Simulation and Analysis Method of Space Charge Distribution in Spacecraft Dielectrics

Abstract

A method for simulating and analyzing the spatial charge distribution of a spacecraft dielectric is disclosed. The method obtains and calculates the actual operating environment parameters of the spacecraft dielectric, including the interaction between electron energy, flow rate, and dielectric material. A self-consistent electron transport model considering drift diffusion is established, which accounts for the ballistic transport of carriers within the dielectric, trapping, detrapping, and recombination of electrons and holes, as well as the passage of electrons through potential barriers at interfaces to become true secondary electrons. The model focuses on the trapping probability of carriers under the influence of traps. The structural parameters and intrinsic properties of the spacecraft dielectric are collected, and the material parameters and electric field boundary conditions are set to establish a charge transport equation. The charge transport equation is calculated, and the simulation results of the internal volume charge, electric field, sample current, and secondary electron emission coefficient of the spacecraft dielectric are obtained by sequentially iteratively solving the continuity equation of a transient solver.

Description

Technical Field

[0001] The present invention relates to the technical field of numerical simulation of space charge measurement of spacecraft dielectrics considering trap modulation, and in particular to a method, system, medium and equipment for numerical simulation of space charge measurement of spacecraft dielectrics. Background Art

[0002] Spacecraft operate in a complex and volatile space environment for extended periods, subject to numerous external factors, including high vacuum, plasma, high-energy particles, and thermal cycling. These factors can interact with the spacecraft and cause various faults. The surface charge-discharge effect on spacecraft refers to the phenomenon in which charged particles in the surrounding space contribute to net charge accumulation, electrostatic potential formation, and electrostatic discharge. Spacecraft are continuously bombarded by plasma, high-energy charged particles, and photoelectron emission caused by solar electromagnetic radiation. Charged particles (generally with energies below 50 keV) interact with spacecraft materials (such as solar panels and transmission cables), inducing surface secondary electron emission and charge trapping and accumulation, resulting in surface potentials reaching thousands or even tens of thousands of volts. Electrostatic discharge (ESD) occurs when the potential difference between different parts of a spacecraft exceeds the discharge threshold. ESD generates electromagnetic pulses that can interfere with or even damage spacecraft communications and electronic systems, leading to equipment malfunctions, malfunctions, and even system failures. Furthermore, arcs formed by discharges can damage spacecraft surface materials, accelerating material aging and shortening their service life, damaging solar panels and affecting the normal operation of the power supply system. Electrostatic discharge can also occur when spacecraft dock due to differences in potential and unequal charges.

[0003] Currently, there are few studies on the numerical simulation of space charge to explain macroscopic experimental phenomena from a microscopic level. Therefore, studying the process of dynamic charge distribution changes in spacecraft dielectric materials under electron beam bombardment has important theoretical significance for in-depth exploration of the mechanism of spacecraft surface charging effects and related characteristic parameters under special environments such as high vacuum and electron irradiation, and can provide theoretical support for the protection design of spacecraft charging and discharging effects.

[0004] The above information disclosed in this Background section is only for enhancement of understanding of the background of the invention and therefore it may contain information that does not form the prior art that is already known to a person of ordinary skill in the art. Summary of the Invention

[0005] The present invention provides a method, system, medium and equipment for simulating and analyzing the spatial charge distribution of spacecraft dielectrics, which overcome the limitations of on-site test conditions, can explain macroscopic phenomena from a microscopic perspective, solve the technical problem of insufficient resolution of measurement equipment, and provide a theoretical basis for the protection design of spacecraft charging and discharging effects.

[0006] A spacecraft dielectric space charge simulation analysis method includes:

[0007] S1. Obtain and calculate the actual operating environment parameters of the spacecraft dielectric, including the interaction between electron energy, flow rate and dielectric material;

[0008] S2. Establish a self-consistent electron transport model that takes drift diffusion into account, focusing on the ballistic transport of carriers within the medium, trapping, detrapping, and recombination of electrons and holes, as well as the electrons crossing the potential barrier at the interface to become true secondary electrons;

[0009] S3. Introducing the probability of carriers being trapped under the influence of traps into the self-consistent electron transport model;

[0010] S4. Collect the structural parameters and intrinsic properties of the spacecraft dielectric, set the material parameters and the boundary conditions of the electric field, and establish the charge transport equation;

[0011] S5. Calculate the charge transport equation and iterate the continuity equation of the transient solver to obtain the simulation results of the internal volume charge, electric field, sample current and secondary electron emission coefficient of the spacecraft dielectric.

[0012] In the spacecraft dielectric space charge distribution simulation analysis method, in step S1, the actual operating environment parameters of the spacecraft dielectric are obtained and calculated as:

[0013] ,

[0014] Where R can be obtained by the following formula:

[0015] ,

[0016] Where, j PE represents the primary electron transmission current in the medium, x represents the carrier depth, j0 represents the electron flux density in the environment, η represents the backscattering coefficient, p represents the exponential transmission parameter, R represents the electron transmission depth, ρ represents the mass density of the spacecraft dielectric, and E0 represents the electron energy in space.

[0017] In the spacecraft dielectric space charge distribution simulation analysis method, in step S2, in the self-consistent electron transport model, the generation of internal secondary electrons from the primary electron excitation is:

[0018] The average generation energy of secondary electrons is linearly related to the band gap:

[0019] ,

[0020] The internal secondary electron generation rate is

[0021] ,

[0022] The deposition of primary electrons is manifested in the form of internal secondary electrons:

[0023] ,

[0024] Where, E i represents the average generation energy of internal secondary electrons, E g represents the band gap of the spacecraft dielectric, g SE Indicates the secondary electron generation rate in the dielectric material, g SH represents the hole generation rate in the dielectric material, x represents the carrier depth, g PE represents the probability of electron deposition in the dielectric material, R represents the electron penetration depth, E0 represents the electron energy in space, j0 represents the electron flux density in the environment, and j PE Represents the transmission current of primary electrons in the medium.

[0025] In the spacecraft dielectric space charge distribution simulation analysis method, in step S2, the calculation formula for the ballistic transport of electrons and holes in the self-consistent electron transport model includes:

[0026] The decay probability during ballistic transport is:

[0027] , ,

[0028] Then the ballistic current can be obtained by differential iteration:

[0029] ,

[0030] ,

[0031] Where λ E0 represents the field-free decay distance of the electron, λ H0 represents the field-free decay distance of holes, β E represents the electron field decay coefficient, β H represents the field decay coefficient of the hole, F represents the electric field strength, W EFR W represents the decay probability of electrons moving to the surface of the dielectric under the action of the electric field. HFR W represents the decay probability of holes moving to the dielectric surface under the action of the electric field. EFT W represents the attenuation probability of electrons moving toward the dielectric substrate under the action of the electric field. HFT represents the attenuation probability of holes moving toward the dielectric substrate under the action of the electric field, j BER and j BHR represents the ballistic current generated by the movement of electrons and holes toward the dielectric surface, j BET and j BHTrepresents the ballistic current generated by the movement of electrons and holes toward the dielectric substrate, x represents the carrier depth, Δx represents a small distance near the x depth, E0 represents the electron energy in space, g SE Indicates the secondary electron generation rate in the dielectric material, g SH represents the hole generation rate in the dielectric material, j0 represents the electron flux density in the environment, g PE Represents the probability of primary electron deposition in the dielectric material.

[0032] In the spacecraft dielectric space charge distribution simulation analysis method, in step S2, the calculation formula for the recombination of electrons and holes in the self-consistent electron transport model includes:

[0033] , ,

[0034] Then the drift current composed of trapping, detrapping and recombination is expressed as:

[0035] ,

[0036] ,

[0037] Where S HE and S HE represents the recombination cross section of electrons and holes, j DER and j DHR represents the drift current of electrons and holes generated by trapping, detrapping and recombination moving to the dielectric surface, j DET and j DHT The drift current of electrons and holes generated by trapping, detrapping and recombination moving toward the substrate is ρ E represents the electron density, ρ H represents the hole density, W E2 represents the electron recombination probability, W H2 represents the hole recombination probability, e0 represents the charge of the electron, Δx represents a small distance near the depth x, and j BER and j BHR represents the ballistic current generated by the movement of electrons and holes toward the dielectric surface, j BET and j BHT Represents the ballistic current generated by the movement of electrons and holes toward the dielectric substrate, W EFR W represents the decay probability of electrons moving to the surface of the dielectric under the action of the electric field. HFR W represents the decay probability of holes moving to the dielectric surface under the action of the electric field. EFT W represents the attenuation probability of electrons moving toward the dielectric substrate under the action of the electric field. HFT represents the attenuation probability of holes moving to the dielectric substrate under the action of the electric field, WE1 and W H1 represents the probability of electrons and holes being trapped under the action of traps, x represents the carrier depth, j SEE is the true secondary electron current escaping from the dielectric surface.

[0038] In the spacecraft dielectric space charge distribution simulation analysis method, in step S2, in the self-consistent electron transport model, the calculation formula for electrons passing through the potential barrier at the interface to become real secondary electrons includes:

[0039] ,

[0040] Where, j SEE is the true secondary electron current escaping from the dielectric surface, E a represents the electron affinity of the medium surface, represents the average kinetic energy of the secondary electrons, j BER Represents the ballistic current generated by electrons moving toward the surface of a dielectric.

[0041] In the spacecraft dielectric space charge distribution simulation analysis method, in step S3, in the self-consistent electron transport model, in the trap adjustment part, the Planck correction is considered, and the calculation formula includes:

[0042] The capture and decapture rates of free charge carriers n over time t can be described by the first-order kinetic equation

[0043] ,

[0044] By using dt=dx / v D Substituting time and shifting phase, the equation is transformed to:

[0045] ,

[0046] The term in brackets is the correction for the capture cross section, and its value ranges from 0 to 1, where the exponential term plays a decisive role in determining the value of the correction coefficient. Therefore, the equation can be simplified and approximated as:

[0047] ,

[0048] The capture cross section obtained by Planck correction is:

[0049] ,

[0050] The carrier trapping probability is:

[0051] ,

[0052] ,

[0053] in ,

[0054] Where N represents the electron trap density, H represents the hole trap density, and ρ E represents the electron density, ρ H represents the hole density, S E represents the electron trap capture cross section, S H represents the hole trap capture cross section, e0 represents the charge of the electron, E E represents the electron thermal excitation energy, E H represents the thermal excitation energy of holes, k represents the Boltzmann constant, T represents the temperature, and ΔE PF represents the field excitation energy, ε0 ​​is the vacuum dielectric constant, ε r is the relative dielectric constant, W E1 and W H1 represents the probability of electrons and holes being trapped under the action of the trap, Δx represents a small distance near the depth x, F represents the electric field strength, and the free carrier is n, v D is the drift velocity, S is the capture cross-sectional area, ρ / e0 is the charge density, f is the escape frequency factor of the Planck effect, S PF is the capture cross section corrected for the Planck effect, S0 is the total cross section at low temperatures, and E T is the thermal excitation energy.

[0055] A system for implementing the method includes:

[0056] The acquisition module acquires and calculates the actual operating environment parameters of the spacecraft dielectric, including the interaction between electron energy, flow rate and dielectric material;

[0057] The self-consistent electron transport module establishes a self-consistent electron transport model, which includes the generation of internal secondary electrons from primary electron excitation, the ballistic transport of electrons and holes, trapping, detrapping and recombination of electrons and holes, and the electrons crossing the potential barrier at the interface to become true secondary electrons. The model focuses on the trapping probability of carriers under the influence of traps;

[0058] The charge transport module collects the structural parameters and intrinsic properties of the spacecraft dielectric, sets the material parameters and the boundary conditions of the electric field, and establishes the charge transport equation;

[0059] The transient solver calculates the charge transport equation and iterates the continuity equation of the transient solver to obtain the simulation results of the internal volume charge, electric field, sample current and secondary electron emission coefficient of the spacecraft dielectric.

[0060] A computer storage medium includes computer instructions, which, when executed on a computer, cause the computer to execute the method described above.

[0061] An electronic device, comprising:

[0062] A memory, a processor, and a computer program stored in the memory and executable on the processor, wherein:

[0063] When the processor executes the program, the method described is implemented.

[0064] Compared with existing technologies, the present invention has the following advantages: Based on a self-consistent electron transport model, it accurately describes the charge behavior in spacecraft dielectrics. This model, composed of the current transport equation, Poisson's equation, and carrier decay equation, is coupled to each other and covers microscopic charge processes such as charge conservation, electron injection, carrier ballistic transport, trapping, detrapping, and recombination. Numerical simulation enables iterative calculations between multiple physical fields, including carrier transport, electric field, and temperature field. This method overcomes the limitations of field test conditions and effectively simulates the dynamic response of space charge in spacecraft dielectrics. It provides a theoretical basis for the design of protection against spacecraft charge and discharge effects, significantly improves the accuracy of dielectric space charge measurements, addresses the technical challenge of low resolution in measurement equipment, and ensures accurate real-time observation of the dynamic response of charge. Taking into account the actual working conditions such as temperature and electric field effects that spacecraft dielectrics need to face when operating in a space environment, numerical simulation is used to realize the multi-physics field coupling cycle iteration of the carrier fluid field, electric field, and temperature field. The distribution of space charge, electric field strength, sample current change, and secondary electron emission coefficient in the spacecraft dielectric are calculated, providing experimental and theoretical references for the later selection of spacecraft insulation materials and the analysis of surface electrical strength and stability. BRIEF DESCRIPTION OF THE DRAWINGS

[0065] Various other advantages and benefits of the present invention will become apparent to those skilled in the art upon reading the detailed description of the preferred embodiments below. The accompanying drawings are intended only to illustrate preferred embodiments and are not to be construed as limiting the present invention. It should be understood that the drawings described below are merely examples of the present invention, and that those skilled in the art will be able to derive other drawings from these drawings without inventive effort. Throughout the drawings, identical reference numerals are used to denote identical components.

[0066] In the attached figure:

[0067] Figure 1 It is a step diagram of the simulation analysis method considering the space charge distribution of the dielectric space of the spacecraft;

[0068] Figure 2 It is a simulation flow chart of the simulation analysis method considering the space charge distribution of the dielectric space of the spacecraft;

[0069] Figures 3(a) to 3(c) are schematic diagrams of charge transport and energy level changes in the self-consistent electron transport model, wherein Figure 3(a) is a schematic diagram of charge transport in the single-layer self-consistent electron transport model, Figure 3(b) is a schematic diagram of charge transport in the double-layer self-consistent electron transport model, and Figure 3(c) is a schematic diagram of energy level changes;

[0070] Figures 4(a) and 4(b) show the space charge distribution diagrams in polyimide and polyimide coated with chromium dioxide film when the space electron energy is 10 keV. Figure 4(a) shows the space charge distribution diagram in a single-layer polyimide, and Figure 4(b) shows the space charge distribution diagram in a polyimide coated with chromium dioxide film.

[0071] Figures 5(a) and 5(b) show the internal electric field distribution diagrams of polyimide, a dielectric material of a spacecraft, and polyimide coated with a chromium dioxide film when the space electron energy is 10 keV. Figure 5(a) shows the spatial charge distribution diagram of a single-layer polyimide, and Figure 5(b) shows the spatial charge distribution diagram of a polyimide coated with a chromium dioxide film.

[0072] Figure 6 This is a graph showing the current variation of samples of spacecraft dielectric materials PI, PET, PTFE, and PE when the space electron energy is 10 keV;

[0073] Figure 7 This is a graph showing the change in secondary electron emission coefficients of spacecraft dielectric materials PI, PET, PTFE, and PE when the space electron energy is 10 keV.

[0074] The present invention will be further explained below with reference to the accompanying drawings and embodiments. DETAILED DESCRIPTION

[0075] Specific embodiments of the present invention will be described in more detail below with reference to the accompanying drawings. Although specific embodiments of the present invention are shown in the accompanying drawings, it should be understood that the present invention can be implemented in various forms and should not be limited by the embodiments set forth herein. Rather, these embodiments are provided to enable a more thorough understanding of the present invention and to fully convey the scope of the present invention to those skilled in the art.

[0076] It should be noted that certain words are used in the specification and claims to refer to specific components. Those skilled in the art should understand that technicians may use different nouns to refer to the same component. This specification and claims do not use the difference in nouns as a way to distinguish components, but use the difference in the functions of the components as the criterion for distinction. As mentioned throughout the specification and claims, "including" or "comprising" is an open term, so it should be interpreted as "including but not limited to". The subsequent description of the specification is a preferred embodiment of the present invention, but the description is based on the general principles of the specification and is not intended to limit the scope of the invention. The scope of protection of the present invention shall be as defined in the attached claims.

[0077] To facilitate understanding of the embodiments of the present invention, further explanation will be given below using specific embodiments as examples in conjunction with the accompanying drawings, and the accompanying drawings do not constitute a limitation on the embodiments of the present invention.

[0078] like Figures 1 to 7 As shown in FIG, the numerical simulation method for measuring the space charge of a spacecraft dielectric includes the following steps:

[0079] S1. Obtain and calculate the actual operating environment parameters of the spacecraft dielectric, including the interaction between electron energy, flow rate and dielectric material;

[0080] S2. Establish a self-consistent electron transport model that takes drift diffusion into account, focusing on the ballistic transport of carriers within the medium, trapping, detrapping, and recombination of electrons and holes, as well as the electrons crossing the potential barrier at the interface to become true secondary electrons;

[0081] S3. The model focuses on the probability of carriers being trapped under the influence of traps;

[0082] S4. Collect the structural parameters (such as thickness, area) and intrinsic properties (such as dielectric constant, conductivity, trap density, electron affinity, band gap) of the spacecraft dielectric material, and set the boundary conditions of the electric field ( ,in represents the electric potential, V0 is the surface potential of the dielectric, and d is the dielectric thickness), and the charge transport equation including the Poisson equation, the continuity equation, and the current density equation is established; the structural parameters and intrinsic properties of the spacecraft dielectric are set, and the material parameters and the boundary conditions of the electric field are set to establish the charge transport equation;

[0083] S5. Calculate the charge transport equation, discretize the physical process using the finite difference method, combine it with the tridiagonal matrix solution, and iterate the continuity equation of the transient solver to obtain the simulation results of the internal volume charge, electric field, sample current and secondary electron emission coefficient of the spacecraft dielectric.

[0084] In a preferred embodiment of the numerical simulation method for measuring space charge of a spacecraft dielectric, in step S1, the actual operating environment parameters of the spacecraft dielectric are obtained and calculated as:

[0085] ,

[0086] Where R can be obtained by the following formula:

[0087] ,

[0088] Where, j PE represents the primary electron transmission current in the medium, x represents the carrier depth, j0 represents the electron flux density in the environment, η represents the backscattering coefficient, p represents the exponential transmission parameter, R represents the electron transmission depth, ρ represents the mass density of the spacecraft dielectric, and E0 represents the electron energy in space.

[0089] In a preferred embodiment of the spacecraft dielectric space charge distribution simulation analysis method, in the self-consistent electron transport model, the generation of internal secondary electrons from the primary electron excitation is:

[0090] The average generation energy of secondary electrons is linearly related to the band gap:

[0091] ,

[0092] The internal secondary electron generation rate is:

[0093] ,

[0094] The deposition of primary electrons is manifested in the form of internal secondary electrons:

[0095] ,

[0096] Where, E i represents the average generation energy of internal secondary electrons, E g represents the band gap of the spacecraft dielectric, g SE Indicates the secondary electron generation rate in the dielectric material, g SH represents the hole generation rate in the dielectric material, x represents the carrier depth, g PE represents the probability of electron deposition in the dielectric material, R represents the electron penetration depth, E0 represents the electron energy in space, j0 represents the electron flux density in the environment, and j PE Represents the transmission current of primary electrons in the medium.

[0097] In a preferred embodiment of the spacecraft dielectric space charge distribution simulation analysis method, the calculation formula for the ballistic transport of electrons and holes in the self-consistent electron transport model includes:

[0098] The decay probability during ballistic transport is:

[0099] , ,

[0100] Then the ballistic current can be obtained by differential iteration:

[0101] ,

[0102] ,

[0103] Where λ E0 represents the field-free decay distance of the electron, λ H0 represents the field-free decay distance of holes, β E represents the electron field decay coefficient, β H represents the field decay coefficient of the hole, F represents the electric field strength, W EFR W represents the decay probability of electrons moving to the surface of the dielectric under the action of the electric field. HFR W represents the decay probability of holes moving to the dielectric surface under the action of the electric field. EFT W represents the attenuation probability of electrons moving toward the dielectric substrate under the action of the electric field. HFT represents the attenuation probability of holes moving toward the dielectric substrate under the action of the electric field, j BER and j BHR represents the ballistic current generated by the movement of electrons and holes toward the dielectric surface, j BET and j BHT represents the ballistic current generated by the movement of electrons and holes toward the dielectric substrate, x represents the carrier depth, Δx represents a small distance near the x depth, E0 represents the electron energy in space, g SE Indicates the secondary electron generation rate in the dielectric material, g SH represents the hole generation rate in the dielectric material, j0 represents the electron flux density in the environment, g PE Represents the probability of primary electron deposition in the dielectric material.

[0104] In a preferred embodiment of the spacecraft dielectric space charge distribution simulation analysis method, in the self-consistent electron transport model, the calculation formulas for electron and hole trapping and detrapping include:

[0105] ,

[0106] ,

[0107] ,

[0108] Where N represents the electron trap density, H represents the hole trap density, and ρ Erepresents the electron density, ρ H represents the hole density, S E represents the electron trap capture cross section, S H represents the hole trap capture cross section, e0 represents the charge of the electron, E E represents the electron thermal excitation energy, E H represents the thermal excitation energy of holes, k represents the Boltzmann constant, T represents the temperature, and ΔE PF represents the field excitation energy, ε0 ​​is the vacuum dielectric constant, ε r is the relative dielectric constant, W E1 and W H1 represents the probability of electrons and holes being trapped under the action of the trap, Δx represents a small distance near the depth x, and F represents the electric field strength.

[0109] In a preferred embodiment of the spacecraft dielectric space charge distribution simulation analysis method, in the self-consistent electron transport model, the calculation formula for the recombination of electrons and holes includes:

[0110] , ,

[0111] Then the drift current composed of trapping, detrapping and recombination is expressed as:

[0112] ,

[0113] ,

[0114] Where S HE and S HE represents the recombination cross section of electrons and holes, j DER and j DHR represents the drift current of electrons and holes generated by trapping, detrapping and recombination moving to the dielectric surface, j DET and j DHT The drift current of electrons and holes generated by trapping, detrapping and recombination moving toward the substrate is ρ E represents the electron density, ρ H represents the hole density, W E2 represents the electron recombination probability, W H2 represents the hole recombination probability, e0 represents the charge of the electron, Δx represents a small distance near the depth x, and j BER and j BHR represents the ballistic current generated by the movement of electrons and holes toward the dielectric surface, j BET and j BHT Represents the ballistic current generated by the movement of electrons and holes toward the dielectric substrate, W EFRW represents the decay probability of electrons moving to the surface of the dielectric under the action of the electric field. HFR W represents the decay probability of holes moving to the dielectric surface under the action of the electric field. EFT W represents the attenuation probability of electrons moving toward the dielectric substrate under the action of the electric field. HFT represents the attenuation probability of holes moving to the dielectric substrate under the action of the electric field, W E1 and W H1 represents the probability of electrons and holes being trapped under the action of traps, x represents the carrier depth, j SEE is the true secondary electron current escaping from the dielectric surface.

[0115] In a preferred embodiment of the spacecraft dielectric space charge distribution simulation analysis method, in the self-consistent electron transport model, the calculation formula for electrons passing through the potential barrier at the interface to become true secondary electrons includes:

[0116] ,

[0117] Where, j SEE is the true secondary electron current escaping from the dielectric surface, E a represents the electron affinity of the medium surface, represents the average kinetic energy of the secondary electrons, j BER Represents the ballistic current generated by electrons moving toward the surface of a dielectric.

[0118] In a preferred embodiment of the spacecraft dielectric space charge distribution simulation analysis method, in the self-consistent electron transport model, the Planck correction is considered in the trap adjustment part:

[0119] The capture and de-capture rates of free charge carriers n over time t can be described by the first-order kinetic equation:

[0120] ,

[0121] By using dt=dx / v D Substituting time and shifting phase, the equation is transformed to:

[0122] ,

[0123] The term in brackets is the correction for the capture cross section, and its value ranges from 0 to 1, where the exponential term plays a decisive role in determining the value of the correction coefficient. Therefore, the equation can be simplified and approximated as:

[0124]

[0125] The capture cross section obtained by Planck correction is:

[0126]

[0127] Where, the free carriers are n, v D is the drift velocity, S is the area of ​​the capture cross section, N is the trap density, ρ / e0 is the charge density, f is the escape frequency factor of the Planck effect, E T is the thermal activation energy, ΔE PF represents the field excitation energy, T represents the thermodynamic temperature, k is the Boltzmann constant, S PF is the capture cross section corrected for the Planck effect, S0 is the total cross section at low temperatures, and E T is the thermal excitation energy.

[0128] A system for implementing the method includes:

[0129] The acquisition module acquires and calculates the actual operating environment parameters of the spacecraft dielectric, including the interaction between electron energy, flow rate and dielectric material;

[0130] The self-consistent electron transport module establishes a self-consistent electron transport model, which includes the generation of internal secondary electrons from primary electron excitation, the ballistic transport of electrons and holes, trapping, detrapping and recombination of electrons and holes, and the electrons crossing the potential barrier at the interface to become true secondary electrons. The model focuses on the trapping probability of carriers under the influence of traps;

[0131] The charge transport module collects the structural parameters and intrinsic properties of the spacecraft dielectric, sets the material parameters and the boundary conditions of the electric field, and establishes the charge transport equation;

[0132] The transient solver calculates the charge transport equation and sequentially iterates the continuity equation of the transient solver to obtain the simulation results of the volume charge inside the spacecraft dielectric.

[0133] A computer storage medium includes computer instructions, which, when executed on a computer, cause the computer to execute the method described above.

[0134] An electronic device, comprising:

[0135] A memory, a processor, and a computer program stored in the memory and executable on the processor, wherein:

[0136] When the processor executes the program, the method described is implemented.

[0137] In one embodiment, in step S4, the material parameters are set, and the mass density, dielectric constant, surface conductivity and charge trap parameters of the medium will respectively affect the electron incidence depth, internal electric field distribution, surface leakage current and the trapping-detrapping process during carrier transport.

[0138] In one embodiment, the method includes: obtaining actual operating environment parameters of the spacecraft dielectric, and calculating the interaction between the electron energy and flow in the environment and the dielectric material; establishing a self-consistent electron transport model, generating internal secondary electrons from the excitation of primary electrons, ballistic transport of electrons and holes, trapping and detrapping, and recombination of electrons and holes, and electrons passing through the potential barrier at the interface to become true secondary electrons; collecting structural parameters and intrinsic properties of the spacecraft dielectric, and setting material parameters, setting boundary conditions of the electric field, and establishing a complete charge transport equation; initializing the charge measurement numerical simulation system of the spacecraft dielectric to configure solver related parameters, and calculating the charge transport equation to obtain simulation results; the present invention overcomes the limitations of field test conditions, ensures an accurate description of the dynamic evolution of charges, and provides an effective tool for the performance evaluation of spacecraft dielectric materials.

[0139] Example 1

[0140] See Figure 1 , the figure shows the steps of the numerical simulation method for measuring space charge of spacecraft dielectric considering trap modulation provided by an embodiment of the present method.

[0141] This method provides a numerical simulation method for measuring space charge of a spacecraft dielectric considering trap modulation, which includes the following steps:

[0142] S1. Obtain and calculate the actual operating environment parameters of the spacecraft dielectric, including the interaction between electron energy, flow rate and dielectric material;

[0143] S2. Establish a self-consistent electron transport model that takes drift diffusion into account, focusing on the ballistic transport of carriers within the medium, trapping, detrapping, and recombination of electrons and holes, as well as the electrons crossing the potential barrier at the interface to become true secondary electrons;

[0144] S3. The model focuses on the probability of carriers being trapped under the influence of traps;

[0145] S4. Collect the structural parameters and intrinsic properties of the spacecraft dielectric, set the material parameters and the boundary conditions of the electric field, and establish the charge transport equation;

[0146] S5. Calculate the charge transport equation and iterate the continuity equation of the transient solver to obtain the simulation results of the internal volume charge, electric field, sample current and secondary electron emission coefficient of the spacecraft dielectric.

[0147] It should be noted that the self-consistent electron transport model is a fluid transport model that includes the energy and flow of particle radiation in the spacecraft environment, the structure and material properties of the spacecraft dielectric material itself, and the temperature field and electric field inside the medium through coupled calculation and cyclic iteration. Please participate. Figure 2 , the horizontal arrows represent the iterative calculation direction when calculating its value at different positions inside the medium, as well as the calculation boundary conditions of different currents on the surface of the medium. The specific contents are as follows: First, the current components at different depths x of the medium under the given model parameters at time t are calculated. The horizontal arrows in the figure represent the iterative calculation direction of each current component at position x inside the medium and the boundary conditions at the surface of the medium (x=0); then the total current j is calculated from each current component. tot (x,t) total charge distribution ρ tot (x, t); then, by performing the respective integral calculations on the charges, the electric field F(x, t) and potential V(x, t) at different positions x are obtained, where V(0, t) represents the potential value on the surface of the medium; finally, the distribution of various parameters at different depth positions x of the medium during the entire radiation time t is obtained through continuous iterative calculations. The intrinsic parameters of the dielectric material have an important influence on the distribution of space charge in the radiation environment. The mass density ρ of the medium is z , dielectric constant , surface conductivity and charge trap parameters will affect the electron incidence depth R, internal electric field distribution F, surface leakage current and the trapping-detrapping process during carrier transport, respectively.

[0148] Figure 2 In, j DER and j DHR represents the drift current of electrons and holes generated by trapping, detrapping and recombination moving to the dielectric surface, j DET and j DHT The drift current of electrons and holes generated by trapping, detrapping and recombination moving toward the substrate, j BER and j BHR represents the ballistic current generated by the movement of electrons and holes toward the dielectric surface, j BET and j BHT represents the ballistic current generated by the movement of electrons and holes toward the dielectric substrate, x represents the carrier depth, j SEE is the real secondary electron current escaping from the dielectric surface, j PE represents the transmission current of an electron in the medium, E0 represents the electron energy in space, E'0 represents the intermediate iteration of energy, t represents the radiation time, j tot represents the total current density, ρ tot represents the total charge density, ρ E1 and ρ E2 Represents the charge density at different energy level depths, ρ H1 and ρ H2represents the hole density at different energy level depths, F represents the electric field strength, and V represents the potential. The calculation flow chart is the core link of simulation modeling and is used to systematically describe the logical structure of the numerical solution process. Complex equations are broken down step by step, the solution order is clarified, and the iterative process is demonstrated. It should be noted that the self-consistent electron transport model mainly includes the following process: an electron with a certain initial energy E0 bombards and enters the medium, exciting the generation of electron-hole pairs; after the excited electrons and holes enter the conduction band and valence band respectively, they move and decay in a ballistic transport manner within a certain distance; they then undergo drift, diffusion, trapping, and electron-hole recombination processes, as shown in Figures 3(a) to 3(b). In the spacecraft environment, electrons interact with the spacecraft dielectric. Electrons with a certain energy are incident into the material and deposited. This process is called the incidence process (indicated by the solid arrow). A single electron bombards and enters the dielectric, exciting the generation of electron-hole pairs. This process is called the excitation process (indicated by the dotted arrow). After the excited electrons and holes enter the conduction band and valence band respectively, they move and decay by ballistic transport within a certain distance. This process is called ballistic transport (indicated by the double-dash arrow). In the dielectric, when the trap energy level is determined and the trapped charges are excited by energy, these charges will escape from the traps and become free charges again. At the same time, some charges may be captured by the traps, forming trapped charges. This process is called the trapping and detrapping process (indicated by the dotted arrow). The free electrons and holes recombine. This process is called recombination (indicated by the triple-dash arrow). The free electrons in the dielectric cross the electron affinity barrier and escape from the dielectric surface to become true secondary electrons. This process is called the escape process (indicated by the double-dash arrow). In practice, this model can describe the migration and interactions of any number of charge carrier types under the influence of an electric field, including trapping and recombination of positive and negative charge carriers. By setting different model boundary conditions, various physical processes of charge injection into a medium and charge escape can be characterized. The electron transport microscopic process diagram is a schematic diagram used to describe the mechanism of electron migration within a material, providing an intuitive description of the charge movement process.

[0149] The set material parameters mainly include the mass density, dielectric constant, surface conductivity, charge trap density, charge trap energy level, conductivity and load factor of the spacecraft dielectric.

[0150] As a preferred embodiment, in step S1, the calculation formula for the interaction between the electron energy, flow rate and dielectric material in the environment includes:

[0151] ,

[0152] Where R can be obtained by the following formula:

[0153] ,

[0154] Where, jPE represents the primary electron transmission current in the medium, x represents the carrier depth, j0 represents the electron flux density in the environment, η represents the backscattering coefficient, p represents the exponential transmission parameter, R represents the electron transmission depth, ρ represents the mass density of the spacecraft dielectric, and E0 represents the electron energy in space.

[0155] It should be noted that the space radiation energy and flow in the spacecraft environment interact with the spacecraft dielectric materials. The first carrier transport equation is the deposition of incident electrons in the dielectric material, and the exponential part is the attenuation term describing the transport process; the second electron deposition equation represents the depth that 1% of the incident electrons can reach.

[0156] As a preferred embodiment, in step S2, the calculation formula for generating internal secondary electrons by primary electron excitation includes:

[0157] The average generation energy of secondary electrons is linearly related to the band gap ,

[0158] The internal secondary electron generation rate is

[0159] ,

[0160] The deposition of primary electrons is manifested in the form of internal secondary electrons:

[0161] ,

[0162] Where, E i represents the average generation energy of internal secondary electrons, E g represents the band gap of the spacecraft dielectric, g SE Indicates the secondary electron generation rate in the dielectric material, g SH represents the hole generation rate in the dielectric material, x represents the carrier depth, g PE represents the probability of electron deposition in the dielectric material, R represents the electron penetration depth, E0 represents the electron energy in space, j0 represents the electron flux density in the environment, and j PE Represents the transmission current of primary electrons in the medium.

[0163] It should be noted that the interaction of charges in the spacecraft environment within the spacecraft dielectric leads to spatial energy loss and the generation of electron-hole pairs. Schematic diagrams of the generation of electron-hole pairs are shown in Figures 3(a) through 3(c). Primary electrons scatter along their paths within the spacecraft dielectric, which stimulates the generation of secondary electron-hole pairs.

[0164] As a preferred embodiment, in step S2, the calculation formula for the ballistic transport of electrons and holes includes:

[0165] The attenuation probability during ballistic transport is , ,

[0166] Then the ballistic current can be obtained by differential iteration:

[0167] ,

[0168] ,

[0169] Where λ E0 represents the field-free decay distance of the electron, λ H0 represents the field-free decay distance of holes, β E represents the electron field decay coefficient, β H represents the field decay coefficient of the hole, F represents the electric field strength, W EFR W represents the decay probability of electrons moving to the surface of the dielectric under the action of the electric field. HFR W represents the decay probability of holes moving to the dielectric surface under the action of the electric field. EFT W represents the attenuation probability of electrons moving toward the dielectric substrate under the action of the electric field. HFT represents the attenuation probability of holes moving toward the dielectric substrate under the action of the electric field, j BER and j BHR represents the ballistic current generated by the movement of electrons and holes toward the dielectric surface, j BET and j BHT represents the ballistic current generated by the movement of electrons and holes toward the dielectric substrate, x represents the carrier depth, Δx represents a small distance near the x depth, E0 represents the electron energy in space, g SE Indicates the secondary electron generation rate in the dielectric material, g SH represents the hole generation rate in the dielectric material, j0 represents the electron flux density in the environment, g PE Represents the probability of primary electron deposition in the dielectric material.

[0170] It should be noted that the electrons and holes inside the dielectric material of the spacecraft decay under the action of the electric field. The decay probability of electrons and holes is expressed in a similar way, and only the positive and negative signs of the parts related to the electric field need to be modified. In the ballistic current transmission equation, the term in curly brackets is the conduction term from the adjacent unit, and the second term is the small distance at the position x of the dielectric material. The generation of internal secondary electrons originates from the deposition of primary electrons at position x, and the exponential term is the decay probability within a distance Δx. The transport of electrons and holes causes changes in the electric field, and electric field distortion also affects mobility and thus carrier transport.

[0171] As a preferred embodiment, in step S2, the calculation formulas for electron and hole trapping and detrapping include:

[0172] ,

[0173] ,

[0174] in ,

[0175] Where N represents the electron trap density, H represents the hole trap density, and ρ E represents the electron density, ρ H represents the hole density, S E represents the electron trap capture cross section, S H represents the hole trap capture cross section, e0 represents the charge of the electron, E E represents the electron thermal excitation energy, E H represents the thermal excitation energy of holes, k represents the Boltzmann constant, T represents the temperature, and ΔE PF represents the field excitation energy, ε0 ​​is the vacuum dielectric constant, ε r is the relative dielectric constant, W E1 and W H1 represents the probability of electrons and holes being trapped under the action of the trap, Δx represents a small distance near the depth x, and F represents the electric field strength.

[0176] It's important to note that carriers within a spacecraft dielectric are ballistically transported over a certain distance, along the field-induced decay length, and then continue to drift until they are trapped. Ballistically transported electrons and holes may be trapped, and similarly, trapped electrons and holes may escape from the trap. The equations describe the probability of carrier entry and de-entrapment, taking into account the Poole-Frenkel effect, which modifies the capture cross section.

[0177] As a preferred embodiment, in step S2, the calculation formula for the recombination of electrons and holes includes:

[0178] , ,

[0179] Then the drift current composed of trapping, detrapping and recombination is expressed as:

[0180] ,

[0181] ,

[0182] Where S HE and S HE represents the recombination cross section of electrons and holes, j DER and j DHR represents the drift current of electrons and holes generated by trapping, detrapping and recombination moving to the dielectric surface, jDET and j DHT The drift current of electrons and holes generated by trapping, detrapping and recombination moving toward the substrate is ρ E represents the electron density, ρ H represents the hole density, W E2 represents the electron recombination probability, W H2 represents the hole recombination probability, e0 represents the charge of the electron, Δx represents a small distance near the depth x, and j BER and j BHR represents the ballistic current generated by the movement of electrons and holes toward the dielectric surface, j BET and j BHT Represents the ballistic current generated by the movement of electrons and holes toward the dielectric substrate, W EFR W represents the decay probability of electrons moving to the surface of the dielectric under the action of the electric field. HFR W represents the decay probability of holes moving to the dielectric surface under the action of the electric field. EFT W represents the attenuation probability of electrons moving toward the dielectric substrate under the action of the electric field. HFT represents the attenuation probability of holes moving to the dielectric substrate under the action of the electric field, W E1 and W H1 represents the probability of electrons and holes being trapped under the action of traps, x represents the carrier depth, j SEE is the true secondary electron current escaping from the dielectric surface.

[0183] It should be noted that, in addition to being trapped, carriers within a spacecraft dielectric can also recombine, with the probability determined by the charge density and recombination cross section. The carrier transport equations describe the drift currents generated by electron and hole trapping, detrapping, and recombination, respectively. The sum of the adjacent units Conducted term, The term is the source term from the decaying and depleted ballistic electrons, The term is the current term subtracted when the internal secondary electrons are emitted into the vacuum to become true secondary electrons. For holes, since true secondary electron emission will not affect holes, there is no need to subtract the true secondary electron emission term. The exponential terms are the probabilities of recombination and trapping during charge transfer.

[0184] As a preferred embodiment, in step S2, the calculation formula for electrons passing through the potential barrier at the interface to become real secondary electrons includes:

[0185] ,

[0186] Where, j SEE is the true secondary electron current escaping from the dielectric surface, E arepresents the electron affinity of the medium surface, represents the average kinetic energy of the secondary electrons, j BER Represents the ballistic current generated by electrons moving toward the surface of a dielectric.

[0187] It should be noted that some of the internal secondary electrons transported toward the dielectric surface will be reflected back into the dielectric when they reach the dielectric surface (x=0). The internal secondary electrons that are not reflected will overcome the surface electron affinity and escape from the surface into the vacuum, becoming true secondary electrons.

[0188] As a preferred embodiment, in step S3, in the trap adjustment part, the Planck correction is considered to include:

[0189] The capture and de-capture rates of free charge carriers n over time t can be described by the first-order kinetic equation:

[0190] ,

[0191] By using dt=dx / v D Substituting time and shifting phase, the equation is transformed to:

[0192] ,

[0193] The term in brackets is the correction for the capture cross section, and its value ranges from 0 to 1, where the exponential term plays a decisive role in determining the value of the correction coefficient. Therefore, the equation can be simplified and approximated as:

[0194] ,

[0195] The capture cross section obtained by Planck correction is:

[0196] ,

[0197] Where, the free carriers are n, v D is the drift velocity, S is the area of ​​the capture cross section, N is the trap density, ρ / e0 is the charge density, f is the escape frequency factor of the Planck effect, E T is the thermal activation energy, ΔE PF represents the field excitation energy, T represents the thermodynamic temperature, k is the Boltzmann constant, S PF is the capture cross section corrected for the Planck effect, S0 is the total cross section at low temperatures, and E T is the thermal excitation energy.

[0198] As a preferred implementation, in step S4, the structural parameters and intrinsic properties of the spacecraft dielectric are collected, and the material parameters and the boundary conditions of the electric field are set.

[0199] As a preferred embodiment, in step S5, the charge measurement numerical simulation system of the spacecraft dielectric is initialized to configure solver related parameters, and the charge transport equation is calculated to obtain simulation results.

[0200] Example 2

[0201] According to Example 1, a spacecraft environment was set up with a space electron radiation energy E0 of 10 keV. The spacecraft dielectric materials were polyimide and polyimide coated with 200nm of chromium oxide. Over a certain radiation period, a gradually varying and deposited space charge was observed. Figures 4(a) and 4(b) show that charge accumulates within the spacecraft dielectric material over time, forming four distinct regions along the depth direction. From 0 to 10nm, the positive charge density increases over time. In this region, surface electrons gain sufficient energy to be emitted into the vacuum, while holes remain trapped in the dielectric. From 10 to 180nm, an alternating pattern of positive and negative charge density is observed. As electrons and holes undergo ballistic transport and drift diffusion, electrons with a longer ballistic decay length penetrate deeper into the dielectric. Due to their opposing motions and different decay characteristics, this results in an alternating charge distribution. In the third region (180-220nm), electrons must overcome a potential barrier to continue penetrating, resulting in a regular change in charge density at the interface. This abrupt change is absent in a single layer of polyimide. At 220 nm, the charge density gradually decreases from negative to zero. As electrons migrate deeper, their energy dissipates, causing the charge density to gradually decrease until it converges to zero. The dielectric materials were selected as polyimide and polyimide coated with a 200 nm chromium oxide film. The dynamic response of the space charge within the dielectric was observed over a certain electron irradiation time.

[0202] The simulation results show that within the dielectric, charge accumulates over time, and four distinct regions emerge along the depth direction:

[0203] 0–10 nm: The positive charge density increases with time. In this region, surface electrons gain enough energy to be emitted into the vacuum, while holes remain trapped in the dielectric.

[0204] 10–180 nm: Displays an alternating pattern of positive and negative charge density. Electrons, due to their larger ballistic attenuation length, penetrate deeper and move in the opposite direction of holes, resulting in an alternating distribution.

[0205] 180–220nm: Electrons need to overcome potential barriers to continue penetrating, resulting in regular changes in charge density at the interface. Single-layer polyimide does not have this region.

[0206] 220+nm: The charge density gradually decreases from negative to zero. As electrons migrate deeper and their energy dissipates, the charge density gradually decreases and stabilizes.

[0207] It can be understood that the structure shown in the figure is only for reference, and the numerical simulation method for measuring space charge of spacecraft dielectrics considering trap modulation may also include more or fewer components than shown in the figure, or have a configuration different from that shown in the figure.

[0208] As shown in Figures 5(a) and 5(b), the field strength of the chromium dioxide-coated polyimide gradually increases over time, affecting carrier dynamics. Notably, the field strength of the coated dielectric is significantly higher than that of the polyimide. This is because the interaction between the two materials leads to an enhanced local electric field, especially in the transition region. Furthermore, the charge movement in the composite material is more intense, indicating increased charge transport. The complexity of the coating structure leads to charge accumulation and transfer at the interface, as well as changes in the electric field at the interface. By optimizing the electric field distribution within the dielectric, its resistance to electrical breakdown can be effectively improved. Strong field concentration areas can lead to excessively strong electric fields in some areas of the dielectric, which can easily trigger electrical breakdown. By optimizing the design and controlling the electric field distribution, the electric field can be made as uniform as possible, thereby enhancing the electrical stability and resistance of the dielectric.

[0209] In the embodiments of the present method, it should be understood that the disclosed method can be implemented in other ways. The above embodiments are only schematic descriptions, and the flowcharts or block diagrams in the figure show possible implementation architectures, functions and operations of the method and computer program product according to multiple embodiments of the present method. In this regard, each box in the flowchart or block diagram may represent a module, program segment or code fragment, which contains one or more executable instructions for implementing the specified logical function. It should be noted that in some alternative implementations, the order of functions shown in the boxes may be different from the order in the accompanying drawings. For example, two consecutive boxes may actually be executed in parallel, or even sometimes in reverse order, depending on the functions involved.

[0210] In various embodiments of the present method, the functional modules can be organized and configured in different ways. Specifically, these modules can be integrated together to form an independent part, or they can exist separately, or two modules can be combined together to form a new independent part.

[0211] If the functions are implemented as software modules and sold or used as standalone products, they can be stored in a computer-readable storage medium. Therefore, the technical solution of this method or its contribution to the prior art can be embodied in the form of a software product stored in the aforementioned storage medium. Specifically, the storage medium contains instructions for causing a computer device (such as a personal computer, server, or network device) to execute all or part of the steps of the method described in each embodiment of this method. The aforementioned storage medium can include various media capable of storing program code, such as USB flash drives, mobile hard drives, read-only memory (ROM), random access memory (RAM), magnetic disks, or optical disks.

[0212] In summary, this method embodiment provides a numerical simulation method for measuring space charge in spacecraft dielectrics, taking into account trap modulation. By establishing a self-consistent electron transport model to describe the internal charge behavior of spacecraft dielectrics in a spacecraft environment, this model, based on the coupled carrier transport equation (including the ballistic transport, trapping, detrapping, and recombination processes of electrons and holes), the Poisson equation, and the field action equation, considers the law of charge conservation and the microscopic physical processes of carriers. Through numerical simulation, iterative calculation and simulation of charge and electric fields within spacecraft dielectrics are achieved, providing a theoretical basis for the design of protection against spacecraft charge and discharge effects. It also significantly improves the accuracy of dielectric space charge measurement, overcomes the technical challenge of low measurement equipment resolution, and ensures accurate real-time observation of charge dynamic responses. This provides experimental and theoretical reference for the selection of spacecraft insulation materials and the analysis of surface dielectric strength and stability.

[0213] In one embodiment, the spacecraft space environment parameters are set as follows:

[0214] Space electron radiation energy E0=10keV

[0215] Select the dielectric material as "polyimide and polyimide coated with 200nm thick chromium dioxide"

[0216] Within a certain electron irradiation time, the dynamic response of the space charge inside the dielectric is observed.

[0217] The simulation results show that within the dielectric, charge accumulates over time, and four distinct regions emerge along the depth direction:

[0218] 0–10 nm: The positive charge density increases with time. In this region, surface electrons gain enough energy to be emitted into the vacuum, while holes remain trapped in the dielectric.

[0219] 10–180 nm: Displays an alternating pattern of positive and negative charge density. Electrons, due to their larger ballistic attenuation length, penetrate deeper and move in the opposite direction of holes, resulting in an alternating distribution.

[0220] 180–220nm: Electrons need to overcome potential barriers to continue penetrating, resulting in regular changes in charge density at the interface. Single-layer polyimide does not have this region.

[0221] 220+nm: The charge density gradually decreases from negative to zero. As electrons migrate deeper and their energy dissipates, the charge density gradually decreases and stabilizes.

[0222] like Figure 7 As shown in the figure, when a medium interacts with space charge, the secondary electron emission coefficient gradually increases over time from a value less than 1 to a steady-state value. This also means that in the steady state, the number of electrons incident on the material is the same as the number of electrons emitted into the vacuum, and there is no change in the net charge inside the medium. The gradual increase in the secondary electron emission coefficient is also due to the accumulation of surface charge, which generates an electric field that causes the energy of electrons reaching the surface of the medium to gradually decrease, ultimately suppressing the secondary electron emission process to an equilibrium state.

[0223] like Figure 6As shown, the sample current curve exhibits an opposite trend to the secondary electron emission coefficient, gradually decreasing from a large initial value to reach a steady-state value of jsc = 0. This trend is also due to charge accumulation, which leads to charge migration within the material, and the trapping and detrapping process gradually reaches a steady state. Similar to the surface potential, both the secondary electron emission coefficient and the sample current density exhibit "inertia," with portions greater than 1 and less than 0, respectively. The charge transport process is highly correlated with the intrinsic physical parameters of the material. Material density affects the maximum electron penetration depth, charge and hole trap density influences the internal current density distribution, surface resistivity affects surface leakage current, dielectric constant influences the electric field distribution, and electron affinity influences the surface reflection current. It can be seen that the variation patterns of these parameters are consistent for different materials, which is the result of the combined effects of these multiple intrinsic parameters during the charging process. However, the parameter curves for PET and PTFE exhibit a significant "inertia" process, which may be due to differences in trap density. The secondary electron emission coefficient and sample current also play an important role in improving electrical resistance. The secondary electron emission coefficient refers to the ratio of the number of secondary electrons released to the number of incident electrons when high-energy electrons impact a surface. This coefficient directly affects the charge accumulation process, and thus affects the distribution and intensity of the electric field. If the secondary electron emission coefficient is high, it may cause excessive accumulation of charge on the surface of the dielectric, forming a strong electric field area, thereby increasing the risk of breakdown. On the contrary, if the secondary electron emission coefficient is low, it helps to reduce the accumulation of surface charge and help improve the electrical stability of the dielectric. The change in sample current reflects the dynamic process of electron emission and charge accumulation. The magnitude and change trend of the current can provide information about the conductivity and charge leakage behavior of the material under the action of the electric field. When the electric field strength is high, the change in sample current can indicate whether there is a local electric field concentration or discharge phenomenon. By controlling the sample current, the electric field distribution can be optimized, thereby improving the resistance to electrical breakdown.

[0224] This invention obtains the actual operating environment parameters of spacecraft dielectrics and models the interaction between electron energy and flux density, establishes an electron incidence model, calculates the deposition behavior of primary electrons in dielectric materials, and accurately describes the initial interaction process between high-energy electrons and dielectric materials in the space environment; provides basic input conditions for subsequent carrier generation; reflects the electron penetration depth and deposition distribution characteristics at different energies, and is the basis for establishing the entire self-consistent model. A self-consistent electron transport model is constructed, covering multiple microscopic charge transport processes, and a self-consistent electron transport model is established that includes the following core physical processes: primary electron excitation to generate internal secondary electrons and holes; ballistic transport of electrons and holes, trapping and detrapping of electrons and holes; carrier recombination; and true secondary electron emission. The essential mechanism of macroscopic charge accumulation phenomena is revealed from a microscopic perspective; accurate prediction of charge dynamic response is achieved through multi-process coupled simulation; theoretical support is provided for analyzing charge transport behavior in complex environments; and the model's reduction and applicability to real physical processes is improved. Modeling the generation of internal secondary electrons by primary electron excitation establishes a carrier generation rate model: This quantifies the number of electron-hole pairs generated by primary electron excitation; this serves as the initial source for subsequent carrier transport and recombination processes, and provides key particle source input for simulations. Ballistic transport modeling (electrons and holes) uses decay probability models and current expressions to describe the ballistic transport behavior of electrons and holes, describing the carrier migration paths and energy loss characteristics under field conditions. This distinguishes the differences in the motion of electrons and holes in the electric field, affecting the final charge distribution and surface potential evolution. Modeling the trapping and detrapping of electrons and holes considers the effects of internal defects on charge accumulation in dielectrics, accounting for the long-term retention and slow release of charge, improving the model's adaptability to real-world material properties, and enabling effective simulation of trap modulation mechanisms. Modeling the recombination of electrons and holes establishes a carrier recombination model: This describes the process by which carriers disappear due to encounters during transport, affecting the charge lifetime and spatial distribution of charge density, and is crucial for evaluating charge stability. The modeling of electrons crossing a potential barrier to become true secondary electrons simulates the process of charge escaping from a material into a vacuum. This is used to assess surface charge states and discharge risks, and provides boundary feedback for surface potential changes. Material parameters are input: mass density, dielectric constant, surface conductivity, charge trap parameters, and electron affinity. Electric field boundary conditions (such as surface potential and substrate grounding) are set. The model is applicable to a variety of commonly used dielectric materials in spacecraft (such as polyimide, polyethylene, polyester, polytetrafluoroethylene, and diamond-like carbon films), ensuring physical consistency between electric field distribution and charge transport. This model also lays the foundation for modeling complex situations such as multilayer structures and heterogeneous interfaces. A transient solver is used to iterate the coupled Poisson equation, continuity equation, and carrier transport equation. Simulation results, including charge density, electric field intensity, and potential distribution, are output.This method enables real-time numerical simulation of dynamic charge evolution; supports coupled calculations of multiple physical fields (electric field, temperature field, and carrier fluid field); significantly improves measurement accuracy, compensating for the insufficient resolution of traditional experimental equipment; and provides data support for the design of spacecraft charge and discharge protection. By constructing a self-consistent electron transport model, combining trap modulation mechanisms with multi-physics field coupled calculations, this method achieves high-precision, full-process simulation of the charge behavior of spacecraft dielectrics in a space environment, providing solid theoretical and technical support for the study of the mechanisms of spacecraft charge and discharge effects and the design of protection.

[0225] Although the embodiments of the present invention have been described above with reference to the accompanying drawings, the present invention is not limited to the above-mentioned specific embodiments and application fields. The above-mentioned specific embodiments are merely illustrative and instructive, and are not restrictive. A person skilled in the art, guided by this specification and without departing from the scope of protection of the claims of the present invention, may also devise various forms, all of which fall within the scope of protection of the present invention.

Claims

1. A method for simulating and analyzing space charge distribution in a spacecraft dielectric, characterized in that: The steps include: S1. Obtain and calculate the actual operating environment parameters of the spacecraft dielectric. The actual operating environment parameters include the interaction between electron energy, flow rate, and dielectric material. The actual operating environment parameters of the spacecraft dielectric are obtained and calculated as: ， Where R can be obtained by the following formula: ， Where, j PE represents the primary electron transmission current in the medium, x represents the carrier depth, j0 represents the electron flux density in the environment, η represents the backscattering coefficient, p represents the exponential transmission parameter, R represents the electron transmission depth, ρ represents the mass density of the spacecraft dielectric, and E0 represents the electron energy in space; S2. Establish a self-consistent electron transport model that takes drift diffusion into account. This model focuses on the ballistic transport of carriers within the medium, trapping, detrapping, and recombination of electrons and holes, as well as the electrons crossing the potential barrier at the interface to become true secondary electrons. S3. The trapping probability of carriers under the influence of traps is introduced into the self-consistent electron transport model. In the self-consistent electron transport model, the Planck correction is considered in the trap adjustment part. The calculation formula includes: The capture and de-capture rates of free charge carriers n over time t are described by the first-order kinetic equation: ， By using dt=dx / v D Substituting time and shifting phase, the equation is transformed to: ， The term in brackets is the correction for the capture cross section, and its value ranges from 0 to 1, where the exponential term plays a decisive role in determining the value of the correction coefficient. Therefore, the equation is simplified and approximated as: ， The capture cross section obtained by Planck correction is: ， The probability of falling into the trap is: ， ， in , Where N represents the electron trap density, H represents the hole trap density, and ρ E represents the electron density, ρ H represents the hole density, S E represents the electron trap capture cross section, S H represents the hole trap capture cross section, e0 represents the charge of the electron, E E represents the electron thermal excitation energy, E H represents the thermal excitation energy of the hole, k represents the Boltzmann constant, T represents the temperature, and ΔE PF represents the field excitation energy, ε0 ​​is the vacuum dielectric constant, ε r is the relative dielectric constant, W E1 and W H1 represents the probability of electrons and holes being trapped under the action of the trap, Δx represents a small distance near the depth x, F represents the electric field strength, and the free carriers are n, v D is the drift velocity, S is the capture cross-sectional area, ρ / e0 is the charge density, f is the escape frequency factor of the Planck effect, S PF is the capture cross section corrected for the Planck effect, S0 is the total cross section at low temperatures, and E T is the thermal excitation energy; S4. Collect the structural parameters and intrinsic properties of the spacecraft dielectric, set the material parameters and the boundary conditions of the electric field, and establish the charge transport equation; S5. Calculate the charge transport equation and iterate the continuity equation of the transient solver to obtain the simulation results of the internal volume charge, electric field, sample current and secondary electron emission coefficient of the spacecraft dielectric.

2. The spacecraft dielectric space charge distribution simulation analysis method according to claim 1, characterized in that: In step S2, in the self-consistent electron transport model, the internal secondary electrons generated from the primary electrons are: The average generation energy of secondary electrons is linearly related to the band gap: ， The internal secondary electron generation rate is: ， The deposition of primary electrons is manifested in the form of secondary electrons ， Where, E i represents the average generation energy of internal secondary electrons, E g represents the band gap of the spacecraft dielectric, g SE Indicates the secondary electron generation rate in the dielectric material, g SH represents the hole generation rate in the dielectric material, x represents the carrier depth, g PE represents the probability of electron deposition in the dielectric material, R represents the electron penetration depth, E0 represents the electron energy in space, j0 represents the electron flux density in the environment, and j PE Represents the transmission current of primary electrons in the medium.

3. The spacecraft dielectric space charge distribution simulation analysis method according to claim 1, characterized in that: In step S2, in the self-consistent electron transport model, the calculation formulas for the ballistic transport of electrons and holes include: The decay probability during ballistic transport is: ， ， Then the ballistic current can be obtained by differential iteration: ， ， Where λ E0 represents the field-free decay distance of the electron, λ H0 represents the field-free decay distance of holes, β E represents the electron field decay coefficient, β H represents the field decay coefficient of the hole, F represents the electric field strength, x represents the carrier depth, Δx represents a small distance near the x depth, E0 represents the electron energy in space, g SE represents the secondary electron generation rate in the dielectric material, j0 represents the electron flux density in the environment, g PE Represents the probability of primary electron deposition in the dielectric material.

4. The spacecraft dielectric space charge distribution simulation analysis method according to claim 1, characterized in that: In step S2, the calculation formula for the recombination of electrons and holes in the self-consistent electron transport model is include: ， ， Then the drift current composed of trapping, detrapping and recombination is expressed as: ， ， Where S HE and S HE represents the electron-hole recombination cross section, ρ E represents the electron density, ρ H represents the hole density, W E2 represents the electron recombination probability, W H2 represents the hole recombination probability, e0 represents the charge of the electron, Δx represents a small distance near the depth x, and W E1 represents the probability of electrons being trapped under the action of traps, x represents the carrier depth, j SEE is the true secondary electron current escaping from the dielectric surface.

5. The spacecraft dielectric space charge distribution simulation analysis method according to claim 1, characterized in that: In step S2, in the self-consistent electron transport model, the calculation formula for electrons passing through the potential barrier at the interface to become real secondary electrons includes: ， Where, j SEE is the true secondary electron current escaping from the dielectric surface, E a represents the electron affinity of the medium surface, represents the average kinetic energy of the secondary electrons, j BER Represents the ballistic current generated by electrons moving toward the surface of a dielectric.

6. A spacecraft dielectric space charge distribution simulation and analysis system, characterized in that: It includes: The acquisition module obtains and calculates the actual operating environment parameters of the spacecraft dielectric. The actual operating environment parameters include the interaction between electron energy, flow rate and dielectric material. The actual operating environment parameters of the spacecraft dielectric are obtained and calculated as: ， Where R can be obtained by the following formula: ， Where, j PE represents the primary electron transmission current in the medium, x represents the carrier depth, j0 represents the electron flux density in the environment, η represents the backscattering coefficient, p represents the exponential transmission parameter, R represents the electron transmission depth, ρ represents the mass density of the spacecraft dielectric, and E0 represents the electron energy in space; The self-consistent electron transport module establishes a self-consistent electron transport model, which includes the generation of internal secondary electrons from primary electron excitation, ballistic transport of electrons and holes, trapping, detrapping and recombination of electrons and holes, and the electrons passing through the potential barrier at the interface to become real secondary electrons. The model focuses on the probability of carriers being trapped under the influence of traps. In the self-consistent electron transport model, the Planck correction is considered in the trap adjustment part. The calculation formula includes: The capture and de-capture rates of free charge carriers n over time t are described by the first-order kinetic equation: ， By using dt=dx / v D Substituting time and shifting phase, the equation is transformed to: ， The term in brackets is the correction for the capture cross section, and its value ranges from 0 to 1, where the exponential term plays a decisive role in determining the value of the correction coefficient. Therefore, the equation is simplified and approximated as: ， The capture cross section obtained by Planck correction is: ， The probability of falling into the trap is: ， ， in , Where N represents the electron trap density, H represents the hole trap density, and ρ E represents the electron density, ρ H represents the hole density, S E represents the electron trap capture cross section, S H represents the hole trap capture cross section, e0 represents the charge of the electron, E E represents the electron thermal excitation energy, E H represents the thermal excitation energy of the hole, k represents the Boltzmann constant, T represents the temperature, and ΔE PF represents the field excitation energy, ε0 ​​is the vacuum dielectric constant, ε r is the relative dielectric constant, W E1 and W H1 represents the probability of electrons and holes being trapped under the action of the trap, Δx represents a small distance near the depth x, F represents the electric field strength, and the free carriers are n, v D is the drift velocity, S is the capture cross-sectional area, ρ / e0 is the charge density, f is the escape frequency factor of the Planck effect, S PF is the capture cross section corrected for the Planck effect, S0 is the total cross section at low temperatures, and E T is the thermal excitation energy; The charge transport module collects the structural parameters and intrinsic properties of the spacecraft dielectric, sets the material parameters and the boundary conditions of the electric field, and establishes the charge transport equation; The transient solver calculates the charge transport equation and iterates the continuity equation of the transient solver to obtain the simulation results of the internal volume charge, electric field, sample current and secondary electron emission coefficient of the spacecraft dielectric.

7. A computer storage medium, characterized in that The storage medium includes computer instructions, which, when executed on a computer, enable the computer to perform the method according to any one of claims 1 to 5.

8. An electronic device, characterized in that: The electronic device comprises: A memory, a processor, and a computer program stored in the memory and executable on the processor, wherein: When the processor executes the program, the method according to any one of claims 1 to 5 is implemented.

Images