A Pulse-Type Electromagnetic Thruster Plume Characteristic Analysis System and Method

Abstract

The present invention discloses a plume characteristic analysis system and method for a pulsed electromagnetic thruster. The system uses a vacuum chamber, a current monitoring system, a multi-probe data acquisition device, an ion current measurement circuit, and a data acquisition and processing system. The multi-probe data acquisition device is used to collect the saturated ion current of the plume plasma of the pulsed electromagnetic thruster and output it as a voltage signal. The ion current measurement circuit is used to convert the voltage signal collected by the multi-probe data acquisition device into an ion current signal. The data acquisition and processing system is used to collect the voltage signal output by the multi-probe data acquisition device and the ion current signal converted by the ion current measurement circuit, convert the ion current signal into a digital signal, and is responsible for fitting the ion current signal to analyze the plume characteristics of the pulsed electromagnetic thruster with superposition of multiple ion groups. The present invention provides a more accurate theoretical basis for the performance optimization of the thruster.

Description

Technical Field

[0001] The present invention relates to the field of aerospace technology, and in particular discloses a plume characteristic analysis system and method for a pulsed electromagnetic thruster with multi-ion group superposition. Background Art

[0002] As an advanced space propulsion technology, the pulsed electromagnetic thruster has been widely used in aerospace fields such as satellite attitude control and orbit transfer. The working principle of this thruster involves complex multi-physical field coupling phenomena, including electromagnetic fields, plasma dynamics, and material ablation. The working medium of the thruster generates ionized components with different ionization degrees and compositions during discharge ionization, so there are also ion groups with various ionization degrees and compositions in its plume. These ion groups have different charge states, generation times, and velocity distribution characteristics. Deeply understanding the characteristics of the thruster plume plasma is of crucial significance for mastering the working principle of the thruster, optimizing its performance, and improving the propulsion efficiency.

[0003] Currently, the research on the characteristics of the pulsed electromagnetic thruster plume plasma mainly relies on experimental diagnostic techniques, such as Langmuir probes, optical emission spectroscopy, and mass spectrometry diagnostic techniques. These techniques can provide key information about plasma parameters, chemical compositions, and particle velocity distributions. However, these techniques have certain limitations in describing the composition and characteristics of ion groups in the plume plasma. For example, optical emission spectroscopy is the spatial superposition integral of the spectral lines of multiple ion components, which is prone to errors when identifying and quantitatively analyzing the emission spectral lines of specific ions. The mass spectrometer has limited selectivity in distinguishing ions with similar mass-to-charge ratios, and due to ionization efficiency differences, some ion signals may be lost; in addition, its sampling representativeness is poor, being greatly affected by position and time, and it has relatively strict requirements for the experimental conditions of a high-vacuum environment. As a traditional technique in the field of plasma diagnostics, the Langmuir probe can analyze the electron density, temperature, and motion velocity of the plasma in a specific region. However, in the research on the plume diagnostics of the pulsed electromagnetic thruster, the plasma parameters provided by the Langmuir probe are usually only the macroscopic average values of the parameters. For example, as mentioned in Patent CN202310686912.8, through time-of-flight (ToF) technology, the ion velocity can be determined by using the peak or other features in the probe signal. However, the ToF technology can only provide the "average" velocity of the plume plasma and cannot distinguish the motion characteristics of different ion groups. Patent CN202111465016.6 proposes using a multi-probe layout for plasma diagnostics, but does not involve parametric model fitting and cannot quantify microscopic characteristic parameters such as the thermal diffusion and divergence rates of ion groups.

[0004] In summary, the prior art has not effectively solved the problem of the superposition effect of multiple ion groups in the plasma plume, and cannot accurately reflect the key characteristics such as the structure, velocity distribution, thermal diffusion, and divergence of the ion group. The inability to accurately analyze the superposition effect of multiple ion groups leads to significant errors in performance evaluation, making it more difficult to deeply understand the physical mechanism in the process of the plasma motion in the thruster plume. Summary of the Invention

[0005] The present invention provides a system and method for analyzing the plume characteristics of a pulsed electromagnetic thruster, aiming to solve at least one defect existing in the above prior art.

[0006] One aspect of the present invention relates to a system for analyzing the plume characteristics of a pulsed electromagnetic thruster, including a vacuum chamber, a current monitoring system, a multi-probe data acquisition device, an ion current measurement circuit, and a data acquisition and processing system. Among them,

[0007] The vacuum chamber is used to provide a space simulation working environment for the operation of the pulsed electromagnetic thruster.

[0008] The current monitoring system is arranged in the vacuum chamber and is used to monitor the main discharge current waveform of the pulsed electromagnetic thruster in real time.

[0009] The multi-probe data acquisition device is arranged in the vacuum chamber and is used to collect the saturated ion current of the plasma plume of the pulsed electromagnetic thruster and output it as a voltage signal.

[0010] The ion current measurement circuit is connected to the multi-probe data acquisition device and is used to convert the voltage signal collected by the multi-probe data acquisition device into an ion current signal.

[0011] The data acquisition and processing system is respectively connected to the multi-probe data acquisition device and the ion current measurement circuit, and is used to collect the voltage signal output by the multi-probe data acquisition device and the ion current signal converted by the ion current measurement circuit, convert the ion current signal into a digital signal, and is responsible for fitting and processing the ion current signal to analyze the plume characteristics of the pulsed electromagnetic thruster with the superposition of multiple ion groups.

[0012] Further, the multi-probe data acquisition device includes a probe body, and the probe body takes a single Langmuir single probe as the core. The Langmuir single probe is made of tungsten wire with a diameter of 50μm - 200μm.

[0013] Further, the system for analyzing the plume characteristics of the pulsed electromagnetic thruster further includes an insulating support. The insulating support is processed into a tubular or columnar shape, and the Langmuir single probe is sleeved inside the insulating support. The length of the insulating support is 3mm - 6mm.

[0014] Further, the multi-probe data acquisition device includes multiple probes arranged at equal intervals along the angular axis of the plume space of the pulsed electromagnetic thruster, and the tips of the probes are perpendicular to the plasma ejection direction.

[0015] Further, the pulsed electromagnetic thruster plume characteristic analysis system further includes a bias power supply, which is connected to the multi-probe data acquisition device and is used to form an ion sheath layer on the probe surface by applying a sufficiently high constant negative bias voltage to the ground, repelling electrons and receiving ions, so as to collect the ion saturation current.

[0016] Further, the pulsed electromagnetic thruster plume characteristic analysis system further includes a protective cover, which is arranged outside the probe.

[0017] Further, the data acquisition and processing system includes a data acquisition card, which is connected to the ion current measurement circuit and is used to convert the ion current signal output by the ion current measurement circuit into a digital signal.

[0018] Another aspect of the present invention relates to a method for analyzing the plume characteristics of a pulsed electromagnetic thruster, which is applied to the above-mentioned method for analyzing the plume characteristics of a pulsed electromagnetic thruster. The method for analyzing the plume characteristics of a pulsed electromagnetic thruster includes the following steps:

[0019] Construct a multi-ion group superposition distribution model;

[0020] As the plasma ejects from the thruster nozzle to form a plume, the plasma sheet expands laterally in a conical form. According to the multi-ion group superposition distribution model, obtain the current density generated by the charge passing through the unit area of the i-th ion group ;

[0021] According to the current density Add up the current densities of the superposition of n ion groups to obtain the total ion current density ;

[0022] According to the total ion current density Obtain the theoretical ion current at the position of the k-th Langmuir probe ;

[0023] Obtain the k experimental measured ion current at the position of the Langmuir probe , and use the optimization objective for parameter fitting to make the theoretical ion current fit the experimental measured ion current , and obtain the best plume characteristic parameters of the pulsed electromagnetic thruster.

[0024] Further, in the step of constructing the multi-ion group superposition distribution model, the distribution of each ion group in the multi-ion group superposition distribution model is independently characterized as shown in the following formula:

[0025]

[0026] wherein, x is the axial position during the axial movement of the ion swarm, is the axial velocity of the ion swarm, describing the movement velocity of ions in the axial direction of the thruster; is the average axial velocity of the ion swarm, representing the average movement velocity of the ion swarm; is the axial thermal velocity of the ion swarm, reflecting the distribution of the thermal movement velocity of the ion swarm in the axial direction; is the charge per unit area of the ion swarm, characterizing the charge density of the ion swarm; is the Dirac δ function, used to represent the locality of the ion swarm in space; is the thruster nozzle position, is the time when the ion swarm moves to the thruster nozzle position, is the th distribution function of the ion swarm.

[0027] Furthermore, in the step of adding the current densities of n ion swarms superimposed according to the current density to obtain the total ion current density , the current density is:

[0028]

[0029] The total ion current density j(x, t) is:

[0030]

[0031] wherein, is the time difference, is the velocity of the ion swarm moving from the thruster exit position to the position at the moment; is the velocity of the ion swarm moving from the thruster exit position to the position at the position and the moment; x is the velocity of the ion swarm moving from the thruster exit position to the is the expression of the current density , is the axial position during the axial movement of the ion swarm, is the thruster nozzle position, is the time when the ion swarm moves to the position, is the time when the ion swarm moves to the thruster exit position, , ; is the number of ion group superpositions.

[0032] The beneficial effects achieved by the present invention are as follows:

[0033] The present invention provides a pulsed electromagnetic thruster plume characteristic analysis system and method. The system adopts a vacuum chamber, a current monitoring system, a multi-probe data acquisition device, an ion current measurement circuit, and a data acquisition and processing system. The vacuum chamber is used to provide a space simulation working environment for the operation of the pulsed electromagnetic thruster; the current monitoring system is used to monitor the main discharge current waveform of the pulsed electromagnetic thruster in real time; the multi-probe data acquisition device is used to collect the saturated ion current of the pulsed electromagnetic thruster plume plasma and output it as a voltage signal; the ion current measurement circuit is used to convert the voltage signal collected by the multi-probe data acquisition device into an ion current signal; the data acquisition and processing system is used to collect the voltage signal output by the multi-probe data acquisition device and the ion current signal converted by the ion current measurement circuit, convert the ion current signal into a digital signal, and is responsible for fitting and processing the ion current signal to analyze the plume characteristics of the pulsed electromagnetic thruster with multi-ion group superposition. The pulsed electromagnetic thruster plume characteristic analysis system and method provided by the present invention have the following beneficial effects:

[0034] 1. Improved accuracy

[0035] Compared with the traditional ToF (Time-of-Flight) technology, the plume plasma reconstruction method of the present invention can more accurately describe the characteristics of ion groups in the plume of the pulsed electromagnetic thruster, including the structure of ion groups, as well as the motion and distribution characteristics such as the average velocity, thermal diffusion, position of the conical expansion vertex, and generation time of each ion group. This helps to deeply understand the physical mechanism of the plasma in the plume and provides a more accurate theoretical basis for the performance optimization of the thruster.

[0036] 2. Deepened physical understanding

[0037] Through the detailed analysis of ion groups, the present invention can reveal the physical processes such as the generation, acceleration, transmission, and interaction of plasma during the operation of the pulsed electromagnetic thruster. By quantifying thermal diffusion and divergence rate, it guides the geometric optimization of the thruster electrodes, provides important theoretical support for further improving the design and performance of the thruster. At the same time, it also helps to discover the deficiencies in the existing plume simulation models of thrusters, provides directions for the improvement and perfection of the models, and promotes the development of pulsed electromagnetic thruster technology.

[0038] 3. Enhanced application value

[0039] The method of the present invention can be applied to fields such as the design, optimization, and fault diagnosis of pulsed electromagnetic thrusters, providing an effective tool for engineers to better understand the working characteristics of thrusters and improve the performance and reliability of thrusters.

[0040] Compared with the prior art, the present invention can provide more comprehensive and accurate plume plasma characteristic information, contributing to the development of more efficient and reliable pulsed electromagnetic thrusters and making contributions to the development of the aerospace field. Brief Description of the Drawings

[0041] Figure 1 It is a schematic flow chart of an embodiment of a method for analyzing plume characteristics of a pulsed electromagnetic thruster of the present invention;

[0042] Figure 2 It is a schematic diagram of the probe distribution in the thruster plume region in a plume characteristic analysis system of a pulsed electromagnetic thruster of the present invention;

[0043] Figure 3 It is a schematic diagram of the change in the distribution of plume ion groups in a plume characteristic analysis system of a pulsed electromagnetic thruster of the present invention;

[0044] Figure 4 It is a schematic diagram of the ion current waveform detected by a probe in a plume characteristic analysis system of a pulsed electromagnetic thruster of the present invention;

[0045] Figure 5 It is a diagram showing the relationship between the discharge current waveform and the plasma density and temperature measured by a Langmuir probe in a plume characteristic analysis system of a pulsed electromagnetic thruster of the present invention;

[0046] Figure 6 It is that the ion current collected by a probe in a plume characteristic analysis system of a pulsed electromagnetic thruster of the present invention is fitted and decomposed into three different ion group currents. Detailed Embodiments

[0047] To better understand the above technical solutions, the above technical solutions will be described in detail below in conjunction with the accompanying drawings of the specification and specific embodiments.

[0048] As Figures 1 to 6As shown in the figure, the first embodiment of the present invention proposes a plume characteristic analysis system for a pulsed electromagnetic thruster, which includes a vacuum chamber, a current monitoring system, a multi-probe data acquisition device, an ion current measurement circuit, and a data acquisition and processing system. Among them, the vacuum chamber is used to provide a space simulation working environment for the operation of the pulsed electromagnetic thruster; the current monitoring system is arranged in the vacuum chamber and is used to monitor the main discharge current waveform of the pulsed electromagnetic thruster in real time; the multi-probe data acquisition device is arranged in the vacuum chamber and is used to collect the saturated ion current of the plume plasma of the pulsed electromagnetic thruster and output it as a voltage signal; the ion current measurement circuit is connected to the multi-probe data acquisition device and is used to convert the voltage signal collected by the multi-probe data acquisition device into an ion current signal; the data acquisition and processing system is respectively connected to the multi-probe data acquisition device and the ion current measurement circuit, and is used to collect the voltage signal output by the multi-probe data acquisition device and the ion current signal converted by the ion current measurement circuit, convert the ion current signal into a digital signal, and is responsible for fitting and processing the ion current signal to analyze the plume characteristics of the pulsed electromagnetic thruster with the superposition of multiple ion groups.

[0049] Further, please refer to Figures 1 to 6 , this embodiment proposes a plume characteristic analysis system for a pulsed electromagnetic thruster, which also includes a bias power supply and a protective cover. The multi-probe data acquisition device includes a probe body, and the probe body takes a single Langmuir single probe as the core. The Langmuir single probe is made of tungsten wire with a diameter of 50μm - 200μm. The plume characteristic analysis system for the pulsed electromagnetic thruster also includes an insulating support, which is processed into a tubular or columnar shape. The Langmuir single probe is sleeved inside the insulating support, and the length of the insulating support is 3mm - 6mm. The multi-probe data acquisition device includes multiple probes arranged at equal intervals along the axis of the plume space angle of the pulsed electromagnetic thruster, and the tip of the probe is perpendicular to the plasma ejection direction. The bias power supply is connected to the multi-probe data acquisition device and is used to form an ion sheath layer on the probe surface by applying a sufficiently high constant negative bias voltage to the ground, repel electrons and receive ions, so as to collect the ion saturation current. The pulse protective cover is arranged outside the probe. The data acquisition and processing system includes a data acquisition card, and the data acquisition card is connected to the ion current measurement circuit and is used to convert the ion current signal output by the ion current measurement circuit into a digital signal. The plume characteristic analysis system for the pulsed electromagnetic thruster proposed by the present invention realizes the real-time monitoring and data acquisition of the plume plasma characteristics of the pulsed plasma thruster, improves the efficiency and accuracy of experimental research; through the reconstruction and processing of probe data, it can accurately describe the characteristics of the ion group in the thruster plume, such as structure, velocity distribution, charge state, thermal diffusion, divergence rate, etc., and provides a reliable theoretical basis for the design, optimization and performance evaluation of the thruster.

[0050] As Figures 1 to 6As shown, the plume characteristic analysis system of the impulse electromagnetic thruster provided in this embodiment has the following working principle:

[0051] A plume characteristic analysis system for a pulsed electromagnetic thruster includes a vacuum chamber, a DC power supply, a trigger controller, a voltage monitoring system, a pulsed electromagnetic thruster (such as a pulsed plasma thruster, a laser electromagnetic induction plasma thruster, a magnetoplasma thruster, etc., which are electric thrusters using capacitive energy storage methods), a plasma diagnostic system, and a data acquisition and processing system.

[0052] The vacuum chamber (vacuum degree < 1×10 -3 Pa) provides a space simulation working environment for the thruster to operate.

[0053] The positive and negative outputs of the DC power supply are connected to the two poles of the energy storage capacitor of the pulsed electromagnetic thruster through transmission lines and charge the energy storage capacitor.

[0054] The current monitoring system uses a Rogowski coil to monitor the main discharge current waveform of the thruster in real time.

[0055] The multi-probe data acquisition device includes a probe body: with a single Langmuir single probe as the core, the probe can be made of tungsten wire with a diameter of 50μm - 200μm, which reduces the disturbance to the plasma while ensuring the mechanical strength of the probe and ensures accurate measurement data.

[0056] Insulating support: To prevent short circuits and ensure stability, insulating and high-temperature-resistant materials such as ceramics and quartz are processed into tubes or columns, with the tungsten wire placed in the center to isolate it from the surrounding conductors. The length of the tungsten wire of each probe exposed outside the insulating support is 3mm - 6mm, and the diameters and exposed lengths of all probes used in the experiment are the same to ensure that the exposed areas of each probe are equal.

[0057] Protective cover: Since there are high-speed particles and strong electromagnetic fields in the plume of the pulsed electromagnetic thruster, a stainless steel protective cover is set outside the probe. Small holes are opened on its surface to allow particles to enter and interact with the tungsten wire, while blocking the impact of high-energy particles. The aperture size is optimized according to experimental requirements and plasma characteristics to balance the protection effect and measurement accuracy.

[0058] Probe layout: At each grid coordinate point in the thruster plume space, the probes are distributed along the axes of each spatial angle. The tip of the probe is perpendicular to the plasma ejection direction. To avoid being affected by the mutual shadow between the probes, the relative positions and spacings of the probes should be reasonably set to cover the plume plasma region that needs to be diagnosed and measured.

[0059] Bias power supply: During measurement, a sufficiently high constant negative bias voltage with respect to ground needs to be applied to the probe to form an ion sheath layer on the probe surface, repelling electrons and receiving ions, thereby collecting the ion saturation current. The bias power supply uses an adjustable DC power supply with an output voltage range of -50V to -100V. Under different parameter settings of the thruster, the voltage is adjusted to ensure that the probe operates in the ion saturation region.

[0060] Ion current measurement circuit: A sampling resistor with a resistance value ranging from 20Ω to 50Ω is connected in series in the Langmuir single-probe measurement circuit. A low-noise, high-sensitivity voltage-current conversion circuit is used to measure the ion current, converting the voltage collected on the sampling resistor into an ion current signal. To improve the accuracy, a low-pass filter with a cut-off frequency ranging from 1kHz to 100kHz is added to filter out the high-frequency noise introduced by the thruster discharge.

[0061] Data acquisition and processing system: The ion current signal output by the ion current measurement circuit is connected to a data acquisition card, converted into a digital signal, and then transmitted to the data acquisition and processing system of the computer. The data acquisition and processing system is responsible for fitting and processing the collected plasma current signals according to the plume characteristics program of the pulsed electromagnetic thruster with multi-ion group superposition.

[0062] For details, see Figures 1 to 6 , this embodiment relates to a method for analyzing the plume characteristics of a pulsed electromagnetic thruster, which is applied to the above method for analyzing the plume characteristics of a pulsed electromagnetic thruster. The method for analyzing the plume characteristics of a pulsed electromagnetic thruster includes the following steps:

[0063] Step S100: Construct a multi-ion group superposition distribution model.

[0064] During the discharge process of the pulsed electromagnetic thruster, ions with different ionization degrees and compositions generated by the ionization of the thruster working medium will form independent groups under the combined action of the electric field and magnetic field, and maintain the relative stability of their charge states and masses during the movement after exiting the thruster. Therefore, the plume of the pulsed electromagnetic thruster is composed of the superposition of multiple independent ion groups, and each ion group has a unified charge state and mass. These ion groups each occupy a specific distribution range in space and exhibit different generation and evolution processes in time.

[0065] Based on the principles of plasma physics and the research results of plasma diagnostics, it can be assumed that the plasma in the thruster plume contains n ion groups ( i =1, 2, 3......n). The movement of each ion group along the axis of the thruster follows the truncated Maxwell charge distribution law. The i th ion group is a plasma sheet at the exit of the thruster nozzle. The distribution of each ion group can be independently characterized as shown in formula (1):

[0066] (1)

[0067] In formula (1), x is the axial position during the axial movement of the ion swarm, is the axial velocity of the ion swarm, describing the movement velocity of the ions in the axial direction of the thruster; is the average axial velocity of the ion swarm, representing the average movement velocity of the ion swarm; is the axial thermal velocity of the ion swarm, reflecting the thermal movement velocity distribution of the ion swarm in the axial direction; is the charge per unit area of the ion swarm, characterizing the charge density of the ion swarm; is the Dirac δ function, used to represent the locality of the ion swarm in space; is the thruster nozzle position, is the time when the ion swarm moves to the thruster nozzle position, is the th distribution function of the ion swarm.

[0068] (2)

[0069] This distribution function well describes the movement behavior of the ion swarm under the action of the electromagnetic field, and at the same time takes into account the thermal movement and spatial distribution characteristics of the ions.

[0070] Step S200: As the plasma ejects from the thruster nozzle to form a plume, the plasma sheet expands laterally in a conical form. According to the multi-ion swarm superposition distribution model, the current density generated by the charge passing through the unit area of the i-th ion swarm is obtained.

[0071] As Figure 3 shown, when t > t s , as the plasma ejects from the thruster nozzle to form a plume, the plasma sheet expands axially along the thruster due to thermal diffusion, and at the same time expands laterally in a conical form. The vertex of the lateral expansion of the cone is located at x s upstream h s position.

[0072] Thus, during the axial movement of the ion swarm, due to axial thermal diffusion and lateral conical expansion, the cross-sectional area at different axial positions x will change, which will cause the change of the ion charge distribution per unit area, and further cause the change of the current density distribution with the lateral expansion of the ion swarm.

[0073] Axial thermal diffusion principle: Ions themselves have the characteristics of thermal motion, which stems from the molecular thermal motion theory in statistical mechanics. A plasma consists of a large number of ions and electrons. After obtaining energy, the ions will be in a continuous state of thermal motion. During the axial movement of the ion group along the thruster, due to the differences in the thermal motion speeds of different ions, the ions with higher thermal speeds will gradually diffuse into the regions with lower speeds, resulting in the gradual expansion of the plasma sheet in the axial direction. This phenomenon conforms to Fick's diffusion law. From the perspective of the microscopic interactions within the plasma, there is a Coulomb interaction between ions, and frequent collisions occur during the movement. The collisions cause the exchange of energy and momentum of the ions, further intensifying the axial diffusion of the ions and making the plasma sheet continuously extend.

[0074] Transverse conical expansion principle: This phenomenon is related to the jet expansion principle in fluid mechanics. When the plasma jets out from the thruster, it can be regarded as a special fluid jet. Without external constraints, the jet will be affected by the surrounding environment. When the plasma jets outwards, there is a pressure difference between its edge part and the surrounding gas or vacuum environment. To achieve pressure balance, the plasma at the edge part will diffuse in all directions. Since the diffusion trends in all directions in the transverse direction are similar, and driven by the axial movement, a conical expansion form is formed. In terms of the characteristics of the plasma itself, it has certain conductivity and magnetism. Under the action of the magnetic field and the induced magnetic field generated by itself, the movement trajectories of the ions will be affected, making the transverse diffusion show a conical characteristic as a whole.

[0075] This causes the x > x s introduction of a conical expansion factor into the distribution function of the ion group at to reflect the change in charge per unit area caused by this transverse conical expansion. Among them, is the conical expansion factor, h s is the distance between the vertex of the conical transverse expansion and the nozzle position. x is the axial position of the ion group during the axial movement, x s is the nozzle position of the thruster. The distribution function of the i th ion group is .

[0076] Thus, the i th ion group at the position x at the time, the current density generated by the charge passing through the unit area can be obtained through formula (3):

[0077] (3)

[0078] In formula (3), is the time difference, is the velocity of the ion swarm when it moves from the thruster exit position to the position at the moment; is the velocity of the ion swarm when it moves from the thruster exit position to the position at the position and moment; x is the current density expression, is the axial position of the ion swarm during axial movement, is the thruster nozzle position, is the time when the ion swarm moves to the position, is the time when the ion swarm moves to the thruster exit position, and , .

[0079] Step S300: According to the current density , sum up the current densities of n superimposed ion swarms to obtain the total ion current density .

[0080] The sum of the current densities of n superimposed ion swarms is the total ion current density , as shown in formula (4):

[0081] (4)

[0082] In formula (4), is the integration result, is the axial position of the ion swarm during axial movement, is the thruster nozzle position, is the time when the ion swarm moves to the x position, is the time when the ion swarm moves to the thruster exit position, , ; is the number of superimposed ion swarms.

[0083] Step S400: Based on the total ion current density , obtain the theoretical ion current at the k-th Langmuir probe position.

[0084] The theoretical ion current at the k-th Langmuir probe position is , where is the theoretical ion current at the k-th Langmuir probe position, is the total ion current collected by the k-th probe, is the effective collection area of the Langmuir probe, and the effective collection areas of all Langmuir probes are the same, i.e., .

[0085] Step S500: Obtain the experimentally measured ion current at the k-th Langmuir probe , and perform parameter fitting using the optimization objective to make the theoretical ion current fit the experimentally measured ion current , and obtain the best plume characteristic parameters of the pulsed electromagnetic thruster.

[0086] Parameter fitting:

[0087] The ion current actually detected at the k-th Langmuir probe is . In order to fit the experimentally measured ion current, the normalized least squares error is defined as the optimization objective as shown in formula (5):

[0088] (5)

[0089] In formula (5), is the normalized least squares error, is the k -th normalized least squares error between the theoretical ion current of the probe and the total ion current collected by the probe. is the theoretical ion current at the k-th Langmuir probe position, is the ion current actually detected at the k-th Langmuir probe.

[0090] In this embodiment, the normalized least squares error is used as the optimization objective to fit the experimentally measured ion current. This approach has considerations in terms of statistical and mathematical principles as well as practical applications. The following is a detailed introduction:

[0091] I. Theoretical basis

[0092] Principle of Least Squares: The least squares method is a classic mathematical optimization technique. Its core idea is to find the best function match for data by minimizing the sum of the squares of errors. In the problem of ion current fitting, there are errors between the experimentally measured ion current and the ion current calculated by the model. Summing the squares of the errors can comprehensively consider the errors at all probe positions and throughout the entire time window. The squaring operation can avoid the cancellation of positive and negative errors, highlighting the impact of larger errors on the overall result, making the fitting result more inclined to reduce the errors of those data points with larger deviations, and thus obtaining fitting parameters that are more in line with the actual situation.

[0093] Statistical Significance of Normalization: In practical applications, the amplitudes of ion currents measured by different probes may vary greatly. If the sum of the squares of errors is directly used for optimization, the errors corresponding to currents with larger amplitudes will dominate in the sum, while the errors of currents with smaller amplitudes may be ignored, resulting in the fitting result not being able to well reflect the characteristics of all data. Through normalization, the sum of the squares of errors for each probe can be relativized, making the errors of currents with different amplitudes have equal weights in the optimization objective. This can more fairly consider the influence of each probe data on the fitting result and improve the accuracy and generality of the fitting.

[0094] II. Considerations in Practical Applications

[0095] Data Stability and Reliability: The data measured in experiments often have certain noise and uncertainties. The normalized least squares error can, to a certain extent, reduce the influence of these noises and uncertainties on the fitting result. Because it comprehensively considers the overall characteristics of the data rather than just focusing on the errors of individual data points, the fitting process becomes more robust, and the obtained fitting parameters are more representative and reliable.

[0096] Facilitating Model Evaluation and Comparison: Using the normalized least squares error as the optimization objective provides a unified evaluation criterion for different fitting models or different parameter settings. By comparing the values in different situations, it can be intuitively judged which model or parameter combination can better fit the experimental data, thus facilitating the screening and optimization of the model. For example, when trying different initial values of ion swarm parameters or changing the number of ion swarms, just compare the corresponding values to quickly determine which setting is better.

[0097] Meet the actual engineering requirements: In actual engineering applications, what is needed is a model that can accurately describe the characteristics of ion current, and the parameters of this model should have certain physical meanings and interpretability. The normalized least-squares error optimization method can, while meeting the fitting accuracy requirements, make the obtained model parameters match the actual physical process, providing a reliable basis for subsequent research and applications. For example, in the design and optimization of plasma thrusters, an accurate ion current fitting model can help engineers better understand the working principle of the thruster and then improve the performance of the thruster.

[0098] Further, taking the ion current detected by the first probe versus time graph as Figure 4 an example, first, the time integration interval needs to be determined according to the probe detection signal window. This interval is the time window for the probe to collect ion current, ensuring that all passing ion currents can be collected within this time period. According to the measurement data of the first probe, in this example, it is ,

[0099] where is the error of each probe, which is determined by calculating the difference between the ion current detected by each probe and the ion current calculated by the model.

[0100] Further, set appropriate initial values for the model parameters. According to the magnitude of the experimental measurement data, set the initial values of the average velocity, thermal diffusion velocity, position of the conical expansion vertex, generation time, and the initial surface charge density multiplied by the effective probe collection area.

[0101] Further, perform parameter fitting. Use optimization algorithms (such as the Levenberg-Marquardt nonlinear least-squares method, Newton's method, gradient descent method, etc.) to iteratively solve the model parameters in formula (4), with the goal of minimizing the error between the current signal calculated by the model and the current signal measured experimentally, generally Stop the iterative solution so that the ion current calculated by the model can better fit the ion current data obtained from experimental measurements.

[0102] Thus, the optimal plume characteristics parameters of the pulsed electromagnetic thruster can be obtained. The optimal plume characteristics parameters of the pulsed electromagnetic thruster include the average velocity, thermal diffusion velocity, position of the conical expansion vertex, initial moment of plume plasma generation, and the surface charge density multiplied by the effective probe collection area, etc.

[0103] Note: The following is a simple description of the algorithm:

[0104] Taking the simple gradient descent method as an example, the implementation steps are as follows:

[0105] 1. Parameter initialization: Initial values are assigned to the parameters to be adjusted in the model, such as the axial average velocity of the ion swarm, axial thermal velocity, transverse expansion vertex distance, initial time, and the product of charge per unit area and effective collection area. These initial values can be based on experience, previous experimental results, or randomly set.

[0106] 2. Calculate the error gradient: According to the current parameter values, calculate the partial derivatives of the normalized least squares error with respect to each parameter to obtain the error gradient. In the fitting of the ion current curve, it is necessary to obtain the expressions of these partial derivatives through derivative operations based on the ion current model formula.

[0107] 3. Update the parameters: According to the gradient descent rule, use the learning rate α to adjust the parameter values. The parameter update formula is the updated parameter value. The learning rate controls the step size of each parameter update, and its value is crucial. If it is too large, it may cause excessive parameter updates, miss the optimal solution, or even increase the error; if it is too small, the convergence speed will be too slow, increasing the calculation time.

[0108] 4. Iterative optimization: Repeat steps 2 and 3, continuously calculate the error gradient and update the parameters until the stopping condition is met. The stopping condition can be that the change in error is less than a certain threshold, indicating that the error has converged; or the change in parameters is less than a certain threshold, meaning that the parameters are close to the optimal value; or the maximum number of iterations set in advance is reached. In practical applications, variants of the gradient descent method such as the Stochastic Gradient Descent (SGD) method and the Mini-Batch Gradient Descent (Mini-Batch GD) method can also be used. When updating the parameters each time, they do not calculate the gradient based on all the data, but based on a randomly selected sample (SGD) or a small batch of samples (Mini-Batch GD), which can speed up the calculation speed and reduce memory occupancy.

[0109] III. Model complexity

[0110] To avoid overfitting, by selecting an appropriate model complexity, the computational amount and model complexity can be reduced while ensuring the accuracy of the model, improving the practicality of the model. In this embodiment, as Figure 5 shown, according to the discharge current oscillation waveform, corresponding to three discharge current peaks, three types of ion swarms are generated, so the maximum number of ion swarms is set to 3, and the initial positions of all ion swarms are set at the thruster exit position.

[0111] As Figures 1 to 6 shown, to better understand the above technical solution, the above technical solution will be described in detail below in combination with the accompanying drawings of the specification and specific implementation manners:

[0112] Taking the pulsed plasma thruster as the example body, the thruster is a thruster with parallel copper electrodes, the channel size is 4.5 cm (length) × 1.5 cm (height) × 1 cm (width), and the thickness of the polytetrafluoroethylene working medium ablation block is 15 mm. Thus, = 4.5 cm.

[0113] Debug and calibrate the discharge current detection system and the plasma diagnostic system to ensure that they can work properly and accurately measure the discharge current and plasma current signals.

[0114] Connect the data acquisition and processing system to ensure that the data can be transmitted and stored in real time.

[0115] I. Parameter Setting

[0116] Set the working parameters of the pulsed plasma thruster, including the capacitance of the capacitor bank, the initial discharge voltage, the discharge frequency, etc. The capacitance value is 6 μF , the capacitor charging voltage is 1000 V, and the discharge frequency is set to 1 Hz.

[0117] Set the parameters of the Langmuir probe, such as the diameter, length, and tip shape of the probe, and set the bias voltage to -50 V to ensure that the probe works in the ion saturation state.

[0118] II. Experimental Measurement

[0119] As Figure 5 shown, for the discharge current measurement - there are three main discharge peaks in the discharge current of the pulsed plasma thruster, and a main type of ion group will be generated corresponding to each peak. Thus, it is assumed that three main ion groups are generated during the discharge, with different plasma densities and temperatures.

[0120] III. Plasma Measurement

[0121] In the example, arrange along the axial center line of the thruster. Please see Figure 2 , three Langmuir probes, with the axial points being 8, 12, and 16 cm probes and the lateral micro-offset being about 0.5 mm to avoid occlusion.

[0122] IV. Data Processing and Analysis

[0123] 1. Data Preprocessing

[0124] Furthermore, perform preliminary processing on the collected voltage and plasma current signals, including noise removal, filtering, and amplification, etc., to improve the signal quality.

[0125] Furthermore, check the integrity and accuracy of the signals, eliminate abnormal data and interference signals, and ensure the reliability of subsequent analysis.

[0126] 2. Model Fitting

[0127] Figure 6 As shown, the ion current collected by a probe is fitted and decomposed into the currents of three different ion groups (IG1, IG2, and IG3).

[0128] Furthermore, initial values of appropriate model parameters are selected. According to the order of magnitude of the experimental measurement data, initial values of the average velocity, thermal diffusion velocity, position of the conical expansion vertex, generation time, and initial surface charge density multiplied by the effective probe collection area are set.

[0129] Furthermore, an optimization algorithm is used to iteratively solve the model parameters. By continuously adjusting the parameter values, the error between the current signal calculated by the model and the experimentally measured current signal is minimized until , the iterative solution is stopped, and the optimal model parameter values are obtained. And the ion current collected by a certain probe can be fitted and decomposed into the superposition of three different ion groups, as Figure 6 shown.

[0130] V. Result Analysis

[0131] Based on the ion group parameters obtained from the fitting, characteristics such as the average velocity, thermal diffusion, position of the conical expansion vertex, and generation time of each ion group are analyzed. The characteristic differences between different ion groups can be compared to understand the structure and motion laws of the ion groups. On this basis, the following analysis is further carried out:

[0132] 1. Analysis of Plume Plasma Characteristics

[0133] Taking into account the characteristics of the ion groups comprehensively, the overall characteristics of the plume plasma of the pulsed plasma thruster are obtained. Explore the variation laws of the plume plasma characteristics with the operating parameters of the pulsed electromagnetic thruster (such as capacitor bank capacitance, discharge initial voltage, discharge frequency, etc.), and compare the plume plasma characteristics under different experimental conditions.

[0134] 2. Trend Analysis

[0135] By analyzing the variation trends of the ion group parameters and plume plasma characteristics with the capacitor capacitance and discharge initial voltage, and constructing a mathematical model to describe the relationship between these parameters. With the help of trend analysis, it provides guidance for the design and optimization of the pulsed plasma thruster, helping engineers optimize the operating parameters and improve the performance and efficiency of the thruster.

[0136] 3. Model Support

[0137] By introducing a truncated Maxwell charge distribution function, the total ion current density model proposed by the present invention not only has the characteristics of simplicity and practicality, but also can effectively describe the motion behavior of ions under the action of electric and magnetic fields. It takes into account both the thermal motion and spatial distribution characteristics of ions, and has a relatively low computational cost, making it convenient for application in actual engineering. Therefore, this model provides a more reliable theoretical support for the design, optimization and performance evaluation of pulsed plasma thrusters.

[0138] Although the preferred embodiments of the present invention have been described, those skilled in the art can make additional changes and modifications to these embodiments once they learn the basic creative concepts. Therefore, the appended claims are intended to be construed to include the preferred embodiments as well as all changes and modifications falling within the scope of the present invention. Obviously, those skilled in the art can make various changes and variations to the present invention without departing from the spirit and scope of the present invention. Thus, if these modifications and variations of the present invention fall within the scope of the claims of the present invention and their equivalent technologies, the present invention is also intended to include these modifications and variations.

Claims

1. A method for analyzing the plume characteristics of a pulsed electromagnetic thruster, which is applied to a system for analyzing the plume characteristics of a pulsed electromagnetic thruster, is characterized in that, The method for analyzing the plume characteristics of the pulsed electromagnetic thruster includes the following steps: Construct a multi-ion group superposition distribution model; As the plasma jets out from the thruster nozzle to form a plume, the plasma sheet expands laterally in a conical form. According to the multi-ion group superposition distribution model, the current density generated by the charge quantity of the i-th ion group passing through a unit area is obtained. ; According to the current density , add the current densities of n ion groups superimposed to obtain the total ion current density ; According to the total ion current density , obtain the theoretical ion current at the k-th Langmuir probe position ; Obtain the k experimentally measured ion current at the th Langmuir probe, and perform parameter fitting using an optimization objective to make the theoretical ion current fit the experimentally measured ion current, and obtain the optimal plume characteristic parameters of the pulsed electromagnetic thruster; The system for analyzing the plume characteristics of the pulsed electromagnetic thruster includes a vacuum chamber, a current monitoring system, a multi-probe data acquisition device, an ion current measurement circuit, and a data acquisition and processing system. Among them, The vacuum chamber is used to provide a space simulation working environment for the operation of the pulsed electromagnetic thruster; The current monitoring system is arranged in the vacuum chamber and is used to monitor the main discharge current waveform of the pulsed electromagnetic thruster in real time; The multi-probe data acquisition device is arranged in the vacuum chamber and is used to collect the saturated ion current of the plume plasma of the pulsed electromagnetic thruster and output it as a voltage signal; The ion current measurement circuit is connected to the multi-probe data acquisition device and is used to convert the voltage signal output by the multi-probe data acquisition device into an ion current signal; The data acquisition and processing system is respectively connected to the multi-probe data acquisition device and the ion current measurement circuit, and is used to collect the voltage signal output by the multi-probe data acquisition device and the ion current signal converted by the ion current measurement circuit, convert the ion current signal into a digital signal, and is responsible for fitting and processing the ion current signal to analyze the plume characteristics of the pulsed electromagnetic thruster with multi-ion group superposition.

2. The plume characteristic analysis method of the pulsed electromagnetic thruster according to claim 1, wherein, In the step of constructing the multi-ion group superposition distribution model, each ion group distribution in the multi-ion group superposition distribution model is independently characterized as shown in the following formula: Among them, x is the axial position during the axial movement of the ion swarm, is the axial velocity of the ion swarm, describing the movement velocity of the ions in the axial direction of the thruster; is the axial average velocity of the ion swarm, representing the average movement velocity of the ion swarm; is the axial thermal velocity of the ion swarm, reflecting the thermal movement velocity distribution of the ion swarm in the axial direction; is the charge per unit area of the ion swarm, characterizing the charge density of the ion swarm; is the Dirac δ function, used to represent the locality of the ion swarm in space; is the thruster nozzle position, is the time when the ion swarm moves to the thruster nozzle position, is the distribution function of the 3. The plume characteristic analysis method of the pulsed electromagnetic thruster according to claim 1, wherein According to the current density , add the current densities of n ion groups to obtain the total ion current density j ( x , t ). In this step, the current density is: The total ion current density j ( x , t ) is as follows: Among them, is the time difference, is the velocity at which the ion swarm moves from the thruster outlet position to the position at the moment; is the velocity at which the ion swarm moves from the thruster outlet position to the position at the position at the moment; is the current density expression, is the axial position during the axial movement of the ion swarm, is the thruster nozzle position, is the time when the ion swarm moves to the position, is the time when the ion swarm moves to the thruster outlet position, , ; is the number of superposed ion swarms.

4. The plume characteristic analysis system of the pulsed electromagnetic thruster according to claim 1, wherein The multi-probe data acquisition device includes a probe body, and the probe body takes a single Langmuir single probe as the core. The Langmuir single probe selects a tungsten wire with a diameter of 50μm - 200μm.

5. The plume characteristic analysis system of the pulsed electromagnetic thruster according to claim 4, characterized in that, The system for analyzing the plume characteristics of the pulsed electromagnetic thruster further includes an insulating support. The insulating support is processed into a tubular or columnar shape. The Langmuir single probe is sleeved in the insulating support, and the length of the insulating support is 3mm - 6mm.

6. The plume characteristic analysis system of the pulsed electromagnetic thruster according to claim 5, wherein, The multi-probe data acquisition device includes a plurality of probes arranged at equal intervals along the plume space angle axis of the pulsed electromagnetic thruster, and the tips of the probes are perpendicular to the plasma ejection direction.

7. The plume characteristic analysis system of the pulsed electromagnetic thruster according to claim 6, characterized in that, The system for analyzing the plume characteristics of the pulsed electromagnetic thruster further includes a bias power supply. The bias power supply is connected to the multi-probe data acquisition device and is used to form an ion sheath layer on the probe surface by applying a negative bias voltage to the ground, repel electrons and receive ions, so as to collect the ion saturation current.

8. The plume characteristic analysis system of the pulsed electromagnetic thruster according to claim 7, characterized in that, The system for analyzing the plume characteristics of the pulsed electromagnetic thruster further includes a protective cover, and the protective cover is arranged outside the probe.

9. The plume characteristic analysis system of the pulsed electromagnetic thruster according to claim 8, characterized in that, The data acquisition and processing system includes a data acquisition card. The data acquisition card is connected to the ion current measurement circuit and is used to convert the ion current signal output by the ion current measurement circuit into a digital signal.

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