# Generalized fluid theory including non-Maxwellian kinetic effects

## Abstract

The results obtained by the plasma physics community for the validation and the prediction of turbulence and transport in magnetized plasmas come mainly from the use of very central processing unit (CPU)-consuming particle-in-cell or (gyro)kinetic codes which naturally include non-Maxwellian kinetic effects. To date, fluid codes are not considered to be relevant for the description of these kinetic effects. Here, after revisiting the limitations of the current fluid theory developed in the 19th century, we generalize the fluid theory including kinetic effects such as non-Maxwellian super-thermal tails with as few fluid equations as possible. The collisionless and collisional fluid closures from the nonlinear Landau Fokker–Planck collision operator are shown for an arbitrary collisionality. Indeed, the first fluid models associated with two examples of collisionless fluid closures are obtained by assuming an analytic non-Maxwellian distribution function. One of the main differences with the literature is our analytic representation of the distribution function in the velocity phase space with as few hidden variables as possible thanks to the use of non-orthogonal basis sets. These new non-Maxwellian fluid equations could initiate the next generation of fluid codes including kinetic effects and can be expanded to other scientific disciplines such as astrophysics, condensed mattermore »

- Authors:

- Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States)

- Publication Date:

- Research Org.:
- Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States)

- Sponsoring Org.:
- USDOE

- OSTI Identifier:
- 1376001

- Report Number(s):
- LLNL-JRNL-696825

Journal ID: ISSN 0022-3778; applab; PII: S0022377817000150

- Grant/Contract Number:
- AC52-07NA27344

- Resource Type:
- Journal Article: Accepted Manuscript

- Journal Name:
- Journal of Plasma Physics

- Additional Journal Information:
- Journal Volume: 83; Journal Issue: 02; Journal ID: ISSN 0022-3778

- Publisher:
- Cambridge University Press

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 42 ENGINEERING; 97 MATHEMATICS, COMPUTING, AND INFORMATION SCIENCE; 70 PLASMA PHYSICS AND FUSION; fusion plasma; magnetized plasmas; plasma confinement

### Citation Formats

```
Izacard, Olivier.
```*Generalized fluid theory including non-Maxwellian kinetic effects*. United States: N. p., 2017.
Web. doi:10.1017/S0022377817000150.

```
Izacard, Olivier.
```*Generalized fluid theory including non-Maxwellian kinetic effects*. United States. doi:10.1017/S0022377817000150.

```
Izacard, Olivier. Wed .
"Generalized fluid theory including non-Maxwellian kinetic effects". United States.
doi:10.1017/S0022377817000150. https://www.osti.gov/servlets/purl/1376001.
```

```
@article{osti_1376001,
```

title = {Generalized fluid theory including non-Maxwellian kinetic effects},

author = {Izacard, Olivier},

abstractNote = {The results obtained by the plasma physics community for the validation and the prediction of turbulence and transport in magnetized plasmas come mainly from the use of very central processing unit (CPU)-consuming particle-in-cell or (gyro)kinetic codes which naturally include non-Maxwellian kinetic effects. To date, fluid codes are not considered to be relevant for the description of these kinetic effects. Here, after revisiting the limitations of the current fluid theory developed in the 19th century, we generalize the fluid theory including kinetic effects such as non-Maxwellian super-thermal tails with as few fluid equations as possible. The collisionless and collisional fluid closures from the nonlinear Landau Fokker–Planck collision operator are shown for an arbitrary collisionality. Indeed, the first fluid models associated with two examples of collisionless fluid closures are obtained by assuming an analytic non-Maxwellian distribution function. One of the main differences with the literature is our analytic representation of the distribution function in the velocity phase space with as few hidden variables as possible thanks to the use of non-orthogonal basis sets. These new non-Maxwellian fluid equations could initiate the next generation of fluid codes including kinetic effects and can be expanded to other scientific disciplines such as astrophysics, condensed matter or hydrodynamics. As a validation test, we perform a numerical simulation based on a minimal reduced INMDF fluid model. The result of this test is the discovery of the origin of particle and heat diffusion. The diffusion is due to the competition between a growing INMDF on short time scales due to spatial gradients and the thermalization on longer time scales. Here, the results shown here could provide the insights to break some of the unsolved puzzles of turbulence.},

doi = {10.1017/S0022377817000150},

journal = {Journal of Plasma Physics},

number = 02,

volume = 83,

place = {United States},

year = {Wed Mar 29 00:00:00 EDT 2017},

month = {Wed Mar 29 00:00:00 EDT 2017}

}

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