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

TL;DR

This paper derives a comprehensive set of collision coefficients for multi-component, multi-temperature plasmas using Grad's method on the linearized Boltzmann operator, highlighting differences from previous models especially at high temperature disparities.

Contribution

It introduces a generalized formulation of collision coefficients for multi-temperature plasmas using the linearized Boltzmann operator, extending previous models and comparing their accuracy.

Findings

Coefficients behave similarly at small temperature differences.

Significant differences appear at high temperature disparities.

New coefficients show improved accuracy over previous models.

Abstract

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.