CN114611251B - Method for designing aperture scaling of grid electrode of ion thruster - Google Patents
Method for designing aperture scaling of grid electrode of ion thruster Download PDFInfo
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Abstract
The application relates to the technical field of space electric propulsion, in particular to a method for designing the aperture scaling of a grid electrode of an ion thruster, which comprises the following steps: step 1: adopting a grid ion method numerical simulation calculation to obtain beam divergence angles corresponding to different screen aperture and thickness combinations under certain electric and gas parameters; step 2: substituting the combination of the screen aperture and the thickness with the same beam divergence angle in the step 1 into a flow guiding calculation formula, and calculating to obtain a corresponding flow guiding coefficient; step 3: and (3) selecting proper parameters from the screen aperture and thickness combination with the same flow conductivity in the step (2) as design parameters according to actual requirements. The method utilizes the structural similarity of the plasma sheath to develop the design of the aperture scaling of the grid electrode of the ion thruster, so that the configuration of the plasma sheath is not changed, and the similarity of the grid electrode system when the geometric dimension is changed is ensured.
Description
Technical Field
The application relates to the technical field of space electric propulsion, in particular to a method for designing the aperture scaling of a grid electrode of an ion thruster.
Background
Realizing high power and superhigh specific impulse is one of the important development directions of ion thrusters. In order to realize high power and ultra-high specific impulse of the ion thruster, the accelerating voltage and beam extraction capacity of the grid system need to be greatly improved. In the traditional double-grid or tri-grid system, the decoupling of the ion acceleration process and the extraction process cannot be realized, and the high power of the thruster can be realized only by enlarging the area of the grid.
Theoretical studies have shown that: the diameter of a grid system of the traditional grid ion thruster is 50cm at maximum, and the maximum power achieved is about 50kW; the two-stage four-grid acceleration technology decouples the extraction process and the acceleration process of ions, so that the high power and the ultrahigh specific impulse of the thruster can be realized by greatly improving the extraction voltage and the acceleration voltage under the condition of not increasing the diameter of a grid electrode. FIG. 1 is a schematic diagram of a dual stage four-grid acceleration system. Theoretical research shows that the accelerating voltage of the two-stage accelerating system can be up to 80kV, the specific impulse of xenon working medium is adopted to exceed 30000s, and the power can reach megawatt.
The grid system is required to bear higher energy deposition under high power no matter the traditional grid ion thruster or the two-stage acceleration ion thruster, and if the thickness of the grid is smaller, serious deformation can be caused to the grid, so that the service life of the grid system is reduced. Research shows that increasing the thickness of the grid electrode can effectively improve the thermal deformation resistance of the grid electrode, but increasing the thickness of the grid electrode requires corresponding increase of the aperture of the grid electrode to ensure that the flow conductivity of the grid electrode system is not reduced. Therefore, it is necessary to develop design method researches of gate aperture and thickness scaling.
Disclosure of Invention
The main purpose of the application is to provide a method for designing the gate aperture scaling of an ion thruster, which is used for designing a large-aperture gate system of a high-power ion thruster.
In order to achieve the above objective, the present application provides a method for designing the scaling of the gate aperture of an ion thruster, comprising the following steps: step 1: adopting a grid ion method numerical simulation calculation to obtain beam divergence angles corresponding to different screen aperture and thickness combinations under certain electric and gas parameters; step 2: substituting the combination of the screen aperture and the thickness with the same beam divergence angle in the step 1 into a flow guiding calculation formula, and calculating to obtain a corresponding flow guiding coefficient; step 3: and (3) selecting proper parameters from the screen aperture and thickness combination with the same flow conductivity in the step (2) as design parameters according to actual requirements.
Further, the calculating of the beam divergence angle in the step 1 includes the following steps: step 1.1: inputting initial parameters such as grid voltage, grid geometric parameters and the like into a simulation system; step 1.2: calculating an initial electrostatic field, dividing an analog calculation area into a large number of grids, taking the voltage applied by each grid as an initial condition, calculating electrostatic potential and electrostatic field of each node by solving a poisson equation, and interpolating electric field intensity at other positions according to the electric field of surrounding nodes; step 1.3: entering particles, wherein the simulated particles comprise propellant ions and electrons in a particle simulation of an ion thruster grid system, the process of entering the propellant ions into a calculation region is realized by adding the simulated particles into the calculation region, and a certain number of simulated particles enter the calculation region from the left boundary of the calculation region at a specific speed in each time step in the simulation; step 1.4: calculating the electric field intensity after charged particles are added, weighting the electric quantity of the charged particles to surrounding grid nodes, calculating the electric potential and the electric field of each node by solving a poisson equation, and interpolating the electric field intensity of the position of the particles according to the electric field of the surrounding nodes; step 1.5: accelerating ions according to newton's second law, the acceleration of ions according to the principle of kinematics can be expressed as: f=m (dv/dt), dx/dt=v; step 1.6: judging whether the electric field is changed, and returning to the step 1.2 if the electric field is changed; step 1.7: the electric field is not changed, and the ion track and the beam divergence angle are calculated.
Further, in step 1.7, calculating an ion track, and calculating an axial position and a radial position of the ion at each time step according to the Newton second law in step 1.5 to obtain a movement track of the ion; and calculating the beam divergence angle according to the axial position x and the radial position y of all ions reaching the right boundary of the calculation region, calculating the beam divergence angle alpha of each ion by using tan alpha = y/x, and calculating the obtained beam divergence angle according to the beam divergence angle definition.
Further, in step 2, the flow guiding calculation formula is:
wherein: epsilon 0 Represents vacuum dielectric constant, e represents electron charge, M i Representing ion mass, ds representing screen aperture diameter, lg representing gate spacing, and ts representing screen thickness.
The invention provides a method for designing the aperture scaling of a grid electrode of an ion thruster, which comprises the following steps of
The beneficial effects are that:
the plasma sheath structure similarity is utilized to develop the grid aperture scaling design of the ion thruster, so that the configuration of the plasma sheath is not changed, the similarity of the grid system when the geometric dimension is changed is ensured, and the grid design can be rapidly developed according to actual needs.
Drawings
The accompanying drawings, which are incorporated in and constitute a part of this application, are included to provide a further understanding of the application and to provide a further understanding of the application with regard to the other features, objects and advantages of the application. The drawings of the illustrative embodiments of the present application and their descriptions are for the purpose of illustrating the present application and are not to be construed as unduly limiting the present application. In the drawings:
FIG. 1 is a schematic diagram of a bipolar four-gate acceleration system;
FIG. 2 is a schematic diagram of plasma sheath configurations and ion trajectories for different screen aperture;
FIG. 3 is a schematic diagram of plasma sheath configuration and ion trajectories with different screen thicknesses;
fig. 4 is a flowchart of a method for designing the scaling of the gate aperture of the ion thruster according to an embodiment of the present application.
Detailed Description
In order to make the present application solution better understood by those skilled in the art, the following description will be made in detail and with reference to the accompanying drawings in the embodiments of the present application, it is apparent that the described embodiments are only some embodiments of the present application, not all embodiments. All other embodiments, which can be made by one of ordinary skill in the art based on the embodiments herein without making any inventive effort, shall fall within the scope of the present application.
It should be noted that the terms "first," "second," and the like in the description and claims of the present application and the above figures are used for distinguishing between similar objects and not necessarily for describing a particular sequential or chronological order. It is to be understood that the data so used may be interchanged where appropriate in order to describe the embodiments of the present application described herein. Furthermore, the terms "comprises," "comprising," and "having," and any variations thereof, are intended to cover a non-exclusive inclusion, such that a process, method, system, article, or apparatus that comprises a list of steps or elements is not necessarily limited to those steps or elements expressly listed but may include other steps or elements not expressly listed or inherent to such process, method, article, or apparatus.
In the present application, the terms "upper", "lower", "left", "right", "front", "rear", "top", "bottom", "inner", "outer", "middle", "vertical", "horizontal", "lateral", "longitudinal" and the like indicate an azimuth or a positional relationship based on that shown in the drawings. These terms are used primarily to better describe the present application and its embodiments and are not intended to limit the indicated device, element or component to a particular orientation or to be constructed and operated in a particular orientation.
Also, some of the terms described above may be used to indicate other meanings in addition to orientation or positional relationships, for example, the term "upper" may also be used to indicate some sort of attachment or connection in some cases. The specific meaning of these terms in this application will be understood by those of ordinary skill in the art as appropriate.
In addition, the term "plurality" shall mean two as well as more than two.
It should be noted that, in the case of no conflict, the embodiments and features in the embodiments may be combined with each other. The present application will be described in detail below with reference to the accompanying drawings in conjunction with embodiments.
As shown in fig. 4, the present application provides a method for designing the scaling of the gate aperture of an ion thruster, which includes the following steps: step 1: adopting a grid ion method numerical simulation calculation to obtain beam divergence angles corresponding to different screen aperture and thickness combinations under certain electric and gas parameters; step 2: substituting the combination of the screen aperture and the thickness with the same beam divergence angle in the step 1 into a flow guiding calculation formula, and calculating to obtain a corresponding flow guiding coefficient; step 3: and (3) selecting proper parameters from the screen aperture and thickness combination with the same flow conductivity in the step (2) as design parameters according to actual requirements.
Specifically, during operation of the ion thruster, a density of plasma is generated within the discharge chamber, which plasma creates a plasma sheath in the vicinity of the screen downstream of the discharge chamber. Since the screen electrode is of a porous structure and a positive potential is applied to the screen electrode, an electric field penetrates into the discharge chamber. Under the combined action of the electric potential generated by the plasma in the discharge chamber and the electric potential penetrating into the discharge chamber, a plasma sheath layer at the tiny hole of the screen grating is formed, and under normal conditions, the plasma sheath layer bends towards one side of the discharge chamber and has convergence effect on the extracted ions, the curvatures are different, the convergence performance is different, the larger the curvature is, and the stronger the convergence effect is. The curvature of the plasma sheath is related to the extraction potential and the plasma density, and also related to the aperture of the small hole of the screen grid and the thickness of the screen grid. According to the grid system design theory, under the condition that electric and gas parameters are unchanged, the aperture and the thickness of the screen grid determine the beam divergence angle and the flow conductivity of the grid system, which are basic parameters of the grid system design, and the geometric parameter design of other grids refers to the two parameters.
Further, the calculating of the beam divergence angle in the step 1 includes the following steps: step 1.1: inputting initial parameters such as grid voltage, grid geometric parameters and the like into a simulation system; step 1.2: calculating an initial electrostatic field, dividing an analog calculation area into a large number of grids, taking the voltage applied by each grid as an initial condition, calculating electrostatic potential and electrostatic field of each node by solving a poisson equation, and interpolating electric field intensity at other positions according to the electric field of surrounding nodes; step 1.3: entering particles, wherein the simulated particles comprise propellant ions and electrons in a particle simulation of an ion thruster grid system, wherein the process of entering the propellant ions into a calculation region is realized by adding the simulated particles into the calculation region, and a certain number of simulated particles enter the calculation region from the left boundary (discharge chamber) of the calculation region at a specific speed in each time step in the simulation; step 1.4: calculating the electric field intensity after charged particles are added, weighting the electric quantity of the charged particles to surrounding grid nodes, calculating the electric potential and the electric field of each node by solving a poisson equation, and interpolating the electric field intensity of the position of the particles according to the electric field of the surrounding nodes; step 1.5: accelerating ions according to newton's second law, the acceleration of ions according to the principle of kinematics can be expressed as: f=m (dv/dt), dx/dt=v; step 1.6: judging whether the electric field is changed, and returning to the step 1.2 if the electric field is changed; step 1.7: the electric field is not changed, and the ion track and the beam divergence angle are calculated.
Further, in step 1.7, calculating an ion track, and calculating an axial position and a radial position of the ion at each time step according to the Newton second law in step 1.5 to obtain a movement track of the ion; and calculating the beam divergence angle according to the axial position x and the radial position y of all ions reaching the right boundary of the calculation region, calculating the beam divergence angle alpha of each ion by using tan alpha = y/x, and calculating the obtained beam divergence angle according to the beam divergence angle definition.
Further, in step 2, the flow guiding calculation formula is:
wherein: ε 0 represents the vacuum dielectric constant, e represents the electron charge, mi represents the ion mass, ds represents the screen aperture diameter, lg represents the gate spacing, and ts represents the screen thickness.
Further, the screen aperture is one of the key factors affecting the position and shape of the plasma sheath. Under the condition that other geometric parameters and electrical parameters are unchanged, the larger the screen electrode aperture is, the plasma sheath layer is deeply arranged towards one side of the discharge chamber, so that the curvature of the plasma sheath layer is increased, on one hand, the ion extraction capacity is improved, and on the other hand, the ion convergence performance is improved. But the curvature is too large, the ion can be over-focused, so that the grid corrosion is aggravated and the beam divergence angle is too large. Fig. 2 shows the effect of different screen aperture on plasma sheath configuration and ion trajectories.
Further, screen gate thickness is yet another key factor affecting plasma sheath position and shape. With other geometrical and electrical parameters unchanged, the screen thickness increases, the plasma sheath moves to the side of the grid, resulting in a decrease in the sheath curvature, which on the one hand will lead to a decrease in the beam extraction capacity of the grid system and on the other hand will impair the ion convergence capacity. But too small a curvature can cause the ions to become unfocused and likewise increase the beam divergence angle. Fig. 3 shows the effect of different screen gate thicknesses on plasma sheath configuration and ion trajectories. Wherein the plasma sheath 1 corresponds to a thick screen and the plasma sheath 2 corresponds to a thin screen.
Thus, the change in the configuration of the plasma sheath necessarily results in a change in the ion focusing performance and extraction capability of the gate system. The screen aperture is increased, the plasma sheath layer moves to one side of the discharge chamber, and the thickness of the screen is increased, and the plasma sheath layer moves to one side of the grid, so that an optimal combination of the screen aperture and the thickness is necessarily present, the configuration of the plasma sheath layer is not changed, and the similarity of the grid system when the geometric dimension is changed is ensured. In the embodiment of the application, firstly, all combinations of different screen aperture and thicknesses are obtained through numerical simulation by utilizing invariance of beam divergence angles; secondly, calculating the combination of different screen aperture and thickness with plasma sheath structure similarity according to a conductance formula by utilizing the invariance of the conductance, wherein the combination of the screen aperture and the thickness with the equal beam divergence angle and the equal flow conductivity is the geometric structure with grid geometric similarity, the corresponding plasma sheath also has structure similarity, and finally, selecting the proper combination parameter of the screen aperture and the thickness from the combination as the design parameter according to the actual requirement.
The foregoing description is only of the preferred embodiments of the present application and is not intended to limit the same, but rather, various modifications and variations may be made by those skilled in the art. Any modification, equivalent replacement, improvement, etc. made within the spirit and principles of the present application should be included in the protection scope of the present application.
Claims (2)
1. The method for designing the grid aperture of the ion thruster is characterized by comprising the following steps of:
step 1: adopting a grid ion method numerical simulation calculation to obtain beam divergence angles corresponding to different screen aperture and thickness combinations under certain electric and gas parameters;
step 1.1: inputting initial parameters such as grid voltage, grid geometric parameters and the like into a simulation system;
step 1.2: calculating an initial electrostatic field, dividing an analog calculation area into a large number of grids, taking the voltage applied by each grid as an initial condition, calculating electrostatic potential and electrostatic field of each node by solving a poisson equation, and interpolating electric field intensity at other positions according to the electric field of surrounding nodes;
step 1.3: entering particles, wherein the simulated particles comprise propellant ions and electrons in a particle simulation of an ion thruster grid system, the process of entering the propellant ions into a calculation region is realized by adding the simulated particles into the calculation region, and a certain number of simulated particles enter the calculation region from the left boundary of the calculation region at a specific speed in each time step in the simulation;
step 1.4: calculating the electric field intensity after charged particles are added, weighting the electric quantity of the charged particles to surrounding grid nodes, calculating the electric potential and the electric field of each node by solving a poisson equation, and interpolating the electric field intensity of the position of the particles according to the electric field of the surrounding nodes;
step 1.5: accelerating ions according to newton's second law, the acceleration of ions according to the principle of kinematics can be expressed as: f=m (dv/dt), dx/dt=v;
step 1.6: judging whether the electric field is changed, and returning to the step 1.2 if the electric field is changed;
step 1.7: calculating an ion track and a beam divergence angle if the electric field is not changed, and calculating the ion track according to the Newton second law in the step 1.5 to obtain the axial position and the radial position of the ions at each time step, so as to obtain the movement track of the ions;
calculating the beam divergence angle according to the axial position x and the radial position y of all ions reaching the right boundary of the calculation region by statistics, calculating the beam divergence angle alpha of each ion by using tan alpha = y/x, and calculating the obtained beam divergence angle according to the beam divergence angle definition;
step 2: substituting the combination of the screen aperture and the thickness with the same beam divergence angle in the step 1 into a flow guiding calculation formula, and calculating to obtain a corresponding flow guiding coefficient;
step 3: and (3) selecting proper parameters from the screen aperture and thickness combination with the same flow conductivity in the step (2) as design parameters according to actual requirements.
2. The method for designing the gate aperture of the ion thruster according to claim 1, wherein in the step 2, the flow guiding calculation formula is:
wherein: epsilon 0 Represents vacuum dielectric constant, e represents electron charge, M i Representing ion mass, ds representing screen aperture diameter, lg representing gate spacing, and ts representing screen thickness.
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