# Fourier-spectral element approximation of the ion–electron Braginskii system with application to tokamak edge plasma in divertor configuration

## Abstract

Due to the extreme conditions required to produce energy by nuclear fusion in tokamaks, simulating the plasma behavior is an important but challenging task. We focus on the edge part of the plasma, where fluid approaches are probably the best suited, and our approach relies on the Braginskii ion–electron model. Assuming that the electric field is electrostatic, this yields a set of 10 strongly coupled and non-linear conservation equations that exhibit multiscale and anisotropy features. The computational domain is a torus of complex geometrical section, that corresponds to the divertor configuration, i.e. with an “X-point” in the magnetic surfaces. To capture the complex physics that is involved, high order methods are used: The time-discretization is based on a Strang splitting, that combines implicit and explicit high order Runge–Kutta schemes, and the space discretization makes use of the spectral element method in the poloidal plane together with Fourier expansions in the toroidal direction. The paper thoroughly describes the algorithms that have been developed, provides some numerical validations of the key algorithms and exhibits the results of preliminary numerical experiments. In particular, we point out that the highest frequency of the system is intermediate between the ion and electron cyclotron frequencies.

- Authors:

- Lab. J. A. Dieudonné, UMR CNRS 7351, Université de Nice-Sophia Antipolis, F-06108 Nice (France)
- (France)

- Publication Date:

- OSTI Identifier:
- 22572351

- Resource Type:
- Journal Article

- Resource Relation:
- Journal Name: Journal of Computational Physics; Journal Volume: 321; Other Information: Copyright (c) 2016 Elsevier Science B.V., Amsterdam, The Netherlands, All rights reserved.; Country of input: International Atomic Energy Agency (IAEA)

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; ALGORITHMS; CONFIGURATION; DIVERTORS; MAGNETIC SURFACES; NONLINEAR PROBLEMS; PLASMA; TOKAMAK DEVICES

### Citation Formats

```
Minjeaud, Sebastian, INRIA project CASTOR, Pasquetti, Richard, E-mail: richard.pasquetti@unice.fr, and INRIA project CASTOR.
```*Fourier-spectral element approximation of the ion–electron Braginskii system with application to tokamak edge plasma in divertor configuration*. United States: N. p., 2016.
Web. doi:10.1016/J.JCP.2016.05.056.

```
Minjeaud, Sebastian, INRIA project CASTOR, Pasquetti, Richard, E-mail: richard.pasquetti@unice.fr, & INRIA project CASTOR.
```*Fourier-spectral element approximation of the ion–electron Braginskii system with application to tokamak edge plasma in divertor configuration*. United States. doi:10.1016/J.JCP.2016.05.056.

```
Minjeaud, Sebastian, INRIA project CASTOR, Pasquetti, Richard, E-mail: richard.pasquetti@unice.fr, and INRIA project CASTOR. Thu .
"Fourier-spectral element approximation of the ion–electron Braginskii system with application to tokamak edge plasma in divertor configuration". United States.
doi:10.1016/J.JCP.2016.05.056.
```

```
@article{osti_22572351,
```

title = {Fourier-spectral element approximation of the ion–electron Braginskii system with application to tokamak edge plasma in divertor configuration},

author = {Minjeaud, Sebastian and INRIA project CASTOR and Pasquetti, Richard, E-mail: richard.pasquetti@unice.fr and INRIA project CASTOR},

abstractNote = {Due to the extreme conditions required to produce energy by nuclear fusion in tokamaks, simulating the plasma behavior is an important but challenging task. We focus on the edge part of the plasma, where fluid approaches are probably the best suited, and our approach relies on the Braginskii ion–electron model. Assuming that the electric field is electrostatic, this yields a set of 10 strongly coupled and non-linear conservation equations that exhibit multiscale and anisotropy features. The computational domain is a torus of complex geometrical section, that corresponds to the divertor configuration, i.e. with an “X-point” in the magnetic surfaces. To capture the complex physics that is involved, high order methods are used: The time-discretization is based on a Strang splitting, that combines implicit and explicit high order Runge–Kutta schemes, and the space discretization makes use of the spectral element method in the poloidal plane together with Fourier expansions in the toroidal direction. The paper thoroughly describes the algorithms that have been developed, provides some numerical validations of the key algorithms and exhibits the results of preliminary numerical experiments. In particular, we point out that the highest frequency of the system is intermediate between the ion and electron cyclotron frequencies.},

doi = {10.1016/J.JCP.2016.05.056},

journal = {Journal of Computational Physics},

number = ,

volume = 321,

place = {United States},

year = {Thu Sep 15 00:00:00 EDT 2016},

month = {Thu Sep 15 00:00:00 EDT 2016}

}