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.
Turbulent MHD transport coefficients: an attempt at self-consistency