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Title: Exact collisional moments for plasma fluid theories

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.
Authors:
ORCiD logo [1] ; ORCiD logo [1] ;  [2]
  1. Princeton Plasma Physics Lab. (PPPL), Princeton, NJ (United States)
  2. Princeton Univ., NJ (United States); Harvard Univ., Cambridge, MA (United States); Harvard-Smithsonian Center for Astrophysics, Cambridge, MA (United States)
Publication Date:
Grant/Contract Number:
AC02-09CH11466; AC02-09-CH11466
Type:
Accepted Manuscript
Journal Name:
Physics of Plasmas
Additional Journal Information:
Journal Volume: 24; Journal Issue: 4; Journal ID: ISSN 1070-664X
Publisher:
American Institute of Physics (AIP)
Research Org:
Princeton Plasma Physics Lab. (PPPL), Princeton, NJ (United States)
Sponsoring Org:
USDOE Office of Science (SC), Fusion Energy Sciences (FES) (SC-24)
Contributing Orgs:
Harvard John A. Paulson School of Engineering and Applied Sciences, Harvard University, Cambridge, Massachusetts 02138, USA; Harvard-Smithsonian Center for Astrophysics, The Institute for Theory and Computation, Cambridge, Massachusetts 02138, USA
Country of Publication:
United States
Language:
English
Subject:
70 PLASMA PHYSICS AND FUSION TECHNOLOGY; Transport; Equation
OSTI Identifier:
1358661
Alternate Identifier(s):
OSTI ID: 1361817

Pfefferlé, D., Hirvijoki, E., and Lingam, M.. Exact collisional moments for plasma fluid theories. United States: N. p., Web. doi:10.1063/1.4979992.
Pfefferlé, D., Hirvijoki, E., & Lingam, M.. Exact collisional moments for plasma fluid theories. United States. doi:10.1063/1.4979992.
Pfefferlé, D., Hirvijoki, E., and Lingam, M.. 2017. "Exact collisional moments for plasma fluid theories". United States. doi:10.1063/1.4979992. https://www.osti.gov/servlets/purl/1358661.
@article{osti_1358661,
title = {Exact collisional moments for plasma fluid theories},
author = {Pfefferlé, D. and Hirvijoki, E. and Lingam, M.},
abstractNote = {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.},
doi = {10.1063/1.4979992},
journal = {Physics of Plasmas},
number = 4,
volume = 24,
place = {United States},
year = {2017},
month = {4}
}