# Comparison of multi-fluid moment models with particle-in-cell simulations of collisionless magnetic reconnection

## Abstract

We introduce an extensible multi-fluid moment model in the context of collisionless magnetic reconnection. This model evolves full Maxwell equations and simultaneously moments of the Vlasov-Maxwell equation for each species in the plasma. Effects like electron inertia and pressure gradient are self-consistently embedded in the resulting multi-fluid moment equations, without the need to explicitly solving a generalized Ohm's law. Two limits of the multi-fluid moment model are discussed, namely, the five-moment limit that evolves a scalar pressures for each species and the ten-moment limit that evolves the full anisotropic, non-gyrotropic pressure tensor for each species. We first demonstrate analytically and numerically that the five-moment model reduces to the widely used Hall magnetohydrodynamics (Hall MHD) model under the assumptions of vanishing electron inertia, infinite speed of light, and quasi-neutrality. Then, we compare ten-moment and fully kinetic particle-in-cell (PIC) simulations of a large scale Harris sheet reconnection problem, where the ten-moment equations are closed with a local linear collisionless approximation for the heat flux. The ten-moment simulation gives reasonable agreement with the PIC results regarding the structures and magnitudes of the electron flows, the polarities and magnitudes of elements of the electron pressure tensor, and the decomposition of the generalized Ohm's law.more »

- Authors:

- Space Science Center and Physics Department, University of New Hampshire, Durham, New Hampshire 03824 (United States)
- Center for Heliophysics, Princeton Plasma Physics Laboratory, Princeton, New Jersey 08543-0451 (United States)

- Publication Date:

- OSTI Identifier:
- 22407986

- Resource Type:
- Journal Article

- Resource Relation:
- Journal Name: Physics of Plasmas; Journal Volume: 22; Journal Issue: 1; 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; ANISOTROPY; BOLTZMANN-VLASOV EQUATION; CLOSURES; COMPARATIVE EVALUATIONS; COMPUTERIZED SIMULATION; ELECTRONS; FLUIDS; HALL EFFECT; HEAT FLUX; MAGNETIC RECONNECTION; MAGNETOHYDRODYNAMICS; MAXWELL EQUATIONS; MOMENT OF INERTIA; MOMENTS METHOD; PLASMA; PLASMA SHEET; PRESSURE GRADIENTS; SCALARS; THREE-DIMENSIONAL CALCULATIONS; VISIBLE RADIATION

### Citation Formats

```
Wang, Liang, E-mail: liang.wang@unh.edu, Germaschewski, K., Hakim, Ammar H., and Bhattacharjee, A..
```*Comparison of multi-fluid moment models with particle-in-cell simulations of collisionless magnetic reconnection*. United States: N. p., 2015.
Web. doi:10.1063/1.4906063.

```
Wang, Liang, E-mail: liang.wang@unh.edu, Germaschewski, K., Hakim, Ammar H., & Bhattacharjee, A..
```*Comparison of multi-fluid moment models with particle-in-cell simulations of collisionless magnetic reconnection*. United States. doi:10.1063/1.4906063.

```
Wang, Liang, E-mail: liang.wang@unh.edu, Germaschewski, K., Hakim, Ammar H., and Bhattacharjee, A.. Thu .
"Comparison of multi-fluid moment models with particle-in-cell simulations of collisionless magnetic reconnection". United States.
doi:10.1063/1.4906063.
```

```
@article{osti_22407986,
```

title = {Comparison of multi-fluid moment models with particle-in-cell simulations of collisionless magnetic reconnection},

author = {Wang, Liang, E-mail: liang.wang@unh.edu and Germaschewski, K. and Hakim, Ammar H. and Bhattacharjee, A.},

abstractNote = {We introduce an extensible multi-fluid moment model in the context of collisionless magnetic reconnection. This model evolves full Maxwell equations and simultaneously moments of the Vlasov-Maxwell equation for each species in the plasma. Effects like electron inertia and pressure gradient are self-consistently embedded in the resulting multi-fluid moment equations, without the need to explicitly solving a generalized Ohm's law. Two limits of the multi-fluid moment model are discussed, namely, the five-moment limit that evolves a scalar pressures for each species and the ten-moment limit that evolves the full anisotropic, non-gyrotropic pressure tensor for each species. We first demonstrate analytically and numerically that the five-moment model reduces to the widely used Hall magnetohydrodynamics (Hall MHD) model under the assumptions of vanishing electron inertia, infinite speed of light, and quasi-neutrality. Then, we compare ten-moment and fully kinetic particle-in-cell (PIC) simulations of a large scale Harris sheet reconnection problem, where the ten-moment equations are closed with a local linear collisionless approximation for the heat flux. The ten-moment simulation gives reasonable agreement with the PIC results regarding the structures and magnitudes of the electron flows, the polarities and magnitudes of elements of the electron pressure tensor, and the decomposition of the generalized Ohm's law. Possible ways to improve the simple local closure towards a nonlocal fully three-dimensional closure are also discussed.},

doi = {10.1063/1.4906063},

journal = {Physics of Plasmas},

number = 1,

volume = 22,

place = {United States},

year = {Thu Jan 15 00:00:00 EST 2015},

month = {Thu Jan 15 00:00:00 EST 2015}

}