Effects of Coupling Oscillations on the Electron Conductivity of Hall Thrusters

It is known that the static magnetic field of a Hall thruster remains unchanged with the product of coil current and coil turn kept constant. This is called the ampere‐turns equivalence principle, which is used in the static magnetic field design of Hall thrusters. It is found that the discharge characteristic is different with the same static magnetic field which is formed by the same ampere‐turns but different coil turns. The effects of the fluctuating magnetic field on the static magnetic field are studied experimentally and theoretically, and the effective collision frequency is calculated based on the dispersion relation of coupling oscillations and the estimation of the fluctuating magnetic field. Results indicate that the different coil turns are accompanied by different coupling intensities which lead to different magnetic field fluctuations. The different magnetic field fluctuations cause differences in the effective electron collision frequency and therefore the electron conductivity and the discharge characteristic of Hall thrusters (© 2012 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

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)     

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.     

磁场梯度对Hall推力器放电特性影响的实验研究

为进一步探索Hall推力器通道内磁场优化设计理论,通过实验分析了强场区磁场梯度对推进剂的电离与加速等放电过程的影响. 研究发现,在本实验设计的磁场梯度范围内,磁场梯度大小对推进剂的电离过程影响较小,但是对离子流的加速特性会产生较为明显的影响.随着磁场梯度的增加,离子束的能量分布会趋于集中,推力器效率提高. 最后,对磁场轴向梯度进一步变大可能会引起的一系列物理问题如有限Larmor半径效应、电子传导机理转变规律和梯度漂移效应等进行了分析和思考.     

Study on the Relation Between Discharge Voltage and Magnetic Field Topography in a Hall Thruster Discharge Channel

The relation between magnetic field topography and operating voltage is investigated in a 1kW Hall thruster discharge channel in order to focus the ion beam effectively and optimize the performance. The curvature of magnetic field line (α) is introduced to characterize the differences of topologies. The optimized magnetic field distribution under each operating voltage is obtained by experiment. Through the curvature transformation, we find that the area of (α > 1) in the channel gradually decreases with the increase of the operating voltage. In response to the results above, two dimensional plasma flows are simulated employing Particle‐in‐Cell method. The distributions of the electric potential, ion density and ion radial velocity are calculated to understand the important influence of the relation above on ion beam focusing. The numerical results indicate that magnetic field curvature and thermal electric field control the ion beam in the ionization and acceleration zone, respectively. The magnetic field topography and discharge voltage interact with each other and together form the focusing electric field. The ion radial mobility is suppressed effectively and the ion beam is focused to the channel centerline. In addition, for a given voltages, when the area of (α > 1) is larger than the optimal scope, the electric potential lines excessively bend to the anode causing ion over focus; contrarily, the electric potential lines will bend to the exit and defocus ions. All these results suggest the relation between magnetic field topography and discharge voltage is important to the ion radial flow control and performance optimization of the Hall thruster (© 2009 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Particle‐in‐cell simulation of an optimized high‐efficiency multistage plasma thruster

Electric propulsion attracts increasing attention in contemporary space missions as an interesting alternative to chemical propulsion because of the high efficiency it offers. The High‐Efficiency Multistage Plasma thruster, a class of cusped field thruster, is able to operate at different anode voltages and operation points and thereby generate different levels of thrust in a stable and efficient way. Since experiments of such thrusters are inherently expensive, multi‐objective design optimization (MDO) is of great interest. Several optimized thruster designs have resulted from a MDO model based on a zero‐dimensional (0D) power balance model. However, the MDO solutions do not warrant self‐consistency due to their dependency on estimation from empirical modelling based on former experimental studies. In this study, one of the optimized thruster designs is investigated by means of particle‐in‐cell (PIC) analysis to examine the predicted performance characteristics with self‐consistent simulations. The 0D power balance model is used to develop additional diagnostics for the PIC simulations to improve the physics analysis. Using input parameters for the 0D power balance model from the PIC simulations allows further improvement for the design optimization.     

Identifying Particle Correlations in Quantum Hall Regime

We introduce a method that allows the disclosure of correlations between particle positions in an arbitrary many‐body system. The method is based on a well‐known simulated annealing algorithm and the proposed artificial distribution technique. Additionally, we investigate correlations in quantum Hall liquids (we consider many‐body wave functions that have been recently determined via the cyclotron subgroup model) and present three‐dimensional plots of configuration probability distributions that have been established from numerical simulations. We demonstrate that the preferred simultaneous positions of particles (configurations of positions, which correspond to large values of a system's probability distribution, ) tend to form complicated geometric structures, which are equivalent to classical Wigner crystals only for Laughlin states. Furthermore, we claim that quantum Hall liquids attributed to non‐Laughlin fillings are correlated on subdomains rather than on a whole particle domain (due to a quantizing magnetic field, which modifies the topology of a system's dynamics). Finally, we characterize Hall‐like internal orders in terms of statistical correlations (one‐dimensional unitary representations of cyclotron subgroups). Our conclusions concerning the stability of many‐body states agree with transport measurements and various numerical studies.     

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.     

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)     

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)     

Semi‐Classical Model of Strongly Correlated Coulomb Systems in Weak Magnetic Field

The integer and fractional quantum Hall effects are two remarkable macroscopic quantum phenomena occurring in two‐dimensional strongly correlated electronic systems at high magnetic fields and low temperatures. Quantization of Hall resistivity in the very high magnetic field regime at partial filling of the lowest Landau level indicates the stabilization of an electronic liquid quantum Hall phase of matter. Other interesting phases that differ from the quantum Hall phases take prominence in weaker magnetic fields when many more Landau levels are filled. These states manifest anisotropic magneto‐transport properties and, under certain conditions, appear to mimic charge density waves and/or liquid crystalline phases. One way to understand such a behavior has been in terms of effective interaction potentials confined to the highest Landau level partially filled with electrons. In this work we show that, for weak magnetic fields, such a quantum treatment of these strongly correlated Coulomb systems resembles a semi‐classical model of rotating electrons in which the time‐averaged interaction potential can be expressed solely in terms of guiding center coordinates. We discuss how the features of this semi‐classical effective potential may affect the stability of various strongly correlated electronic phases in the weak magnetic field regime (© 2011 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

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.     

Magnetotransport and superconductivity of α-uranium

We have measured the electrical resistivity, magnetoresistance and Hall effect on several new single-crystal samples and one polycrystalline sample of α-U. The residual resistivity ratios of these samples vary from 13 to 315. Matthiessen's law appears to hold above the onset of the charge-density wave phase transitions that begin near 43?K, but not below this temperature. Sharp features at all three charge-density wave transitions are observed and the effects of high magnetic fields on them are presented and discussed. The magnetoresistance is anisotropic, reaches 1000% at 2?K and 18?T and does not exhibit Kohler scaling. The Hall coefficient is positive, independent of magnetic field and slightly temperature dependent above about 40?K in agreement with earlier studies. Below 40?K the Hall coefficient changes sign as the temperature falls, varies with field and becomes much more strongly negative at the lowest temperatures than has been reported. Some of our results suggest that a spin-density wave may coexist with the charge-density wave states. Superconductivity is observed in two of our samples; we argue that it is intrinsic to α-U and suggest that it is consistent with a two-band model. Several parameters characterizing the transport and superconductivity of α-U are estimated.     

A 100 kW, 140 GHz pulsed gyrotron

The design and operation of a 100 kW, 140 GHz pulsed gyrotron are reported. To our knowledge, this is the highest frequency at which high gyrotron output power (>-100 kW) has been achieved. Results are presented for gyrotron operation in the range of magnetic field from 4 to 7 T, voltage from 23 to 80 kV and current up to 7.5 A. Near a value of magnetic field of 5.4 T, and output power of 100 kW was obtained at 140.4 GHz in single mode operation in the TE₀₃₁ resonator mode.     

霍尔效应推力器放电双稳态机理研究

实验发现霍尔效应推力器在自励磁模式下具有两个稳定的放电工作点,且运 行过程中在这两个工作点上往复跳变,很大程度上影响了推力器通道内等离子体的放 电物理过程及其综合性能.本文结合推力器放电磁安特性曲线与励磁电流曲线的相互关 系,给出了推力器放电双稳态特性形成的物理机理．在此基础上提出了通过改变励磁电 流曲线斜率,使推力器稳定工作于单放电工作点的方法,结合一维动态流体模型给予了物 理解释,并通过实验加以验证.     

基于霍尔效应的土沉降监测方法及装置

针对我国目前土沉降监测的自动化程度及仪器可靠性低、监测数据不及时、测量精度不高等问题,提出了一种新型基于霍尔效应的科学监测方法;这种方法采用多个霍尔器件组成阵列,将沉降磁环分布在土中,土的沉降会带动沉降磁环的跟随沉降,于是便会引起霍尔器件周围磁场强度发生相应的变化;利用霍尔效应监测霍尔器件周围磁场强弱并转化为相应的电信号,采用RS485总线通讯方式将采集到的数据实时上传至实验主机,主机对实验数据进行科学建模处理找到沉降磁环沉降位移与电信号的关系,并设计监测管理平台以实现对土沉降实时在线监测;通过实验验证这种监测方法监测精度高最大误差在0.4 mm、稳定性好,可以对多点实时在线监测,从而实现对土沉降的智能化高精度监测;在设计中可结合当前远程传输控制技术实现数据远程共享,具有更加广泛的应用前景。     

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.     

Hall coefficient and conduction mechanism in intermediate concentration n-Ge at helium temperatures

Hall coefficient measurements for intermediate concentration n-type Ge were carried out at liquid helium temperatures. The measurements show that the Hall coefficient and mobility increase with decreasing temperature down to 1.7 K and with increasing magnetic field up to 25 KG. These behaviours are opposite to what was observed in low concentration samples. We conclude that the thermal activated localised hopping motion does not exist in our concentration level, 6 × 10¹⁶ cm^?3, but rather the delocalised quasi-free carriers still dominate the overall conduction for temperature as low as 1.7 K. A model is suggested to explain the Hall mobility behaviour. The model based on the decrease of the dominant scattering mechanism, ionised impurity scattering in our case, as the temperature is lowered and when the magnetic field is increased. From the Hall coefficient behaviour at 4.2 and 1.7 K as well as the resistivity measurements, we found no effect of magnetic field on the unique activation energy existing in this concentration level.     

A Basic Predator‐Prey Type Model for Low Frequency Discharge Oscilations in Hall Thrusters

The mechanism of low frequency oscillations in Hall thrusters is usually explained using the predator‐prey type model, but the reasonable boundary conditions for the model have not been given. Analyses on thrusters' model equations show that besides the processes of neutral replenishment and ionization avalanche, the effects of dynamic electric field are also necessary for low frequency oscillations. The dynamic electric field reflects the interaction of ionization zone with acceleration zone, and is embodied in boundary conditions of the predator‐prey type model. Furthermore, a basic predator‐prey type model with reasonable boundary conditions and complete physical mechanism is proposed. And the effects of electric field on low frequency oscillations are verified by experiment (© 2011 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)