Kaganovich I, Misina M, Berezhnoi SV, Gijbels R
Department of Chemical Engineering, University of Houston, 4800 Calhoun Rd., Houston, Texas 77204-4792, USA.
Phys Rev E Stat Phys Plasmas Fluids Relat Interdiscip Topics. 2000 Feb;61(2):1875-89. doi: 10.1103/physreve.61.1875.
The electron distribution function (EDF) in an electron cyclotron resonance (ECR) discharge is far from Maxwellian. The self-consistent simulation of ECR discharges requires a calculation of the EDF on every magnetic line for various ion density profiles. The straightforward self-consistent simulation of ECR discharges using the Monte Carlo technique for the EDF calculation is very computer time expensive, since the electron and ion time scales are very different. An electron Boltzmann kinetic equation averaged over the fast electron bouncing and pitch-angle scattering was derived in order to develop an effective and operative tool for the fast modeling (FM) of low-pressure ECR discharges. An analytical solution for the EDF in a loss cone was derived. To check the validity of the FM, one-dimensional (in coordinate) and two-dimensional (in velocity) Monte Carlo simulation codes were developed. The validity of the fast modeling method is proved by comparison with the Monte Carlo simulations. The complete system of equations for FM is presented and ready for use in a comprehensive study of ECR discharges. The variations of plasma density and of wall and sheath potentials are analyzed by solving a self-consistent set of equations for the EDF.
电子回旋共振（ECR）放电中的电子分布函数（EDF）远非麦克斯韦分布。ECR放电的自洽模拟需要针对各种离子密度分布计算每条磁力线上的EDF。使用蒙特卡罗技术计算EDF来直接对ECR放电进行自洽模拟非常耗费计算机时间，因为电子和离子的时间尺度差异很大。为了开发一种用于低压ECR放电快速建模（FM）的有效且实用的工具，推导了一个在快速电子弹跳和俯仰角散射上平均的电子玻尔兹曼动力学方程。推导了损失锥中EDF的解析解。为了检验FM的有效性，开发了一维（坐标）和二维（速度）蒙特卡罗模拟代码。通过与蒙特卡罗模拟比较证明了快速建模方法的有效性。给出了FM的完整方程组，可用于对ECR放电进行全面研究。通过求解一组关于EDF的自洽方程，分析了等离子体密度以及壁和鞘层电位的变化。
