2017
1.
Pfefferlé, D; Hirvijoki, E; Lingam, M
Exact collisional moments for plasma fluid theories Journal Article
In: Physics of Plasmas, vol. 24, no. 4, pp. 042118, 2017.
Abstract | Links | BibTeX | Tags: chapman-enskog, collisional moments, collisions, fluid theory, hermite polynomials, non-linear resistivity
@article{pfefferle-exact,
title = {Exact collisional moments for plasma fluid theories},
author = {D Pfefferl\'{e} and E Hirvijoki and M Lingam},
doi = {10.1063/1.4979992},
year = {2017},
date = {2017-04-20},
journal = {Physics of Plasmas},
volume = {24},
number = {4},
pages = {042118},
abstract = {The velocity-space moments of the often troublesome nonlinear Landau collision operator are expressed exactly in terms of multi-index Hermite-polynomial moments of distribution functions. The collisional moments are shown to be generated by derivatives of two well-known functions, namely, the Rosenbluth-MacDonald-Judd-Trubnikov potentials for a Gaussian distribution. The resulting formula has a nonlinear dependency on the relative mean flow of the colliding species normalised to the root-mean-square of the corresponding thermal velocities and a bilinear dependency on densities and higher-order velocity moments of the distribution functions, with no restriction on temperature, flow, or mass ratio of the species. The result can be applied to both the classic transport theory of plasmas that relies on the Chapman-Enskog method, as well as to derive collisional fluid equations that follow Grad's moment approach. As an illustrative example, we provide the collisional ten-moment equations with exact conservation laws for momentum- and energy-transfer rates.},
keywords = {chapman-enskog, collisional moments, collisions, fluid theory, hermite polynomials, non-linear resistivity},
pubstate = {published},
tppubtype = {article}
}
The velocity-space moments of the often troublesome nonlinear Landau collision operator are expressed exactly in terms of multi-index Hermite-polynomial moments of distribution functions. The collisional moments are shown to be generated by derivatives of two well-known functions, namely, the Rosenbluth-MacDonald-Judd-Trubnikov potentials for a Gaussian distribution. The resulting formula has a nonlinear dependency on the relative mean flow of the colliding species normalised to the root-mean-square of the corresponding thermal velocities and a bilinear dependency on densities and higher-order velocity moments of the distribution functions, with no restriction on temperature, flow, or mass ratio of the species. The result can be applied to both the classic transport theory of plasmas that relies on the Chapman-Enskog method, as well as to derive collisional fluid equations that follow Grad's moment approach. As an illustrative example, we provide the collisional ten-moment equations with exact conservation laws for momentum- and energy-transfer rates.