A method for calculating a grid hole compensation coefficient of a grid assembly of an ion thruster

Abstract

The application relates to the technical field of space electric propulsion, in particular to a method for calculating a grid hole compensation coefficient of an ion thruster grid assembly, which comprehensively considers the influence of grid hole asymmetry on the geometric structure parameters, working parameters, performance and working life of the grid assembly, determines the corresponding grid hole compensation coefficient when the performance of the thruster is best and the life is longest, can provide technical support in the process of ion thruster product development or optimization design, and can greatly shorten the product development cycle and reduce the product development cost.

Description

Technical Field

[0001] This application relates to the field of space electric propulsion technology, and more specifically, to a method for calculating the gate hole compensation coefficient of an ion thruster gate assembly. Background Technology

[0002] Electric propulsion is a technology that uses electrical energy to heat, dissociate, and accelerate a working propellant to form a high-speed jet, thereby generating thrust. Depending on the acceleration method, electric propulsion is divided into three types: electrostatic, electromagnetic, and electrothermal. Ion electric propulsion is a type of electrostatic electric propulsion. Compared to other types, ion electric propulsion has advantages such as high specific impulse, long lifespan, high thrust, and continuously adjustable resolution. It can significantly improve the satellite's payload capacity, reduce overall satellite costs, and significantly improve satellite orbit coupling control, enabling ultra-high precision orbit maintenance.

[0003] When a thruster is operating in orbit, its thrust vector direction must be continuously adjusted according to changes in the satellite's center of mass. However, the thruster itself lacks the capability for thrust vector adjustment and requires external assistance to eliminate attitude disturbance torques caused by thrust deviations. To address this issue, the satellite is designed with a thrust vector adjustment mechanism to rapidly eliminate yaw and pitch moments caused by forces perpendicular to the thrust direction, and to eliminate roll moments caused by forces parallel to the thrust direction using chemical propulsion or momentum wheels. This measure is effective for near-field exploration missions, but for long-range deep space exploration missions, the ion thruster requires real-time attitude adjustments. Once roll moments are generated, chemical propulsion or momentum wheels need to operate. This necessitates the satellite carrying additional propellant for chemical propulsion or momentum wheel operation, and also reduces the satellite's on-orbit reliability due to the operation of chemical propulsion or momentum wheels.

[0004] Currently, the solution to the main factor causing rolling torque, gate aperture asymmetry, is gate aperture compensation. However, the determination of this coefficient depends solely on the geometric parameters of the gate assembly. In fact, the offset of the gate aperture displacement also affects the extracted beam current of the gate aperture, i.e., the performance of the thruster, and also determines the intercepted current of the acceleration gate, i.e., the working life of the thruster. Therefore, during the design process, it is necessary to comprehensively consider the thruster performance and life to determine the gate aperture compensation coefficient applicable to specific structures and operating parameters. Summary of the Invention

[0005] This application provides a method for calculating the gate hole compensation coefficient of an ion thruster gate assembly, which can determine the gate hole compensation coefficient corresponding to the best performance and longest lifespan of the ion thruster.

[0006] To achieve the above objectives, this application provides a method for calculating the gate aperture compensation coefficient of an ion thruster gate assembly, comprising the following steps: Step 1: Determine the beam current and screen voltage based on the ion thruster performance parameters; Step 2: Determine the accelerating gate voltage based on the electron backflow limit requirements; Step 3: Obtain the total accelerating voltage using the screen voltage obtained in Step 1 and the accelerating gate voltage obtained in Step 2; Step 4: Obtain the maximum current conductivity based on the relationship between the gate aperture conductivity and the beam current and total accelerating voltage; Step 5: Determine the screen gate thickness, aperture, and gate spacing based on the relationship between the maximum current conductivity and the gate geometry; Step 6: Determine the corresponding beam current extraction ratio based on the relationship between the beam extraction ratio and the gate geometry parameters and operating parameters; Step 7: Establish the gate... A highly asymmetric numerical simulation model is used to determine the beam focusing situation. Finite element analysis is employed to perform simulation calculations for different beam extraction ratios, grid thickness, aperture, and grid spacing, obtaining the grid geometry and operating parameters under normal beam focusing conditions. Step 8: By changing the positional offset of the accelerating grid aperture relative to the center of the grid aperture, the simulation model is revised. Simulation calculations are used to simulate the beam focusing performance under different displacement offsets, and the maximum extracted beam current and the intercepted current of the accelerating grid corresponding to different offsets are statistically analyzed. Step 9: The extracted beam current and the intercepted current of the accelerating grid under different offsets are analyzed. The offset of the accelerating grid relative to the center of the grid aperture that results in the maximum extracted beam current and the minimum intercepted current of the accelerating grid is selected to obtain the grid aperture compensation coefficient.

[0007] Furthermore, in step 1, the process of determining the beam current and grid voltage based on the performance parameters of the ion thruster is as follows: Step 1.1: Based on the relationship between the specific impulse and the ion ejection velocity of the ion thruster, the ion ejection velocity under a specific specific impulse is obtained using the following formula:

[0008]

[0009] Among them, I SP For the specific impulse of the ion thruster, v i Let g be the ion ejection velocity and g be the gravitational acceleration; Step 1.2: Based on the relationship between the ion ejection velocity and the grid voltage, the grid voltage is obtained using the following formula:

[0010]

[0011] Where e is the electron charge, V b Where is the grid voltage and M is the ion mass; Step 1.3: Based on the relationship between thrust and beam voltage, the beam current is obtained using the following formula:

[0012]

[0013] Among them, I bγ represents the ion thruster beam, T represents the thrust, and γ represents the correction factor.

[0014] Furthermore, in step 2, based on the electron backflow limit requirement, the accelerating gate voltage is determined using the following formula:

[0015]

[0016] Among them, V a To accelerate the gate voltage.

[0017] Furthermore, in step 3, the total accelerating voltage is calculated using the following formula:

[0018]

[0019] Furthermore, in step 4, the maximum conductivity coefficient is calculated using the following formula:

[0020]

[0021] Among them, P max This represents the maximum conductivity coefficient of the gate aperture.

[0022] Furthermore, in step 5, the grating thickness, aperture, and grating spacing are calculated using the following formulas:

[0023]

[0024] Where: ε0 is the vacuum permittivity, d s t is the diameter of the screen aperture. s For the thickness of the screen grid, l g This represents the grid spacing.

[0025] Furthermore, in step 6, the beam extraction ratio is calculated using the following formula:

[0026]

[0027] Furthermore, in step 7, the numerical simulation calculation model for gate asymmetry is established using the following steps: Step 7.1: Select the outermost gate-screen aperture with the largest displacement relative to the center of the screen gate and its corresponding acceleration gate aperture as the simulation calculation research object; Step 7.2: Considering the symmetry of the aperture, select half of the screen gate and acceleration gate as the numerical calculation region; Step 7.3: Based on the screen gate thickness, aperture diameter and gate spacing obtained in step 5, establish the numerical simulation calculation model for gate asymmetry.

[0028] The present invention provides a method for calculating the gate aperture compensation coefficient of an ion thruster gate assembly, which has the following beneficial effects:

[0029] This application comprehensively considers the impact of gate aperture asymmetry on the geometric parameters, operating parameters, thruster performance, and service life of the gate assembly, and determines the gate aperture compensation coefficient corresponding to the best thruster performance and longest service life. It can provide technical support for the development or optimization design of ion thruster products, and can significantly shorten the product development cycle and reduce product development costs. Attached Figure Description

[0030] The accompanying drawings, which form part of this application, are used to provide a further understanding of the application and to make other features, objects, and advantages of the application more apparent. The illustrative embodiments and descriptions of this application are used to explain the application and do not constitute an undue limitation of the application. In the drawings:

[0031] Figure 1 This is a numerical simulation calculation model diagram of gate asymmetry provided in the embodiments of this application;

[0032] Figure 2 This is a graph showing the relationship between the beam extraction ratio and the acceleration gate interception current according to an embodiment of this application.

[0033] Figure 3 This is a graph showing the relationship between the beam current drawn out of the gate aperture, the current intercepted by the accelerating gate, and the position offset of the gate aperture, according to an embodiment of this application. Detailed Implementation

[0034] To enable those skilled in the art to better understand the present application, the technical solutions in the embodiments of the present application will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present application, and not all embodiments. Based on the embodiments in the present application, all other embodiments obtained by those of ordinary skill in the art without creative effort should fall within the scope of protection of the present application.

[0035] It should be noted that the terms "first," "second," etc., in the specification, claims, and accompanying drawings of this application are used to distinguish similar objects and are not necessarily used to describe a specific order or sequence. It should be understood that such data can be interchanged where appropriate for the embodiments of this application described herein. Furthermore, the terms "comprising" and "having," and any variations thereof, are intended to cover non-exclusive inclusion; for example, a process, method, system, product, or apparatus that comprises a series of steps or units is not necessarily limited to those steps or units explicitly listed, but may include other steps or units not explicitly listed or inherent to such processes, methods, products, or apparatus.

[0036] In this application, the terms "upper," "lower," "left," "right," "front," "rear," "top," "bottom," "inner," "outer," "middle," "vertical," "horizontal," "lateral," and "longitudinal" indicate the orientation or positional relationship based on the orientation or positional relationship shown in the accompanying drawings. These terms are primarily for the purpose of better describing this application and its embodiments, and are not intended to limit the indicated device, element, or component to having a specific orientation, or to be constructed and operated in a specific orientation.

[0037] Furthermore, in addition to indicating location or positional relationship, some of the aforementioned terms may also have other meanings. For example, the term "above" may also be used in some cases to indicate a certain dependency or connection relationship. Those skilled in the art can understand the specific meaning of these terms in this application based on the specific circumstances.

[0038] In addition, the term "multiple" should mean two or more.

[0039] 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.

[0040] Gate aperture asymmetry is a major factor causing the rolling torque of ion thrusters. Because the gate assembly is a thin-walled, convex metal structure, the gate plate forming process inevitably causes a certain offset between the gate apertures of the gate and the accelerating gate relative to the central axis. The gate aperture displacement is smaller in the central region and larger towards the edge. To address this issue, gate aperture compensation methods are commonly used domestically and internationally, compensating by changing the gate aperture spacing of the accelerating gate. The compensation coefficient is related to the geometric parameters of the gate assembly. However, the gate aperture displacement also determines the beam deflection angle, i.e., thrust loss, and directly affects the interception current of the accelerating gate, i.e., the thruster's operating life. Therefore, the compensation coefficient cannot be solely determined by the geometric parameters of the gate assembly. The gate aperture compensation coefficient calculation method for ion thruster gate assemblies provided in this application comprehensively considers the impact of gate aperture asymmetry on the geometric parameters, operating parameters, thruster performance, and operating life of the gate assembly, determining the gate aperture compensation coefficient corresponding to the best thruster performance and longest lifespan. Figure 1 As shown, the specific steps include the following:

[0041] Step 1: Determine the beam current and grid voltage based on the performance parameters of the ion thruster. The specific process is as follows:

[0042] Step 1.1: Based on the relationship between the specific impulse of the ion thruster and the ion ejection velocity, the ion ejection velocity at a specific specific impulse is obtained using the following formula:

[0043]

[0044] Among them, I SP For the specific impulse of the ion thruster, v i where g is the ion ejection velocity and g is the gravitational acceleration.

[0045] Step 1.2: Based on the relationship between ion ejection velocity and grid voltage, the grid voltage is obtained using the following formula:

[0046]

[0047] Where e is the electron charge, V b Where is the grid voltage and M is the ion mass; Step 1.3: Based on the relationship between thrust and beam voltage, the beam current is obtained using the following formula:

[0048]

[0049] Among them, I b γ represents the ion thruster beam, T represents the thrust, and γ represents the correction factor.

[0050] Step 2: Based on the electron backflow limit requirement, determine the accelerating gate voltage using the following formula:

[0051]

[0052] Among them, V a To accelerate the gate voltage.

[0053] Step 3: Using the grid voltage obtained in Step 1 and the acceleration grid voltage obtained in Step 2, the total acceleration voltage is obtained. The total acceleration voltage is calculated using the following formula:

[0054]

[0055] Step 4: Based on the relationship between the grid aperture conductivity and the beam current and total accelerating voltage, the maximum grid aperture conductivity is obtained. The maximum conductivity is calculated using the following formula:

[0056]

[0057] Among them, P max This represents the maximum conductivity coefficient of the gate aperture.

[0058] Step 5: Determine the gate thickness, aperture, and gate spacing by using the relationship between the maximum conductivity and the gate geometry, using the following formula:

[0059]

[0060] Where: ε0 is the vacuum permittivity, d st is the diameter of the screen aperture. s For the thickness of the screen grid, l g The grid spacing is used for calculation. During the calculation process, the maximum conductivity coefficient is maximized by adjusting the grid hole diameter and grid thickness. In this process, it is also necessary to ensure that the grid thickness is not too small in order to ensure the thruster's service life.

[0061] Step 6: Based on the relationship between the beam extraction ratio and the gate geometry parameters and operating parameters, determine the corresponding beam extraction ratio using the following formula:

[0062]

[0063] Step 7: As Figure 1 As shown, a numerical simulation model for gate asymmetry is established, and the specific steps are as follows:

[0064] Step 7.1: Select the outermost gate-to-gate aperture with the largest displacement relative to the center of the gate-to-gate acceleration gate and its corresponding acceleration gate aperture as the simulation calculation research object;

[0065] Step 7.2: Considering the symmetry of the grating aperture, half of the screen grating and the acceleration grating are selected as the numerical calculation region;

[0066] Step 7.3: Based on the grid thickness, aperture and grid spacing obtained in Step 5, establish a numerical simulation calculation model for grid asymmetry;

[0067] Then, numerical calculation methods were used to verify the correctness of the design values ​​of the gate geometry parameters and operating parameters. Subsequently, finite element analysis was used to numerically simulate the beam-ion acceleration focusing extraction process under different beam extraction ratios, gate thicknesses, apertures, and gate spacings, such as... Figure 2 As shown, the statistical acceleration gate intercept current I a The size of I a If the value is greater than 0, the beam is under-focused or over-focused; otherwise, it is normally focused. The gate geometry parameters and operating parameters corresponding to normal beam focusing are obtained based on the calculation results.

[0068] Step 8: By changing the position offset d of the acceleration grid aperture relative to the center of the screen grid aperture, the calculation simulation model is revised. The beam focusing performance under different displacement offsets is simulated using simulation calculation methods. The maximum extracted beam current of the grid aperture and the intercepted current of the acceleration grid corresponding to different offsets are statistically analyzed.

[0069] Step 9: As Figure 3 As shown, the beam current extracted from the grid aperture and the current intercepted by the accelerating grid under different offsets are analyzed. The offset of the accelerating grid relative to the center of the screen grid aperture is selected when the beam current is the largest and the current intercepted by the accelerating grid is the smallest, and the grid aperture compensation coefficient is obtained.

[0070] The above description is merely a preferred embodiment of this application and is not intended to limit this application. Various modifications and variations can be made to this application by those skilled in the art. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of this application should be included within the protection scope of this application.

Claims

1. A method for calculating the gate aperture compensation coefficient of an ion thruster gate assembly, characterized in that, Includes the following steps: Step 1: Determine the beam current and grid voltage based on the performance parameters of the ion thruster; Step 2: Determine the accelerating gate voltage according to the requirements of the electron backflow limit; Step 3: Using the grid voltage obtained in Step 1 and the acceleration grid voltage obtained in Step 2, obtain the total acceleration voltage; Step 4: Obtain the maximum conductivity based on the relationship between the grid aperture conductivity and the beam current and total accelerating voltage; Step 5: Determine the gate thickness, aperture, and gate spacing by using the relationship between the maximum conductivity and the gate geometry; Step 6: Determine the corresponding beam extraction ratio based on the relationship between the beam extraction ratio and the gate geometry parameters and operating parameters; Step 7: Establish a numerical simulation model of gate asymmetry, determine the beam focusing situation, and use the finite element analysis method to carry out simulation calculations for different beam extraction ratios, screen thickness, aperture and gate spacing to obtain the gate geometric structure parameters and operating parameters under normal beam focusing conditions; Step 8: By changing the positional offset of the acceleration grid aperture relative to the center of the screen grid aperture, the calculation simulation model is revised again. The beam focusing performance under different displacement offsets is simulated using simulation calculation methods. The maximum extracted beam current of the grid aperture and the intercepted current of the acceleration grid corresponding to different offsets are statistically analyzed. Step 9: Analyze the beam current extracted from the grid aperture and the current intercepted by the accelerating grid under different offsets, and select the offset of the accelerating grid relative to the center of the screen aperture that has the largest extracted beam current and the smallest current intercepted by the accelerating grid to obtain the aperture compensation coefficient.

2. The method for calculating the gate aperture compensation coefficient of the ion thruster gate assembly according to claim 1, characterized in that, In step 1, the process of determining the beam current and grid voltage based on the performance parameters of the ion thruster is as follows: Step 1.1: Based on the relationship between the specific impulse of the ion thruster and the ion ejection velocity, the ion ejection velocity at a specific specific impulse is obtained using the following formula: Among them, I SP For the specific impulse of the ion thruster, v i where g is the ion ejection velocity and g is the gravitational acceleration. Step 1.2: Based on the relationship between ion ejection velocity and grid voltage, the grid voltage is obtained using the following formula: Where e is the electron charge, V b Where is the grid voltage, and M is the ion mass; Step 1.3: Based on the relationship between thrust and beam voltage, the beam current is obtained using the following formula: Among them, I b γ represents the ion thruster beam, T represents the thrust, and γ represents the correction factor.

3. The method for calculating the gate aperture compensation coefficient of the ion thruster gate assembly according to claim 2, characterized in that, In step 2, based on the electron backflow limit requirement, the accelerating gate voltage is determined using the following formula: Among them, V a To accelerate the gate voltage.

4. The method for calculating the gate aperture compensation coefficient of the ion thruster gate assembly according to claim 3, characterized in that, In step 3, the total accelerating voltage is calculated using the following formula:

5. The method for calculating the gate aperture compensation coefficient of the ion thruster gate assembly according to claim 4, characterized in that, In step 4, the maximum conductivity coefficient is calculated using the following formula: Among them, P max This represents the maximum conductivity coefficient of the gate aperture.

6. The method for calculating the gate aperture compensation coefficient of the ion thruster gate assembly according to claim 5, characterized in that, In step 5, the screen thickness, aperture, and screen spacing are calculated using the following formulas: Where: ε0 is the vacuum permittivity, d s t is the diameter of the screen aperture. s For the thickness of the screen grid, l g This represents the grid spacing.

7. The method for calculating the gate aperture compensation coefficient of the ion thruster gate assembly according to claim 6, characterized in that, In step 6, the beam extraction ratio is calculated using the following formula:

8. The method for calculating the gate aperture compensation coefficient of the ion thruster gate assembly according to claim 6, characterized in that, In step 7, the numerical simulation model for gate asymmetry is established using the following steps: Step 7.1: Select the outermost gate-to-gate aperture with the largest displacement relative to the center of the gate-to-gate acceleration gate and its corresponding acceleration gate aperture as the simulation calculation research object; Step 7.2: Considering the symmetry of the grating aperture, half of the screen grating and the acceleration grating are selected as the numerical calculation region; Step 7.3: Based on the grid thickness, aperture and grid spacing obtained in Step 5, establish a numerical simulation calculation model for grid asymmetry.

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