3D calculation method and system of spatial plasma resistance based on multi-channel discrete

Abstract

The present invention provides a 3D calculation method and system for spatial plasma resistance based on multi-channel discretization, which is suitable for calculating spatial resistance between charged surfaces in a plasma environment. The method is based on the equivalent of plasma space to a multi-channel circuit, and the grid of the calculation domain is divided by the electric field lines and equipotential surfaces between the charged surfaces, that is, the calculation domain is discretized into multiple spatial channels, and each channel is further discretized into multiple microelement channel bodies. Then, the resistivity and resistance of each microelement channel body are calculated, and then the spatial plasma resistance between the charged surfaces is calculated through the series or parallel relationship between each microelement channel body. The calculation speed of the present invention is relatively high, and the conductivity and conduction current between charged surfaces in a space plasma environment can be calculated.

Description

Technical Field

[0001] The present invention relates to the field of computing, and in particular to a 3D computing method and system for spatial plasma resistance based on multi-channel discreteness. Background Art

[0002] Plasma is a conductive medium. When it is stably distributed in space, it exhibits the characteristics of resistance, which allows charges to be transferred and conducted in space. Here, the equivalent resistance value of plasma in space is called the spatial resistance of plasma. The solution of spatial resistance involves scientific problems in multiple engineering fields, such as the breakdown problem of suspended electrode surfaces in the fields of plasma spraying and coating, the parasitic current and electrostatic field discharge problems on the surfaces of various components, thrusters or solar wings on the surface of spacecraft, the influence of discharge resistance on luminous efficiency during xenon lamp discharge, and the short-circuit discharge problem of equipment in the low-temperature plasma ground environment chamber. The above problems all involve the discharge conduction mechanism between charged surfaces. Therefore, the design of spatial plasma resistance between charged surfaces is of great significance for controlling the transmission current of the above-mentioned breakdown, conduction and other discharge processes.

[0003] At present, the calculation methods of plasma resistance are mainly based on two categories. One is based on various theoretical algorithms and numerical algorithms derived from the basic theory of plasma, and the other is based on empirical formulas fitted by experimental data. The literature "Robert S Cohen, et al. The Electrical Conductivity of an Ionized Gas. Physical Review 80 (2), 1950" obtained a method for calculating the resistivity of uniform plasma by accurately solving the Boltzmann equations of plasma. This method has high calculation accuracy in zero-dimensional or one-dimensional problems. The literature "Zhang Y, et al. Influence of Plasma Resistivity on Peeling-Ballooning modes. Physics of Plasmas 24, 2017" proposed two numerical calculation methods, linear and nonlinear, for the plasma fluid dynamics equations, which can perform 2D simulation of the resistivity of two different plasma boundary parameter states. The literature "Chen Jia et al. Study on plasma resistance during pulsed xenon lamp discharge. Laser & Infrared 39(2), 2009" measured the volt-ampere characteristics of xenon lamp discharge under different structural parameters and working parameters, and obtained the relationship between columnar plasma resistance and plasma current density and structural size and the fitting formula.

[0004] In summary, the theoretical algorithm can achieve a higher and more convenient calculation process, but the applicable problems are mostly charged surface conditions with simple structures or configurations; the numerical method has a wide range of applications, but the calculation efficiency is low. It has advantages in studying the influence mechanism of plasma layout resistivity, but lacks engineering application value for rapid estimation and optimization adjustment of a large number of conditions; although the experimental fitting formula has high calculation accuracy, it has a small scope of application and high time and economic costs. Therefore, in the face of various engineering problems in the field of plasma conduction discharge, it is urgent to develop a calculation model with a wide range of applications and high calculation speed. Summary of the invention

[0005] In view of the defects in the prior art, the purpose of the present invention is to provide a 3D calculation method and system for spatial plasma resistance based on multi-channel discreteness.

[0006] According to the present invention, a 3D calculation method of spatial plasma resistance based on multi-channel discreteness includes the following steps:

[0007] Channel division step: the plasma space is equivalent to a multi-channel circuit, and then the multi-channel circuit is divided into a number of micro-element channel bodies;

[0008] The steps of calculating the resistivity and resistance of micro-element channel bodies are as follows: calculating the resistivity and resistance of each micro-element channel body;

[0009] Steps for calculating spatial resistance: Calculate the spatial resistance between charged surfaces based on the series or parallel relationship between each microelement channel body.

[0010] Preferably, the channel division step comprises:

[0011] Discrete setting step: setting the voltages of the first charged surface and the second charged surface, and discretizing the first charged surface into a plurality of surface nodes;

[0012] The step of solving the spatial electric field line distribution is as follows: solving the spatial electric field line distribution according to the electric field intensity distribution data between the first charged surface and the second charged surface;

[0013] Steps for setting the micro-element channel body: the arc cylinder surrounded by each of four adjacent electric field lines is set as a space channel, and the small cylinders divided by a number of equipotential surfaces in an arc cylinder are set as micro-element channel bodies.

[0014] Preferably, the method for generating the electric field lines is:

[0015] Node position determination step: determining a node position of the first charged surface;

[0016] Pointing direction solving steps: obtain the three-way electric field intensity components and the total electric field intensity value of the node, and solve the pointing direction of the electric field of the node;

[0017] Extended position solution step: solve the coordinates of the end point of the electric field line extending outward from the node at a distance of Δs;

[0018] Derivation step: derive the electric field lines to the second charged surface to realize the calculation network division.

[0019] Preferably, the determined node is numbered (i, j, 0) and has coordinates (x0, y0, z0), and the endpoint of the electric field line extending outward by a distance of Δs is numbered (i, j, 1 / k) and has coordinates (x 1 / k ,y 1 / k , z 1 / k ),but:

[0020]

[0021]

[0022]

[0023] Preferably, after the spatial position of the microelement channel body is determined, the resistance of the microelement channel body is solved:

[0024]

[0025] Among them, ρ i,j,m is the resistivity of the microelement channel, l i,j,m is the length of the microelement channel, A i,j,m is the area of ​​the microelement channel, l i,j,m Characterized by the distance between the center points of the two end faces, A i,j,m Characterized by the average of the two end surface areas;

[0026]

[0027] Where Z is the number of ion charges, m is the mass of the electron, lnΛ is the Coulomb logarithm, ε0 is the vacuum dielectric constant, and k B is the Boltzmann constant, T i,j,m is the local plasma temperature;

[0028]

[0029] Among them, n i,j,m is the local plasma number density.

[0030] Preferably, after the resistance of all the microelement channel bodies in the computational domain is solved, the resistance of each channel is composed of the resistances of all the microelement channel bodies connected in series. Assuming that a channel contains n microelement channel bodies, the resistance of each channel is solved as follows:

[0031]

[0032] The spatial resistance is solved as follows:

[0033]

[0034] Preferably, the conduction current between the two surfaces is calculated as follows:

[0035]

[0036] According to the present invention, a 3D calculation system for spatial plasma resistance based on multi-channel discreteness is provided, comprising the following modules:

[0037] Channel division module: the plasma space is equivalent to a multi-channel circuit, and then the multi-channel circuit is divided into several micro-element channel bodies;

[0038] Micro-element channel body resistivity and resistance calculation module: calculate the resistivity and resistance of each micro-element channel body;

[0039] Spatial resistance calculation module: Calculates the spatial resistance between charged surfaces based on the series or parallel relationship between each microelement channel body.

[0040] Compared with the prior art, the present invention has the following beneficial effects:

[0041] 1. The present invention provides a 3D calculation method for spatial plasma resistance based on multi-channel discreteness, which can be directly applied to the calculation of conduction current between charged surfaces in a plasma environment, and provides a numerical method for estimating short-circuit current, parasitic current, etc. between various charged surfaces based on plasma conduction.

[0042] 2. The calculation time of the calculation model of the present invention is relatively short. The calculation time under general working conditions is generally between 1 and 3 seconds. For most surface conduction current estimation problems in plasma environments, the present invention can achieve efficient and accurate estimation and optimization. BRIEF DESCRIPTION OF THE DRAWINGS

[0043] Other features, objects and advantages of the present invention will become more apparent from the detailed description of non-limiting embodiments made with reference to the following drawings:

[0044] Figure 1 Schematic diagram of channel generation for the 3D calculation method of spatial plasma resistance based on multi-channel discretization.

[0045] Figure 2 Schematic diagram of electric field line extension based on multi-channel discrete 3D calculation method of spatial plasma resistance.

[0046] Figure 3Schematic diagram of the microelement channel body based on the 3D calculation method of spatial plasma resistance based on multi-channel discretization. DETAILED DESCRIPTION

[0047] The present invention is described in detail below in conjunction with specific embodiments. The following embodiments will help those skilled in the art to further understand the present invention, but are not intended to limit the present invention in any form. It should be noted that, for those of ordinary skill in the art, several changes and improvements can also be made without departing from the concept of the present invention. These all belong to the protection scope of the present invention.

[0048] like Figures 1 to 3 As shown, the present invention provides a 3D calculation method and system for spatial plasma resistance based on multi-channel discreteness, the method comprising the following steps:

[0049] Step 1: Equivalent the plasma space to a multi-channel circuit, and then divide the multi-channel circuit into several micro-element channel bodies;

[0050] Step 2: Calculate the resistivity and resistance of each microelement channel body;

[0051] Step 3: Calculate the spatial resistance between the charged surfaces based on the series or parallel relationship between each microelement channel body.

[0052] More specifically, for step 1, Figure 1 As shown, the voltage on surface 1 is set to U1, the voltage on surface 2 is set to U2, and surface 1 is discretized into multiple surface nodes; secondly, according to the electric field intensity distribution data between surface 1 and surface 2, the spatial electric field line distribution is solved. The method for generating electric field lines is as follows Figure 2 , after the position of a node (numbered i, j, 0) on surface 1 is determined, that is, the coordinates are (x0, y0, z0), the three-dimensional electric field intensity components and the total electric field intensity value of the node are obtained by interpolation method, and then the direction of the electric field of the node is solved (the cosine value of the angle in the three directions can be solved). Assuming that the change of electric field intensity within a very small distance Δs can be ignored, the coordinates of the position of the endpoint of the electric field line (numbered i, j, 1 / k) extending outward from this node on surface 1 at a distance of Δs can be solved, see formula (1),

[0053]

[0054]

[0055]

[0056] Then, when the electric field lines are extended in this way for several (set to k) Δs distances, so that the electric potential at this moment is exactly equal to or approximately equal to ΔU, the derivation process of the electric field lines from node (i, j, 0) to node (i, j, 1) is realized. By analogy, the derivation of node (i, j, 1) to node (i, j, 2), the derivation of node (i, j, 2) to node (i, j, 3), ..., can be realized until the electric field lines are derived to surface 2. Therefore, the spatial calculation nodes of the entire calculation domain and the surface nodes of surface 2 can be deduced to realize the calculation grid division.

[0057] Here, the space electric field lines are orthogonal to the equipotential surfaces, and the arc cylinder surrounded by each of the four adjacent electric field lines is set as a space channel, and the small cylinders divided by several equipotential surfaces in each space channel are set as microelement channel bodies. The potential difference between adjacent equipotential surfaces is set to a constant value ΔU, and the number of equipotential surfaces can be determined, thus realizing the division of the computational grid. Generally speaking, the more equipotential surfaces there are, the higher the computational accuracy is, but the longer the computational time is, which can be determined according to the actual computational conditions.

[0058] Step 2: After the spatial position of the micro-element channel body is determined (each micro-element channel body corresponds to 8 node coordinates), Figure 3 As shown, the resistance of the infinitesimal channel body can be solved by formula (2):

[0059]

[0060] Among them, ρ i,j,m is the resistivity of the microelement channel, l i,j,m is the length of the microelement channel, A i,j,m is the area of ​​the microelement channel. i,j,m It can be solved by formula (3), l i,j,m It can be characterized by the distance between the center points of the two end faces (equipotential surfaces), A i,j,m It can be characterized by the average of the two end surface areas.

[0061]

[0062] Where Z is the number of ion charges (generally 1), which can be averaged from the number densities corresponding to the eight nodes, m is the electron mass, lnΛ is the Coulomb logarithm (which can be solved by formula (4)), ε0 is the vacuum dielectric constant, and k B is the Boltzmann constant, T i,j,m is the local plasma temperature, which can be solved by taking the average value of the plasma temperatures corresponding to the 8 nodes.

[0063]

[0064] Among them, n i,j,mis the local plasma number density, which can be solved by taking the average value of the plasma number density corresponding to the 8 nodes.

[0065] The calculation method of the spatial plasma resistance described in step 3 is as follows. After the resistance of all microelement channel bodies in the calculation domain is solved, the resistance of each channel can be composed of the series connection of the resistances of all microelement channel bodies on it. The solution is as follows (assuming that a channel contains n microelement channel bodies):

[0066]

[0067] Next, the resistance between each channel is in parallel, so the spatial resistance can be described by the following formula:

[0068]

[0069] Once the spatial resistance is solved, the conduction current between the two surfaces can be calculated:

[0070]

[0071] The present invention also provides a 3D calculation system for spatial plasma resistance based on multi-channel discreteness, comprising:

[0072] Channel division module: the plasma space is equivalent to a multi-channel circuit, and then the multi-channel circuit is divided into several micro-element channel bodies; micro-element channel body resistivity and resistance calculation module: the resistivity and resistance of each micro-element channel body are calculated; spatial resistance calculation module: the spatial resistance between charged surfaces is calculated according to the series or parallel relationship between each micro-element channel body.

[0073] The channel division module includes: a discrete setting module: setting the voltage of the first charged surface and the second charged surface, and discretizing the first charged surface into multiple surface nodes; a spatial electric field line distribution solving module: solving the spatial electric field line distribution according to the electric field intensity distribution data between the first charged surface and the second charged surface; a micro-element channel body setting module: an arc column surrounded by every four adjacent electric field lines is set as a spatial channel, and a small column divided by a plurality of equipotential surfaces of an arc column is set as a micro-element channel body.

[0074] Furthermore, the method for generating electric field lines is as follows: determine the position of a node on the first charged surface; obtain the three-dimensional electric field intensity components and the total electric field intensity value of the node, and solve the direction of the electric field at the node; solve the coordinates of the endpoint position of the electric field line extending outward from the node by a distance of Δs; derive the electric field lines to the second charged surface to realize the division of the computational network.

[0075] Assume that the node number is (i, j, 0) and the coordinates are (x0, y0, z0). The endpoint of the electric field line extending outward by a distance of Δs is numbered (i, j, 1 / k) and the coordinates are (x 1 / k ,y 1 / k , z 1 / k ),but:

[0076]

[0077]

[0078]

[0079] When the spatial position of the infinitesimal channel body is determined, the resistance of the infinitesimal channel body is solved:

[0080]

[0081] Among them, ρ i,j,m is the resistivity of the microelement channel, l i,j,m is the length of the microelement channel, A i,j,m is the area of ​​the microelement channel, l i,j,m Characterized by the distance between the center points of the two end faces, A i,j,m Characterized by the average of the two end surface areas;

[0082]

[0083] Where Z is the number of ion charges, m is the mass of the electron, lnΛ is the Coulomb logarithm, ε0 is the vacuum dielectric constant, and k B is the Boltzmann constant, T i,j,m is the local plasma temperature;

[0084]

[0085] Among them, n i,j,m is the local plasma number density.

[0086] When the resistance of all the micro-element channel bodies in the computational domain is solved, the resistance of each channel is composed of the resistance of all the micro-element channel bodies connected in series. Assuming that a channel contains n micro-element channel bodies, the resistance of each channel is solved as follows:

[0087]

[0088] The spatial resistance is solved as follows:

[0089]

[0090] The conduction current between the two surfaces is calculated as follows:

[0091]

[0092] The calculation time of the calculation model of the present invention is relatively short. For general working conditions: plasma environment (number density: 10 14 m -3 , temperature: 2eV), the charged surface area is 20cm 2 , 1m apart, 20° included angle, the spatial calculation domain is divided into 1000 channels, each channel is divided into 200 microelement channel bodies. Using a computer with common configuration (CPU i5 4500, 8Gb memory), the calculation time is generally between 1 and 3 seconds. For most of the surface conduction current estimation problems in plasma environments, the present invention can achieve efficient and accurate estimation and optimization.

[0093] The spirit and principles of the present invention should include: first, based on the electric field lines between charged surfaces, the calculation domain of the space plasma environment is discretized into multiple channel circuits, and then these channel circuits are discretized into a large number of micro-element channel bodies by orthogonality of the electric field lines and equipotential surfaces; second, the method of generating electric field lines is based on the electric field intensity data and uses the cosine values ​​of the three directions of the field intensity to extend the coordinates of the endpoints of the electric field lines; third, the resistances of each micro-element channel body in a channel are in a series relationship, and the resistances of each channel are in a parallel relationship, and the space resistance is solved based on this series-parallel relationship. All surface structure changes, surface material and gas type replacements, and formula equivalent deformations carried out within this spirit and principle should be included in the protection scope of the present invention.

[0094] The above describes the specific embodiments of the present invention. It should be understood that the present invention is not limited to the above specific embodiments, and those skilled in the art can make various changes or modifications within the scope of the claims, which does not affect the essence of the present invention. In the absence of conflict, the embodiments of the present application and the features in the embodiments can be combined with each other arbitrarily.

Claims

1. A 3D calculation method of spatial plasma resistance based on multi-channel discreteness, characterized in that: The steps include: Channel division step: the plasma space is equivalent to a multi-channel circuit, and then the multi-channel circuit is divided into a number of micro-element channel bodies; The steps of calculating the resistivity and resistance of micro-element channel bodies are as follows: calculating the resistivity and resistance of each micro-element channel body; Steps for calculating spatial resistance: Calculate the spatial resistance between charged surfaces based on the series or parallel relationship between each microelement channel body; When the spatial position of the infinitesimal channel body is determined, the resistance of the infinitesimal channel body is solved: Among them, ρ i,j,m is the resistivity of the microelement channel, l i,j,m is the length of the microelement channel, A i,j,m is the area of ​​the microelement channel, l i,j,m Characterized by the distance between the center points of the two end faces, A i,j,m Characterized by the average of the two end surface areas; Where Z is the number of ion charges, m is the mass of the electron, lnΛ is the Coulomb logarithm, ε0 is the vacuum dielectric constant, and k B is the Boltzmann constant, T i,j,m is the local plasma temperature; Among them, n i,j,m is the local plasma number density, When the resistance of all the micro-element channel bodies in the computational domain is solved, the resistance of each channel is composed of the resistance of all the micro-element channel bodies connected in series. Assuming that a channel contains n micro-element channel bodies, the resistance of each channel is solved as follows: The spatial resistance is solved as follows: The channel division step comprises: Discrete setting step: setting the voltages of the first charged surface and the second charged surface, and discretizing the first charged surface into a plurality of surface nodes; The step of solving the spatial electric field line distribution is as follows: solving the spatial electric field line distribution according to the electric field intensity distribution data between the first charged surface and the second charged surface; Steps for setting the micro-element channel body: the arc cylinder surrounded by each of four adjacent electric field lines is set as a space channel, and the small cylinders divided by a number of equipotential surfaces in an arc cylinder are set as micro-element channel bodies.

2. The 3D calculation method of spatial plasma resistance based on multi-channel discreteness according to claim 1 is characterized in that: The method for generating electric field lines is: Node position determination step: determining a node position of the first charged surface; Pointing direction solving steps: obtain the three-way electric field intensity components and the total electric field intensity value of the node, and solve the pointing direction of the electric field of the node; Extended position solution step: solve the coordinates of the end point of the electric field line extending outward from the node at a distance of Δs; Derivation step: derive the electric field lines to the second charged surface to realize the calculation network division.

3. The 3D calculation method of spatial plasma resistance based on multi-channel discreteness according to claim 2 is characterized in that: Assume that the node number is (i, j, 0) and the coordinates are (x0, y0, z0). The endpoint of the electric field line extending outward by a distance of Δs is numbered (i, j, 1 / k) and the coordinates are (x 1 / k ,y 1 / k , z 1 / k ),but:

4. The 3D calculation method of spatial plasma resistance based on multi-channel discreteness according to claim 1 is characterized in that: The conduction current between the two surfaces is calculated as follows:

5. A 3D calculation system for spatial plasma resistance based on multi-channel discreteness, characterized in that: Includes the following modules: Channel division module: the plasma space is equivalent to a multi-channel circuit, and then the multi-channel circuit is divided into several micro-element channel bodies; Micro-element channel body resistivity and resistance calculation module: calculate the resistivity and resistance of each micro-element channel body; Spatial resistance calculation module: calculates the spatial resistance between charged surfaces according to the series or parallel relationship between each microelement channel body; When the spatial position of the infinitesimal channel body is determined, the resistance of the infinitesimal channel body is solved: Among them, ρ i,j,m is the resistivity of the microelement channel, l i,j,m is the length of the microelement channel, A i,j,m is the area of ​​the microelement channel, l i,j,m Characterized by the distance between the center points of the two end faces, A i,j,m Characterized by the average of the two end surface areas; Where Z is the number of ion charges, m is the mass of the electron, lnΛ is the Coulomb logarithm, ε0 is the vacuum dielectric constant, and k B is the Boltzmann constant, T i,j,m is the local plasma temperature; Among them, n i,j,m is the local plasma number density, When the resistance of all the micro-element channel bodies in the computational domain is solved, the resistance of each channel is composed of the resistance of all the micro-element channel bodies connected in series. Assuming that a channel contains n micro-element channel bodies, the resistance of each channel is solved as follows: The spatial resistance is solved as follows: The channel division step comprises: Discrete setting step: setting the voltages of the first charged surface and the second charged surface, and discretizing the first charged surface into a plurality of surface nodes; The step of solving the spatial electric field line distribution is as follows: solving the spatial electric field line distribution according to the electric field intensity distribution data between the first charged surface and the second charged surface; Steps for setting the micro-element channel body: the arc cylinder surrounded by each of four adjacent electric field lines is set as a space channel, and the small cylinders divided by a number of equipotential surfaces in an arc cylinder are set as micro-element channel bodies.

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