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)     

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)     

The Hall effect and oscillating decay of a magnetic field

The decay of a strong magnetic field in a conducting matter is considered. It is shown that nondissipative Hall currents can considerably change the behavior of the field when it decays. The nonlinear character of the Hall effect leads to the generation of fields of high multipolarity even for most simple initial magnetic configurations. In particular, the evolution of an initially dipole configuration may give rise not only to quadrupole or higher poloidal harmonics but also to a toroidal field that is other than zero only inside the conductor. The nonlinear Hall currents relate different harmonics to each other and, in a sufficiently strong field, may provide efficient energy exchange between them. Due to this redistribution of the magnetic energy, the evolution of different harmonics has an oscillating character. The oscillation period is determined by the characteristic time of Hall drift and may be fairly short in strong magnetic fields.     

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.     

Calculation of the electric potential and the Lorentz force in a transverse flow past a circular cylinder in a nonuniform magnetic field for various configurations of a locally ionized region at the cylinder surface

We obtain a solution to the equation for the electric potential in a locally ionized transverse magnetohydrodynamic flow past a circular cylinder in a nonuniform magnetic field produced by a linear conductor for various configurations of the ionization region. Analytical formulas are derived for the volume density of the Lorentz force acting on the flow in a locally ionized region. The effect of the Hall parameter and of the configuration of the region of the magnetohydrodynamic interaction on the Lorentz force is analyzed. It is shown that an increase in the Hall parameter leads to a decrease in the Lorentz force acting on the flow, and a change in the configuration of the locally ionized region makes it possible to suppress the effect of the Hall parameter on the Lorentz force.     

永磁体辅助下单畴GdBCO超导体和永磁体之间的磁悬浮力研究

通过对永磁体辅助下单畴GdBCO超导体和圆柱形永磁体在液氮温度、零场冷、轴对称情况下磁悬浮力的测量,研究了两种不同组态下辅助永磁体对超导体磁悬浮力特性的影响.实验结果表明,当长方体辅助永磁体水平磁化、且磁极N指向超导体时,超导体的最大磁悬浮力从没有引入辅助永磁体的29.8 N增加到61.5 N,增加为没有引入辅助永磁体时的206%.当长方体辅助永磁体的N极与圆柱形永磁体的N极反平行时,超导体的最大磁悬浮力从没有引入辅助永磁体的29.8 N减小到19.6 N,减小为无辅助永磁体时的65.8%.这些研究结果说明,通过科学合理地设计超导体和永磁体的组合方式,能有效地提高超导体的磁悬浮力.该研究结果对促进超导体的应用具有重要的指导意义. 关键词： 单畴GdBCO 永磁体 磁悬浮力     

Model fractional quantum Hall states and Jack polynomials

We describe an occupation-number-like picture of fractional quantum Hall states in terms of polynomial wave functions characterized by a dominant occupation-number configuration. The bosonic variants of single-component Abelian and non-Abelian fractional quantum Hall states are modeled by Jack symmetric polynomials (Jacks), characterized by dominant occupation-number configurations satisfying a generalized Pauli principle. In a series of well-known quantum Hall states, including the Laughlin, Read-Moore, and Read-Rezayi, the Jack polynomials naturally implement a "squeezing rule" that constrains allowed configurations to be restricted to those obtained by squeezing the dominant configuration. The Jacks presented in this Letter describe new trial uniform states, but it is yet to be determined to which actual experimental fractional quantum Hall effect states they apply.     

Cylindrical gauge field configurations. A signal of confinement in QCD

An infrared approximation to the field equations of QCD is proposed which generates a mapping of configuration space into two dimensions (one time, one space dimension). The associated cylindrical gauge field configurations insure confinement whenever nontrivial interactions in two dimensions remain. This feature distinguishes abelian from nonabelian gauge theories.     

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)     

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.     

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.     

辅助永磁体磁化方式对单畴GdBCO超导块材捕获磁场分布及其磁悬浮力的影响

通过对方形永磁体和方形辅助永磁体在液氮温度下对GdBCO超导体磁化后超导磁悬浮力的测量, 研究了两种组态中方形辅助永磁体对超导体的磁化方式对单畴GdBCO超导块材磁场分布及其磁悬浮力的影响. 结果发现, 方形辅助永磁体的下表面和超导体上表面保持在同一个水平面上, 磁化进程中方形辅助永磁体在GdBCO超导体上表面水平面内沿直径方向的位置x从–15 mm增加到+15 mm时, 超导磁悬浮力大小与超导体的磁化方式有着密切关系(以Z=0.1 mm为例): 1) 当方形辅助永磁体N极垂直向上且场冷后去掉辅助永磁体时, 超导体最大磁悬浮力先从16.7 N增大到23.1 N, 再减小到16.6 N; 2) 当方形辅助永磁体N极垂直向下且场冷后去掉辅助永磁体时, 超导体最大磁悬浮力先从17.7 N减小到7 N, 再增加到17.6 N; 3) 两种组态中最大磁悬浮力不相等, 而且与零场冷下的最大磁悬浮力(17.1 N)也不同. 这些结果说明: 只有通过科学合理地设计超导体和永磁体的组合方式, 才能获得较高的磁场强度, 有效地提高超导体的磁悬浮力特性, 该结果对促进超导体的应用具有重要的指导意义. 关键词： 单畴GdBCO 永磁体 捕获磁场 磁悬浮力     

Properties of static fluid cylinders and plane layers in general relativity

Exact solutions of field equations representing static perfect fluid cylinders and plane layers, with possible inclusion of electromagnetic or scalar field, are constructed and discussed. For the case of cylindrical symmetry, conditions at a regular axis are formulated and examples of regular solutions are presented. For planar and pseudoplanar configurations some limitations are obtained concerning existence of mirror symmetry in the thickness direction. These limitations make such symmetry rather unprobable, thus giving evidence that realistic models for equilibrium disklike configurations should be nonstatic (rotating). A configuration described by Teixeira, Wolk, and Som, possessing planar plus mirror symmetry (the case of disordered radiation), is shown to be unphysical.     

Hall Effects on Magnetic Relaxation

A generalized vorticity is introduced whose self-linkage (the hybrid helicity) and flux are invariants of ideal incompressible magnetohydrodynamics (MHD) when the Hall term is included. A model of magnetofluid relaxation is constructed for Hall magnetohydrodynamics by assuming that the energy seeks the minimum value compatible with constrained values of magnetic helicity, hybrid helicity, axial magnetic flux, and fluid vorticity flux. As a result of the coupling of magnetic field to fluid vorticity in the generalized vorticity, it is found that the relaxed magnetic-field configuration need not be force free. The presence of a nonvanishing fluid vorticity is shown to be necessary for the existence of relaxed magnetic-field configurations that confine a finite plasma pressure. The study has potential relevance to the dynamics and morphology of space and cosmic plasmas, as well as to pressure confinement and current drive in fusion plasmas.     

磁场强度对霍尔推力器放电特性影响的实验研究

为探索霍尔推力器通道内优化磁场的标准,本文研究了磁场强度对其放电特性的影响规律.通过在保持磁场形貌不变（“聚焦”形）下改变磁场强度的大小,使用朗缪尔探针、光谱仪等测量手段分析了工作于不同磁安特性曲线段的推力器放电特性.研究表明：当磁场强度小于优化值时,电子横越磁场的传导以近壁传导机制为主;反之,当磁场强度大于优化值时,放电电流反常变化,而现有的电子输运传导机制不能解释这种现象. 关键词： 霍尔推力器 磁场强度 放电特性     

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.     

The interior solution of axially symmetric,stationary and rigidly rotating dust configurations

It is shown that the interior solution of axially symmetric, stationary and rigidly rotating dust configurations is completely determined by the mass density along the axis of rotation. The particularly interesting case of a mass density, which is cylindrical symmetric in the interior of the dust configuration, is presented. Among other things, this proves the non-existence of homogeneous dust configurations.     

等离子体融断开关磁场Hall渗透机制的模拟研究

 利用自行研制的2-1/2维全电磁柱坐标粒子模拟程序对等离子体融断开关磁场渗透机制进行了模拟研究。模拟结果表明在磁场Hall渗透机制特征长度远远小于等离子体离子的无碰撞趋肤深度的条件下,等离子体内部磁场渗透过程主要由电子流体运动的Hall项来控制。对于等离子体空间分布存在较大的密度梯度的物理问题,必须考虑二维空间特性对磁场渗透速度的影响。在磁场已渗透经过的等离子体区域中,等离子体呈现非电中性,离子受静电场的作用会加速运动到达阴极,最终形成真空鞘层。     

Experimental and numerical investigation of a Hall thruster with a chamfered channel wall

A discharge channel with a chamfered wall not only has application in the design of modern Hall thrusters, but also exists where the channel wall is eroded, and so is a common status for these units. In this paper, the laws and mechanisms that govern the effect of the chamfered wall on the performance of a Hall thruster are investigated. By applying both experimental measurement and particle-in-cell simulation, it is determined that there is a moderate chamfer angle that can further improve the optimal performance obtained with a straight channel. This is because the chamfering of the wall near the channel exit can enhance ion acceleration and effectively reduce ion recombination on the wall, which is favorable to the promotion of the thrust and efficiency. However, the chamfer angle should not be too large; otherwise, both the density of the propellant gas and the distribution of the plasma potential in the channel are influenced, which is undesirable for efficient propellant utilization and beam concentration. Therefore, it is suggested that the chamfer shape of the channel wall is an important factor that must be carefully considered in the design of Hall thrusters.     

辅助永磁体厚度对单畴GdBCO超导体捕获磁场分布及其磁悬浮力的影响

研究了两种磁悬浮系统组态中圆台形辅助永磁体厚度对高温超导体捕获磁场和超导磁悬浮力的影响。结果表明,圆台形辅助永磁体的下表面和GdBCO超导体上表面同处在一个水平面上,磁化用圆台形辅助永磁体的厚度H从5 mm增加到45 mm时,超导体捕获磁场和磁悬浮力与圆台形辅助永磁体的厚度直接相关。（1）当圆台形辅助永磁体的北极垂直向上且用液氮冷却后移除辅助永磁体时,最大磁悬浮力从21.8 N增大到26.5 N,再减小到22.9 N;（2）当圆台形辅助永磁体的北极垂直向下且用液氮冷却后移除辅助永磁体时,最大磁悬浮力从20.5 N减小到11.9 N ,再增加到20.4 N;（3）两种磁悬浮系统组态中最大磁悬浮力不一致,与零场冷情况下的最大磁悬浮力14.6 N也不同。在超导磁悬浮应用系统设计中,只有科学选择辅助永磁体形状和尺寸,合理设计组合方式,才能获得较强的磁场强度,提高超导磁悬浮力特性,该结果对促进高温超导体的实际应用具有重要的指导作用。