Exact collisional moments for plasma fluid theories
Abstract
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:
 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:
 Research Org.:
 Princeton Plasma Physics Lab. (PPPL), Princeton, NJ (United States)
 Sponsoring Org.:
 USDOE Office of Science (SC), Fusion Energy Sciences (FES) (SC24)
 Contributing Org.:
 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
 OSTI Identifier:
 1358661
 Alternate Identifier(s):
 OSTI ID: 1361817
 Grant/Contract Number:
 AC0209CH11466; AC0209CH11466
 Resource Type:
 Journal Article: 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)
 Country of Publication:
 United States
 Language:
 English
 Subject:
 70 PLASMA PHYSICS AND FUSION TECHNOLOGY; Transport; Equation
Citation Formats
Pfefferlé, D., Hirvijoki, E., and Lingam, M. Exact collisional moments for plasma fluid theories. United States: N. p., 2017.
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. Sat .
"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 = {Sat Apr 01 00:00:00 EDT 2017},
month = {Sat Apr 01 00:00:00 EDT 2017}
}
Web of Science

A fluid treatment of the plasma presheath for collisionless and collisional plasmas
The presheath region of an unmagnetized plasma is treated using ion fluid equations in the collisional and collisionless regimes. Effects of neutral gasplasma interactions are included through source terms in the fluid equations. Ionion collisional effects are included through the closure conditions of the fluid equations. In the collisionless regime, the perpendicular ion temperature is assumed constant and independent of the parallel ion temperature. In the collisional limit, the parallel and perpendicular temperatures are assumed equal throughout the presheath. Profiles of ion density, flow velocity, parallel temperature, and energy flux obtained by integrating the fluid equations compare well to previouslymore » 
A multifluid stagnationflow plasma model with selfconsistent treatment of the collisional sheath
A twotemperature, multifluid model of a plasma in stagnation flow against a cooled, electrically biased surface is presented in this paper. The model couples bulk fluid motion, species diffusion and convection, electron and bulk energy equations, and net finiterate ionization with Poisson`s equation for the electric field in a generalized formulation. Application of the model to argon flow reveals important interactions between thermal, hydrodynamic, chemical and electrical boundary layers, with implications to currentlimiting regimes of arcjet operation. The analysis also examines the response of a planar, Langmuir probe in contact with a collisional, flowing plasma. Determinations of currentvoltage behavior comparemore » 
Implicit collisional threefluid simulation of the plasma erosion opening switch
The plasma erosion opening switch (PEOS) has been studied with the aid of the ANTHEM implicit simulation code. This switch consists of fill plasma injected into a transmission line. The plasma is ultimately removed by selfelectrical forces, permitting energy delivery to a load. Here, ANTHEM treats the ions and electrons of the fill plasma and the electrons emitted from the transmissionline cathode as three distinct Eulerian fluids  with electron inertia retained. This permits analysis of charge separation effects, and avoids the singularities that plague conventional MHD codes at low density. E and BETA fields are computed by the implicitmore »