# Heat flux viscosity in collisional magnetized plasmas

## Abstract

Momentum transport in collisional magnetized plasmas due to gradients in the heat flux, a “heat flux viscosity,” is demonstrated. Even though no net particle flux is associated with a heat flux, in a plasma there can still be momentum transport owing to the velocity dependence of the Coulomb collision frequency, analogous to the thermal force. This heat-flux viscosity may play an important role in numerous plasma environments, in particular, in strongly driven high-energy-density plasma, where strong heat flux can dominate over ordinary plasma flows. The heat flux viscosity can influence the dynamics of the magnetic field in plasmas through the generalized Ohm's law and may therefore play an important role as a dissipation mechanism allowing magnetic field line reconnection. The heat flux viscosity is calculated directly using the finite-difference method of Epperlein and Haines [Phys. Fluids 29, 1029 (1986)], which is shown to be more accurate than Braginskii's method [S. I. Braginskii, Rev. Plasma Phys. 1, 205 (1965)], and confirmed with one-dimensional collisional particle-in-cell simulations. The resulting transport coefficients are tabulated for ease of application.

- Authors:

- Princeton University, Princeton, New Jersey 08544 (United States)
- Princeton Plasma Physics Laboratory, Princeton, New Jersey 08543 (United States)
- (United States)

- Publication Date:

- OSTI Identifier:
- 22410343

- Resource Type:
- Journal Article

- Resource Relation:
- Journal Name: Physics of Plasmas; Journal Volume: 22; Journal Issue: 5; Other Information: (c) 2015 AIP Publishing LLC; Country of input: International Atomic Energy Agency (IAEA)

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 70 PLASMA PHYSICS AND FUSION TECHNOLOGY; COLLISIONS; COMPUTERIZED SIMULATION; COULOMB FIELD; ENERGY DENSITY; FINITE DIFFERENCE METHOD; HEAT FLUX; MAGNETIC FIELDS; PARTIAL DIFFERENTIAL EQUATIONS; PARTICLES; PLASMA; PLASMA DENSITY; VISCOSITY

### Citation Formats

```
Liu, C., E-mail: cliu@pppl.gov, Fox, W., Bhattacharjee, A., and Princeton Plasma Physics Laboratory, Princeton, New Jersey 08543.
```*Heat flux viscosity in collisional magnetized plasmas*. United States: N. p., 2015.
Web. doi:10.1063/1.4918941.

```
Liu, C., E-mail: cliu@pppl.gov, Fox, W., Bhattacharjee, A., & Princeton Plasma Physics Laboratory, Princeton, New Jersey 08543.
```*Heat flux viscosity in collisional magnetized plasmas*. United States. doi:10.1063/1.4918941.

```
Liu, C., E-mail: cliu@pppl.gov, Fox, W., Bhattacharjee, A., and Princeton Plasma Physics Laboratory, Princeton, New Jersey 08543. Fri .
"Heat flux viscosity in collisional magnetized plasmas". United States. doi:10.1063/1.4918941.
```

```
@article{osti_22410343,
```

title = {Heat flux viscosity in collisional magnetized plasmas},

author = {Liu, C., E-mail: cliu@pppl.gov and Fox, W. and Bhattacharjee, A. and Princeton Plasma Physics Laboratory, Princeton, New Jersey 08543},

abstractNote = {Momentum transport in collisional magnetized plasmas due to gradients in the heat flux, a “heat flux viscosity,” is demonstrated. Even though no net particle flux is associated with a heat flux, in a plasma there can still be momentum transport owing to the velocity dependence of the Coulomb collision frequency, analogous to the thermal force. This heat-flux viscosity may play an important role in numerous plasma environments, in particular, in strongly driven high-energy-density plasma, where strong heat flux can dominate over ordinary plasma flows. The heat flux viscosity can influence the dynamics of the magnetic field in plasmas through the generalized Ohm's law and may therefore play an important role as a dissipation mechanism allowing magnetic field line reconnection. The heat flux viscosity is calculated directly using the finite-difference method of Epperlein and Haines [Phys. Fluids 29, 1029 (1986)], which is shown to be more accurate than Braginskii's method [S. I. Braginskii, Rev. Plasma Phys. 1, 205 (1965)], and confirmed with one-dimensional collisional particle-in-cell simulations. The resulting transport coefficients are tabulated for ease of application.},

doi = {10.1063/1.4918941},

journal = {Physics of Plasmas},

number = 5,

volume = 22,

place = {United States},

year = {Fri May 15 00:00:00 EDT 2015},

month = {Fri May 15 00:00:00 EDT 2015}

}