Ion thruster acceleration gate downstream pit-groove corrosion morphology prediction method

Abstract

The invention discloses an ion thruster acceleration gate downstream pit-groove corrosion morphology prediction method, which comprises the following steps: establishing a computational domain, and determining boundary conditions of the computational domain; ions are injected from the left boundary of the computational domain, charges carried by all the ions are mapped to grid nodes of the computational domain through a weight distribution method, and space charge density distribution is obtained; solving three-dimensional potential distribution and three-dimensional electric field distribution in a computational domain based on space charge density distribution and set boundary conditions; pushing the ions to move based on the three-dimensional electric field distribution, and updating the positions and speeds of all the ions; simulating a charge exchange collision process of ions and neutral atoms based on the updated ion position and speed, and updating the state of the collided ions; counting information of charge exchange ions impacting the downstream surface of the acceleration gate within a set time; and calculating the three-dimensional corrosion morphology of the downstream surface of the acceleration gate based on charge exchange ion information in combination with a sputtering yield model and gate material attributes.

Description

Technical Field

[0001] This invention belongs to the field of plasma propulsion technology, and in particular relates to a method for predicting the "pit-groove" corrosion morphology downstream of the accelerator grid of an ion thruster. Background Technology

[0002] Ion thrusters are characterized by low thrust, high specific impulse, and long lifespan, and are widely used in space propulsion, such as spacecraft attitude control, position holding, orbital maneuvers, and interplanetary flight. With the development of my country's space program, space exploration missions are evolving towards higher payloads, longer distances, and longer durations.

[0003] During operation, charged ions bombard components such as the hollow cathode, screen grid, and accelerating grid, causing corrosion. Due to the large negative potential of the accelerating grid, the corrosion caused by ions downstream of the accelerating grid is the most severe, becoming a key factor limiting the lifespan of the ion thruster.

[0004] Traditional ion thruster gate corrosion measurement experiments are lengthy, typically lasting thousands of hours, and even tens of thousands of hours for sputter-resistant carbon-carbon gates. Numerical simulation can simulate the extraction of ions from the gate beam and the sputtering corrosion process on the gate, making it an efficient method for predicting the evolution of gate corrosion morphology. Existing gate corrosion models, based on the two-dimensional axisymmetric assumption, can only predict the corrosion morphology of the gate's hole walls. However, for ion thruster gate assemblies, CEX ions, drawn by the negative voltage of the accelerating gate, bombard the downstream surface of the accelerating gate, resulting in typical "pit" and "groove" corrosion profiles, commonly known as "pit-groove" corrosion. Since "pit-groove" corrosion leads to structural failure of the accelerating gate holes, ultimately preventing the gate assembly from extracting the ion beam normally, accurate calculation of the accelerating gate's "pit-groove" corrosion morphology is crucial for predicting the service life of the gate assembly. However, current two-dimensional simulation models of gate components, based on the axisymmetric assumption, can only accurately predict the corrosion morphology of the gate apertures, but cannot quantitatively assess the intensity of the "pit-groove" corrosion downstream of the accelerating gate. Therefore, this invention proposes a method for predicting the "pit-groove" corrosion morphology downstream of the accelerating gate in an ion thruster. Summary of the Invention

[0005] To address the aforementioned technical problems, this invention proposes a method for predicting the "pit-groove" corrosion morphology downstream of the ion thruster acceleration grid, thereby resolving the issues present in the prior art.

[0006] To achieve the above objectives, the present invention provides a method for predicting the "pit-groove" corrosion morphology downstream of the accelerator gate of an ion thruster, comprising: A computational domain comprising a screen, an acceleration grid, and a downstream plume region is established, and the boundary conditions of the computational domain are determined. Ions are injected from the left boundary of the computational domain, and the charges carried by all ions are mapped to the grid nodes of the computational domain through a weighted allocation method to obtain the space charge density distribution. Based on the space charge density distribution and the set boundary conditions, the three-dimensional electric potential distribution and three-dimensional electric field distribution in the computational domain are solved. Based on the aforementioned three-dimensional electric field distribution, the movement of ions is driven, and the position and velocity of all ions are updated. Based on the updated ion positions and velocities, the process of charge exchange collisions between ions and neutral atoms is simulated, and the states of the colliding ions are updated. Collect information on charge-exchange ions that collide with the downstream surface of the acceleration gate within a set time period; Based on the charge-exchange ion information, combined with the sputtering yield model and gate material properties, the three-dimensional corrosion morphology of the downstream surface of the accelerating gate is calculated.

[0007] Optionally, the process of establishing the computational domain and determining the boundary conditions of the computational domain includes: The computational domain is obtained by selecting a quarter region based on the gate center hole structure; A spatial coordinate system is constructed by processing the spatial positions of the nodes in the computational domain using a Cartesian coordinate system. The physical constraints based on the electric field set the left boundary of the computational domain as the first type of boundary condition, and set the upper boundary, lower boundary, right boundary, front boundary and back boundary of the computational domain as the second type of boundary condition. The potentials of the screen gate and the acceleration gate are set to fixed values ​​based on the gate voltage parameters; Based on particle collision characteristics, the left boundary, right boundary, screen grid, and acceleration grid are set as ion absorption boundaries, while the upper boundary, lower boundary, front boundary, and rear boundary are set as ion reflection boundaries.

[0008] Optionally, the process of injecting ions from the left boundary of the computational domain includes: The number of ions ejected in a single step is determined based on the upstream plasma density, Bohm velocity, and time step. The initial ion ejection position is determined based on the radial grid position; The ion lateral velocity is assigned a value using Bohm velocity, and the longitudinal and vertical velocities of the ions are processed using Maxwell distribution to obtain the ion dispersion velocity.

[0009] Optionally, based on the space charge density distribution and the set boundary conditions, the process of solving for the three-dimensional potential distribution and the three-dimensional electric field distribution in the computational domain includes: Electron density distribution is calculated using the Boltzmann relation based on electron temperature and boundary potential; Based on the space charge density distribution and electron density distribution, the Poisson equation is discretized using the finite difference method to obtain a system of difference equations. The three-dimensional potential distribution is obtained by iteratively solving the difference equations using the over-relaxation iterative method to obtain the potential values ​​of each grid node in the computational domain. The electric potential distribution is processed using the central difference method to obtain the electric field intensity components of each grid node in three directions, thus obtaining the three-dimensional electric field distribution.

[0010] Optionally, the process of updating the position and velocity of all ions based on the three-dimensional electric field distribution to drive ion motion includes: The electric force on the ion is calculated based on the three-dimensional electric field distribution. Ion acceleration is calculated using Newton's second law based on the electric field force acting on the ion and the ion's mass. The acceleration is integrated over time using the frog-leap algorithm. By advancing the velocity of the current time step forward by half a step, the velocity is updated based on the acceleration. The updated velocity is then used to advance the ion position by a full time step, resulting in the updated ion position and velocity.

[0011] Optionally, the process of simulating charge-exchange collisions between ions and neutral atoms based on the updated ion positions and velocities, and updating the states of the colliding ions, includes: The collision probability is calculated based on the neutral atom density, ion velocity, and charge exchange collision cross section at the current position of the ion. The collision probability is processed using the Monte Carlo collision method to obtain the collision judgment result; The positions and velocities of ions that undergo charge exchange collisions are updated based on the collision determination results.

[0012] Optionally, the process of calculating the three-dimensional corrosion morphology of the downstream surface of the acceleration gate includes: Energy-dependent sputtering yields were calculated using the Eckstein formula based on the incident energy of charge-exchange ions. Angle-dependent sputtering yield is calculated using the Wei formula based on the incident angle of charge-exchange ions; The total sputtering yield is calculated based on the energy-dependent sputtering yield and the angle-dependent sputtering yield. The corrosion rate of each grid is calculated based on the total sputtering yield, the atomic mass of the gate material, the material density, and the grid area. The three-dimensional corrosion morphology of the downstream surface of the acceleration gate is obtained based on the corrosion rate of each grid.

[0013] Compared with the prior art, the present invention has the following advantages and technical effects: This invention establishes a three-dimensional simulation model of the ion thruster gate assembly based on the PIC-MCC method, effectively overcoming the technical limitation of traditional two-dimensional axisymmetric models in simulating the three-dimensional corrosion morphology downstream of the accelerating gate. This method accurately predicts the unique "pit-groove" corrosion morphology evolution in this region by fully simulating beam ion extraction, charge exchange collisions, and the sputtering process of CEX ions on the downstream surface of the accelerating gate. Compared with time-consuming ground experiments, this method significantly improves the efficiency of corrosion morphology prediction, providing a reliable numerical analysis tool for the lifetime assessment and structural optimization of ion thruster gate assemblies.

[0014] Based on the PIC-MCC method, this invention develops a three-dimensional simulation model of the gate assembly, which can accurately accelerate the corrosion rate and morphological evolution process of the downstream "pit" through numerical simulation calculation. It can be combined with the parameterization study of the gate structure to optimize the design of the gate assembly of the ion engine and improve the service life of the ion engine. Attached Figure Description

[0015] The accompanying drawings, which form part of this application, are used to provide a further understanding of this application. The illustrative embodiments and descriptions of this application are used to explain this application and do not constitute an undue limitation of this application. In the drawings: Figure 1 This is a schematic diagram illustrating the selection of the simulation object (dashed circle) and the setting of the simulation calculation domain in an embodiment of the present invention; Figure 2 This is a flowchart illustrating a method for predicting the "pit-groove" corrosion morphology downstream of an ion thruster accelerator grid according to an embodiment of the present invention. Figure 3 This is a schematic diagram of three-dimensional ion interpolation in an embodiment of the present invention; Figure 4 This is a schematic diagram of the frog-jumping format of the present invention; Figure 5 This is a schematic diagram of the gate beam in an embodiment of the present invention, wherein (a) is the spatial distribution of beam ions after convergence, and (b) is the corrosion rate of the "pits" and "grooves" on the downstream surface of the accelerated gate. Detailed Implementation

[0016] It should be noted that, unless otherwise specified, the embodiments and features described in this application can be combined with each other. This application will now be described in detail with reference to the accompanying drawings and embodiments.

[0017] It should be noted that the steps shown in the flowchart in the accompanying drawings can be executed in a computer system such as a set of computer-executable instructions, and although a logical order is shown in the flowchart, in some cases the steps shown or described may be executed in a different order than that shown here.

[0018] Example 1 This embodiment provides a method for predicting the "pit-groove" corrosion morphology downstream of the accelerating gate of an ion thruster. Based on fundamental experimental measurements, this method employs numerical simulation to accurately predict the evolution of the corrosion morphology of the ion thruster gate. Specifically, it includes the following steps: S1. Establish a computational domain that includes the screen, acceleration screen, and downstream plume region, and determine the boundary conditions of the computational domain.

[0019] This invention selects the central hole of the gate as the research object for the study of accelerated gate "pit-trench" corrosion. To ensure computational efficiency, this embodiment selects 1 / 4 of a single hole as the computational domain, and uses a Cartesian coordinate system to describe the spatial position of the gate node to construct a spatial coordinate system. The computational domain is as follows: Figure 1 As shown. Set the bottom left corner of the computation domain as the origin, with the x-axis pointing to the right (horizontal), the y-axis pointing upwards (vertical), and the z-axis pointing backwards (vertical). Name the origin of the computation domain A, and name the other points as follows: Figure 1 As shown. The left boundary (ABCD) is set to the side closest to the discharge chamber, and the right boundary (EFGH) is set to the neutralization point of the downstream beam ions of the thruster. From the left boundary (ABCD) to the right, the components are, in order, the discharge chamber, the screen grid, the inter-grid region, the acceleration grid, and the downstream plume region. The x-axis length is set to X, the y-axis length is set to Y, and the z-axis length is set to Z. The distance from the screen grid (subscript s) to the left boundary (AB) is set to lp, the screen grid thickness is set to ts, the grid spacing is set to lg, the acceleration grid thickness is set to ta, the screen grid aperture radius is set to ds / 2, and the acceleration grid aperture radius is set to da / 2.

[0020] The physical constraints based on the electric field set the left boundary of the computational domain as the first type of boundary condition, and set the upper boundary, lower boundary, right boundary, front boundary and back boundary of the computational domain as the second type of boundary condition.

[0021] The potential conditions at the computational domain boundaries and the gate potential are set as follows: the left boundary (ABCD) is set as a first-type boundary condition, and the upper boundary (DCGH), lower boundary (ABFE), right boundary (EFGH), front boundary (ADHE), and rear boundary (BCGF) are all set as second-type boundary conditions. Furthermore, the gate potential is set to a fixed value to simulate a real DC gate voltage setting. The second-type boundary conditions for the upper boundary (DCGH) and lower boundary (ABFE) are set according to a longitudinal potential derivative of 0, the second-type boundary condition for the right boundary (EFGH) is set according to a transverse potential derivative of 0, and the second-type boundary conditions for the front boundary (ADHE) and rear boundary (BCGF) are set according to a vertical potential derivative of 0. At the boundaries between surfaces, the potential at points on the line will have derivatives of 0 in both directions.

[0022] The potentials of the screen gate and the acceleration gate are set to fixed values ​​based on the gate voltage parameters; the left boundary, right boundary, screen gate and acceleration gate are set as ion absorption boundaries based on particle collision characteristics, and the upper boundary, lower boundary, front boundary and rear boundary are set as ion reflection boundaries.

[0023] When ions within the computational domain collide with the boundaries and the gate, the collision conditions are set as follows: 1) The left boundary (ABCD) and the right boundary (EFGH) are set as absorption boundaries, meaning that when ions collide with the left and right boundaries, the ions are absorbed; 2) The upper boundary (DCGH), the lower boundary (ABFE), the front boundary (ADHE), and the rear boundary (BCGF) are set as reflection boundaries, meaning that when ions collide with the upper and lower boundaries and the front and rear boundaries, the ions undergo specular reflection to simulate the situation where the beam from adjacent apertures enters this computational domain; 3) The screen and the accelerating gate are set as absorption boundaries.

[0024] S2. Ion Spraying: Ions are injected from the left boundary of the computational domain. The charge carried by all ions is mapped to the grid nodes of the computational domain using a weighted distribution method to obtain the space charge density distribution. This process includes: determining the number of ions sprayed in a single step based on the upstream plasma density, Bohm velocity, and time step; determining the initial spraying position of each ion based on the radial grid position; assigning Bohm velocity to the transverse velocity of the ions, and processing the longitudinal and vertical velocities of the ions using Maxwell distribution to obtain the ion spraying velocity.

[0025] Using the left boundary of the computational domain (ABCD) as the boundary for ion implantation, the number of ions ejected in a single step can be determined by the following formula: The location where the ions are sprayed is: here, v Bohm The Bohm velocity of the ion. k Boltzmann's constant, T e For electron temperature, M i is the relative atomic mass of the ion. n ref For the upstream plasma density, Δt For time step, r j For radial grid positions, Δr = Δz For grid spacing, rand It is a random number between (0,1).

[0026] The ion ejection velocities are set as follows: the lateral velocity is set to the Bohm velocity, and the longitudinal and vertical velocities follow the Maxwell distribution. For the Maxwell distribution of ion velocities and neutral atom velocities, this invention employs the "Box-Muller" partitioning method.

[0027] S3. Electric Field Solution: Based on the space charge density distribution and the established boundary conditions, the three-dimensional potential and electric field distributions within the computational domain are solved. This process includes: calculating the electron density distribution using the Boltzmann relation based on electron temperature and boundary potential; discretizing the Poisson equation using the finite difference method based on the space charge density and electron density distributions to obtain a system of difference equations; iteratively solving the system of difference equations using the over-relaxation iteration method to obtain the potential values ​​of each grid node within the computational domain, thus obtaining the three-dimensional potential distribution; and processing the potential distribution using the central difference method to obtain the electric field intensity components of each grid node in three directions, thus obtaining the three-dimensional electric field distribution.

[0028] In establishing the three-dimensional model of the accelerated gate "pit" corrosion, this invention neglects the influence of the magnetic field on the gate beam extraction process, considering only the influence of the electric field on ion movement. Based on the above analysis, solving the entire Maxwell's equations can be simplified to solving only the Poisson equation. This invention uses the finite difference method to solve the Poisson equation, where the ion density of the grid nodes is obtained by indexing the entire linked list, and the volume weight method is used to interpolate the ions at the current position to the node.

[0029] Assume the current ion's horizontal, vertical, and center positions are as follows: x pos , y pos , z pos The bottom left corner of the current grid A The horizontal grid index is i ( i The value range is 0, 1, 2, 3, …, I ), the vertical grid index is j ( j The value range is 0, 1, 2, 3, …, J ), vertical grid index is k ( k The value range is 0, 1, 2, 3, …, K The horizontal distance from the origin is x i The vertical distance from the origin is y j The vertical distance from the origin is z k The grid points are numbered as follows: Figure 3 As shown. The volume of the mesh. V g The solution can be obtained using the following formula: Ions are interpolated to each grid node using a volume-weighted method, which involves multiplying the charge of the ion at the current position by the ratio of the volume of a small block to the volume of the entire grid. This can be solved using the following formula: Since all examples in this embodiment use regular quadrilateral meshes, therefore, in the above formula... x i+1 - x i , y j+1 - y j , z k+1 - z k It can be simplified to .

[0030] Similar to the two-dimensional model, since electrons are about six orders of magnitude lighter than xenon ions, if electrons are also treated as particles, the time step will be set very small due to the limitations of the PIC time step. To improve computational efficiency, the three-dimensional model established in this embodiment also treats electrons as fluids, and the calculation method is the same as that of the two-dimensional model, which will not be repeated here.

[0031] After determining the ion and electron densities, the three-dimensional model in this embodiment also performs numerical discretization of the Poisson equation to solve it. The Poisson equation can be transformed into various forms. Since the three-dimensional model uses a Cartesian coordinate system, the Poisson equation is transformed into the following form: here n ion and n e Here, represents the ion number density and the electron number density, respectively, and e is the unit charge. ε 0Given the vacuum permittivity, this embodiment uses the finite difference method to solve the Poisson equation. For the three-dimensional model, a seven-point difference method is used to discretize the Poisson equation into a difference equation: Here, Δ represents the spatial step size. Rearranging the above equations, we obtain: To improve the solution speed, this embodiment uses the Successive Over Relaxation (SOR) method to solve the above equations. Similar to the two-dimensional model, the over-relaxation factor is... w The value is 1.5. The above equation is transformed into an over-relaxed iterative form: For the left boundary (ABCD) and the gate potential, since it is a first-type boundary condition, it is not necessary to solve the above formula. Simply substitute the fixed potential into the above formula when solving for the potentials of adjacent nodes. For the upper boundary (DCGH), lower boundary (ABFE), right boundary (EFGH), front boundary (ADHE), and rear boundary (BCGF), since a second-type boundary condition is used, the over-relaxed iterative form of the Poisson equation on the boundaries can be obtained. For the iterative form on the surface, the upper boundary (DCGH) and lower boundary (ABFE) are respectively: The right boundary (EFGH) is: The front boundary (ADHE) and the back boundary (BCGF) are as follows: For the iterative form on the boundary line between surfaces, the line AE is: Line DH is: Line BF is: The line CG is: Line EH is: Line EF is: Line FG is: Line GH is: After obtaining the electric potential in the computational domain through iterative calculation using the above formula, the electric field strength at the grid nodes can be solved using the following formula. E : Similar to the two-dimensional model, the central difference method is used to solve the above equation. The nodes are then solved using the following equation. i , j , k The transverse, longitudinal, and vertical electric fields at the location are: S4. Ion Motion Simulation: Based on the three-dimensional electric field distribution, ion motion is driven, and the positions and velocities of all ions are updated. This process includes: calculating the electric force on the ions based on the three-dimensional electric field distribution; calculating the ion acceleration based on the electric force on the ions and the ion mass using Newton's second law; using the frog-jumping algorithm to integrate the acceleration over time, by advancing the velocity of the current time step forward by half a step, updating the velocity based on the acceleration, and using the updated velocity to advance the ion position by a full time step, thus obtaining the updated ion position and velocity.

[0032] Ion motion is mainly calculated by solving for the electric force acting on the ion, substituting the electric force into Newton's second law to obtain the ion's acceleration, and then substituting the acceleration into the equation of motion to obtain the ion's velocity and position at the next time step. The leap-frog algorithm is used to accelerate the calculation of ion motion. For example... Figure 4 As shown, the leap-frog algorithm is a method that discretizes time to handle the dependency between motion and time. It works by initially shifting the velocity forward by half a time step, then updating the velocity based on forces to obtain the velocity at half a time step. This velocity is then used to update the ion position at the current time step to the ion position at the next time step, and this process is repeated. Its principle is illustrated in the figure below. The leap-frog algorithm has second-order accuracy in terms of time; as Δt approaches 0, the computational error also approaches 0. Therefore, it can improve the computational efficiency of the PIC method while maintaining computational accuracy.

[0033] S5. Electronic simulation.

[0034] Electrons carry a single unit of negative charge, and their mass is far less than that of commonly used propellant atoms such as argon, krypton, and xenon. In plasma, electrons and ions have the same temperature, but due to the significant mass difference, the average thermal velocity of electrons is much higher than that of ions, nearly 500 times faster. Therefore, treating electrons as particles in plasma simulations severely reduces the simulation time step, leading to a significant increase in simulation time costs. In ion thruster plasma simulations, to improve simulation efficiency, electrons are treated as fluids, and based on their isothermal and collision-free characteristics, their number density distribution follows a Boltzmann distribution.

[0035] Because both the screen and the accelerating gate have a significant repulsive effect on electrons, the electron density drops drastically as electrons approach the gate. Therefore, there is almost no electron distribution between the gates, and the upstream of the screen and the downstream of the accelerating gate are the main electron distribution regions. The electron number density distribution upstream of the screen is as follows: In the formula, 0 It is the upstream plasma potential, which in the program is the potential at the left boundary of the computational domain. T e0 It refers to the electron temperature within the upstream plasma region.

[0036] Similarly, downstream of the accelerating gate, the electron number density is In the formula, It accelerates the plasma potential downstream of the gate. It accelerates the temperature of electrons downstream of the gate. It is the average plasma number density downstream of the accelerated gate.

[0037] S6. Charge exchange collision and gate corrosion rate calculation: Based on the updated ion position and velocity, the process of charge exchange collision between ions and neutral atoms is simulated, and the state statistics of the colliding ions are updated to include the charge exchange ion information that impacts the downstream surface of the accelerating gate within a set time. Based on the charge exchange ion information, combined with the sputtering yield model and gate material properties, the three-dimensional corrosion morphology of the downstream surface of the accelerating gate is calculated.

[0038] The process of updating the state of colliding ions includes: calculating the collision probability based on the neutral atom density, ion velocity, and charge exchange collision cross section at the current position of the ion; processing the collision probability using the Monte Carlo collision method to obtain the collision judgment result; and updating the position and velocity of the ion that has undergone charge exchange collision based on the collision judgment result.

[0039] Unlike the two-dimensional axisymmetric model, the three-dimensional corrosion model requires calculating the velocity in the third dimension when solving for ion collision velocities, and statistically analyzing the CEX ions downstream of the impact acceleration gate after calculating charge exchange collisions. The formula for charge exchange collisions (CEX collisions) between ions and neutral atoms is: In gate simulation n The value can be 1 or 2. The generated slow-moving ions, known as CEX ions, can affect beam performance and sputtering corrosion of the gate assembly. Therefore, a Monte Carlo Collision (MCC) module is added to the PIC particle simulation program to simulate the generation process of CEX ions.

[0040] Any ion in space interacts with a neutral atom The frequency of collisions occurring within time t is: Therefore, the collision probability is: In the formula: This represents the number density of neutral atoms at the current position of the ion; The velocity of charged ions; This represents the collision cross section for ion charge exchange.

[0041] The ion charge exchange collision cross section is calculated using the following formula: In the formula: k 1 , k 2 The constant is given for a charge-exchange ion in a single valence state. k 1 Take 87.3, k 2 Take 13.6; divalent k 1 Take 45.7, k 2 Take 8.9.

[0042] The relative velocity between the ions and neutral atoms is denoted by . Since the ion velocity is much greater than the atom velocity, the ion velocity is used instead in the simulation.

[0043] Since the collision probability between ions and atoms is very small, but the collision probability and collision cross-section need to be calculated at each time step, this has a significant impact on computational efficiency. Therefore, this embodiment uses the empty collision technique to accelerate the calculation of the collision process.

[0044] First, calculate the maximum collision frequency of all ions. : Assume that there are in the computational domain at this time N i If there are ions, then randomly select them in the program. N i × P null Each ion is subjected to collisions (eliminating duplicates). The collision frequency of each selected ion is calculated. ν Then, a random number is generated by the program. RAND ,if If a collision occurs, the ion is considered to have undergone a charge exchange collision; otherwise, it is considered to have undergone an empty collision (no processing is performed). It is important to note that when sampling random numbers, due to the large sample size, a denser random number sequence is needed to more accurately reflect this random process. After an ion undergoes a charge exchange collision, the atomic position and velocity at that location are assigned to the current ion. The ion that caused the charge exchange collision will participate in the electric field calculations and ion motion in the following time steps.

[0045] The process of calculating the three-dimensional corrosion morphology of the downstream surface of the accelerating gate includes: calculating the energy-dependent sputtering yield based on the incident energy of charge-exchange ions using the Eckstein formula; calculating the angle-dependent sputtering yield based on the incident angle of charge-exchange ions using the Wei formula; calculating the total sputtering yield based on the energy-dependent sputtering yield and the angle-dependent sputtering yield; calculating the corrosion rate of each grid based on the total sputtering yield, the atomic mass of the gate material, the material density, and the grid area; and obtaining the three-dimensional corrosion morphology of the downstream surface of the accelerating gate based on the corrosion rate of each grid.

[0046] The accelerated gate "pit" corrosion rate was calculated using Eckstein and Wei's sputtering yield formula. The relationship between sputtering yield and ion energy was calculated using Eckstein's formula: here, Scaling parameters for experience, E The incident energy of the ions. It is an experience index item. This represents the sputtering threshold energy. For graphite carbon... Take values ​​of 4, 0.8, 1.8, and 21 respectively. The reduced nucleus stopping energy is based on the Krypton-Carbon (KC) potential.

[0047] The relationship between sputtering yield and incident angle is obtained by solving the Wei formula: Where 'a' represents the projected energy range, and α and β represent the longitudinal and transverse discrete ranges, respectively. β / α and a / α represent the ratio of the transverse to the longitudinal discrete range and the ratio of the projected energy range to the longitudinal discrete range, respectively.

[0048] The final sputtering output was: After calculating the sputtering yield of a single CEX ion, the total sputtering yield caused by all CEX ions within one time step for each grid on the gate surface is calculated using the following formula. .

[0049] In the formula, N This represents the total number of ions. Substituting into the following formula, the corrosion rate of a certain grid on the gate surface per unit time can be calculated. R E .

[0050] In the formula, m n,grid The absolute mass of the gate material atoms. A Let be the area of ​​a certain grid on the gate surface. ρ grid denoted as gate material density.

[0051] Example 2 The ion thruster gate is a screen structure composed of a screen grid and an acceleration grid. To improve computational efficiency, one-quarter of the central aperture is selected as the simulation computational domain, and the spatial position of the gate node is described using a Cartesian coordinate system. The distance from the screen grid to the left boundary is kept constant at 1 mm. The plasma density at the upstream sheath edge is set to 1.0 × 10⁻⁶. 17 m -3 The upstream sheath potential was set to 35V. The upstream electron temperature was set to 5eV, and the downstream electron temperature was set to 1.5eV. Xenon was used as the propellant in the simulation, and the neutral atom density was set to be equal at all locations, at 5.0 × 10⁻⁶. 18 m -3 The horizontal x-length of the computational domain is set to 27.5 mm, and the vertical y-length and z-length are both set to 1.1 mm.

[0052] like Figure 2 As shown, a method for predicting the "pit-groove" corrosion morphology downstream of an ion thruster accelerator grid includes the following steps: S1. Input gate parameters, plasma parameters and initialize grid, boundary potential and gate potential and other conditions; S2. Spray ions from the left boundary of the computational domain (assign initial velocity, position, weight, and other parameters to the ions); S3. Interpolate the charges of all ions in the computational domain to the corresponding grid nodes to solve for the ion density, and use a fluid method to solve for the electron density; S4. The electric potential of the grid nodes is solved by the over-relaxation iterative method, and then the electric field of the grid nodes is solved. S5. Interpolate the electric field of the grid nodes back to the ion position, solve for the force on the ion and drive the ion's motion; S6. Traverse the ions in the computational domain, determine whether the ions have undergone charge exchange collisions and process them accordingly; S7. Compare whether the total number of ions in the current computational domain has changed relative to the previous time step. If the change is greater than 1‰, repeat steps 1-6; otherwise, proceed to the next step. S8. Continue running for 5000-10000 steps, and collect the position, velocity, and weight information of CEX ions that collide with the downstream surface of the acceleration gate at each time step. Figure 5 (a) shows the spatial distribution of beam ions after calculation convergence; S9. Based on the CEX ion information impacting the downstream surface of the accelerating gate, and combined with the corrosion rate calculation formula, the corrosion rates of the "pits" and "grooves" on the downstream surface of the accelerating gate are calculated, such as... Figure 5 As shown in (b).

[0053] The above are merely preferred embodiments of this application, but the scope of protection of this application is not limited thereto. Any variations or substitutions that can be easily conceived by those skilled in the art within the scope of the technology disclosed in this application should be included within the scope of protection of this application. Therefore, the scope of protection of this application should be determined by the scope of the claims.

Claims

1. A method for predicting the "pit-groove" corrosion morphology downstream of an ion thruster accelerator grid, characterized in that, Includes the following steps: A computational domain comprising a screen, an acceleration grid, and a downstream plume region is established, and the boundary conditions of the computational domain are determined. Ions are injected from the left boundary of the computational domain, and the charges carried by all ions are mapped to the grid nodes of the computational domain through a weighted allocation method to obtain the space charge density distribution. Based on the space charge density distribution and the set boundary conditions, the three-dimensional electric potential distribution and three-dimensional electric field distribution in the computational domain are solved. Based on the aforementioned three-dimensional electric field distribution, the movement of ions is driven, and the position and velocity of all ions are updated. Based on the updated ion positions and velocities, the process of charge exchange collisions between ions and neutral atoms is simulated, and the states of the colliding ions are updated. Collect information on charge-exchange ions that collide with the downstream surface of the acceleration gate within a set time period; Based on the charge-exchange ion information, combined with the sputtering yield model and gate material properties, the three-dimensional corrosion morphology of the downstream surface of the accelerating gate is calculated.

2. The method for predicting the "pit-groove" corrosion morphology downstream of the ion thruster acceleration grid according to claim 1, characterized in that, The process of establishing a computational domain and determining the boundary conditions of the computational domain includes: The computational domain is obtained by selecting a quarter region based on the gate center hole structure; A spatial coordinate system is constructed by processing the spatial positions of the nodes in the computational domain using a Cartesian coordinate system. The physical constraints based on the electric field set the left boundary of the computational domain as the first type of boundary condition, and set the upper boundary, lower boundary, right boundary, front boundary and back boundary of the computational domain as the second type of boundary condition. The potentials of the screen gate and the acceleration gate are set to fixed values ​​based on the gate voltage parameters; Based on particle collision characteristics, the left boundary, right boundary, screen grid, and acceleration grid are set as ion absorption boundaries, while the upper boundary, lower boundary, front boundary, and rear boundary are set as ion reflection boundaries.

3. The method for predicting the "pit-groove" corrosion morphology downstream of the ion thruster acceleration grid according to claim 1, characterized in that, The process of injecting ions from the left boundary of the computational domain includes: The number of ions ejected in a single step is determined based on the upstream plasma density, Bohm velocity, and time step. The initial ion ejection position is determined based on the radial grid position; The ion lateral velocity is assigned a value using Bohm velocity, and the longitudinal and vertical velocities of the ions are processed using Maxwell distribution to obtain the ion dispersion velocity.

4. The method for predicting the "pit-groove" corrosion morphology downstream of the ion thruster acceleration grid according to claim 1, characterized in that, Based on the aforementioned space charge density distribution and the established boundary conditions, the process of solving for the three-dimensional potential distribution and three-dimensional electric field distribution within the computational domain includes: Electron density distribution is calculated using the Boltzmann relation based on electron temperature and boundary potential; Based on the space charge density distribution and electron density distribution, the Poisson equation is discretized using the finite difference method to obtain a system of difference equations. The three-dimensional potential distribution is obtained by iteratively solving the difference equations using the over-relaxation iterative method to obtain the potential values ​​of each grid node in the computational domain. The electric potential distribution is processed using the central difference method to obtain the electric field intensity components of each grid node in three directions, thus obtaining the three-dimensional electric field distribution.

5. The method for predicting the "pit-groove" corrosion morphology downstream of the ion thruster acceleration grid according to claim 1, characterized in that, The process of updating the position and velocity of all ions based on the three-dimensional electric field distribution that drives ion movement includes: The electric force on the ion is calculated based on the three-dimensional electric field distribution. Ion acceleration is calculated using Newton's second law based on the electric field force acting on the ion and the ion's mass. The acceleration is integrated over time using the frog-leap algorithm. By advancing the velocity of the current time step forward by half a step, the velocity is updated based on the acceleration. The updated velocity is then used to advance the ion position by a full time step, resulting in the updated ion position and velocity.

6. The method for predicting the "pit-groove" corrosion morphology downstream of the ion thruster acceleration grid according to claim 1, characterized in that, Based on the updated ion positions and velocities, the process of simulating charge-exchange collisions between ions and neutral atoms, and updating the states of the colliding ions, includes: The collision probability is calculated based on the neutral atom density, ion velocity, and charge exchange collision cross section at the current position of the ion. The collision probability is processed using the Monte Carlo collision method to obtain the collision judgment result; The positions and velocities of ions that undergo charge exchange collisions are updated based on the collision determination results.

7. The method for predicting the "pit-groove" corrosion morphology downstream of the ion thruster accelerating grid according to claim 1, characterized in that, The process of calculating the three-dimensional corrosion morphology of the downstream surface of the acceleration gate includes: Energy-dependent sputtering yields were calculated using the Eckstein formula based on the incident energy of charge-exchange ions. Angle-dependent sputtering yield is calculated using the Wei formula based on the incident angle of charge-exchange ions; The total sputtering yield is calculated based on the energy-dependent sputtering yield and the angle-dependent sputtering yield. The corrosion rate of each grid is calculated based on the total sputtering yield, the atomic mass of the gate material, the material density, and the grid area. The three-dimensional corrosion morphology of the downstream surface of the acceleration gate is obtained based on the corrosion rate of each grid.

Images