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# Mean force kinetic theory: A convergent kinetic theory for weakly and strongly coupled plasmas

## Abstract

A new closure of the BBGKY hierarchy is developed, which results in a convergent kinetic equation that provides a rigorous extension of plasma kinetic theory into the regime of strong Coulomb coupling. The approach is based on a single expansion parameter which enforces that the exact equilibrium limit is maintained at all orders. Because the expansion parameter does not explicitly depend on the range or the strength of the interaction potential, the resulting kinetic theory does not suffer from the typical divergences at short and long length scales encountered when applying the standard kinetic equations to Coulomb interactions. Here, the approach demonstrates that particles effectively interact via the potential of mean force and that the range of this force determines the size of the collision volume. When applied to a plasma, the collision operator is shown to be related to the effective potential theory [S. D. Baalrud and J. Daligault, Phys. Rev. Lett. 110, 235001 (2013)]. In addition to the collision operator, this systematic derivation reveals a second term that is related to the excess (nonideal) components of the pressure and internal energy in the hydrodynamic limit. The relationship between this and previous kinetic theories is discussed.

- Authors:

- Univ. of Iowa, Iowa City, IA (United States)
- 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 Laboratory Directed Research and Development (LDRD) Program

- OSTI Identifier:
- 1565899

- Alternate Identifier(s):
- OSTI ID: 1548581

- Report Number(s):
- LA-UR-19-22330

Journal ID: ISSN 1070-664X

- Grant/Contract Number:
- 89233218CNA000001

- Resource Type:
- Accepted Manuscript

- Journal Name:
- Physics of Plasmas

- Additional Journal Information:
- Journal Volume: 26; 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

### Citation Formats

```
Baalrud, Scott D., and Daligault, Jérôme Olivier. Mean force kinetic theory: A convergent kinetic theory for weakly and strongly coupled plasmas. United States: N. p., 2019.
Web. doi:10.1063/1.5095655.
```

```
Baalrud, Scott D., & Daligault, Jérôme Olivier. Mean force kinetic theory: A convergent kinetic theory for weakly and strongly coupled plasmas. United States. doi:10.1063/1.5095655.
```

```
Baalrud, Scott D., and Daligault, Jérôme Olivier. Thu .
"Mean force kinetic theory: A convergent kinetic theory for weakly and strongly coupled plasmas". United States. doi:10.1063/1.5095655.
```

```
@article{osti_1565899,
```

title = {Mean force kinetic theory: A convergent kinetic theory for weakly and strongly coupled plasmas},

author = {Baalrud, Scott D. and Daligault, Jérôme Olivier},

abstractNote = {A new closure of the BBGKY hierarchy is developed, which results in a convergent kinetic equation that provides a rigorous extension of plasma kinetic theory into the regime of strong Coulomb coupling. The approach is based on a single expansion parameter which enforces that the exact equilibrium limit is maintained at all orders. Because the expansion parameter does not explicitly depend on the range or the strength of the interaction potential, the resulting kinetic theory does not suffer from the typical divergences at short and long length scales encountered when applying the standard kinetic equations to Coulomb interactions. Here, the approach demonstrates that particles effectively interact via the potential of mean force and that the range of this force determines the size of the collision volume. When applied to a plasma, the collision operator is shown to be related to the effective potential theory [S. D. Baalrud and J. Daligault, Phys. Rev. Lett. 110, 235001 (2013)]. In addition to the collision operator, this systematic derivation reveals a second term that is related to the excess (nonideal) components of the pressure and internal energy in the hydrodynamic limit. The relationship between this and previous kinetic theories is discussed.},

doi = {10.1063/1.5095655},

journal = {Physics of Plasmas},

number = 8,

volume = 26,

place = {United States},

year = {2019},

month = {8}

}

*Citation information provided by*

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