# Electron parallel transport for arbitrary collisionality

## Abstract

Integral (nonlocal) closures [J.-Y. Ji and E. D. Held, Phys. Plasmas 21, 122116 (2014)] are combined with the momentum balance equation to derive electron parallel transport relations. For a single harmonic fluctuation, the relations take the same form as the classical Spitzer theory (with possible additional terms): The electric current and heat flux densities are connected to the modified electric field and temperature gradient by transport coefficients. In contrast to the classical theory, the dimensionless coefficients depend on the collisionality quantified by a Knudsen number, the ratio of the collision length to the angular wavelength. The key difference comes from the proper treatment of the viscosity and friction terms in the momentum balance equation, accurately reflecting the free streaming and collision terms in the kinetic equation. For an arbitrary fluctuation, the transport relations may be expressed by a Fourier series or transform. Finally, for low collisionality, the electric resistivity can be significantly larger than that of classical theory and may predict the correct timescale for fast magnetic reconnection.

- Authors:

- Utah State Univ., Logan, UT (United States). Dept. of Physics
- Pohang Univ. of Science and Technology (POSTECH) (Korea, Republic of). Dept. of Physics
- Seoul National Univ. (Korea, Republic of). Dept. of Nuclear Engineering

- Publication Date:

- Research Org.:
- Utah State Univ., Logan, UT (United States)

- Sponsoring Org.:
- USDOE

- OSTI Identifier:
- 1524578

- Alternate Identifier(s):
- OSTI ID: 1410466

- Grant/Contract Number:
- FC02-08ER54973; SC0014033, SC0016256, DE-FC02-08ER54973; FG02-04ER54746

- Resource Type:
- Accepted Manuscript

- Journal Name:
- Physics of Plasmas

- Additional Journal Information:
- Journal Volume: 24; Journal Issue: 11; 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

### Citation Formats

```
Ji, Jeong-Young, Yun, Gunsu S., Na, Yong-Su, and Held, Eric D. Electron parallel transport for arbitrary collisionality. United States: N. p., 2017.
Web. doi:10.1063/1.5004531.
```

```
Ji, Jeong-Young, Yun, Gunsu S., Na, Yong-Su, & Held, Eric D. Electron parallel transport for arbitrary collisionality. United States. doi:10.1063/1.5004531.
```

```
Ji, Jeong-Young, Yun, Gunsu S., Na, Yong-Su, and Held, Eric D. Tue .
"Electron parallel transport for arbitrary collisionality". United States. doi:10.1063/1.5004531. https://www.osti.gov/servlets/purl/1524578.
```

```
@article{osti_1524578,
```

title = {Electron parallel transport for arbitrary collisionality},

author = {Ji, Jeong-Young and Yun, Gunsu S. and Na, Yong-Su and Held, Eric D.},

abstractNote = {Integral (nonlocal) closures [J.-Y. Ji and E. D. Held, Phys. Plasmas 21, 122116 (2014)] are combined with the momentum balance equation to derive electron parallel transport relations. For a single harmonic fluctuation, the relations take the same form as the classical Spitzer theory (with possible additional terms): The electric current and heat flux densities are connected to the modified electric field and temperature gradient by transport coefficients. In contrast to the classical theory, the dimensionless coefficients depend on the collisionality quantified by a Knudsen number, the ratio of the collision length to the angular wavelength. The key difference comes from the proper treatment of the viscosity and friction terms in the momentum balance equation, accurately reflecting the free streaming and collision terms in the kinetic equation. For an arbitrary fluctuation, the transport relations may be expressed by a Fourier series or transform. Finally, for low collisionality, the electric resistivity can be significantly larger than that of classical theory and may predict the correct timescale for fast magnetic reconnection.},

doi = {10.1063/1.5004531},

journal = {Physics of Plasmas},

number = 11,

volume = 24,

place = {United States},

year = {2017},

month = {11}

}

*Citation information provided by*

Web of Science

Web of Science

#### Figures / Tables:

_{AB}(–k) = K̂

_{AB}(k) for AB= $hh, hR, RR$, and $\pi\pi$ and K̂

_{AB}(–k)= K̂

_{AB}(k) for AB= h$\pi$more »

Works referenced in this record:

##
Laser Absorption and Heat Transport by Non-Maxwell-Boltzmann Electron Distributions

journal, June 1983

- Albritton, J. R.
- Physical Review Letters, Vol. 50, Issue 26

##
Nonlinear magnetohydrodynamics simulation using high-order finite elements

journal, March 2004

- Sovinec, C. R.; Glasser, A. H.; Gianakon, T. A.
- Journal of Computational Physics, Vol. 195, Issue 1

##
Electron energy transport in ion waves and its relevance to laser-produced plasmas

journal, January 1983

- Bell, A. R.
- Physics of Fluids, Vol. 26, Issue 1

##
Unified fluid/kinetic description of plasma microinstabilities. Part II: Applications

journal, May 1992

- Chang, Zuoyang; Callen, J. D.
- Physics of Fluids B: Plasma Physics, Vol. 4, Issue 5

##
Unified fluid/kinetic description of plasma microinstabilities. Part I: Basic equations in a sheared slab geometry

journal, May 1992

- Chang, Zuoyang; Callen, J. D.
- Physics of Fluids B: Plasma Physics, Vol. 4, Issue 5

##
Erratum: “Electron parallel closures for arbitrary collisionality” [Phys. Plasmas **21** , 122116 (2014)]

journal, December 2015

- Ji, Jeong-Young; Held, Eric D.
- Physics of Plasmas, Vol. 22, Issue 12

##
Damping of ion-acoustic waves in the presence of electron-ion collisions

journal, September 1992

- Epperlein, E. M.; Short, R. W.; Simon, A.
- Physical Review Letters, Vol. 69, Issue 12

##
BOUT++: A framework for parallel plasma fluid simulations

journal, September 2009

- Dudson, B. D.; Umansky, M. V.; Xu, X. Q.
- Computer Physics Communications, Vol. 180, Issue 9

##
Electron parallel closures for arbitrary collisionality

journal, December 2014

- Ji, Jeong-Young; Held, Eric D.
- Physics of Plasmas, Vol. 21, Issue 12

##
Transport Phenomena in a Completely Ionized Gas

journal, March 1953

- Spitzer, Lyman; Härm, Richard
- Physical Review, Vol. 89, Issue 5

##
Transport Phenomena in a Completely Ionized Gas in Presence of a Magnetic Field

journal, October 1949

- Landshoff, Rolf
- Physical Review, Vol. 76, Issue 7

##
Closure and transport theory for high-collisionality electron-ion plasmas

journal, April 2013

- Ji, Jeong-Young; Held, Eric D.
- Physics of Plasmas, Vol. 20, Issue 4

##
Kinetic theory of laser filamentation in plasmas

journal, October 1990

- Epperlein, Eduardo M.
- Physical Review Letters, Vol. 65, Issue 17

##
Linearly exact parallel closures for slab geometry

journal, August 2013

- Ji, Jeong-Young; Held, Eric D.; Jhang, Hogun
- Physics of Plasmas, Vol. 20, Issue 8

##
Electron parallel closures for various ion charge numbers

journal, March 2016

- Ji, Jeong-Young; Kim, Sang-Kyeun; Held, Eric D.
- Physics of Plasmas, Vol. 23, Issue 3

##
A fast non-Fourier method for Landau-fluid operators

journal, May 2014

- Dimits, A. M.; Joseph, I.; Umansky, M. V.
- Physics of Plasmas, Vol. 21, Issue 5

*Figures/Tables have been extracted from DOE-funded journal article accepted manuscripts.*