# Collisional transport coefficients of dense high-temperature plasmas within the quantum Landau-Fokker-Planck framework

## Abstract

In this paper, we extend the long-established formulas for the transport coefficients of classical plasmas inside the dense plasma regime for temperatures and densities where the classical Landau equation breaks down but its quantum extension that includes quantum degeneracy effects is valid. To this end, the quantum Landau kinetic equation is solved by the Chapman-Enskog method. The mathematical derivation is done in full generality, i.e., for multicomponent systems and to all orders of the polynomials expansion used to approximate the distribution functions. We apply the general results to two important examples, the electron gas model and an electron-ion plasma model consisting of one type of ions of any charge. We discuss the combined effects of the Pauli exclusion principle, of the electron-electron, and of the electron-ion collisions on the transport coefficients and on the convergence of the Chapman-Enskog method. For the electron gas model, the effect of the Pauli exclusion principle on the transport coefficients rapidly becomes non-negligible outside the domain of validity of the classical Landau equation. For the electron-ion plasmas, the effect of the Pauli exclusion principle depends sensitively on the ion charge Z and varies non-monotonically with Θ. For instance, for ion charge Z = 1, the electrical conductivity is increased by up to ~30% compared to its classical value over the range of degeneracy parameters studied, the thermal conductivity is reduced by up to ~9%, and the shear viscosity coefficient is increased by up to ~13%. Finally, in the Lorentz gas ( $Z\to \infty $) limit, the electrical conductivity is reduced by up to ~14% compared to its classical value over the range of degeneracy parameters studied, the thermal conductivity is reduced by up to ~39%, and the shear viscosity coefficient is not affected.

- Authors:

- Los Alamos National Lab. (LANL), Los Alamos, NM (United States)

- Publication Date:

- Research Org.:
- Los Alamos National Lab. (LANL), Los Alamos, NM (United States)

- Sponsoring Org.:
- USDOE; LANL Laboratory Directed Research and Development (LDRD) Program

- OSTI Identifier:
- 1467341

- Alternate Identifier(s):
- OSTI ID: 1463382

- Report Number(s):
- LA-UR-18-23684

Journal ID: ISSN 1070-664X

- Grant/Contract Number:
- AC52-06NA25396

- Resource Type:
- Accepted Manuscript

- Journal Name:
- Physics of Plasmas

- Additional Journal Information:
- Journal Volume: 25; Journal Issue: 8; 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; electrical conductivity; stochastic processes; plasma dynamics; viscosity; thermal conductivity; electron gas

### Citation Formats

```
Daligault, Jérôme. Collisional transport coefficients of dense high-temperature plasmas within the quantum Landau-Fokker-Planck framework. United States: N. p., 2018.
Web. doi:10.1063/1.5045330.
```

```
Daligault, Jérôme. Collisional transport coefficients of dense high-temperature plasmas within the quantum Landau-Fokker-Planck framework. United States. doi:10.1063/1.5045330.
```

```
Daligault, Jérôme. Wed .
"Collisional transport coefficients of dense high-temperature plasmas within the quantum Landau-Fokker-Planck framework". United States. doi:10.1063/1.5045330. https://www.osti.gov/servlets/purl/1467341.
```

```
@article{osti_1467341,
```

title = {Collisional transport coefficients of dense high-temperature plasmas within the quantum Landau-Fokker-Planck framework},

author = {Daligault, Jérôme},

abstractNote = {In this paper, we extend the long-established formulas for the transport coefficients of classical plasmas inside the dense plasma regime for temperatures and densities where the classical Landau equation breaks down but its quantum extension that includes quantum degeneracy effects is valid. To this end, the quantum Landau kinetic equation is solved by the Chapman-Enskog method. The mathematical derivation is done in full generality, i.e., for multicomponent systems and to all orders of the polynomials expansion used to approximate the distribution functions. We apply the general results to two important examples, the electron gas model and an electron-ion plasma model consisting of one type of ions of any charge. We discuss the combined effects of the Pauli exclusion principle, of the electron-electron, and of the electron-ion collisions on the transport coefficients and on the convergence of the Chapman-Enskog method. For the electron gas model, the effect of the Pauli exclusion principle on the transport coefficients rapidly becomes non-negligible outside the domain of validity of the classical Landau equation. For the electron-ion plasmas, the effect of the Pauli exclusion principle depends sensitively on the ion charge Z and varies non-monotonically with Θ. For instance, for ion charge Z = 1, the electrical conductivity is increased by up to ~30% compared to its classical value over the range of degeneracy parameters studied, the thermal conductivity is reduced by up to ~9%, and the shear viscosity coefficient is increased by up to ~13%. Finally, in the Lorentz gas (Z→∞) limit, the electrical conductivity is reduced by up to ~14% compared to its classical value over the range of degeneracy parameters studied, the thermal conductivity is reduced by up to ~39%, and the shear viscosity coefficient is not affected.},

doi = {10.1063/1.5045330},

journal = {Physics of Plasmas},

number = 8,

volume = 25,

place = {United States},

year = {2018},

month = {8}

}

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