# Nonlinear resistivity for magnetohydrodynamical models

## Abstract

A new formulation of the plasma resistivity that stems from the collisional momentum-transfer rate between electrons and ions is presented. The resistivity computed herein is shown to depend not only on the temperature and density but also on all other polynomial velocity-space moments of the distribution function, such as the pressure tensor and heat flux vector. The full expression for the collisional momentum-transfer rate is determined and is used to formulate the nonlinear anisotropic resistivity. The new formalism recovers the Spitzer resistivity, as well as the concept of thermal force if the heat flux is assumed to be proportional to a temperature gradient. Furthermore, if the pressure tensor is related to viscous stress, the latter enters the expression for the resistivity. The relative importance of the nonlinear term(s) with respect to the well-established electron inertia and Hall terms is also examined. Lastly, the subtle implications of the nonlinear resistivity, and its dependence on the fluid variables, are discussed in the context of magnetized plasma environments and phenomena such as magnetic reconnection.

- Authors:

- Princeton Univ., NJ (United States). Dept. of Astrophysical Sciences; Harvard Univ., Cambridge, MA (United States). John A. Paulson School of Engineering and Applied Sciences; Harvard-Smithsonian Center for Astrophysics, Cambridge, MA (United States)
- Princeton Plasma Physics Lab. (PPPL), Princeton, NJ (United States)
- Princeton Univ., NJ (United States). Dept. of Astrophysical Sciences; Princeton Plasma Physics Lab. (PPPL), Princeton, NJ (United States)

- Publication Date:

- Research Org.:
- Princeton Plasma Physics Lab. (PPPL), Princeton, NJ (United States)

- Sponsoring Org.:
- USDOE Office of Science (SC), Fusion Energy Sciences (FES) (SC-24); National Science Foundation (NSF)

- OSTI Identifier:
- 1358667

- Alternate Identifier(s):
- OSTI ID: 1361822

- Grant/Contract Number:
- AC02-09CH11466; AGS-1338944; AGS-1552142

- Resource Type:
- Journal Article: Accepted Manuscript

- Journal Name:
- Physics of Plasmas

- Additional Journal Information:
- Journal Volume: 24; Journal Issue: 4; Journal ID: ISSN 1070-664X

- Publisher:
- American Institute of Physics (AIP)

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 70 PLASMA PHYSICS AND FUSION TECHNOLOGY; collisionless magnetic reconnection; dynamo; simulations; plasmas; electrical resistivity; anisotropy; viscosity; maxwell equations; tensor methods

### Citation Formats

```
Lingam, M., Hirvijoki, E., Pfefferlé, D., Comisso, L., and Bhattacharjee, A.
```*Nonlinear resistivity for magnetohydrodynamical models*. United States: N. p., 2017.
Web. doi:10.1063/1.4980838.

```
Lingam, M., Hirvijoki, E., Pfefferlé, D., Comisso, L., & Bhattacharjee, A.
```*Nonlinear resistivity for magnetohydrodynamical models*. United States. doi:10.1063/1.4980838.

```
Lingam, M., Hirvijoki, E., Pfefferlé, D., Comisso, L., and Bhattacharjee, A. Thu .
"Nonlinear resistivity for magnetohydrodynamical models". United States.
doi:10.1063/1.4980838. https://www.osti.gov/servlets/purl/1358667.
```

```
@article{osti_1358667,
```

title = {Nonlinear resistivity for magnetohydrodynamical models},

author = {Lingam, M. and Hirvijoki, E. and Pfefferlé, D. and Comisso, L. and Bhattacharjee, A.},

abstractNote = {A new formulation of the plasma resistivity that stems from the collisional momentum-transfer rate between electrons and ions is presented. The resistivity computed herein is shown to depend not only on the temperature and density but also on all other polynomial velocity-space moments of the distribution function, such as the pressure tensor and heat flux vector. The full expression for the collisional momentum-transfer rate is determined and is used to formulate the nonlinear anisotropic resistivity. The new formalism recovers the Spitzer resistivity, as well as the concept of thermal force if the heat flux is assumed to be proportional to a temperature gradient. Furthermore, if the pressure tensor is related to viscous stress, the latter enters the expression for the resistivity. The relative importance of the nonlinear term(s) with respect to the well-established electron inertia and Hall terms is also examined. Lastly, the subtle implications of the nonlinear resistivity, and its dependence on the fluid variables, are discussed in the context of magnetized plasma environments and phenomena such as magnetic reconnection.},

doi = {10.1063/1.4980838},

journal = {Physics of Plasmas},

number = 4,

volume = 24,

place = {United States},

year = {Thu Apr 20 00:00:00 EDT 2017},

month = {Thu Apr 20 00:00:00 EDT 2017}

}

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