A Numerical Solution of the Boltzmann Equation
A Numerical Solution of the Boltzmann Equation
复制标题
玻尔兹曼方程的数值解
DOI：
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发表时间：
1983
期刊：
影响因子：
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通讯作者：
L. Pitchford
中科院分区：
文献类型：
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作者：
L. Pitchford
由电子中性散射截面描述的电子的微观行为与电子群的宏观行为之间的数学联系是通过玻尔兹曼方程，玻尔兹曼方程描述了相空间中电子能量分布函数（EEDF）的时间演化。玻尔兹曼方程可以被求解以产生EEDF，各种积分在群实验中产生可测量的参数（Huxley和Crompton，1974）。两个preceeding文件描述的数学基础（Skullerud，1981年）和分析的勒让德展开解决方案的玻尔兹曼方程以及渐近形式的解决方案（阿利斯，1981年）。对于应用，几乎总是需要数值求解玻尔兹曼方程。本文介绍了数值求解技术的一些最新工作。
The mathematical connection between the microscopic behavior of electrons as described by electron-neutral scattering cross sections and the macroscopic behavior of an electron swarm is through the Boltzmann equation which describes the time-evolution of the electron energy distribution function (EEDF) in phase space. The Boltzmann equation can be solved to yield the EEDF, various integrals over which yield the measurable parameters in a swarm experiment (Huxley and Crompton, 1974). Two preceeding papers describe the mathematical foundation (Skullerud, 1981) and analysis of the Legendre expansion solution of the Boltzmann equation as well as asymptotic forms of the solutions (Allis, 1981). For applications, it is almost always necessary to solve the Boltzmann equation numerically. This article describes some recent work in numerical solution techniques.