基于玻尔兹曼方程的不同密度等离子体电子弛豫相似性研究  

Research on Similarity of Electron Relaxation in Plasmas With Different Densities Based on Boltzmann Equation

作　　者：蔡新景[1] 王新新[2] 邹晓兵[2] 鲁志伟[1] CAI Xinjingl;WANG Xinxin;ZOU Xiaobing;LU Zhiwei(College of Electrical Engineering, Northeast Dianli University, Jilin 132012, Jilin Province, China;State Key Laboratory of Control and Simulation of Power Systems and Generation Equipments （Department of Electrical Engineering, Tsinghua University）, Haidian District, Beijing 100084, China)

机构地区：[1]东北电力大学电气工程学院,吉林省吉林市132012 [2]电力系统及发电设备控制与仿真国家实验室(清华大学电机系),北京市海淀区100084

出　　处：《中国电机工程学报》2018年第10期3109-3115,共7页Proceedings of the CSEE

摘　　要：了解等离子体的弛豫过程是低温等离子体应用领域所面临的共性关键科学问题。为了研究不同密度等离子体在交叉电磁场下弛豫特性，该文采用改进的多项近似法解玻尔兹曼方程计算电子的弛豫特性。对不同气体密度Reid模型气体进行电子弛豫特性计算，发现：1）x轴方向体漂移速度WBx、z轴方向体漂移速度坼k和扩散系数Dii均随着时间t呈衰减震荡变化，而电子平均能量s随着时间t呈单调变化；2）电子弛豫至少有三个典型的弛豫时间：电子回旋时间搔动量弛豫时间Ym和能量弛豫时间γe，且满足托〈γg〈γm〈γe）当施加的约化电场强度E／n0和约化磁感应强度B／n0相同时，不同密度气体的体漂移速度WBx和WBx、电子平均能量s、扩散系数Dii与气体密度的组合参量noDjj随无量纲时间n0t的弛豫过程完全相同。最后从无量纲化和物理意义两个方面对电子弛豫的相似性作了解释。从无量纲化上看，体漂移速度WBi、电子平均能量s、not、n0Dii均为不变量或组合不变量；从物理意义上看，碰撞频率v∞n0，n0t∞vt为无量纲时间，体漂移速度WBi∞E/n0，电子平均能量ε仅与约化电场和磁感应强度相关，扩散系数Dii∞1／n0。Research on the temporal relaxation of plasmas is of significance in the applications of low temperature plasmal In order to study the temporal relaxation of plasmas with different densities under the action of crossed electric and magnetic fields, electron relaxation properties were calculated based on multi-term approximation of the Boltzmarm equation. Firstly electron relaxation properties of Reid model gas with different densities were calculated. It is shown that： 1） bulk drift velocity WBx in the x-axis direction, bulk drift velocity WBx in the z-axis direction, diffusion coefficients Dii exhibit damped periodic decay as the time t increases, while relaxation of electron mean energy c is monotonic; 2） there is three distinct timescales： the electron gyration period yg, the momentum relaxation time γm and the energy relaxation time γc. And the timescales satisfy yg 〈 Ym 〈 Ye; 3） bulk drift velocity WBx, bulk drift velocity WBz, electron mean energy e, combination parameter n0Dii of plasmas with different densities as a function of dimensionless time not all show similarity laws. In the end the similarity laws of electron relaxation was explained from dimensionless approach and physical meaning. From the perspective of dimensionless approach, bulk drift velocity WBi, electron mean energy ε, combination parameter not and noOii are all invariants or combination invariants. From the perspective of physical meaning, collision frequency v is proportional to gas density no, so combination parameter not is a dimensionless time, bulk drift velocity WBi is proportional to reduced electric field E/no, electron mean energy ε only relates to reduced electric and magnetic field, diffusion coefficients Dii is inversely proportional to gas density no.

关 键 词：多项近似 玻尔兹曼方程 电子输运 电子弛豫 相似性 无量纲化参量 不变量 碰撞频率 

分 类 号：TM85[电气工程—高电压与绝缘技术]