在5 kW级PPS $\circledR$ X 000霍尔推力器低频放电电流振荡（$\sim$ ~14 kHz）过程中，记录了$^+$离子轴向速度分布函数（VDF）的时间特性。的离子轴向速度分量的时间的演变监测的激光诱导荧光诊断工具的时间分辨率为100纳秒。由于在如此短的时间内荧光光子的数量非常低，因此使用自制的脉冲计数锁定系统来执行背景光子和荧光光子之间的实时区分。在时间上的离子VDF的演变，观察到在三个位置沿推力器通道轴后，快速关闭的推力器电源。阳极放电电流在5 $μ$ s期间以2 kHz关闭，与电流振荡周期没有任何同步。这种方法允许检查的时间行为的离子VDF在放电的衰减和点火过程中，以及在强制和自然等离子体振荡。测量结果表明，在强迫和自然的情况下，在一个频率接近电流振荡频率的时间周期性变化的分布函数的轴向分量的$^+$离子。离子密度和平均速度振荡，而速度色散保持不变，这表明电离层和加速层具有相同的动力学。最后，随着时间的推移的电场的变化是第一次实验证明在交叉场放电。
英文摘要：
The temporal characteristics of the Xe$^+$ ion axial Velocity Distribution Function (VDF) were recorded in the course of low-frequency discharge current oscillations ($\sim$~14 kHz) of the 5 kW-class PPS$\circledR$X000 Hall thruster. The evolution in time of the ion axial velocity component is monitored by means of a laser induced fluorescence diagnostic tool with a time resolution of 100 ns. As the number of fluorescence photons is very low during such a short time period, a hom-made pulse-counting lock-in system was used to perform real-time discrimination between background photons and fluorescence photons. The evolution in time of the ion VDF was observed at three locations along the thruster channel axis after a fast shut down of the thruster power. The anode discharge current is switched off at 2 kHz during 5 $μ$s without any synchronization with the current oscillation cycle. This approach allows to examine the temporal behavior of the ion VDF during decay and ignition of the discharge as well as during forced and natural plasma oscillations. Measurements show that the distribution function of the axial component of the Xe$^+$ ion does change periodically in time with a frequency close to the current oscillation frequency in both forced and natural cases. The ion density and the mean velocity are found to oscillate whereas the velocity dispersion stays constant, which indicates that ionization and acceleration layers have identical dynamics. Finally, variations over time of the electric field are for the first time experimentally evidenced in a crossed-field discharge.
A two-dimensional simulation is conducted to investigate the effect of cross-field electron transport enhancement in the Hall thruster discharge caused by the nonuniform propellant supply in azimuth. The Hall thruster operation with azimuthally nonuniform propellant supply is expected to be a good test case to understand the influences of azimuthal plasma property distributions on the axial electron transport. A particle-fluid hybrid model is developed with a two-dimensional magnetized electron fluid model incorporated with an empirical anomalous electron mobility model. The calculation result…
In this paper, a coaxial pulsed plasma thruster was designed, built, and tested. This design confirmed PPT operation at substantially reduced discharge voltages of 100 to 200 V across the discharge plasma at a discharge current level of 10.4 kA similar to magnetoplasmadynamic arcs. The PPT cathode was imaged with an ICCD camera over a wide range of pressures, and the photos indicated "spotless" diffuse arc attachment to the cathode at higher pressures, and the appearance of conventional cathode spots at lower pressures. Cathode erosion rate measurements support the conclusion of "spotless" ope…
The electron cross-field transport by the induced azimuthal electric field in a Hall thruster exhibits the mobility scaled by $1/B$. This study investigates parameters affecting this transport over a Hall thruster's distinct regions, such as the ionization, acceleration, and plume region. The main focus is on the nonzero equilibrium azimuthal electric field induced by an azimuthally inhomogeneous neutral supply. A fast Fourier transform analysis of the plasma structure reveals that the wavenumber $k$ of the azimuthal plasma structure increases from $k=2$, which is the input condition, to $k=4$…
Conventional snowplow/1-D models assume the existence of single completely ionized plasma sheet in the discharge chamber of pulsed plasma thrusters (PPTs). However, extensive experimental analysis and observations suggest the presence of multiple plasma streams and partial ionization of the propellant gas. A multi-layered plasma-neutral mass sheet one-dimensional numerical model is developed for PPTs in the present paper. The model accounts for the secondary plasma sheets generated due to the crowbar breakdowns as well as the neutral gas generated after the main discharge. The model accurately…
Azimuthal spoke-like modes commonly occur in ExB discharges. The natural occurrence of the spoke mode is correlated with changes of plasma parameters. Here, instead of allowing these changes to occur naturally, we report a technique for actively controlling the spoke by adjusting the boundary condition at the anode. The technique is demonstrated using a cylindrical Hall thruster equipped with a segmented anode. By varying the voltage and the relative phases of the anode segments, properties of the azimuthal mode can be altered substantially, as shown by fast camera images and probe diagnostics…
Hall Thrusters typically operate at thrust densities on the order of 10 N/m2, which is well below the thrust density limits discussed in previous literature. These limits have been considered here and each component of thrust density is analyzed to demonstrate the relative contribution to the total thrust density. Dependencies of the thrust density limits upon the thruster geometry, electron mobility, and the applied magnetic field are revealed and compared with experimental data.
Along with crossed electric and magnetic fields in a Hall thruster, a radial component of electric field is generated that takes ions toward the walls, which causes sputtering and produces dust contamination in the thruster plasma. Considering negatively charged dust particles in the Hall thruster, we approach analytically the resistive instability by taking into account the oscillations of dust particles, ions and electrons along with finite temperatures of ions and electrons. In typical Hall thruster regimes, the resistive instability growth rate increases with higher collision rates in the …
The genesis of the ion axial velocity distribution function (VDF) is analyzed for collisionless Hall thruster discharges. An analytical form for the VDF is obtained from the Vlasov equation, by applying the Tonks-Langmuir theory in the thruster channel, under the simplifying assumptions of monoenergetic creation of ions and steady state. The equivalent set of 1D unsteady anisotropic moment equations is derived from the Vlasov equation, and simple phenomenological closures are formulated, assuming a polynomial shape for the ions VDF. The analytical results and the anisotropic moment equations a…
A model calculation is presented to characterize the anomalous cross-field transport of electrons in a Hall thruster geometry. The anomalous nature of the transport is attributed to the chaotic dynamics of the electrons arising from their interaction with fluctuating unstable electrostatic fields of the electron cyclotron drift instability that is endemic in these devices. Electrons gain energy from these background waves leading to a significant increase in their temperature along the perpendicular direction $T_\perp / T_\parallel \sim 4$ and an enhanced cross-field electron transport along t…
In this study, wall ion loss and erosion rate are evaluated in the RAIJIN thruster. The novelty of this work is the detailed analysis of measured guard-ring (metallic channel wall) current, which enables a fast evaluation of the wall ion loss and erosion rate. The current-voltage characteristics of the guard-ring current indicate that the sheath on the guard rings is in the ion saturation regime and that the guard-ring current can be used as a wall ion flux indicator. The experimental results demonstrate that the wall ion loss can be significantly reduced in the magnetic configuration of RAIJI…
An axial-azimuthal two-dimensional Hall thruster discharge model was developed for analyzing gradient drift instability (GDI) and cross-field electron transport enhancement induced solely by the GDI. A hybrid particle-fluid model was used for the partially ionized plasma, where the inertialess electron fluid in the quasineutral plasma was assumed. A nonoscillatory numerical method was proposed for the potential solver in the electron fluid model to avoid numerical instability and analyze the physics of GDI accurately. A simulation is performed for a 1 kW-class anode-layer-type Hall thruster, a…
Hall-effect thrusters (HETs) are widely used for modern near-earth spacecraft propulsion and are vital for future deep-space missions. Methods of modeling HETs are developing rapidly. However, such methods are not yet precise enough and cannot reliably predict the parameters of a newly designed thruster, mostly due to the enormous computational cost of a HET plasma simulation. Another approach is to use scaling techniques based on available experimental data. This paper proposes an approach for scaling HETs using neural networks and other modern machine learning methods. The new scaling model …
The advent of high-power Hall thrusters and the increasing interest towards their use as a primary propulsion system for various missions have given a new boost to the efforts aiming at self-consistent predictive modeling of this thruster technology. In this article, we present a novel approach, which allows enhancing the predictive capability of one-dimensional Particle-in-Cell (PIC) simulations to self-consistently capture the wave-induced electron transport due to the azimuthal instabilities in Hall thrusters. The so-called "pseudo-2D" PIC scheme resulting from this approach is extensively …
The low-frequency rotating plasma instability (spoke) in the ISCT200 thruster operating in the wall-less configuration was simulated with a 3 dimensional PIC MCC code. In the simulations an m = 1 spoke rotating with a velocity of 6.5 km/s in the ExB direction was observed. The rotating electron density structure in the spoke is accompanied by a strongly depleted region of the neutral gas, which clearly shows that the spoke instability is of an ionization nature, similar to the axial breathing mode oscillations. In the simulation the electron cross-field transport through the spoke core was cau…
Ions in Hall effect thrusters are often characterized by a low collisionality. In the presence of acceleration fields and azimuthal electric field waves, this results in strong deviations from thermodynamic equilibrium, introducing kinetic effects. This work investigates the application of the 14-moment maximum-entropy model to this problem. This method consists in a set of 14 PDEs for the density, momentum, pressure tensor components, heat flux vector and fourth-order moment associated to the particle velocity distribution function. The model is applied to the study of collisionless ion dynam…
Hall-effect thrusters (HETs) operated with xenon are one of the most commonly used electric propulsion technologies for a wide range of space missions, including drag compensation in low Earth orbit, station-keeping, and orbital insertion, as access to space becomes more affordable. Although anomalous electron transport, the electron drift instability (EDI), and secondary electron emission (SEE) have been studied experimentally and numerically in xenon-based HETs, the impact of alternative propellants is still poorly characterized. In this work, a two-dimensional particle-in-cell/Monte Carlo c…
A Hybrid Simulation Code for Hall Thrusters and its Sensitivity to Numerical Parameters
Lab of Plasma Propulsion, Harbin Institute of Technology（哈尔滨工业大学等离子体推进实验室）；Key Laboratory of Advanced Aerospace Propulsion Technology, Ministry of Industry and Information Technology（工业和信息化部航空航天推进技术重点实验室）；Aviation Key Laboratory of Science and Technology on Aerodynamics of High Speed and High Reynolds Number, AVIC Aerodynamics Research Institute（中国航空工业集团公司空气动力研究院高速高雷诺数气动技术航空科技重点实验室）；China Jiuyuan Hi-Tech Equipment Co., Ltd.（中国九元高科技设备有限公司）；CAEP Software Center for High Performance Numerical Simulation（中国工程物理研究院高性能数值模拟软件中心）；School of Mechanical and Power Engineering, Harbin University of Science and Technology（哈尔滨科技大学机械与动力工程学院）
Free-Molecular Face-Flux Preprocessing for Reduced Neutral-Continuity Modeling in Hall Thrusters: Particle-Based Reference and Deterministic SN-DFEM Realization
School of Energy Science and Engineering, Harbin Institute of Technology（哈尔滨工业大学能源学院）
In this article, we introduce a novel dimensionality reduction formulation for the Poisson's equation in the Vlasov-Poisson system that yields a reduced-order particle-in-cell scheme. This scheme allows a remarkable reduction in the computational cost of self-consistent kinetic simulations of Hall thrusters. The formulation of the dimensionality reduction approach, together with its verification for a general Poisson's problem, is presented. Moreover, we show the results of several "quasi-2D" axial-azimuthal simulations we performed with the conditions of a well-established 2D3V reference case…
Traditional expressions and definitions describing performance of plasma thrusters, including the thrust, specific impulse, and the thruster efficiency, assume a steady state plasma flow with a constant flow velocity. However, it is very common for these thrusters that the plasma exhibits unstable behavior resulting in time-variations of the thrust and the exhaust velocity. For example, in Hall thrusters, the ionization instability leads to strong oscillations of the discharge current (so-called breathing oscillations), plasma density, ion energy, and as a result the ion flow. In this paper, w…
Hall thrusters are susceptible to large-amplitude plasma oscillations that impact thruster performance and lifetime and are also difficult to model. High-speed cameras are a popular tool to study these dynamics due to their spatial resolution and are a popular, nonintrusive complement to in-situ probes. High-speed video of thruster oscillations can be isolated (decomposed) into coherent structures (modes) with algorithms that help us better understand the evolution and interactions of each. This work provides an introduction, comparison, and step-by-step tutorial on established Fourier and new…
The microwave power absorption efficiency of the mu10 ECR ion thruster, utilized in the Japanese asteroid explorers Hayabusa and Hayabusa2, is investigated in order to allow performance measurement and provide information for its improvement. A model detailing the local electron behavior in a real ECR plasma discharge, based the magnetic field characteristics, is presented. Three methods to evaluate the microwave power absorption efficiency are proposed: an estimation based on the chamber geometry and magnetic field characteristics, a measuremen based on performance parameters and a measuremen…
One special interest for the industrial development of Hall thruster is characterizing the anomalous cross-field electron transport observed after the channel exit. Since the ionization efficiency is more than 90%, the neutral atom density in that domain is so low that the electron collisions cannot explain the high electron flux observed experimentally. Indeed this is 100 times higher than the collisional transport. In Hall thruster geometry, as ions are not magnetized the electric and magnetic field configuration creates a huge difference in drift velocity between electrons and ions, which g…
A reversed gas feed configuration for Hall thrusters is proposed and studied numerically. As an alternative to standard direct injection, we investigate the effect of injecting the propellant near the channel exit and directing it backwards, towards the anode. The resulting neutral density and average velocity fields are studied with the Direct Simulation Monte Carlo method for both cold and warm anode conditions. The residence time of neutral particles inside the channel and in the ionization region is computed using a test-particle Monte Carlo method. The computations indicate that the rever…
Reduced-order particle-in-cell (PIC) scheme is a novel modeling approach that enables computationally efficient electrostatic kinetic simulations of plasma. In our previous publications, we demonstrated the potentials of a preliminary implementation of this PIC scheme to resolve the multi-dimensional plasma processes in a Hall thruster in a manner close to traditional multi-dimensional PIC simulations. In this work, we first introduce a mathematically mature formulation for the dimensionality reduction of Poisson's equation, which enables the generalized "quasi-multi-dimensional" PIC scheme. W…
Low frequency ionization oscillations involving plasma and neutral density (breathing modes) are the most violent perturbations in Hall thrusters for electric propulsion. Because of its simplicity, the zero-dimensional (0-D) predator-prey model of two nonlinearly coupled ordinary differential equations for plasma and neutral density has been often used for the characterization of such oscillations and scaling estimates. We investigate the properties of its continuum analog, the one-dimensional (1-D) system of two nonlinearly coupled equations in partial derivatives (PDE) for plasma and neutral…
Low-frequency axial oscillations (5-50 kHz) stand out as a pervasive feature observed in many types of Hall thrusters. While it is widely recognized that the ionization effects play the central role in this mode, as manifested via the large scale oscillations of neutral and plasma density, the exact mechanism(s) of the instabilities remain unclear. To gain further insights into the physics of the breathing mode and evaluate the role of kinetic effects, a one-dimensional time-dependent full nonlinear low-frequency model describing neutral atoms, ions, and electrons, is developed in full fluid f…
The spoke instability in an $E\times B$ Penning discharge is shown to be strongly affected by the boundary that is perpendicular to $B$ field lines. The instability is the strongest when bounded by dielectric walls. With a conducting wall, biased to collect electron current from the plasma, the spoke becomes faster, less coherent and localised closer to the axis. The corresponding anomalous cross-field transport is assessed via simultaneous time-resolved measurements of plasma potential and density. This shows a dominant large-scale $E\times B$ anomalous character of the electron cross-field c…
