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)     

使用不同工质的会切磁场等离子体推力器

会切磁场等离子体推力器是一种利用磁镜约束等离子体产生推力的新型推力器,具有寿命长、推力大范围连续可调等优点,在无拖曳控制领域具有较大的应用前景.分别采用Xe,Kr和Ar三种不同工质,开展了会切磁场等离子体推力器实验.首先,对所用的推力器进行了简要的原理和设计介绍;然后,对三种工质的点火电压分别进行了测试,发现Xe是最容易点火成功的,Kr和Ar点火难度较大.在阳极电流、推力、效率和比冲等性能方面,三种工质在同等条件下也存在明显的区别.分析发现,三者的工质利用率高低导致了性能上的差别,通过提升通流密度能够大幅提升Kr和Ar的工质利用率.在羽流结构方面,法拉第测量结果表明三者都存在明显的空心羽流,且离子电流密度峰值出现的角度随着原子量的减小而逐渐减小.     

霍尔推力器磁场位形及其优化的数值研究

基于麦克斯韦方程,在轴对称假设下建立了霍尔推力器磁场的数学模型.用有限差分方法对模型进行了离散.给出了数值求解模型的迭代法.通过对模型的数值求解,得到了相应的数值结果.通过对所得数值结果的分析,研究了磁场线圈电流变化对霍尔推力器磁场位形的影响.通过调整磁场线圈电流的大小找到了理想磁场位形.研究表明,对于理想磁场位形,内通道的磁镜比在3—3.5之间,外通道的磁镜比在0.4—0.9之间;增加磁场线圈的电流,出口的磁场强度随着增加,但不能增加磁镜比.通道内部的磁场强度几乎不随着磁场线圈电流的变化而变化. 关键词： 霍尔推力器 磁场位形 磁场线圈电流 磁镜比     

外磁场作用下的磁等离子体动力学过程仿真

磁等离子体动力学推力器是空间高功率电推进装置的典型代表,磁等离子体动力学过程是其核心工作机制.为深入理解外磁场对其工作特性的影响,本文采用粒子云(particle in cell,PIC)方法结合基于自相似准则的缩比模型,进行外加磁场作用下磁等离子体动力学推力器工作过程的建模仿真,通过与实验结果对比验证模型和方法的可靠性,并重点分析推力器点火启动过程的等离子特性参数分布,以及外磁场和阴极电流对推力器工作性能的影响.研究结果表明:阴阳极放电电弧构建是推力器启动和高效工作的关键步骤;外磁场强度较低工况不利于构建稳定放电电弧,等离子体束流集中于轴线附近,推力主要产生机制是自身场加速;外磁场强度较高时,阴阳极放电电弧稳定,推力产生主要机制是涡旋加速,推力、比冲随外磁场强度线性增大;推力器效率随阴极电流和外磁场强度增大而增大;放电电压随阴极电流增大而增大,但随外磁场强度的增大表现出先减小后增大的趋势.     

外磁场作用下的磁等离子体动力学过程仿真

磁等离子体动力学推力器是空间高功率电推进装置的典型代表,磁等离子体动力学过程是其核心工作机制.为深入理解外磁场对其工作特性的影响,本文采用粒子云(particle in cell,PIC)方法结合基于自相似准则的缩比模型,进行外加磁场作用下磁等离子体动力学推力器工作过程的建模仿真,通过与实验结果对比验证模型和方法的可靠性,并重点分析推力器点火启动过程的等离子特性参数分布,以及外磁场和阴极电流对推力器工作性能的影响.研究结果表明:阴阳极放电电弧构建是推力器启动和高效工作的关键步骤;外磁场强度较低工况不利于构建稳定放电电弧,等离子体束流集中于轴线附近,推力主要产生机制是自身场加速;外磁场强度较高时,阴阳极放电电弧稳定,推力产生主要机制是涡旋加速,推力、比冲随外磁场强度线性增大;推力器效率随阴极电流和外磁场强度增大而增大;放电电压随阴极电流增大而增大,但随外磁场强度的增大表现出先减小后增大的趋势.     

2 cm电子回旋共振离子推力器离子源中磁场对等离子体特性与壁面电流影响的数值模拟

电子回旋共振离子推力器(electron cyclotron resonance ion thruster,ECRIT)离子源内等离子体分布会影响束流引出,而磁场结构决定的ECR区与天线的相对位置共同影响了等离子体分布.在鞘层作用下,等离子体中的离子或电子被加速对壁面产生溅射,形成壁面离子或电子电流,造成壁面磨损和等离子体损失,因此研究壁面电流与等离子体特征十分重要.为此本文建立2 cm ECRIT的粒子PIC/MCC(particle-in-cell with Monte Carlo collision)仿真模型,数值模拟研究磁场结构对离子源内等离子体与壁面电流特性的影响.计算表明,当ECR区位于天线上游时,等离子体集中在天线上游和内外磁环间,栅极前离子密度最低,故离子源引出束流、磁环端面电流和天线壁面电流较低.ECR区位于天线下游时,天线和栅极上游附近的等离子体密度较高,故离子源引出束流、天线壁面电流和磁环端面电流较高.腔体壁面等离子体分布与电流受磁场影响最小.     

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.     

Measurements of the Drift Current Oscillations in Thrusters with Closed Electron Drift

An induction method used to measure the drift current in thrusters with anode layer (TAL) has been applied for measuring the integral distortion of the magnetic field in the channel of a low-power stationary plasma thruster (SPT). Experiments are described in which the integral level of magnetic field oscillations in the narrow channel of a thruster with closed electron drift was determined. Experimental data show that when a discharge is ignited in an SPT, the drift current completely demagnetizes the discharge gap (the ratio between the self-magnetic and external fields reaches 90%). The same effect has been observed in TALs. In thrusters of both types, the total discharge current is one and a half order of magnitude higher than that typical of the stationary discharge and the plasma glow is observed not only inside but also outside the discharge channel. Drift current oscillations have been measured under steady-state conditions. It has been shown, in particular, that when the oscillations are intense (in weak magnetic fields on the order of 100 G), the drift-current-induced distortion of the magnetic field may reach 33%. Under rated operating conditions (200 G), the distortion does not exceed 8%. Beyond optimal operating conditions, the type of oscillation in SPTs and TALs and their performances differ. For example, in SPTs, a critical magnetic field at which the “turbulent” regime sets in is absent. In general, the discharge current is weakly dependent on the magnetic field.     

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.     

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.     

Influence of channel length on discharge performance of anode layer Hall thruster studied by particle-in-cell simulation

Hall thruster has the advantages of simple structure, high specific impulse, high efficiency, and long service life, and so on. It is suitable for spacecraft attitude control, North and South position keeping, and other track tasks. The anode layer Hall thruster is a kind of Hall thruster. The thruster has a longer anode area and a relatively short discharge channel.In this paper, the effect of the channel length on the performance of the anode layer Hall thruster is simulated by the PIC simulation method. The simulation results show that the change of the channel length has significant effect on the plasma parameters, such as potential and plasma density and so on. The ionization region mainly concentrates at the hollow anode outlet position, and can gradually move toward the channel outlet as the channel length decreases. The collision between the ions and the wall increases with the channel length increasing. So the proper shortening of the channel length can increase the life of the thruster. Besides, the results show that there is a best choice of the channel length for obtaining the best performance. In this paper, thruster has the best performance under a channel length of 5 mm.     

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)     

离子推力器放电腔数值模拟

 为更好地理解放电腔内等离子体物理机制,对Kaufman型离子推力器放电腔进行了数值研究,其中初始电子采用粒子模拟的方法处理,二次电子和离子采用漂移-扩散流体近似描述。模拟结果与已有实验测量数据进行对比表明：所采用计算方法适用于放电腔内等离子体流动规律的数值研究;模拟得到的稳态下等离子体分布及变化规律与实验测量数据相吻合;磁场的设计对初始电子起到显著的约束作用,有效地提高了其与工质气体的电离碰撞几率;二次电子的精确描述还需在流体方程中耦合磁场效应。     

Particle-in-cell simulation for the effect of magnetic cusp on discharge characteristics in a cylindrical Hall thruster

The cylindrical Hall thruster has the good prospect of serving as a miniaturized electric propulsion device.A 2 D-3 V particle-in-cell plus Monte Carlo(PIC-MCC) method is used to study the effect of the magnetic cusp on discharge characteristics of a cylindrical Hall thruster.The simulation results show that the main ionization region and the main potential drop of the thruster are located at the upstream of the discharge channel.When the magnetic cusp moves toward the anode side,the main ionization region is compressed and weakened,moving upstream correspondingly.The ionization near the cusp is enhanced,and the interaction between the plasma and the wall increases.The simulation results suggest that the magnetic cusp should be located near the channel exit.     

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)     

The effects of a small transverse magnetic field upon acapacitively coupled RF discharge

A capacitively-coupled RF argon discharge at a pressure of 10 mTorr with a plate separation of 7.5 cm has been studied both experimentally and using a one-dimensional particle in cell simulation with Monte Carlo collisions. A magnetic field of 0 to 60 G is applied in the direction parallel to the capacitor plates. In the simulation it was found that as the magnetic field was increased such that the electron cyclotron orbit radius of the hot electrons became smaller than of the order of the discharge length, the electron heating in the bulk of the discharge increased. The dominant electron heating mechanism was observed to change from a stochastic sheath to a bulk ohmic electron heating mode, with a variation of field from a to 10 G. This was accompanied by a drop in the plasma density at small magnetic fields, which was also observed experimentally. At higher magnetic fields the plasma density was found to increase, A detailed discussion of the simulation results is presented drawing comparisons with the experimental results, with which there is good agreement, and a simple magnetohydrodynamic model for the bulk heating     

一种耦合外部电路的脉冲感应推力器磁流体力学数值仿真模型

为了深入研究脉冲感应推力器的工作原理,预测其推进性能,建立了一种耦合外部电路的磁流体力学模型,实现了对加速通道内等离子体二维流场结构演化过程及驱动电路放电过程的同步耦合求解.模拟计算所得美国MK-1推力器加速通道内的等离子体瞬态参数分布及推力器比冲、效率等性能参数均与实验数据一致;计算结果成功复现了推力器的工作物理图景.借助这一新模型,实现了对电路-等离子体双向耦合作用的定量分析,分析结果表明:耦合等离子体导致驱动电路等效电阻增大,电感减小;激励线圈与等离子体之间的互感随等离子体整体远离线圈表面而逐渐减小.     

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在非对称磁镜场微波ECR等离子体中引入了磁电加热系统,研究了电极环大小、轴向位置以及双环加热对离子温度的影响.结果表明,大小合适的电极环能有效提高离子的加热温度,且最优电极环尺寸主要取决于离子回旋半径.电极环轴向位置的选择主要与磁镜场位形有关,将电极环置于磁镜场中部的弱磁场位置时最有利于离子温度的提高.采用双电极环加热能进一步提高离子温度,并且其加热效果是单环加热的两倍.     

Ionization equilibrium of atoms in a strong magnetic field (the saha formula)

The effect of an external magnetic field on the ionization equilibrium of atoms in the nondegenerate nonrelativistic plasma is examined. When taken into account that the interaction of the magnetic moments of electrons with the magnetic field immediately changes their kinetic energy, which is incorrect, the degree of ionization of atoms will increase with increase in the magnetic field strength compared to the atomic concentration in the absence of a magnetic field at the same temperature. When taken into account that this energy changes in view of the Pauli principle and spontaneous minimization of the quantum system, the degree of ionization must decrease with increase in the external magnetic field strength, that is, a strong magnetic field suppresses ionization of atoms in the nonrelativistic plasma at a given temperature. Byelorussian State University; Brest State University. Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 7, pp. 36–39, July, 1999.     

Dependence of the transverse dynamics of the plasma electrons in the ion focus regime on the ratio of the radius of a relativistic electron beam to the radius of the ion channel

A study is made of the effect of the magnetic self-field of a relativistic electron beam propagating in the ion focus regime on the transverse dynamics of plasma electrons. For Gaussian radial profiles of the beam and the ion density in the channel, the maximum deviation of the plasma electrons from the axis of the beam-plasma system is determined as a function of the space-charge neutralization fraction, the ratio of the characteristic beam radius to the channel radius, and the net beam current.