Lawrence Livermore National Laboratory, Livermore, California 94550, USA.
Departament de Matematiques, Universitat Autònoma de Barcelona, 08193 Bellaterra-Barcelona, Spain.
Phys Rev E. 2018 Jan;97(1-1):013205. doi: 10.1103/PhysRevE.97.013205.
In this work, we elucidate the mathematical structure of the integral that arises when computing the electron-ion temperature equilibration time for a homogeneous weakly coupled plasma from the Lenard-Balescu equation. With some minor approximations, we derive an analytic formula, requiring no input Coulomb logarithm, for the equilibration rate that is valid for moderate electron-ion temperature ratios and arbitrary electron degeneracy. For large temperature ratios, we derive the necessary correction to account for the coupled-mode effect, which can be evaluated very efficiently using ordinary Gaussian quadrature.
在这项工作中，我们阐明了在从 Lenard-Balescu 方程计算均匀弱耦合等离子体的电子-离子温度平衡时间时出现的积分的数学结构。通过一些微小的近似，我们推导出了一个解析公式，用于平衡率，该公式不需要输入库仑对数，对于中等电子-离子温度比和任意电子简并度都是有效的。对于大的温度比，我们推导出了考虑耦合模式效应的必要修正，这可以使用普通高斯求积法非常有效地进行评估。
