# Influence of a finite initial ion density gradient on plasma expansion into a vacuum

## Abstract

The influence of a finite initial ion density gradient on a plasma expansion into a vacuum is studied with a numerical model that takes into account the charge-separation effects and assumes a Boltzmann equilibrium for the electrons. The cases of a semi-infinite plasma and of a finite plasma slab are treated. In both cases it is shown that the finite initial ion density gradient of the plasma surface leads to two phases in the plasma expansion, separated by a wave breaking of the ion flow. An ion front forms after the wave breaking and, in the semi-infinite plasma case, the plasma expansion becomes closer and closer to the initially sharp boundary case, the maximum ion velocity increasing logarithmically with time. In the finite plasma slab case, the energy conservation has to be taken into account, the thermal electron energy being progressively converted into the kinetic energy of the ions. When the initial ion density scale length l{sub ss} is larger than a few percent of the total plasma slab width, the final maximum ion velocity decreases with l{sub ss}.

- Authors:

- Centre de Physique Theorique, Unite Mixte de recherche 7644 du Centre National de la Recherche Scientifique (CNRS), Ecole Polytechnique, 91128 Palaiseau Cedex (France)

- Publication Date:

- OSTI Identifier:
- 20782538

- Resource Type:
- Journal Article

- Resource Relation:
- Journal Name: Physics of Plasmas; Journal Volume: 13; Journal Issue: 3; Other Information: DOI: 10.1063/1.2178653; (c) 2006 American Institute of Physics; Country of input: International Atomic Energy Agency (IAEA)

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 70 PLASMA PHYSICS AND FUSION TECHNOLOGY; CHARGED-PARTICLE TRANSPORT; ELECTRONS; ENERGY CONSERVATION; EQUILIBRIUM; ION DENSITY; IONS; KINETIC ENERGY; NUMERICAL ANALYSIS; PLASMA; PLASMA DENSITY; PLASMA EXPANSION; SURFACES; THERMODYNAMICS; VELOCITY

### Citation Formats

```
Grismayer, T., and Mora, P.
```*Influence of a finite initial ion density gradient on plasma expansion into a vacuum*. United States: N. p., 2006.
Web. doi:10.1063/1.2178653.

```
Grismayer, T., & Mora, P.
```*Influence of a finite initial ion density gradient on plasma expansion into a vacuum*. United States. doi:10.1063/1.2178653.

```
Grismayer, T., and Mora, P. Wed .
"Influence of a finite initial ion density gradient on plasma expansion into a vacuum". United States.
doi:10.1063/1.2178653.
```

```
@article{osti_20782538,
```

title = {Influence of a finite initial ion density gradient on plasma expansion into a vacuum},

author = {Grismayer, T. and Mora, P.},

abstractNote = {The influence of a finite initial ion density gradient on a plasma expansion into a vacuum is studied with a numerical model that takes into account the charge-separation effects and assumes a Boltzmann equilibrium for the electrons. The cases of a semi-infinite plasma and of a finite plasma slab are treated. In both cases it is shown that the finite initial ion density gradient of the plasma surface leads to two phases in the plasma expansion, separated by a wave breaking of the ion flow. An ion front forms after the wave breaking and, in the semi-infinite plasma case, the plasma expansion becomes closer and closer to the initially sharp boundary case, the maximum ion velocity increasing logarithmically with time. In the finite plasma slab case, the energy conservation has to be taken into account, the thermal electron energy being progressively converted into the kinetic energy of the ions. When the initial ion density scale length l{sub ss} is larger than a few percent of the total plasma slab width, the final maximum ion velocity decreases with l{sub ss}.},

doi = {10.1063/1.2178653},

journal = {Physics of Plasmas},

number = 3,

volume = 13,

place = {United States},

year = {Wed Mar 15 00:00:00 EST 2006},

month = {Wed Mar 15 00:00:00 EST 2006}

}