2017
3.
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.
2.
Lingam, M; Hirvijoki, E; Pfefferlé, D; Comisso, L; Bhattacharjee, A
Nonlinear resistivity for magnetohydrodynamical models Journal Article
In: Physics of Plasmas, vol. 24, no. 4, pp. 042120, 2017.
Abstract | Links | BibTeX | Tags: collisional moments, collisions, fluid theory, hermite polynomials, non-linear resistivity
@article{lingam-nonlinear,
title = {Nonlinear resistivity for magnetohydrodynamical models},
author = {M Lingam and E Hirvijoki and D Pfefferl\'{e} and L Comisso and A Bhattacharjee},
doi = {10.1063/1.4980838},
year = {2017},
date = {2017-04-20},
journal = {Physics of Plasmas},
volume = {24},
number = {4},
pages = {042120},
abstract = {A new formulation of the plasma resistivity that stems from the collisional momentum-transfer rate between electrons and ions is presented. The resistivity computed herein is shown to depend not only on the temperature and density but also on all other polynomial velocity-space moments of the distribution function, such as the pressure tensor and heat flux vector. The full expression for the collisional momentum-transfer rate is determined and is used to formulate the nonlinear anisotropic resistivity. The new formalism recovers the Spitzer resistivity, as well as the concept of thermal force if the heat flux is assumed to be proportional to a temperature gradient. Furthermore, if the pressure tensor is related to viscous stress, the latter enters the expression for the resistivity. The relative importance of the nonlinear term(s) with respect to the well-established electron inertia and Hall terms is also examined. The subtle implications of the nonlinear resistivity, and its dependence on the fluid variables, are discussed in the context of magnetized plasma environments and phenomena such as magnetic reconnection.},
keywords = {collisional moments, collisions, fluid theory, hermite polynomials, non-linear resistivity},
pubstate = {published},
tppubtype = {article}
}
A new formulation of the plasma resistivity that stems from the collisional momentum-transfer rate between electrons and ions is presented. The resistivity computed herein is shown to depend not only on the temperature and density but also on all other polynomial velocity-space moments of the distribution function, such as the pressure tensor and heat flux vector. The full expression for the collisional momentum-transfer rate is determined and is used to formulate the nonlinear anisotropic resistivity. The new formalism recovers the Spitzer resistivity, as well as the concept of thermal force if the heat flux is assumed to be proportional to a temperature gradient. Furthermore, if the pressure tensor is related to viscous stress, the latter enters the expression for the resistivity. The relative importance of the nonlinear term(s) with respect to the well-established electron inertia and Hall terms is also examined. The subtle implications of the nonlinear resistivity, and its dependence on the fluid variables, are discussed in the context of magnetized plasma environments and phenomena such as magnetic reconnection.
2016
1.
Hirvijoki, E; Lingam, M; Pfefferlé, D
Fluid moments of the nonlinear Landau collision operator Journal Article
In: Physics of Plasmas, vol. 23, no. 8, pp. 080701, 2016.
Abstract | Links | BibTeX | Tags: collisional moments, collisions, fluid theory, hermite polynomials
@article{hirvijoki-2016,
title = {Fluid moments of the nonlinear Landau collision operator},
author = {E Hirvijoki and M Lingam and D Pfefferl\'{e}},
url = {http://dx.doi.org/10.1063/1.4960669},
doi = {10.1063/1.4960669},
year = {2016},
date = {2016-08-09},
journal = {Physics of Plasmas},
volume = {23},
number = {8},
pages = {080701},
abstract = {An important problem in plasma physics is the lack of an accurate and complete description of Coulomb collisions in associated fluid models. To shed light on the problem, this Letter introduces an integral identity involving the multivariate Hermite tensor polynomials and presents a method for computing exact expressions for the fluid moments of the nonlinear Landau collision operator. The proposed methodology provides a systematic and rigorous means of extending the validity of fluid models that have an underlying inverse-square force particle dynamics to arbitrary collisionality and flow.},
keywords = {collisional moments, collisions, fluid theory, hermite polynomials},
pubstate = {published},
tppubtype = {article}
}
An important problem in plasma physics is the lack of an accurate and complete description of Coulomb collisions in associated fluid models. To shed light on the problem, this Letter introduces an integral identity involving the multivariate Hermite tensor polynomials and presents a method for computing exact expressions for the fluid moments of the nonlinear Landau collision operator. The proposed methodology provides a systematic and rigorous means of extending the validity of fluid models that have an underlying inverse-square force particle dynamics to arbitrary collisionality and flow.