Fund Project:Project supported by the National Natural Science Foundation of China (Grant Nos. 51937009, 51807147) and the Natural Science Foundation of Shaanxi Province, China (Grant No. 2019JM-158)
Received Date:14 October 2020
Accepted Date:10 November 2020
Available Online:24 February 2021
Published Online:05 March 2021
Abstract:Vacuum arc is a special metal vapor discharge phenomenon, because its discharge medium totally comes from the evaporation and ionization of electrode materials. In the case of low current, the vacuum arc is completely composed of plasma jets emitted from discrete cathode spots on the cathode surface and the current carried by each spot depends on the cathode material. When the arc current exceeds a certain value, a certain number of cathode spot plasma jets will appear. Vacuum arcs play a very important role in some industrial applications such as vacuum circuit breakers, vacuum coatings and electric thrusters. As an important plasma control method, the external axial magnetic field (AMF) has an important influence on the macroscopic morphology and microscopic parameter distribution of the vacuum arc. Various studies of vacuum arc under AMF have been carried out and some progress has been made. However, the existing literature about the simulation research of vacuum arc is mostly concentrated in the case of large current, and less attention is paid to the case of small current. The reason is that the traditional methods, magneto-hydrodynamics or particle-in-cell, are limited by either accuracy or efficiency, and cannot be effectively applied to the low current vacuum arc plasma jet simulations. In this paper, we develop a fully three-dimensional hybrid plasma simulation algorithm to study the single cathode spot vacuum arc plasma jet under AMF. In this model, ions are modelled as particles while electrons are treated as massless fluid, and the self-generated magnetic field is also considered. To simplify the condition, the cathode spot in our model only exists as a plasma jet source, thus the detailed mechanism of producing plasmas is neglected. And the movement of the cathode spot is not considered either. The results show that the single cathode spot plasma jet diffuses into the interelectrode in a cone shape after leaving the cathode spot, and the ion density drops rapidly from cathode to anode. Under the simulation conditions in this paper (I ≤ 150 A), the self-generated magnetic field will not have a significant influence on the plasma jet itself in the case of low current. The external AMF has a compressive effect on the diffusion of the vacuum arc plasma jet. Under the AMF, the radial movement of the ions is suppressed, and the decrease of the ion radial velocity leads to a smaller diffusion radius of the jet. This compression effect of the AMF on the plasma jet is related to both the intensity of the external AMF and the magnitude of the arc current. In the case of a constant arc current magnitude, the compression effect gradually increases as the value of the AMF intensity gradually increases; in the case of a constant value of the external AMF, the compression effect gradually decreases as the current gradually becomes larger. Keywords:vacuum arc/ plasma jet/ hybrid model/ axial magnetic field
式中: φsh表示阳极鞘层电压; jth表示随机电子电流密度, 和电子温度相关; je表示电子电流密度. 3.仿真结果在本文中, 模拟区域大小为20 mm × 20 mm × 10 mm, 阴极和阳极分别位于z = 0和z = 10 mm处, 阴极斑点被设置在阴极中心, 外施纵向磁场在整个仿真区域中均匀分布. 三维空间的离子数密度分布如图3所示. 电弧电流为30 A, 无外施纵向磁场(Bz = 0 mT). 从图3可以看到, 等离子体射流在离开阴极斑点后呈锥形扩散状, 离子数密度从阴极到阳极逐渐减小, 且射流中心的离子数密度大于射流边缘处的离子数密度. 对于单阴极斑点的等离子体射流来说, 由于电荷电流较小, 所以其自生磁场对等离子体射流的影响较弱. 所以等离子体射流的形状受离子初始喷射角的影响较大. 图 3 三维空间离子数密度分布 Figure3. The distribution of ion number density in 3D space.
由于在本文中只考虑了单个阴极斑点等离子体射流, 因此等离子体参数在x-z平面和y-z平面具有相同的对称分布, 因此在图4中仅展示了电流和自生磁场在x-z平面的分布. 在图4(a)中轴向电流的方向从阳极指向阴极, 由图3可知在等离子体射流从阴极向阳极运动的过程中, 作为电流载流体的等离子体横截面逐渐增大, 所以在图4(a)中可以观察到轴向电流密度从阴极到阳极逐渐减小. 值得注意的是, 等离子体射流电流密度分布可能与等离子体密度分布不同. 原因是等离子体密度分布主要和离子与电子的位置有关, 而电流密度的分布则主要受电子的漂移速度影响. 在真空电弧中, 由于电中性条件, 电子和离子的密度相同, 但是由于离子电流只占总电流的10%[23], 因此从(8)式中可以计算得到电子的漂移速度约为离子的11倍. 图 4 (a) 轴向电流密度分布; (b)自生磁感应强度分布 I = 30 A, Bz = 0 mT Figure4. (a) The distribution of axial current density; (b) the distribution of self-generated azimuthal magnetic field I = 30 A, Bz = 0 mT
图6展示了电弧电流为30 A时, 不同外施纵向磁场强度下轴线上(x = y = 0)从阴极到阳极的离子数密度变化. 从图6可以看到, 不同外施纵向磁场情况下, 离子数密度的最大值相同且均出现在阴极表面, 然后从阴极到阳极逐渐降低. 同时与图5相对应, 施加纵向磁场后, 离子径向扩散减少导致等离子体被压缩, 使得轴线上离子数密度升高. 并且外施纵向磁场越大, 轴线上离子数密度越高. 在阴极斑点附近(z = 0—0.5 mm), 离子数密度的变化趋势受纵向磁场的影响不明显. 图 6 不同外施纵磁条件下轴线上离子数密度变化 Figure6. Ion number density distributions along the axis under different external AMFs.
图7展示了电弧电流为30 A时, 外施纵向磁场分别为0 mT和50 mT时, 离子沿x正方向的速度在x-z平面的相空间分布. 从图中的粒子分布可以看到, 在外施纵向磁场的作用下单阴极斑点等离子体射流沿径向的扩散减少, 说明外施纵向磁场对等离子体射流的扩散起到了很强的束缚作用, 这一现象和图5中的离子数密度分布相对应. 同时观察离子沿x方向的速度分布可以看出, 在外施纵向磁场的作用下, 离子沿径向速度的绝对值也因受到限制而变小. 图 7 不同外施磁场条件下离子沿x方向速度在x-z平面的相空间分布 Figure7. Phase diagram of ion velocity along x-direction in x-z plane under different external AMFs.
图8展示了外施纵向磁场为75 mT时不同电弧电流大小 (30, 60, 90, 120 A)下离子数密度在x-z平面的分布. 从图中可以看到, 当外施纵向磁场强度不变时, 随着电弧电流的逐渐增大, 等离子体射流的形状逐渐从圆柱形变成锥形, 离子在径向上的扩散逐渐增多. 这说明对于单阴极斑点等离子体射流来说, 增大电弧电流可以抑制外施纵向磁场对于等离子体射流的压缩效应. 图 8 在Bz = 75 mT时不同电弧电流条件下离子数密度分布 (a) I = 30 A; (b) I = 60 A; (c) I = 90 A; (d) I = 120 A Figure8. Ion number density distributions with different arc currents at Bz = 75 mT: (a) I = 30 A; (b) I = 60 A; (c) I = 90 A; (d) I = 120 A.
可以用轴线上阳极处离子密度和阴极处离子密度的比值来衡量外施纵向磁场对等离子体射流的压缩效应. 不同情况下阳极处离子数密度与阴极处离子数密度的比值如图9所示. 当无外施纵向磁场时, 等离子体射流的扩散不受影响, 不同电弧电流所对应的比值几乎相等. 在同等电弧电流情况下, 随着纵向磁场强度的增加, 轴线上阳极处离子数密度与阴极处离子数密度的比值也随之变大. 由于电弧电流相同时阴极处离子数密度一致(图6), 这说明阳极处离子数密度随着外施纵向磁场的增大而逐渐升高. 由此可知纵向磁场对等离子体射流的压缩效应会随着纵向磁场强度的增加而越来越强. 在同等外施纵向磁场情况下, 随着电弧电流的逐渐增大, 比值随之变小. 这说明电弧电流的升高会抑制纵向磁场对等离子体射流的压缩效应. 图 9 轴线上阳极处离子数密度与阴极处离子数密度的比值 Figure9. The ratios of the ion number density at the anode to that at the cathode on the axis.