Particle‐in‐cell simulation of the effect of curved magnetic field on wall bombardment and erosion in a hall thruster

A curved, convex towards the channel bottom magnetic field is an important feature of an advanced Hall thruster that allows confining the plasma flow in the channel center, reducing the divergence angle of the ejected ion beam, and improving the discharge performance. In this article, the discharge behaviour of a Hall thruster in magnetic fields with different degrees of curvature is simulated with a particle‐in‐cell numerical method, and the effect of curved magnetic field on the ion bombardment and wall erosion and the associated mechanisms are studied and analysed. The results show that, as the curvature of the magnetic field increases, the propellant ionization becomes more confined at the channel center, the potential drop inside the channel decreases, and the acceleration region shifts outside the channel, which lead to the attenuation of the ion energy bombarding the wall and the deviation of the bombardment angle from the optimal sputtering angle. Conversely, the ion flux bombarding the wall near the channel exit increases. Nevertheless, the bombardment energy and angle are the dominant factors for the wall erosion, and the wall erosion rate clearly decreases with the increasing curvature of the magnetic field. These findings are closely related to the behaviour of electron conduction under a curved magnetic field; the relevant mechanisms are clarified in this article.     

Effect of permanent magnet configuration on discharge characteristics in cylindrical Hall thrusters

Magnetic field design is important in cylindrical Hall thrusters and using permanent magnets to generate magnetic field is very promising in the future. In two typical permanent magnet configurations (i.e., ring and cylindrical configurations) of cylindrical Hall thrusters, discharge characteristics are compared in this paper through the experiments and simulations. The study shows that the cylindrical configuration can bring about higher thruster performance in the same working condition. The reason is that the potential drop of the cylindrical configuration is mainly concentrated in the channel, which is beneficial for the electrons to obtain energy to promote the ionization of the propellant. However, the voltage regulation range of the cylindrical configuration is lower because the anode is more easily overheated.     

Study on Similarity Criteria of Hall Effect Thrusters

The scaling design of Hall effect thrusters is based on similarity criteria. Up to now, few of the similarity criteria proposed concern about the inside physical processes of the thruster except Melikov‐Morozov similarity criterion which embodies the ionization of propellant. As many other significant processes, such as electron conduction, ion acceleration and energy exchange, are out of consideration, it is far from enough to direct the thruster design appropriately at present. Therefore, in this paper, we have deduced out many new similarity criteria by analyzing the neutral continuity equation, the ion/electron momentum equations and the electron energy equation with the equation analysis method. By further comparing the magnitudes of source terms of those equations, we obtain certain similarity criteria which are primary and should be guaranteed for modeling design of thrusters. These dominant similarity criteria are finally verified in experiments (© 2009 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

The Effect of Magnetic Mirror on Near Wall Conductivity in Hall Thrusters

The effect of magnetic mirror on near wall conductivity is studied in the acceleration region of Hall thrusters. The electron dynamics process in the plasma is described by test particle method, in which electrons are randomly emitted from the centerline towards the inner wall of the channel. It is found that the effective collision coefficient, i.e. the rate of electrons colliding with the wall, changes dramatically with the magnetic mirror effect being considered; and that it decreases further with the increase of magnetic mirror ratio to enhance the electron mobility accordingly. In particular, under anistropic electron velocity distribution conditions, the magnetic mirror effect becomes even more prominent. Furthermore, due to decrease in magnetic mirror ratio from the exhaust plane to the anode in Hall thrusters, the axial gradient of electron mobility with magnetic mirror effect is greater than without it. The magnetic mirror effects on electron mobility are derived analytically and the results are found in agreement with the simulation. (© 2008 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Flow visualization and local mass transfer studies for turbulent flow in a wind tunnel with chamfered ribs

The paper presents results of flow visualization and mass transfer studies for fully developed turbulent flow of air in a square section wind tunnel with repeated chamfered rib roughness on the bottom of the tunnel (rib head chamfer angles ϕ of -15°, 0°, and 15°; relative roughness pitchp/e = 3, 5, 7.5, and 10). Direct video recordings of flow patterns were made using a simple technique of particles visualization. For the positively chamfered closely spaced ribs (p/e <- 5) vigorous vortex shedding has been seen compared to the square or negatively chamfered ribs, which is found to be a function of the Reynolds number. For the widely spaced ribs, the study shows flow separation at the ribs and reattachment in the inter-rib region. Local mass transfer studies, based on the variation in colour of cobaltous chloride solution impregnated paper due to evaporation of water, showed a significant improvement in mass transfer rate in the recirculating region in the wake of ribs with the change in the chamfer angle from -15° to 15°. The positively chamfered 15° ribs are found to be better than square section ribs atp/e <- 7.5. The performance of negatively chamfered ribs is found to be poor compared to other ribs irrespective of the relative roughness pitch.     

Study of low‐frequency oscillations in a double‐stage Hall thruster

The characteristics of low‐frequency oscillations of double‐stage Hall thrusters are quite different from those of conventional single‐stage Hall thrusters. In this paper, the effects of double‐stage discharge on the low‐frequency oscillations are experimentally investigated. The results indicate that the amplitude significantly decreases with increasing magnetic field strength and voltage during the ionization stage. Meanwhile, data analysis reveals that ionization occurs in both stages and that the transport ion current between the two stages is the key factor that affects the amplitude and main frequency of the oscillations. Two new processes, namely the ion transport and ion recombination caused by double‐stage discharge, are found to be relevant to the change in the current oscillations. To summarize, the ionization stage relieves the oscillations in the acceleration stage, leading to a reduction in the amplitude of the discharge current.     

Particle‐in‐Cell Simulations for Ion Thrusters

The Particle‐in‐Cell (PIC) method was used to study two different ion thruster concepts: Hall Effect Thrusters (HETs) and High Efficiency Multistage Plasma Thrusters (HEMPs), in particular the plasma properties in the discharge chamber due to the different magnetic field configurations. Special attention was paid to the simulation of plasma particles fluxes on the thrusters inner surfaces. In both cases PIC proved itself as a powerful tool, delivering important insight into the basic physics of the different thruster concepts.The simulations demonstrated that the new HEMP thruster concept allows for a high thermal efficiency due to both minimal energy dissipation and high acceleration efficiency. In the HEMP thruster the plasma contact to the wall is limited only to very small areas of the magnetic field cusps, which results in much smaller ion flux to the thruster channel surface as compared to HET. (© 2009 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

真空背压对霍尔推力器放电特性影响的实验研究

真空背压的变化会改变进入霍尔推力器放电通道内的背景气体量,对工质的电离、电子的传导等物理过程产生影响,从而进一步影响到推力器的宏观放电特性.为分析真空背压对推力器放电的影响规律,通过向真空罐输入流量可控的氪气改变真空背压,在不同真空背压下测量通道内原子、离子的发光特性以及出口处离子流的伏安特性.分析结果表明:背景气体返流对通道内工质放电过程具有全局性的影响,提高背压会使通道内的电子温度降低、电离效率降低,并会在通道内形成一个新的电离区,且背压越高,该电离区距推力器阳极越近.     

Scaling Design and Experimental Study on Hall Thrusters with Curved Magnetic Field

The existing scaling theories of Hall thrusters are based on the hypothesis of a one‐dimensional straight magnetic field, which is not suitable for the design of modern thrusters with a two‐dimensional curved magnetic field. In this paper, using the equation analysis method, we derive new similarity criterions in a curved magnetic field by analyzing the momentum equations of charged particles; consequently, we propose a new modeling design method for Hall thrusters with a constant discharge voltage. This method is further validated by experiments. A designed model with a power of 1.5 kW is made based on our proposed method from a prototype model with a power of 1 kW. The experimental results demonstrate that these two thrusters have little differences in performance and physical processes as expected from the scaling. Therefore, our method is well suited for designing a Hall thruster with a curved magnetic field (© 2011 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Acoustic characteristics of chamfered Hartmann whistles

Experimental studies are conducted to investigate the effect of internal chamfer at the mouth of Hartmann resonators. Studies involve a range of nozzle pressure ratios from 4 to 6, and chamfer angles 15°, 30°, and 45°. Further, the effects of cavity length and stand-off distance are also considered. The spectra, directivity, and acoustic power characteristics are studied in detail. Detailed numerical simulations are carried out to capture the flow oscillations inside as well as at the outside of the mouth of the chamfered cavities. Computations show flow diversion in chamfered cavities and explain the shift in the directivity observed experimentally. The fundamental frequency of cavities with 15° and 30° chamfers is observed to be higher than that of regular cavities. Resonance is intensified by the presence of chamfer resulting in higher overall sound pressure levels of chamfered whistles. Thus, chamfered Hartmann whistles are found to emit more than twice the acoustic power of a regular cylindrical whistle. The tonal quality of sound is analyzed using a new metric termed as “resonance index”.     

Space electric propulsion plasmas

Electric thrusters offer the promise of a substantial improvement in performance over that of conventional chemical rockets currently used in space propulsion applications. There are three basically different ways in which electrical power and propellant inputs might be combined to produce thrust: (1) propellant can be heated electrically and then expanded through a nozzle; (2) electromagnetic body forces can be applied to accelerate a plasma to the desired exhaust velocity; or (3) electrostatic body forces can be applied to accelerate charged particles. Electric thrusters are classified in accordance with the mechanism by which they induce thrust as electrothermal, electromagnetic, and electrostatic. The characteristics of plasmas in electric thrusters along these lines are considered     

离子推力器工作性能参数控制模型

为了研究离子推力器工作参数对输出特性的影响,通过离子推力器工作性能参数的理论计算公式,建立起离子推力器输入参数与输出参数的Simulink控制模型,根据模型分别对我国研制的30 cm口径以及20 cm口径离子推力器的工作输出参数进行了理论计算,并通过推力测量试验对理论值进行了比对和分析。比对结果表明:在推力理论计算过程中引入二价Xe离子比率和束流密度分布推力修正,以及推力均方误差修正后,推力理论值与实测值符合性较好,计算误差小于1 mN,证明了推力修正方法的合理性。     

A 200-W permanent magnet Hall thruster discharge with graphite channel wall

A 200-W Hall thruster was designed using permanent magnets placing the axial maximum magnetic field outside of the channel, and the anode/gas distributor as an integrated U-shaped structure. A split structure is adopted for the discharge channel to conveniently change the wall material. With the initial conditions that the anode mass flow is maintained at 0.8 mg/s, 1.0 mg/s and 1.2 mg/s over a voltage range of 150–400 V (at 50 V intervals), the discharge properties were determined for the two thruster models with the channel walls composed of graphite and boron nitride (BN). The results demonstrate that under identical operating parameters, the properties of the thruster with the graphite channel walls are similar to the properties of the thruster with the BN channel walls. The maximum difference of the discharge current between the two wall materials is 6.2%; the maximum difference of the thrust and the specific impulse is 3.3%, and that of the anode efficiency is 1.7% (absolute value). These differences are smaller than the corresponding parameter differences observed from changing wall materials in other common Hall thrusters.     

电子温度各向异性对霍尔推力器BN绝缘壁面鞘层特性的影响

建立多价态多组分等离子体一维流体鞘层模型,引入电子温度各向异性系数并考虑出射电子速度分布,研究了电子温度各向异性对霍尔推力器中的BN绝缘壁面鞘层特性和近壁电子流的影响.分析结果表明,相比于纯一价氙等离子体鞘层参数,推力器中的多价态氙等离子体鞘层电势降略有降低,电子壁面损失增加,临界二次电子发射系数减小.推力器中的电子温度各向异性现象可以显著地加大出射电子能量系数,进而降低鞘层电势降,增强电子壁面相互作用.数值结果表明,空间电荷饱和机制下电子温度各向异性对鞘层空间电势分布影响显著. 关键词： 霍尔推力器 电子温度各向异性 空间电荷饱和鞘层     

Similarity scaling-application and limits for high-efficiency-multistage-plasma-thruster particle-in-cell modelling

To suit a wide variety of space mission profiles, different designs of ion thrusters were developed, such as the High-Efficiency-Multistage-Plasma thrusters (HEMP-T). In the past, the optimization of ion thrusters was a difficult and time-consuming process and evolved experimentally. Because the construction of new designs is expensive, cheaper methods for optimization were sought-after. Computer-based simulations are a cheap and useful method towards predictive modelling. The physics in HEMP-T requires a kinetic model. The Particle-in-Cell (PIC) method delivers self-consistent solutions for the plasmas of ion thrusters, but it is limited by the high amount of computing time required to study a specific system. Therefore, it is not suited to explore a wide operational and design space. An approach to decrease computing time is self-similarity scaling schemes, which can be derived from the kinetic equations. One specific self-similarity scheme is investigated quantitatively in this work for selected HEMP-Ts, using PIC simulations. The possible application of the scaling is explained and the limits of this approach are derived.     

Influence of the erosion of the discharge channel wall on the efficiency of a stationary plasma thruster

The integral characteristics of stationary plasma thrusters are studied experimentally during their long-term operation. It is shown that the monotonic fall of the thrust efficiency and specific impulse within the initial 500?C1000 h of operation is explained, in particular, by a decrease in the propellant utilization efficiency. A physical mechanism underlying this phenomenon is suggested, and expressions predicting the variation of the output characteristics of the thrusters during the operating life are derived. Satisfactory agreement is observed between experimental and predicted results on the anode specific impulse variation in the course of testing several thrusters with different powers for endurance. An experimentally found correlation between the magnetic field configuration and the position of the erosion zone boundary on the discharge chamber wall is accounted for.     

Aero-acoustic features of internal and external chamfered Hartmann whistles: A comparative study

The efficient way of chamfering at the mouth of Hartmann whistles in generating higher acoustic emission levels are experimentally demonstrated in this paper. The relevant parameters of the present work comprise internal and external-chamfer angles (15°, 30°), cavity-length, nozzle-to-cavity-distance and jet pressure ratios. The frequency and amplitude characteristics of internal and external, chamfered-Hartmann whistles are compared in detail to ascertain the role of chamfering in enhancing acoustic radiations. The high frequencies possessed by the internal chamfered whistles as compared to the external ones indicate that it amplifies the resonance. It is observed that the internal chamfered whistles exhibit higher directivity than the external chamfered ones. Further, it is noticed that the acoustic-power and efficiency are also higher for the internal chamfered whistles. The shadowgraph sequences reveal the variance in flow-shock oscillations as well as the spill-over features at the mouth of internal and external, chamfered cavities. The presence of large mass flow as well as its subsequent increase of spill-over as a result of enlarged mouth in internal chamfered whistles, leads to the generation of high intensity acoustic radiation than the external chamfered ones. Thus, the internal chamfer proves to be the best passive control device for augmented sound pressure levels and acoustic efficiencies in resonance cavities.     

Magnetic confinement studies for performance enhancement of a 5-cmion thruster

Several magnet assemblies relevant to ion thrusters were investigated using a numerical code to calculate the primary electron mean containment time. An analytical model was used to determine, consistently with the plasma stability condition, the ion thruster performance parameters, namely, the plasma ion energy cost, the plasma density, the plasma potential, and the doubly charged ion production rate as a function of the propellant mass flow rate. The numerical code was checked by reproducing the experimental performance parameters obtained from a 7-m checkerboard ion thruster. Using this approach, performance curves were obtained for a 5-cm ion thruster devised to produce a 1-mN thrust with low power and propellant consumption     

On the Effect of the Surface State and Geometry of the Discharge- Chamber Edges and Sizes of Morozov’s Stationary Plasma Thruster upon its Long-Term Operation

The results of long-term tests of Morozov’s stationary plasma thrusters are presented. It is revealed how the surface state and geometry of the discharge chamber’s edges influence the thruster’s parameters. It is shown that, during the ground tests of thrusters with cylindrical geometry of the acceleration channel under initial stage of operation, material sputtered from the discharge chambers’ walls is deposited onto the nearanode segment of the walls. Films of deposited material fail during thruster operation causing fragment formation, which jut out towards the discharge volume and disturb the motion of drifting electrons in the area of their acceleration. As a result the thruster reactive force and specific impulse decrease. The way in which the forming fragments influence thruster performance and operation is examined. It is shown that it decreases under long-term operation and significant channel widening since the ion flux to the wall and the quantity of the sputtered material decrease, and since the profile of the walls changes due to their wear and cleaning effect of the discharge. As a result the thruster’s parameters are restored to a level close to the initial one. It is shown that the dynamics of thruster parameters variation in space and during ground tests is different. This means that it is necessary to simulate more properly the conditions of thruster operation in space when conducting ground development tests. Thrusters with a long lifetime should be designed with widening of the acceleration channel beyond the loop which surrounds the magnetic system so that areas of acceleration and the erosion of walls are located in the widened part of the channel.     

Characteristics of wall sheath and secondary electron emission under different electron temperatures in a Hall thruster

In this paper, a two-dimensional physical model is established in a Hall thruster sheath region to investigate the influences of the electron temperature and the propellant on the sheath potential drop and the secondary electron emission in the Hall thruster, by the particle-in-cell(PIC) method. The numerical results show that when the electron temperature is relatively low, the change of sheath potential drop is relatively large, the surface potential maintains a stable value and the stability of the sheath is good. When the electron temperature is relatively high, the surface potential maintains a persistent oscillation, and the stability of the sheath reduces. As the electron temperature increases, the secondary electron emission coefficient on the wall increases. For three kinds of propellants(Ar, Kr, and Xe), as the ion mass increases the sheath potentials and the secondary electron emission coefficients reduce in sequence.