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 (2002 Transport Processes in Multicomponent Plasma (London: Taylor and Francis)) 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.

Grad 方法用于线性化 Boltzmann 碰撞算子，以推导出最高 2 级的多组分、多温度等离子体的碰撞系数的最通用表达式。在这样做时，碰撞系数然后被表示为纯温度系数和质量比乘以截面相关的 Chapman-Cowling 积分的系列和。这些碰撞系数与 Zhdanov（2002年多组分等离子体传输过程（伦敦：泰勒和弗朗西斯））先前获得的系数进行了比较，以获得13 N矩多温度方案。首先直接比较系数的差异，然后比较粘度和摩擦力的一阶近似差异。对于 13 N-moment 多温度系数，发现它们在小温差下表现相当相似，但当温差高时，系数以及粘度和摩擦力值显示出显着差异。此外，将得到的系数与Zhdanov等人提供的21 N矩单温度近似值进行比较，可以看出差异高于13 N矩多温度系数，甚至在等温附近，特别是对于粘度和摩擦力计算。