Hydrodynamic description of an unmagnetized plasma with multiple ion species. I. General formulation
Abstract
A generalization of the Braginskii ion fluid description [S. I. Braginskii, Sov. Phys. JETP 6, 358 (1958)] to the case of an unmagnetized collisional plasma with multiple ion species is presented. An asymptotic expansion in the ion Knudsen number is used to derive the individual ion species continuity, as well as the total ion mass density, momentum, and energy evolution equations accurate through the second order. Expressions for the individual ion species drift velocities with respect to the center of mass reference frame, as well as for the total ion heat flux and viscosity, which are required to close the fluid equations, are evaluated in terms of the first-order corrections to the lowest order Maxwellian ion velocity distribution functions. A variational formulation for evaluating such corrections and its relation to the plasma entropy are presented. Employing trial functions for the corrections, written in terms of expansions in generalized Laguerre polynomials, and maximizing the resulting functionals produces two systems of linear equations (for “vector” and “tensor” portions of the corrections) for the expansion coefficients. A general matrix formulation of the linear systems as well as expressions for the resulting transport fluxes are presented in forms convenient for numerical implementation. The generalmore »
- Authors:
-
- Los Alamos National Lab. (LANL), Los Alamos, NM (United States). Computational Physics Division
- Publication Date:
- Research Org.:
- Los Alamos National Lab. (LANL), Los Alamos, NM (United States)
- Sponsoring Org.:
- USDOE National Nuclear Security Administration (NNSA)
- OSTI Identifier:
- 1304814
- Alternate Identifier(s):
- OSTI ID: 1242321
- Report Number(s):
- LA-UR-16-20406-01
Journal ID: ISSN 1070-664X; 1089-7674 (Electronic)
- Grant/Contract Number:
- AC52-06NA25396
- Resource Type:
- Accepted Manuscript
- Journal Name:
- Physics of Plasmas
- Additional Journal Information:
- Journal Volume: 23; Journal Issue: 3; Journal ID: ISSN 1070-664X
- Publisher:
- American Institute of Physics (AIP)
- Country of Publication:
- United States
- Language:
- English
- Subject:
- 70 PLASMA PHYSICS AND FUSION TECHNOLOGY
Citation Formats
Simakov, Andrei Nikolaevich, and Molvig, Kim. Hydrodynamic description of an unmagnetized plasma with multiple ion species. I. General formulation. United States: N. p., 2016.
Web. doi:10.1063/1.4943894.
Simakov, Andrei Nikolaevich, & Molvig, Kim. Hydrodynamic description of an unmagnetized plasma with multiple ion species. I. General formulation. United States. https://doi.org/10.1063/1.4943894
Simakov, Andrei Nikolaevich, and Molvig, Kim. Thu .
"Hydrodynamic description of an unmagnetized plasma with multiple ion species. I. General formulation". United States. https://doi.org/10.1063/1.4943894. https://www.osti.gov/servlets/purl/1304814.
@article{osti_1304814,
title = {Hydrodynamic description of an unmagnetized plasma with multiple ion species. I. General formulation},
author = {Simakov, Andrei Nikolaevich and Molvig, Kim},
abstractNote = {A generalization of the Braginskii ion fluid description [S. I. Braginskii, Sov. Phys. JETP 6, 358 (1958)] to the case of an unmagnetized collisional plasma with multiple ion species is presented. An asymptotic expansion in the ion Knudsen number is used to derive the individual ion species continuity, as well as the total ion mass density, momentum, and energy evolution equations accurate through the second order. Expressions for the individual ion species drift velocities with respect to the center of mass reference frame, as well as for the total ion heat flux and viscosity, which are required to close the fluid equations, are evaluated in terms of the first-order corrections to the lowest order Maxwellian ion velocity distribution functions. A variational formulation for evaluating such corrections and its relation to the plasma entropy are presented. Employing trial functions for the corrections, written in terms of expansions in generalized Laguerre polynomials, and maximizing the resulting functionals produces two systems of linear equations (for “vector” and “tensor” portions of the corrections) for the expansion coefficients. A general matrix formulation of the linear systems as well as expressions for the resulting transport fluxes are presented in forms convenient for numerical implementation. The general formulation is employed in the companion paper [A. N. Simakov and K. Molvig, Hydrodynamic description of an unmagnetized plasma with multiple ion species. II. Two and three ion species plasmas, submitted to Phys. Plasmas (2015)] to evaluate the individual ion drift velocities and the total ion heat flux and viscosity for specific cases of two and three ion species plasmas.},
doi = {10.1063/1.4943894},
journal = {Physics of Plasmas},
number = 3,
volume = 23,
place = {United States},
year = {Thu Mar 17 00:00:00 EDT 2016},
month = {Thu Mar 17 00:00:00 EDT 2016}
}
Web of Science
Works referenced in this record:
A drift ordered short mean free path description for magnetized plasma allowing strong spatial anisotropy
journal, January 2004
- Catto, Peter J.; Simakov, Andrei N.
- Physics of Plasmas, Vol. 11, Issue 1
Transport Processes in Multicomponent Plasma
journal, September 2002
- Zhdanov, V. M.
- Plasma Physics and Controlled Fusion, Vol. 44, Issue 10
The potential role of electric fields and plasma barodiffusion on the inertial confinement fusion database
journal, May 2011
- Amendt, Peter; Wilks, S. C.; Bellei, C.
- Physics of Plasmas, Vol. 18, Issue 5
Proton radiography of dynamic electric and magnetic fields in laser-produced high-energy-density plasmas
journal, May 2009
- Li, C. K.; Séguin, F. H.; Frenje, J. A.
- Physics of Plasmas, Vol. 16, Issue 5
Initial performance results of the OMEGA laser system
journal, January 1997
- Boehly, T. R.; Brown, D. L.; Craxton, R. S.
- Optics Communications, Vol. 133, Issue 1-6
On the kinetic theory of rarefied gases
journal, December 1949
- Grad, Harold
- Communications on Pure and Applied Mathematics, Vol. 2, Issue 4
Hydrodynamic description of an unmagnetized plasma with multiple ion species. II. Two and three ion species plasmas
journal, March 2016
- Simakov, Andrei N.; Molvig, Kim
- Physics of Plasmas, Vol. 23, Issue 3
A drift-ordered short mean-free path description of a partially ionized magnetized plasma
journal, February 2009
- Simakov, Andrei N.
- Plasma Physics and Controlled Fusion, Vol. 51, Issue 5
Classical transport equations for burning gas-metal plasmas
journal, September 2014
- Molvig, Kim; Simakov, Andrei N.; Vold, Erik L.
- Physics of Plasmas, Vol. 21, Issue 9
Self-generated magnetic fields in direct-drive implosion experiments
journal, June 2014
- Igumenshchev, I. V.; Zylstra, A. B.; Li, C. K.
- Physics of Plasmas, Vol. 21, Issue 6
Proton Radiography of Inertial Fusion Implosions
journal, February 2008
- Rygg, J. R.; Seguin, F. H.; Li, C. K.
- Science, Vol. 319, Issue 5867
Electron transport in a collisional plasma with multiple ion species
journal, February 2014
- Simakov, Andrei N.; Molvig, Kim
- Physics of Plasmas, Vol. 21, Issue 2
Monoenergetic-Proton-Radiography Measurements of Implosion Dynamics in Direct-Drive Inertial-Confinement Fusion
journal, June 2008
- Li, C. K.; Séguin, F. H.; Rygg, J. R.
- Physical Review Letters, Vol. 100, Issue 22
Ion Thermal Decoupling and Species Separation in Shock-Driven Implosions
journal, January 2015
- Rinderknecht, Hans G.; Rosenberg, M. J.; Li, C. K.
- Physical Review Letters, Vol. 114, Issue 2
Nonlinear Structure of the Diffusing Gas-Metal Interface in a Thermonuclear Plasma
journal, October 2014
- Molvig, Kim; Vold, Erik L.; Dodd, Evan S.
- Physical Review Letters, Vol. 113, Issue 14
Effects of Self-Generated Magnetic Field on Rayleigh–Taylor Instability
journal, January 2002
- Nishiguchi, Akio
- Japanese Journal of Applied Physics, Vol. 41, Issue Part 1, No. 1
Works referencing / citing this record:
Plasma kinetic effects on interfacial mix
journal, November 2016
- Yin, L.; Albright, B. J.; Taitano, W.
- Physics of Plasmas, Vol. 23, Issue 11
Self-similar solutions for multi-species plasma mixing by gradient driven transport
journal, March 2018
- Vold, E.; Kagan, G.; Simakov, A. N.
- Plasma Physics and Controlled Fusion, Vol. 60, Issue 5
Mass diffusion and liner material effect in a MagLIF fusion-like plasma
journal, August 2018
- García-Rubio, F.; Sanz, J.
- Physics of Plasmas, Vol. 25, Issue 8
Ion species stratification within strong shocks in two-ion plasmas
journal, March 2018
- Keenan, Brett D.; Simakov, Andrei N.; Taitano, William T.
- Physics of Plasmas, Vol. 25, Issue 3
Plasma ion stratification by weak planar shocks
journal, September 2017
- Simakov, Andrei N.; Keenan, Brett D.; Taitano, William T.
- Physics of Plasmas, Vol. 24, Issue 9
Multi-species plasma transport in 1D direct-drive ICF simulations
journal, March 2019
- Vold, E.; Rauenzahn, R.; Simakov, A. N.
- Physics of Plasmas, Vol. 26, Issue 3
Turbulent mixing and transition criteria of flows induced by hydrodynamic instabilities
journal, August 2019
- Zhou, Ye; Clark, Timothy T.; Clark, Daniel S.
- Physics of Plasmas, Vol. 26, Issue 8
Kinetic physics in ICF: present understanding and future directions
journal, April 2018
- Rinderknecht, Hans G.; Amendt, P. A.; Wilks, S. C.
- Plasma Physics and Controlled Fusion, Vol. 60, Issue 6
Hydrodynamic description of an unmagnetized plasma with multiple ion species. II. Two and three ion species plasmas
journal, March 2016
- Simakov, Andrei N.; Molvig, Kim
- Physics of Plasmas, Vol. 23, Issue 3
Plasma transport in an Eulerian AMR code
journal, April 2017
- Vold, E. L.; Rauenzahn, R. M.; Aldrich, C. H.
- Physics of Plasmas, Vol. 24, Issue 4
Diffusion-driven fluid dynamics in ideal gases and plasmas
journal, June 2018
- Vold, E. L.; Yin, L.; Taitano, W.
- Physics of Plasmas, Vol. 25, Issue 6
Plasma kinetic effects on interfacial mix and burn rates in multispatial dimensions
journal, June 2019
- Yin, L.; Albright, B. J.; Vold, E. L.
- Physics of Plasmas, Vol. 26, Issue 6
Deciphering the Kinetic Structure of Multi-Ion Plasma Shocks
text, January 2017
- Keenan, Brett D.; Simakov, Andrei N.; Chacon, Luis
- arXiv
Ion Species Stratification Within Strong Shocks in Two-Ion Plasmas
text, January 2017
- Keenan, Brett D.; Simakov, Andrei N.; Taitano, William T.
- arXiv