## 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. doi: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. doi: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 = {2016},

month = {3}

}

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