The Effect of the Flow of Atoms Sputtered from the Anode on the Flow of Current in a Vacuum Arc

The paper deals with the problem on the effect of atoms sputtered from the anode on the flow of fast cathode ions in a vacuum discharge at relatively low (100 A/cm²) values of current density. The problem is solved using a model of instantaneous ionization and a model allowing for the finite ionization length. The calculations result in determining the boundary of the region of stable passage of current depending on the density of arc current, the density of the flow of sputtered atoms, and on their velocity. It is demonstrated that, in the studied range of currents, it is impractical to include the fast ion pressure in the equations of motion and balance for energy, because these ions hardly collide with one another during the time of their transit through the discharge gap. The calculation results enable one to determine the range of validity of the model of instantaneous ionization beyond which one must allow for the dynamics of the process of ionization of atoms in the anode region.     

Critical Conditions of a High-Current Vacuum Arc

A one-dimensional three-fluid (electrons, slow and fast ions) model of high-current vacuum arc is used to investigate the peculiar features of motion of fast cations and slow anions. The model enables one to calculate the distribution of the concentrations, velocities, and temperatures of the components with due regard for the boundary conditions at the anode and cathode boundaries of plasma. It is demonstrated that, in a three-component plasma, the fast and slow ions have limits restricting the maximum velocity of slow ions from above and the minimum velocity of fast ions from below. In a three-component plasma, these limiting velocities differ from the ion sound velocities of the respective components. The presence of the limiting velocity of slow ions results in the impossibility of their complete flow to the cathode, and the existence of the limiting velocity of fast ions restricts the range of existence of the quasistationary mode of current flow. The calculation results are given, which demonstrate the dependence of the limiting velocities on the parameters of the vacuum arc.     

Two-dimensional kinetic model of short high-current vacuum-arc discharge

A two-dimensional mathematical model of a short high-current vacuum-arc discharge is developed, according to which magnetized electrons move in a hydrodynamic regime and fast cathode ions propagate in a free flight regime in a two-dimensional electric field. The proposed model takes into account the distribution of ions with respect to their escape angles from the cathode plasma boundary. A method for calculation of the plasma density distribution in the interelectrode gap is proposed. Two-dimensional distributions of the plasma density, electric field, and discharge current density in an external magnetic field are calculated. It is shown that ion trajectories exhibit mutual intersections, partly return to the cathode, and partly rotate in the oppositely oriented electric field at the side boundary of plasma. A decrease in the applied magnetic field intensity leads to a decrease in the number of ion trajectories reaching the anode (ion starvation), which can result in the violation of a stationary current transfer.     

基于MHD的小间隙真空电弧仿真研究

真空开关电弧电流过零前的电弧等离子体状态对真空开关能否顺利开断具有十分重要的影响。本文在建立小间隙真空电弧磁流体动力学(MHD)模型的基础上,采用通用计算流体力学仿真软件对电弧电流过零前0.5 ms时的电弧等离子体的特性进行数值仿真研究。计算得到了真空电弧等离子体压力、等离子体密度、离子纵向速度、阳极表面纵向电流密度和电弧电压等的空间分布。仿真结果表明:从阴极到阳极,真空电弧等离子体压力和密度逐渐增大,而等离子体速度逐渐减小;阳极表面电流密度存在较大径向梯度,最大值低于形成阳极斑点的极限收缩电流,阳极仍不活跃。仿真得到的等离子体密度分布与高速摄像机拍摄得到的CMOS图像光强基本吻合,计算得到的电弧电压与测得的电弧电压是一致的,从而验证了本模型的可行性。     

A two-dimensional mathematical model of a short vacuum arc in external magnetic field: results of numerical calculations

The paper deals with the investigation of the impact made by two-dimensional effects on the process of passage of current in a short vacuum arc in an axial magnetic field. A two-fluid mathematical model is used, which is based on hydrodynamic and electrodynamic equations. The axial magnetic field B _z affects significantly the magnitude of two-dimensional effects: the two-dimensional effects increase with decreasing B _z . The simulation results demonstrate that the contraction of plasma density exceeds that of current density. The distribution of anode drop of potential on the anode surface is nonuniform; in the case of certain (critical) values of current, the anode drop goes to zero on the external boundary of plasma. The dependence of the critical current on B _z is determined. The distribution of current density on the starting plane is nonuniform with a maximum on the axis, and the ion trajectories are inclined to the discharge axis. The possibility is discussed of matching the solution in the plasma region of vacuum arc with that for cathode flames.     

Boundary Transparency of a Discharge in the Knudsen Regime

An integral characteristic of the balance, namely, the boundary transparency defined as the ratio of a flux of neutrals via the side surface of the discharge to their flux from the cathode, is treated in application to vacuum discharges with gas-active cathodes. This quantity is determined with due regard for the burn-out and angular distribution of the flux on cathode in the Knudsen regime of the motion of neutrals. Singularities of the behavior of concentration and hydrodynamic flow velocity under these conditions are revealed.     

A Two-Dimensional Mathematical Model of a Short Vacuum Arc in External Magnetic Field

A mathematical model of a short high-current vacuum arc is developed. The model involves equations of motion and continuity for electrons and ions, as well as electrodynamic equations. The boundary conditions are formulated on the cathode and anode boundaries of plasma and on the side surface of plasma. The model is based on the method of trajectories, in the case of which a set of partial equations can be reduced to a set of ordinary differential equations written for derivatives along ion trajectories. The model is used to determine the region of steady-state solutions and to calculate the distribution of the parameters of arc plasma in this region.     

Singularities of interaction between a cathode stream and anode vapors in a vacuum arc: Numerical simulation results

Numerical simulation is performed of the process of interaction of cathode and anode ions in a highcurrent vacuum arc with evaporating anode. The presence of the friction force between ion flows, as well as of the friction work, leads to heating and acceleration of slow anode ions and deceleration of fast cathode ions. The boundaries of stable passage of current are determined, associated with the presence of the limiting value of density of anode vapors     

Ion acceleration in a high-current cathode plasma jet expanding in vacuum

Ion acceleration in a high-current cathode plasma jet of a low-voltage vacuum spark discharge has been studied. It is established that an increase in the discharge current amplitude leads to a growth in both the density and velocity of the ion flux emitted from the discharge gap. The dependence of the ion velocity on the discharge current amplitude in the range below 10 kA is well described by a simple hydrodynamic model of the current-carrying jet with allowance for plasma compression by the intrinsic magnetic field of the discharge current. For discharge current amplitudes exceeding 10 kA, the ion velocity ceases to grow and exhibits a considerable scatter of values measured in different shots.     

A simple model for the interaction of a low-current vacuum arc with a copper cathode

Experimental and theoretical studies of the arc-cathode region have been made for several decades, but the task is not yet complete, despite many efforts and much progress. In this work, a numerical model describing the arc-cathode region is developed. The arc is treated as a steady-state phenomenon. The model is then applied to a vacuum arc discharge interacting with a Cu cathode at low current of 4–50 A. The model yields the temperature and electric field strength at the cathode surface, density of the current of the electrons emitted, total current density, cathode spot radius, different kinds of power densities in heating and cooling the cathode, and the plasma electron density. The comparison with experimental results shows good agreement. Published in Inzhenerno-Fizicheskii Zhurnal, Vol. 80, No. 6, pp. 63–72, November–December, 2007.     

Dynamics of plasma and ion flux in a vacuum neutron tube

Results of the numerical simulation of the formation of the ion beam in the accelerating gap of a vacuum neutron tube are presented. Calculations are performed with the KARAT code in a two-dimensional nonstationary formulation for plasma formed in arc discharge and inflowing into an accelerating gap with the given time dependences of parameters (density, expansion velocity). The small duration of the vacuum arc leads to a considerable change of parameters of inflowing plasma during the accelerating pulse. Two geometries are considered: the conventional and sectioned diode, in which the total voltage is divided between the anode, intermediate electrode, and cathode.     

Plasma flow crisis and the limiting electron temperature in a vacuum arc in axial magnetic field

The possibility of supersonic motion of cathode plasma in a low-current vacuum arc in an axial magnetic field has been studied. It is shown that an increase in the electron temperature unavoidably leads to a plasma flow crisis, whereby the plasma velocity decreases to the sound velocity. The dependence of the limiting length of a stationary flow on the magnetic field has been studied. The maximum possible electron temperature T _cr in the plasma is determined by the initial ion energy and can be estimated as T _cr ≈ 3T _m, where T _m is the maximum electron temperature in the cathode spot region.     

The Simulation of a Beam-Plasma Discharge with the Beam Current Exceeding the Limiting Vacuum Current

Results are given of simulation of the space-time dynamics of a beam-plasma discharge with the beam current exceeding the limiting vacuum current. It is found that the process of discharge development has three characteristic stages, namely, a stationary virtual cathode (VC), a progressively moving VC, and an ordinary beam-plasma discharge. It is further found that the ensemble of ions in the second stage is divided into two parts, namely, plasma ions and ions captured to collective acceleration by the moving VC.     

微阴极电弧推力器放电特性研究

相对于大型卫星, 微纳卫星具有模块化、发射灵活、可编队飞行等特点。微阴极电弧推力器 (μ-CAT) 是一种适用于微纳卫星的推进装置, 具有体积小、质量轻、功耗小等特点。本文分析了μ-CAT的工作原理, 对推力器结构进行了设计, 并利用高真空电推进实验平台, 完成了对推力器放电特性实验装置的搭建。在高真空条件下对μ-CAT进行了点火试验, 测试了推力器放电时的伏安特性曲线, 分析了单脉冲周期的电压电流变化规律。随后分别在有无外加磁场的条件下, 采用法拉第探针测量了μ-CAT等离子体离子电流空间分布情况, 实验结果表明磁场具有减小等离子体羽流发散角的作用。研究工作可为后续推力器放电参数优化设计和羽流测量工作提供理论指导。     

Electron emission in a flat cathode-curved anode system in the space-charge-limited current regime

The process of electron emission in a vacuum diode with curved cathode in the space-charge-limited current regime has been theoretically studied. The space charge density, electric field, and velocity field distributions in the interelectrode gap are determined by means of expansion with respect to a small parameter representing the ratio of the characteristic transverse and longitudinal scales. Based on these results, the current density distribution over the cathode surface is analytically described. The analytical results are compared to the data of numerical calculations available in the literature.     

The current column contraction and ion charge increase induced by the current build-up in a pulsed vacuum discharge

It is shown that three current build-up regimes may be realized in a pulsed vacuum discharge, depending on the relationship between the pulse duration τ and the characteristic times of the plasma flow (τ_L) and the cathode spot spreading (τ_S). For a rapid build-up (τ<τ_L), the cathode plasma jet exhibits the neck formation with high values of the plasma temperature and density. At a slow current increase (τ_L<τ<τ_S), the current column is subject to a uniform magnetic contraction, while at a very slow current growth rate (τ>τ_S), the contraction becomes insignificant. The first two cases give rise to additional nonequilibrium ionization in the current column, which leads to the ion charge increasing with the current. The third case is characterized by a “frozen” ion composition corresponding to the plasma parameters in the near-cathode region.     

磁控电弧离子镀阴极斑点特性的高速摄影研究

利用高速摄影技术，对磁控电弧离子镀中阴极斑点大小、寿命及运动轨迹进行了观测，获得了阴极斑点电流密度、运动速度随磁场、电弧电流及背景气体压力改变而变化的关系曲线。