Generalized Collisional Fluid Theory for Multi-Component, Multi-Temperature Plasma Using The Linearized Boltzmann Collision Operator for Scrape-Off Layer/Edge Applications
Madhusudan Raghunathan, Yannick Marandet, Hugo Bufferand, Guido Ciraolo, Philippe Ghendrih, Patrick Tamain, Eric Serre
备注：
Corrected some typos from the previous version. Accepted by Plasma Physics and Controlled Fusion (April 9,2021)
本文利用Grad方法作用于线性化玻尔兹曼碰撞算符，推导出多组分、多温度等离子体直至秩-2的最一般碰撞系数表达式。由此，碰撞系数被表示为温度比和质量比的纯系数级数与依赖于截面的Chapman-Cowling积分相乘之和。将这些碰撞系数与Zhdanov等人先前在13N矩多温度方案中获得的系数[Zhdanov V.M., Transport processes in multi-component plasma, Taylor and Francis (2002)]进行比较。首先直接比较系数的差异，然后比较粘性和摩擦力的一阶近似差异。对于13N矩多温度系数，发现在温度差较小时它们表现得相当相似，但当温度差较大时，无论是系数本身还是粘性和摩擦力值都表现出显著差异。此外，将所得系数与Zhdanov等人提供的21N矩单温度近似进行比较，发现其差异大于13N矩多温度系数，即使在温度接近相等的附近也存在显著差异，尤其是在粘性和摩擦力计算方面。
英文摘要：
Grad's method is used on the linearized Boltzmann collision operator to derive the most general expressions for the collision coefficients for a multi-component, multi-temperature plasma up to rank-2. In doing so, the collision coefficients then get expressed as series sum of pure coefficients of temperature and mass ratios multiplied by the cross-section dependent Chapman-Cowling integrals. These collisional coefficients are compared to previously obtained coefficients by Zhdanov et al [Zhdanov V.M., Transport processes in multi-component plasma, Taylor and Francis (2002)] for 13N-moment multi-temperature scheme. First, the differences in coefficients are compared directly, and then the differences in first approximation to viscosity and friction force are compared. For the 13N-moment multi-temperature coefficients, it is found that they behave reasonably similarly for small temperature differences, but display substantial differences in the coefficients when the temperature differences are high, both for the coefficients and for viscosity and friction force values. Furthermore, the obtained coefficients are compared to the 21N-moment single-temperature approximation provided by Zhdanov et al, and it is seen that the differences are higher than the 13N-moment multi-temperature coefficients, and have substantial differences even in the vicinity of equal temperatures, especially for the viscosity and friction force calculations.
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Institute of Plasma Physics, Hefei Institutes of Physical Science, Chinese Academy of Sciences（中国科学院合肥物质科学研究院等离子体物理研究所）；University of Science and Technology of China（中国科学技术大学）
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