determine the plasma phase space governing equation.

Images