# Electron cooling and finite potential drop in a magnetized plasma expansion

## Abstract

The steady, collisionless, slender flow of a magnetized plasma into a surrounding vacuum is considered. The ion component is modeled as mono-energetic, while electrons are assumed Maxwellian upstream. The magnetic field has a convergent-divergent geometry, and attention is restricted to its paraxial region, so that 2D and drift effects are ignored. By using the conservation of energy and magnetic moment of particles and the quasi-neutrality condition, the ambipolar electric field and the distribution functions of both species are calculated self-consistently, paying attention to the existence of effective potential barriers associated to magnetic mirroring. The solution is used to find the total potential drop for a set of upstream conditions, plus the axial evolution of various moments of interest (density, temperatures, and heat fluxes). The results illuminate the behavior of magnetic nozzles, plasma jets, and other configurations of interest, showing, in particular, in the divergent plasma the collisionless cooling of electrons, and the generation of collisionless electron heat fluxes.

- Authors:

- Department of Aeronautics and Astronautics, Massachusetts Institute of Technology, 77 Massachusetts Avenue, Cambridge, Massachusetts 02139 (United States)
- Escuela Técnica Superior de Ingeniería Aeronáutica y del Espacio, Universidad Politécnica de Madrid, Plaza Cardenal Cisneros 3, Madrid 28040 (Spain)
- Departamento de Bioingeniería e Ingeniería Aeroespacial, Universidad Carlos III de Madrid, Avda. Universidad 30, Leganés 28911, Madrid (Spain)

- Publication Date:

- OSTI Identifier:
- 22410345

- Resource Type:
- Journal Article

- Journal Name:
- Physics of Plasmas

- Additional Journal Information:
- Journal Volume: 22; Journal Issue: 5; Other Information: (c) 2015 AIP Publishing LLC; Country of input: International Atomic Energy Agency (IAEA); Journal ID: ISSN 1070-664X

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 70 PLASMA PHYSICS AND FUSION TECHNOLOGY; DISTRIBUTION FUNCTIONS; ELECTRIC FIELDS; ELECTRON COOLING; ELECTRONS; HEAT FLUX; MAGNETIC FIELDS; MAGNETIC MIRRORS; MAGNETIC MOMENTS; MATHEMATICAL SOLUTIONS; NOZZLES; PLASMA EXPANSION; PLASMA JETS

### Citation Formats

```
Martinez-Sanchez, M., Navarro-Cavallé, J., and Ahedo, E.
```*Electron cooling and finite potential drop in a magnetized plasma expansion*. United States: N. p., 2015.
Web. doi:10.1063/1.4919627.

```
Martinez-Sanchez, M., Navarro-Cavallé, J., & Ahedo, E.
```*Electron cooling and finite potential drop in a magnetized plasma expansion*. United States. doi:10.1063/1.4919627.

```
Martinez-Sanchez, M., Navarro-Cavallé, J., and Ahedo, E. Fri .
"Electron cooling and finite potential drop in a magnetized plasma expansion". United States. doi:10.1063/1.4919627.
```

```
@article{osti_22410345,
```

title = {Electron cooling and finite potential drop in a magnetized plasma expansion},

author = {Martinez-Sanchez, M. and Navarro-Cavallé, J. and Ahedo, E.},

abstractNote = {The steady, collisionless, slender flow of a magnetized plasma into a surrounding vacuum is considered. The ion component is modeled as mono-energetic, while electrons are assumed Maxwellian upstream. The magnetic field has a convergent-divergent geometry, and attention is restricted to its paraxial region, so that 2D and drift effects are ignored. By using the conservation of energy and magnetic moment of particles and the quasi-neutrality condition, the ambipolar electric field and the distribution functions of both species are calculated self-consistently, paying attention to the existence of effective potential barriers associated to magnetic mirroring. The solution is used to find the total potential drop for a set of upstream conditions, plus the axial evolution of various moments of interest (density, temperatures, and heat fluxes). The results illuminate the behavior of magnetic nozzles, plasma jets, and other configurations of interest, showing, in particular, in the divergent plasma the collisionless cooling of electrons, and the generation of collisionless electron heat fluxes.},

doi = {10.1063/1.4919627},

journal = {Physics of Plasmas},

issn = {1070-664X},

number = 5,

volume = 22,

place = {United States},

year = {2015},

month = {5}

}