A Variable Scaling Method for PIC-MCC Models

Abstract

This invention proposes a variable scaling method for PIC-MCC models, comprising: establishing an initial PIC-MCC physical model; selecting a scaling factor and, following the discharge similarity law, constructing variable scaling relationships between plasma density, collision cross section, and particle kinetic energy in a scaled-down PIC-MCC simulation model corresponding to the PIC-MCC physical model; determining variable scaling relationships between thermocurrent density, plasma frequency, particle collision frequency, and particle collision probability in the scaled-down PIC-MCC simulation model; determining the variable scaling relationship parameters in the scaled-down PIC-MCC simulation model, conducting plasma particle simulation, and mapping the calculation results of the scaled-down PIC-MCC simulation model back to the initial PIC-MCC physical model. This invention solves the problems of existing scaling techniques exacerbating plasma instability and local electric field effects, and maintains undistorted simulation results even at large scaling ratios, significantly improving calculation accuracy.

Description

Technical Field

[0001] This invention belongs to the field of numerical simulation technology of plasma, and relates to the PIC-MCC model of plasma. Specifically, it is a variable scaling method for the PIC-MCC model. Background Technology

[0002] The PIC-MCC model is a plasma simulation model that accurately simulates the motion behavior of plasma. The model can reflect the microscopic motion characteristics of single plasma particles in an electromagnetic field, and can also describe the collective motion behavior of plasma. Its accuracy is far superior to other models such as those for fluid dynamics, and it is also known as a quasi-experimental method or model. It is currently widely used in the field of plasma research.

[0003] Because the PIC-MCC model uses a large number of single particles as simulation units, the simulation process involves a large amount of computation, a long computation time, and consumes a lot of computing resources. Without adopting efficient computation methods, the calculation will become extremely difficult.

[0004] To address the aforementioned problems, patent application CN 109979543 ​​A proposes a particle simulation method for high-density, large-size plasmas, solving the challenge of rapid computation for such plasmas. This method follows the discharge similarity law when applying a scaled-down model to handle the scaling relationships of particle collision processes.

[0005] nσ~ζ -1

[0006] Where 1 / ζ is the scaling factor, the collision cross section σ between particles is considered a constant, and the plasma density n is increased by a factor of 1 / ζ, that is:

[0007]

[0008] However, increasing the plasma density in the PIC-MCC model exacerbates plasma instability and local electric field effects, especially when the simulation model is scaled up significantly. This leads to distorted simulation results, causing the PIC-MCC model to lose its original accurate simulation characteristics and greatly limiting the application of particle simulation methods. Summary of the Invention

[0009] To address the problem of simulation distortion at large scaling ratios in existing scaling techniques, this invention proposes a variable scaling method for PIC-MCC models.

[0010] To achieve the above objectives, the technical solution adopted by the present invention is as follows:

[0011] On one hand, the present invention provides a variable scaling method for PIC-MCC models, comprising:

[0012] Establish the initial PIC-MCC physical model;

[0013] By selecting a scaling factor and following the discharge similarity law, a variable scaling relationship between plasma density, collision cross section and particle kinetic energy is constructed in the PIC-MCC scaled-down simulation model corresponding to the PIC-MCC physical model.

[0014] Determine the variable scaling relationships of thermal current density, plasma frequency, particle collision frequency, and particle collision probability in the PIC-MCC scaled-down simulation model;

[0015] Determine the variable scaling relationship between the total number of simulated particles and the total simulation time in the PIC-MCC scaled-down simulation model;

[0016] Determine the variable scaling relation parameters in the PIC-MCC scaled-down simulation model, conduct plasma particle simulation, and map the calculation results of the PIC-MCC scaled-down simulation model to the initial PIC-MCC physical model.

[0017] Compared with existing technologies, the variable scaling method for PIC-MCC models proposed in this invention has the following advantages:

[0018] (1) This invention proposes a variable scaling relation for the PIC-MCC model, which solves the problems of the existing scaling technology exacerbating plasma instability and local electric field effects. The simulation results are not distorted when the scaling factor is large, and the calculation accuracy is significantly improved.

[0019] (2) This invention inherits and develops the advantages of existing scaling methods, and can improve computational efficiency in terms of both simulation time and the total number of simulated particles. Under the same scaling model conditions, the total number of simulated particles is less and the computational efficiency is higher when using the method of this invention.

[0020] (3) The variable scaling relation proposed in this invention can be matched and selected according to the computational resources and time requirements. This method can make the plasma PIC-MCC model more operable and interactive. Attached Figure Description

[0021] To more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are only some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on the structures shown in these drawings without creative effort.

[0022] Figure 1 This is a flowchart of an embodiment of the present invention;

[0023] Figure 2 This is a diagram illustrating the relationship between the collision cross section of CO2 molecules and the kinetic energy of electrons in one embodiment. Detailed Implementation

[0024] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only a part of the embodiments of the present invention, and not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those of ordinary skill in the art without creative effort are within the scope of protection of the present invention.

[0025] Reference Figure 1 One embodiment provides a variable scaling method for PIC-MCC models, comprising:

[0026] (S1) Establish the initial PIC-MCC physical model;

[0027] (S2) Select a scaling factor and follow the discharge similarity law to construct the variable scaling relationship between plasma density, collision cross section and particle kinetic energy in the PIC-MCC scaled simulation model corresponding to the PIC-MCC physical model;

[0028] (S3) Determine the variable scaling relationships of thermal current density, plasma frequency, particle collision frequency and particle collision probability in the PIC-MCC scaled-down simulation model;

[0029] (S4) Determine the variable scaling relationship between the total number of simulated particles and the total simulation time in the PIC-MCC scaled-down simulation model;

[0030] (S5) Determine the variable scaling relation parameters in the PIC-MCC scaled-down simulation model, conduct plasma particle simulation, and map the calculation results of the PIC-MCC scaled-down simulation model to the initial PIC-MCC physical model.

[0031] In one embodiment, the method for implementing step (S2) includes:

[0032] (S2.1) Select a scaling factor and follow the discharge similarity law to construct the variable scaling relationship between plasma density and collision cross section in the PIC-MCC scaled simulation model corresponding to the PIC-MCC physical model;

[0033] (S2.2) Based on the variable scaling relationship between plasma density and collision cross section in the PIC-MCC scaled-down simulation model, for different particle collision types in the PIC-MCC physical model, construct the correspondence between collision cross section and particle kinetic energy in the PIC-MCC scaled-down simulation model.

[0034] It is understood that the specific implementation method of establishing the initial PIC-MCC physical model in step (S1) of this invention is not limited, and those skilled in the art can make reasonable choices based on existing technology. Without loss of generality, in one embodiment, a method for establishing the initial PIC-MCC physical model is proposed, with the following specific steps: For the PIC process, based on the spatiotemporal characteristics of plasma in the studied physical model, the electromagnetic field solution equation is determined, and the model boundary conditions and calculation parameters are set; for the MCC process, the different collision types between particles during plasma motion are determined.

[0035] In step (S2) of one embodiment, a specific implementation method is proposed as follows: Let the scaling factor ζ∈(0,1), construct the variable scaling relationship between plasma density n and collision cross section σ in the PIC-MCC scaled simulation model corresponding to the PIC-MCC physical model, as follows:

[0036]

[0037] In the formula, i and j are two variable scaling parameters in the PIC-MCC scaled-down simulation model. Preferably, i + j = -1, i ≥ 0, j ≥ -1.

[0038] Next, we construct the collision cross section σ, plasma density n, and particle kinetic energy E. th The variable scaling relation is as follows:

[0039]

[0040] In the formula, i and j are two variable scaling parameters in the PIC-MCC scaled-down simulation model, and E th Let i be the particle kinetic energy corresponding to the collision cross section in the scaled-down simulation model of PIC-MCC. Preferably, i+j=-1, i≥0, j≥-1.

[0041] In one embodiment, assuming ζ is 0.001, taking the carbon dioxide discharge process as an example, the original relationship between the collision cross section and the electron kinetic energy in the three processes of elastic collision, excitation, and ionization of CO2 molecules with electrons, as well as the scaling relationship constructed by the scaled model, are as follows: Figure 2 As shown.

[0042] In one embodiment (S3), the variable scaling relationships of thermal current density, plasma frequency, particle collision frequency, and particle collision probability in the PIC-MCC scaled-down simulation model are determined as follows:

[0043]

[0044] In the formula, j th Represents the heat current density, ω peThe plasma frequency is represented by ν, the particle collision frequency by P, the particle collision probability by e, and the electron charge by n. e Let ε0 represent electron density, v represent electron velocity, ε0 represent vacuum permittivity, and m represent electron density. e Δt represents the electron mass, and Δt represents the collision interval time.

[0045] In the PIC-MCC simulation model, the total simulation time before and after scaling up can be considered positively correlated with the time difference of a single particle entering and leaving the simulation area, assuming the total probability of particle collisions remains unchanged. Based on the scaling relationship between the simulation area length and particle velocity, the variable scaling relationship of the total simulation time t in the scaled-up PIC-MCC simulation model in step (S4) is obtained as follows:

[0046] t~ζ 1 / 2

[0047] The total number of simulated particles N is related to the dimension of the coordinate space of the established simulation model. For PIC-MCC models with different dimensions, it is assumed that the dimension of the model coordinate space is k and the particle number density is n. p Then, in step (S4), the variable scaling relationship of the total number of simulated particles in the PIC-MCC scaled-down simulation model is as follows:

[0048] N = n p L k ~ζ j+k

[0049] In the formula, L represents the size of the one-dimensional coordinate space. Preferably, k∈[0,3] takes integer values.

[0050] For the PIC-MCC scaled-down simulation model with a selected scaling factor ζ, the specific values ​​of the variable scaling relation parameters i and j in the PIC-MCC scaled-down simulation model are determined by comprehensively considering the available computer computing resources, simulation requirements for computation time and accuracy, plasma particle simulation is carried out, and the calculation results of the PIC-MCC scaled-down simulation model are mapped to the initial PIC-MCC physical model according to the scaling relation.

[0051] This invention proposes a variable scaling method for PIC-MCC models, addressing the problems of increased plasma instability and local electric field effects caused by existing scaling techniques. The simulation results remain accurate even at large scaling ratios, significantly improving computational accuracy. This invention inherits and develops the advantages of existing scaling methods, enabling PIC-MCC models to reduce the number of simulated particles and shorten simulation time, thereby improving computational efficiency. Furthermore, under the same scaling model conditions, the method of this invention requires fewer simulated particles and achieves higher computational efficiency.

[0052] In one embodiment, a variable scaling device for a PIC-MCC model is provided, comprising:

[0053] The first module is used to establish the initial PIC-MCC physical model;

[0054] The second module is used to select the scaling factor, follow the discharge similarity law, and construct the variable scaling relationship between plasma density, collision cross section and particle kinetic energy in the PIC-MCC scaled-down simulation model corresponding to the PIC-MCC physical model.

[0055] The third module is used to determine the variable scaling relationships of thermal current density, plasma frequency, particle collision frequency, and particle collision probability in the PIC-MCC scaled-down simulation model.

[0056] The fourth module is used to determine the variable scaling relationship between the total number of simulated particles and the total simulation time in the PIC-MCC scaled-down simulation model;

[0057] The fifth module is used to determine the variable scaling relationship parameters in the PIC-MCC scaled-down simulation model, conduct plasma particle simulation, and map the calculation results of the PIC-MCC scaled-down simulation model to the initial PIC-MCC physical model.

[0058] The implementation methods of the above modules and the construction of the model can all adopt the methods described in any of the foregoing embodiments, and will not be repeated here.

[0059] Matters not covered in this invention are common knowledge.

[0060] The technical features of the above embodiments can be combined in any way. For the sake of brevity, not all possible combinations of the technical features in the above embodiments are described. However, as long as there is no contradiction in the combination of these technical features, they should be considered to be within the scope of this specification.

[0061] The embodiments described above are merely illustrative of several implementation methods of this application, and while the descriptions are relatively specific and detailed, they should not be construed as limiting the scope of the invention patent. It should be noted that those skilled in the art can make various modifications and improvements without departing from the concept of this application, and these all fall within the protection scope of this application. Therefore, the protection scope of this patent application should be determined by the appended claims.

[0062] The above description is merely a preferred embodiment of the present invention and is not intended to limit the invention. Various modifications and variations can be made to the present invention by those skilled in the art. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of the present invention should be included within the scope of protection of the present invention.

Claims

1. A variable scaling method for PIC-MCC models, characterized in that, include: Establish the initial PIC-MCC physical model; By selecting a scaling factor and following the discharge similarity rule, the plasma density in the PIC-MCC scaled-down simulation model corresponding to the PIC-MCC physical model is constructed. n Collision cross section σ With particle kinetic energy E th The variable scaling relation is as follows: In the formula, E th This represents the particle kinetic energy corresponding to the collision cross section in the scaled-down simulation model of PIC-MCC. i , j These are two variable scaling relationship parameters in the PIC-MCC scaled-down simulation model. This is the scaling factor; Determine the variable scaling relationships of thermal current density, plasma frequency, particle collision frequency, and particle collision probability in the PIC-MCC scaled-down simulation model; Determine the variable scaling relationship between the total number of simulated particles and the total simulation time in the PIC-MCC scaled-down simulation model; Determine the variable scaling relation parameters in the PIC-MCC scaled-down simulation model, conduct plasma particle simulation, and map the calculation results of the PIC-MCC scaled-down simulation model to the initial PIC-MCC physical model.

2. The variable scaling method for PIC-MCC models according to claim 1, characterized in that, i+j =-1， i 0， j -1。 3. The variable scaling method for PIC-MCC models according to claim 1 or 2, characterized in that, scaling factor .

4. The variable scaling method for PIC-MCC models according to claim 3, characterized in that, The variable scaling relationships of thermal current density, plasma frequency, particle collision frequency, and particle collision probability in the PIC-MCC scaled-down simulation model are as follows: In the formula, j th Represents heat current density ω pe Indicates plasma frequency, ν Indicates the frequency of particle collisions. P Indicates the probability of particle collision. e Indicates the amount of electron charge. n e Represents electron density, v Indicates electron velocity, ɛ 0 represents the vacuum permittivity. m e Indicates electron mass, t This indicates the collision interval time.

5. The variable scaling method for PIC-MCC models according to claim 1, 2, or 4, characterized in that, Total simulation time in PIC-MCC scaled-down simulation model t The variable scaling relation is as follows: In the formula t This represents the total simulation time.

6. The variable scaling method for PIC-MCC models according to claim 5, characterized in that, Total number of simulated particles in the PIC-MCC scaled-down simulation model N The variable scaling relation is as follows: In the formula L Represents the size of a one-dimensional coordinate space. k Represents the dimension of the model's coordinate space. n p Represents particle number density.

7. The variable scaling method for PIC-MCC models according to claim 6, characterized in that, k [0,3] takes the integer part.

8. The variable scaling method for PIC-MCC models according to claim 1, 2, 4, 6, or 7, characterized in that, Based on the requirements of computer computing resources, computing time, and computing accuracy, determine the two variable scaling relationship parameters in the PIC-MCC scaled-down simulation model. i , j .

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