Solving the Boltzmann equation to obtain electron transport coefficients and rate coefficients for fluid models
Solving the Boltzmann equation to obtain electron transport coefficients and rate coefficients for fluid models
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DOI：
10.1088/0963-0252/14/4/011
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发表时间：
2005-11-01
影响因子：
3.8
通讯作者：
Pitchford, LC
中科院分区：
文献类型：
--
作者：
Hagelaar, GJM;Pitchford, LC
气体放电的流体模型需要输运系数和速率系数的输入，取决于电子能量分布函数。这些系数通常通过求解电子玻尔兹曼方程（BE）从碰撞截面数据计算。在本文中，我们提出了一个新的用户友好的BE求解器，特别是为此目的，免费提供的名称BOLSIG+，这是更一般，更容易使用比大多数其他BE求解器。求解器提供了稳态的BE的电子在一个均匀的电场中，使用经典的两项扩展的解决方案，并能够占不同的增长模型，准静态和振荡场，电子中性碰撞和电子-电子碰撞。我们表明，我们使用的近似，BE采取的形式的对流扩散连续方程的非本地源项在能量空间。为了求解这个方程，我们使用了对流扩散问题中常用的指数格式。计算的电子传输系数和速率系数的定义，以确保最大的一致性与流体方程。我们讨论了如何在流体模型中最好地使用这些系数，并说明了一些基本参数和近似值的影响。
Fluid models of gas discharges require the input of transport coefficients and rate coefficients that depend on the electron energy distribution function. Such coefficients are usually calculated from collision cross-section data by solving the electron Boltzmann equation (BE). In this paper we present a new user-friendly BE solver developed especially for this purpose, freely available under the name BOLSIG+, which is more general and easier to use than most other BE solvers available. The solver provides steady-state solutions of the BE for electrons in a uniform electric field, using the classical two-term expansion, and is able to account for different growth models, quasi-stationary and oscillating fields, electron-neutral collisions and electron-electron collisions. We show that for the approximations we use, the BE takes the form of a convection-diffusion continuity-equation with a non-local source term in energy space. To solve this equation we use an exponential scheme commonly used for convection-diffusion problems. The calculated electron transport coefficients and rate coefficients are defined so as to ensure maximum consistency with the fluid equations. We discuss how these coefficients are best used in fluid models and illustrate the influence of some essential parameters and approximations.