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Grad's method is used on the linearized Boltzmann collision operator toderive the most general expressions for the collision coefficients for amulti-component, multi-temperature plasma up to rank-2. In doing so, thecollision coefficients then get expressed as series sum of pure coefficients oftemperature and mass ratios multiplied by the cross-section dependentChapman-Cowling integrals. These collisional coefficients are compared topreviously obtained coefficients by Zhdanov et al [Zhdanov V.M., Transportprocesses in multi-component plasma, Taylor and Francis (2002)] for 13N-momentmulti-temperature scheme. First, the differences in coefficients are compareddirectly, and then the differences in first approximation to viscosity andfriction force are compared. For the 13N-moment multi-temperature coefficients,it is found that they behave reasonably similarly for small temperaturedifferences, but display substantial differences in the coefficients when thetemperature differences are high, both for the coefficients and for viscosityand friction force values. Furthermore, the obtained coefficients are comparedto the 21N-moment single-temperature approximation provided by Zhdanov et al,and it is seen that the differences are higher than the 13N-momentmulti-temperature coefficients, and have substantial differences even in thevicinity of equal temperatures, especially for the viscosity and friction forcecalculations.

plasma physics and controlled fusion

Generalized Collisional Fluid Theory for Multi-Component,  Multi-Temperature Plasma Using The Linearized Boltzmann Collision Operator  for Scrape-Off Layer/Edge Applications