# Parameter-Space Survey of Linear G-mode and Interchange in Extended Magnetohydrodynamics

## Abstract

The extended magnetohydrodynamic stability of interchange modes is studied in two configurations. In slab geometry, a local dispersion relation for the gravitational interchange mode (g-mode) with three different extensions of the MHD model [P. Zhu, et al., Phys. Rev. Lett. 101, 085005 (2008)] is analyzed. Our results delineate where drifts stablize the g-mode with gyroviscosity alone and with a two-fluid Ohm’s law alone. Including the two-fluid Ohm’s law produces an ion drift wave that interacts with the g-mode. This interaction then gives rise to a second instability at finite k _{y}. A second instability is also observed in numerical extended MHD computations of linear interchange in cylindrical screw-pinch equilibria, the second configuration. Particularly with incomplete models, this mode limits the regions of stability for physically realistic conditions. But, applying a consistent two-temperature extended MHD model that includes the diamagnetic heat flux density ($$\vec{q}$$ _{*}) makes the onset of the second mode occur at larger Hall parameter. For conditions relevant to the SSPX experiment [E.B. Hooper, Plasma Phys. Controlled Fusion 54, 113001 (2012)], significant stabilization is observed for Suydam parameters as large as unity (D _{s}≲1).

- Authors:

- Univ. of Wisconsin, Madison, WI (United States). Dept. of Engineering Physics

- Publication Date:

- Research Org.:
- Univ. of Wisconsin, Madison, WI (United States)

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

- OSTI Identifier:
- 1390175

- Alternate Identifier(s):
- OSTI ID: 1395917; OSTI ID: 1436977

- Report Number(s):
- UW-CPTC 17-5

Journal ID: ISSN 1070-664X

- Grant/Contract Number:
- FG02-06ER54850; FC02-05ER54813; FC02-08ER54975

- Resource Type:
- Journal Article: Accepted Manuscript

- Journal Name:
- Physics of Plasmas

- Additional Journal Information:
- Journal Volume: 24; Journal Issue: 10; 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; mathematical foundations: fluid and multi-fluid theory; instabilities: hydromagnetic; computer simulation: MHD

### Citation Formats

```
Howell, E. C., and Sovinec, C. R.
```*Parameter-Space Survey of Linear G-mode and Interchange in Extended Magnetohydrodynamics*. United States: N. p., 2017.
Web. doi:10.1063/1.4993440.

```
Howell, E. C., & Sovinec, C. R.
```*Parameter-Space Survey of Linear G-mode and Interchange in Extended Magnetohydrodynamics*. United States. doi:10.1063/1.4993440.

```
Howell, E. C., and Sovinec, C. R. Mon .
"Parameter-Space Survey of Linear G-mode and Interchange in Extended Magnetohydrodynamics". United States.
doi:10.1063/1.4993440. https://www.osti.gov/servlets/purl/1390175.
```

```
@article{osti_1390175,
```

title = {Parameter-Space Survey of Linear G-mode and Interchange in Extended Magnetohydrodynamics},

author = {Howell, E. C. and Sovinec, C. R.},

abstractNote = {The extended magnetohydrodynamic stability of interchange modes is studied in two configurations. In slab geometry, a local dispersion relation for the gravitational interchange mode (g-mode) with three different extensions of the MHD model [P. Zhu, et al., Phys. Rev. Lett. 101, 085005 (2008)] is analyzed. Our results delineate where drifts stablize the g-mode with gyroviscosity alone and with a two-fluid Ohm’s law alone. Including the two-fluid Ohm’s law produces an ion drift wave that interacts with the g-mode. This interaction then gives rise to a second instability at finite ky. A second instability is also observed in numerical extended MHD computations of linear interchange in cylindrical screw-pinch equilibria, the second configuration. Particularly with incomplete models, this mode limits the regions of stability for physically realistic conditions. But, applying a consistent two-temperature extended MHD model that includes the diamagnetic heat flux density ($\vec{q}$*) makes the onset of the second mode occur at larger Hall parameter. For conditions relevant to the SSPX experiment [E.B. Hooper, Plasma Phys. Controlled Fusion 54, 113001 (2012)], significant stabilization is observed for Suydam parameters as large as unity (Ds≲1).},

doi = {10.1063/1.4993440},

journal = {Physics of Plasmas},

number = 10,

volume = 24,

place = {United States},

year = {Mon Sep 11 00:00:00 EDT 2017},

month = {Mon Sep 11 00:00:00 EDT 2017}

}