Exact collisional moments for plasma fluid theories
The velocityspace moments of the often troublesome nonlinear Landau collision operator are expressed exactly in terms of multiindex Hermitepolynomial moments of distribution functions. The collisional moments are shown to be generated by derivatives of two wellknown functions, namely, the RosenbluthMacDonaldJuddTrubnikov potentials for a Gaussian distribution. The resulting formula has a nonlinear dependency on the relative mean flow of the colliding species normalised to the rootmeansquare of the corresponding thermal velocities and a bilinear dependency on densities and higherorder 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 ChapmanEnskog method, as well as to derive collisional fluid equations that follow Grad's moment approach. As an illustrative example, we provide the collisional tenmoment equations with exact conservation laws for momentumand energytransfer rates.
 Authors:

^{[1]}
;
^{[1]}
;
^{[2]}
 Princeton Plasma Physics Lab. (PPPL), Princeton, NJ (United States)
 Princeton Univ., NJ (United States); Harvard Univ., Cambridge, MA (United States); HarvardSmithsonian Center for Astrophysics, Cambridge, MA (United States)
 Publication Date:
 Grant/Contract Number:
 AC0209CH11466; AC0209CH11466
 Type:
 Accepted Manuscript
 Journal Name:
 Physics of Plasmas
 Additional Journal Information:
 Journal Volume: 24; Journal Issue: 4; Journal ID: ISSN 1070664X
 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) (SC24)
 Contributing Orgs:
 Harvard John A. Paulson School of Engineering and Applied Sciences, Harvard University, Cambridge, Massachusetts 02138, USA; HarvardSmithsonian 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 velocityspace moments of the often troublesome nonlinear Landau collision operator are expressed exactly in terms of multiindex Hermitepolynomial moments of distribution functions. The collisional moments are shown to be generated by derivatives of two wellknown functions, namely, the RosenbluthMacDonaldJuddTrubnikov potentials for a Gaussian distribution. The resulting formula has a nonlinear dependency on the relative mean flow of the colliding species normalised to the rootmeansquare of the corresponding thermal velocities and a bilinear dependency on densities and higherorder 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 ChapmanEnskog method, as well as to derive collisional fluid equations that follow Grad's moment approach. As an illustrative example, we provide the collisional tenmoment equations with exact conservation laws for momentumand energytransfer rates.},
doi = {10.1063/1.4979992},
journal = {Physics of Plasmas},
number = 4,
volume = 24,
place = {United States},
year = {2017},
month = {4}
}