# Nonlinear viscosity and its role in drift-Alfven modes

## Abstract

The moment approach is used to analyze the part of the magnetized plasma viscosity related to the nonlinear character of the Landau collision integral in the Boltzmann kinetic equation (nonlinear viscosity), pointed out by Catto and Simakov [Phys. Plasmas 11, 90 (2004)]. It is shown that the results of these authors, who have used an alternative procedure based on a more detailed analysis of the kinetic equation, correspond to a 15-moment approach. In comparison with the 13-moment approach (density, temperature, velocity, heat flux, and the viscosity tensor) of Grad, the 15-moment approach takes into account two higher-order moments, one of which is the vector-type moment similar to the parallel heat flux and the second is the tensor-type moment similar to the parallel projection of the viscosity tensor. Both these higher-order moments enter into the Braginskii approximation. The nonlinear viscosity calculated in the scope of the 13-moment Grad approach is qualitatively the same as that found by Catto and Simakov. Its role is investigated for drift-Alfven modes, driven by the combined effect of the dissipative part of perpendicular heat conductivity and the standard collisional viscosity, and it is shown to be essential for the radial transport of these modes. It ismore »

- Authors:

- Physics Institute, University of Sao Paulo, Cidade Universitaria, 05508-900, Sao Paulo (Brazil)
- (Russian Federation) and Nonlinear Physics Laboratory, Moscow Institute of Physics and Technology, Institutskii per. 9, Dolgoprudnyi 141700, Moscow Region (Russian Federation)
- (Russian Federation) and Moscow Engineering Physics Institute, Kashirskoe Shosse 31, Moscow 115409 (Russian Federation)
- (Russian Federation) and Institute of Nuclear Fusion, Russian Research Centre Kurchatov Institute, Kurchatov Sq., 1, Moscow 123182 (Russian Federation)
- (Russian Federation)
- (Brazil) and Brazilian Center for Research in Physics, Rua Xavier Sigaud, 150, 22290-180, Rio de Janeiro (Brazil)

- Publication Date:

- OSTI Identifier:
- 20782394

- Resource Type:
- Journal Article

- Resource Relation:
- Journal Name: Physics of Plasmas; Journal Volume: 12; Journal Issue: 12; Other Information: DOI: 10.1063/1.2151169; (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; ALFVEN WAVES; APPROXIMATIONS; BOLTZMANN EQUATION; CHARGED-PARTICLE TRANSPORT; COLLISION INTEGRALS; COMPARATIVE EVALUATIONS; ELECTRON TEMPERATURE; ELECTRONS; HEAT FLUX; ION TEMPERATURE; NONLINEAR PROBLEMS; PLASMA; PLASMA DENSITY; PLASMA DIAMAGNETISM; PLASMA DRIFT; PLASMA PRESSURE; PRESSURE GRADIENTS; TEMPERATURE GRADIENTS; VECTORS; VISCOSITY; WAVE PACKETS

### Citation Formats

```
Tsypin, V.S., Mikhailovskii, A.B., Shirokov, M.S., Kovalishen, E.A., Konovalov, S.V., Galvao, R.M.O., Institute of Nuclear Fusion, Russian Research Centre Kurchatov Institute, Kurchatov Sq., 1, Moscow 123182, Institute of Nuclear Fusion, Russian Research Centre Kurchatov Institute, Kurchatov Sq., 1, Moscow 123182, Nonlinear Physics Laboratory, Moscow Institute of Physics and Technology, Institutskii per. 9, Dolgoprudnyi 141700, Institute of Nuclear Fusion, Russian Research Centre Kurchatov Institute, Kurchatov Sq., 1, Moscow 123182, and Physics Institute, University of Sao Paulo, Cidade Universitaria, 05508-900, Sao Paulo.
```*Nonlinear viscosity and its role in drift-Alfven modes*. United States: N. p., 2005.
Web. doi:10.1063/1.2151169.

```
Tsypin, V.S., Mikhailovskii, A.B., Shirokov, M.S., Kovalishen, E.A., Konovalov, S.V., Galvao, R.M.O., Institute of Nuclear Fusion, Russian Research Centre Kurchatov Institute, Kurchatov Sq., 1, Moscow 123182, Institute of Nuclear Fusion, Russian Research Centre Kurchatov Institute, Kurchatov Sq., 1, Moscow 123182, Nonlinear Physics Laboratory, Moscow Institute of Physics and Technology, Institutskii per. 9, Dolgoprudnyi 141700, Institute of Nuclear Fusion, Russian Research Centre Kurchatov Institute, Kurchatov Sq., 1, Moscow 123182, & Physics Institute, University of Sao Paulo, Cidade Universitaria, 05508-900, Sao Paulo.
```*Nonlinear viscosity and its role in drift-Alfven modes*. United States. doi:10.1063/1.2151169.

```
Tsypin, V.S., Mikhailovskii, A.B., Shirokov, M.S., Kovalishen, E.A., Konovalov, S.V., Galvao, R.M.O., Institute of Nuclear Fusion, Russian Research Centre Kurchatov Institute, Kurchatov Sq., 1, Moscow 123182, Institute of Nuclear Fusion, Russian Research Centre Kurchatov Institute, Kurchatov Sq., 1, Moscow 123182, Nonlinear Physics Laboratory, Moscow Institute of Physics and Technology, Institutskii per. 9, Dolgoprudnyi 141700, Institute of Nuclear Fusion, Russian Research Centre Kurchatov Institute, Kurchatov Sq., 1, Moscow 123182, and Physics Institute, University of Sao Paulo, Cidade Universitaria, 05508-900, Sao Paulo. Thu .
"Nonlinear viscosity and its role in drift-Alfven modes". United States.
doi:10.1063/1.2151169.
```

```
@article{osti_20782394,
```

title = {Nonlinear viscosity and its role in drift-Alfven modes},

author = {Tsypin, V.S. and Mikhailovskii, A.B. and Shirokov, M.S. and Kovalishen, E.A. and Konovalov, S.V. and Galvao, R.M.O. and Institute of Nuclear Fusion, Russian Research Centre Kurchatov Institute, Kurchatov Sq., 1, Moscow 123182 and Institute of Nuclear Fusion, Russian Research Centre Kurchatov Institute, Kurchatov Sq., 1, Moscow 123182 and Nonlinear Physics Laboratory, Moscow Institute of Physics and Technology, Institutskii per. 9, Dolgoprudnyi 141700 and Institute of Nuclear Fusion, Russian Research Centre Kurchatov Institute, Kurchatov Sq., 1, Moscow 123182 and Physics Institute, University of Sao Paulo, Cidade Universitaria, 05508-900, Sao Paulo},

abstractNote = {The moment approach is used to analyze the part of the magnetized plasma viscosity related to the nonlinear character of the Landau collision integral in the Boltzmann kinetic equation (nonlinear viscosity), pointed out by Catto and Simakov [Phys. Plasmas 11, 90 (2004)]. It is shown that the results of these authors, who have used an alternative procedure based on a more detailed analysis of the kinetic equation, correspond to a 15-moment approach. In comparison with the 13-moment approach (density, temperature, velocity, heat flux, and the viscosity tensor) of Grad, the 15-moment approach takes into account two higher-order moments, one of which is the vector-type moment similar to the parallel heat flux and the second is the tensor-type moment similar to the parallel projection of the viscosity tensor. Both these higher-order moments enter into the Braginskii approximation. The nonlinear viscosity calculated in the scope of the 13-moment Grad approach is qualitatively the same as that found by Catto and Simakov. Its role is investigated for drift-Alfven modes, driven by the combined effect of the dissipative part of perpendicular heat conductivity and the standard collisional viscosity, and it is shown to be essential for the radial transport of these modes. It is shown that the wave packet of drift-Alfven modes, propagating in the diamagnetic drift direction and driven for reversed temperature gradient, is transported down the pressure gradient. In contrast to this, the wave packet propagating in the electron diamagnetic drift direction and driven for positive temperature gradient is transported up the pressure gradient.},

doi = {10.1063/1.2151169},

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}

}