# Vortex formation in an electron plasma with a sheared flow

## Abstract

The formation of vortex structures in an electron plasma with a sheared flow is investigated. The electron fluid is drifting in a self-electric field generated by an unshielded electron population. This setting is linearly unstable and an instability of diocotron (slipping-stream) type occurs. The time scale of the dynamics is assumed to be much shorter than the ion plasma and ion gyroperiods. Consequently, the ions do not respond to the wave potential and serve only as a neutralizing background. An equation determining the nonlinear evolution of the electrostatic potential in a plane perpendicular to an external magnetic field is derived within the drift approximation. The governing equation is then analyzed for the case with a localized shear in the electron fluid velocity. Possible final states of the diocotron instability are investigated analytically and solutions in the form of a tripolar vortex, a zonal flow, and a vortex street are found. The nonlinear time evolution of the diocotron instability is investigated by solving the governing equation numerically. In particular, the dynamics of nonlinearly saturated states and the formation of such states are discussed. Numerical solutions show a vortex street structure in a saturated state. The relevance of our investigation for spacemore »

- Authors:

- Institut fuer Theoretische Physik IV, Fakultaet fuer Physik und Astronomie, Ruhr-Universitaet Bochum, D-44780 Bochum (Germany)

- Publication Date:

- OSTI Identifier:
- 20782374

- Resource Type:
- Journal Article

- Resource Relation:
- Journal Name: Physics of Plasmas; Journal Volume: 12; Journal Issue: 12; Other Information: DOI: 10.1063/1.2039547; (c) 2005 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; APPROXIMATIONS; ELECTRIC FIELDS; ELECTRONS; IONS; MAGNETIC FIELDS; NONLINEAR PROBLEMS; NUMERICAL ANALYSIS; NUMERICAL SOLUTION; PLASMA; PLASMA DRIFT; PLASMA INSTABILITY; PLASMA POTENTIAL; PLASMA WAVES; SHEAR; VORTICES

### Citation Formats

```
Hall, J.O., and Shukla, P.K.
```*Vortex formation in an electron plasma with a sheared flow*. United States: N. p., 2005.
Web. doi:10.1063/1.2039547.

```
Hall, J.O., & Shukla, P.K.
```*Vortex formation in an electron plasma with a sheared flow*. United States. doi:10.1063/1.2039547.

```
Hall, J.O., and Shukla, P.K. Thu .
"Vortex formation in an electron plasma with a sheared flow". United States.
doi:10.1063/1.2039547.
```

```
@article{osti_20782374,
```

title = {Vortex formation in an electron plasma with a sheared flow},

author = {Hall, J.O. and Shukla, P.K.},

abstractNote = {The formation of vortex structures in an electron plasma with a sheared flow is investigated. The electron fluid is drifting in a self-electric field generated by an unshielded electron population. This setting is linearly unstable and an instability of diocotron (slipping-stream) type occurs. The time scale of the dynamics is assumed to be much shorter than the ion plasma and ion gyroperiods. Consequently, the ions do not respond to the wave potential and serve only as a neutralizing background. An equation determining the nonlinear evolution of the electrostatic potential in a plane perpendicular to an external magnetic field is derived within the drift approximation. The governing equation is then analyzed for the case with a localized shear in the electron fluid velocity. Possible final states of the diocotron instability are investigated analytically and solutions in the form of a tripolar vortex, a zonal flow, and a vortex street are found. The nonlinear time evolution of the diocotron instability is investigated by solving the governing equation numerically. In particular, the dynamics of nonlinearly saturated states and the formation of such states are discussed. Numerical solutions show a vortex street structure in a saturated state. The relevance of our investigation for space and laboratory plasmas is discussed.},

doi = {10.1063/1.2039547},

journal = {Physics of Plasmas},

number = 12,

volume = 12,

place = {United States},

year = {Thu Dec 15 00:00:00 EST 2005},

month = {Thu Dec 15 00:00:00 EST 2005}

}