# Three species one-dimensional kinetic model for weakly ionized plasmas

## Abstract

A three species one-dimensional kinetic model is presented for a spatially homogeneous weakly ionized plasma subjected to the action of a time varying electric field. Planar geometry is assumed, which means that the plasma evolves in the privileged direction of the field. The energy transmitted to the electric charges is channelized to the neutrals thanks to collisions, a mechanism that influences the plasma dynamics. Charge-charge interactions have been designed as a one-dimensional collision term equivalent to the Landau operator used for fully ionized plasmas. Charge-neutral collisions are modelled by a conservative drift-diffusion operator in the Dougherty's form. The resulting set of coupled integro-differential equations is solved with the stable and robust propagator integral method. This semi–analytical method feasibility accounts for non–linear effects without appealing to linearisation or simplifications, providing conservative physically meaningful solutions even for initial or emerging sharp velocity distribution function profiles. It is found that charge-neutral collisions exert a significant effect since a quite different plasma evolution arises if compared to the collisionless limit. In addition, substantial differences in the system motion are found for constant and temperature dependent collision frequencies cases.

- Authors:

- Department of Applied Physics, Escuela Técnica Superior de Ingeniería Aeronáutica y del Espacio, Universidad Politécnica de Madrid, 28040 Madrid (Spain)

- Publication Date:

- OSTI Identifier:
- 22598988

- Resource Type:
- Journal Article

- Resource Relation:
- Journal Name: Physics of Plasmas; Journal Volume: 23; Journal Issue: 6; Other Information: (c) 2016 Author(s); Country of input: International Atomic Energy Agency (IAEA)

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 70 PLASMA PHYSICS AND FUSION TECHNOLOGY; APPEALS; COLLISIONS; COMPARATIVE EVALUATIONS; DISTRIBUTION FUNCTIONS; ELECTRIC CHARGES; ELECTRIC FIELDS; GEOMETRY; INTEGRO-DIFFERENTIAL EQUATIONS; LANDAU DAMPING; NONLINEAR PROBLEMS; ONE-DIMENSIONAL CALCULATIONS; PLASMA; SOLUTIONS; TEMPERATURE DEPENDENCE

### Citation Formats

```
Gonzalez, J., E-mail: jorge.gonzalez@upm.es, Donoso, J. M., and Tierno, S. P..
```*Three species one-dimensional kinetic model for weakly ionized plasmas*. United States: N. p., 2016.
Web. doi:10.1063/1.4953901.

```
Gonzalez, J., E-mail: jorge.gonzalez@upm.es, Donoso, J. M., & Tierno, S. P..
```*Three species one-dimensional kinetic model for weakly ionized plasmas*. United States. doi:10.1063/1.4953901.

```
Gonzalez, J., E-mail: jorge.gonzalez@upm.es, Donoso, J. M., and Tierno, S. P.. Wed .
"Three species one-dimensional kinetic model for weakly ionized plasmas". United States.
doi:10.1063/1.4953901.
```

```
@article{osti_22598988,
```

title = {Three species one-dimensional kinetic model for weakly ionized plasmas},

author = {Gonzalez, J., E-mail: jorge.gonzalez@upm.es and Donoso, J. M. and Tierno, S. P.},

abstractNote = {A three species one-dimensional kinetic model is presented for a spatially homogeneous weakly ionized plasma subjected to the action of a time varying electric field. Planar geometry is assumed, which means that the plasma evolves in the privileged direction of the field. The energy transmitted to the electric charges is channelized to the neutrals thanks to collisions, a mechanism that influences the plasma dynamics. Charge-charge interactions have been designed as a one-dimensional collision term equivalent to the Landau operator used for fully ionized plasmas. Charge-neutral collisions are modelled by a conservative drift-diffusion operator in the Dougherty's form. The resulting set of coupled integro-differential equations is solved with the stable and robust propagator integral method. This semi–analytical method feasibility accounts for non–linear effects without appealing to linearisation or simplifications, providing conservative physically meaningful solutions even for initial or emerging sharp velocity distribution function profiles. It is found that charge-neutral collisions exert a significant effect since a quite different plasma evolution arises if compared to the collisionless limit. In addition, substantial differences in the system motion are found for constant and temperature dependent collision frequencies cases.},

doi = {10.1063/1.4953901},

journal = {Physics of Plasmas},

number = 6,

volume = 23,

place = {United States},

year = {Wed Jun 15 00:00:00 EDT 2016},

month = {Wed Jun 15 00:00:00 EDT 2016}

}