Effects of reflection of electrons and negative ions on magnetized electronegative and collisional plasma sheath

Abstract

The effects of the reflection of electrons and negative ions in magnetized electronegative and collisional plasma sheath on the Bohm criterion and the sheath structure are numerically investigated. The Bohm criterion expression of the sheath with considering the reflection of electrons and negative ions is derived theoretically. The lower limit of ion Mach number versus parameters and the distribution curve of charged particle density in sheath are obtained by numerical simulation when Boltzmannian model and reflection model are applied to electrons and negative ions. The results show that the upper limit of ion Mach number is identical to that of Boltzmannian model, but their lower limit expressions are different. The lower limit of ion Mach number in the reflection model is also related to the wall potential, and with the increase of the wall potential, ion Mach number first increases and then remains unchanged after reaching the same value as that from Boltzmannian model, and the speeds of their reaching the maximum values are different due to the difference in sheath edge negative ion concentration and temperature. In both Boltzmannian and the reflection model, the lower limit of the ion Mach number decreases with the concentration of the negative ion at the sheath edge increasing and the negative ion temperature decreasing, but the maximum value is smaller in the reflection model. The lower limit of ion Mach number for each of the two models increases with sheath edge electric field increasing, but increases faster and the final value is larger in Boltzmannian model. The lower limit of ion Mach number for each of the two models decreases with the increase of collision parameter or magnetic field angle, but decreases faster in Boltzmannian model with the increase of collision parameter or magnetic field angle. The lower limits of ion Mach number in the two models tend to be the same with the increase of magnetic field angle. When the wall potential is small, the reflection of electrons and negative ions has a great influence on the sheath structure. When the wall potential is large, the reflection of electrons and negative ions have little effect on the density distribution of charged particles in the sheath.

Structure of collisional magnetized plasma sheath with non-extensive distribution of electrons

“…式 与电子满足麦克斯韦分布时的等离子体磁鞘的下 限条件 [12] 一致. 由Tsallis的非广延分布理论, 当 时, 所有的结果可以回到经典的麦克斯韦分 时这个减小的趋势更加明显, 这个结论与Hatami [14] 的研究结果相似.…”

“…q 为了更好地了解电子满足非广延分布情况下 的碰撞等离子体磁鞘的结构, 本文采用流体力学方 法和数值模拟模拟了具有非广延分布电子的碰撞 等离子体磁鞘模型, 研究对比了麦克斯韦分布 [12] 与非广延分布两种碰撞磁鞘的玻姆判据, 以及由参 [18] . 对 速 率 分 布函数积分, 可得电子的密度为 [14,15,18,19] n e = n e0…”

The structure of an electronegative magnetized plasma sheath with non-extensive electron distribution

“…The structure of the plasma sheath plays an important role in many processes such as plasma etching and material surface modification. Therefore, relevant theoretical and experimental research works are still a special topic of interest [1][2][3][4][5][6][7][8][9][10][11][12][13][14]. These works have studied many plasma sheath layers with different physical conditions, such as the collision between ions and neutral particles, ion temperature and applied magnetic field.…”

“…In these research works, it is assumed that both the electron and negative ion satisfy the Boltzmann distribution at low pressure [1][2][3][4][5][6][7][8][9][10][11][12][13][14]. In 2009, Ghim and Hershkowitz [4] proved that the negative ions follow the Boltzmann distribution through experiments.…”

“…Zhao et al [9] studied the influence of negative ions on the Bohm criterion of the non-collision plasma sheath and believed that the critical value of the ion Mach number would decrease with the increase of the charge carried by the negative ion. We also have done a lot of research on the electronegative magnetized plasma sheath [7,[10][11][12][13][14]. The main conclusion is that the magnetic field has great effects on the plasma sheath structure.…”