# Gyrokinetic theory of slab universal modes and the non-existence of the gradient drift coupling (GDC) instability

## Abstract

A gyrokinetic linear stability analysis of a collisionless slab geometry in the local approximation is introduced. We focus on k _{∥}=0 universal (or entropy) modes driven by plasma gradients at small and large plasma β. These are small scale non-MHD instabilities with growth rates that typically peak near k _{⊥}ρi~1 and vanish in the long wavelength k _{⊥}→0 limit. This report also discusses a mode known as the Gradient Drift Coupling (GDC) instability previously reported in the gyrokinetic literature, which has a finite growth rate γ= $$\sqrt{β/[2(1+β)]C_{s}/|L_{p}|}$$ with C$$^{2}_{s}$$ =p _{0}/ρ _{0} for k _{⊥}→0 and is universally unstable for 1/L _{p}≠0. Here, we show that the GDC instability is a spurious, unphysical artifact that erroneously arises due to the failure to respect the total equilibrium pressure balance p _{0}+B$$^{2}_{0}$$ /(8π)=constant, which renders the assumption B$$^{\prime}_{0}$$ 0 =0 inconsistent if p$$^{\prime}_{0}$$ ≠0.

- Authors:

- Dartmouth College, Hanover, NH (United States)

- Publication Date:

- Research Org.:
- Dartmouth College, Hanover, NH (United States)

- Sponsoring Org.:
- USDOE Office of Science (SC)

- OSTI Identifier:
- 1540179

- Alternate Identifier(s):
- OSTI ID: 1437336

- Grant/Contract Number:
- SC0010508; DOE-SC-0010508

- Resource Type:
- Accepted Manuscript

- Journal Name:
- Physics of Plasmas

- Additional Journal Information:
- Journal Volume: 25; Journal Issue: 5; Journal ID: ISSN 1070-664X

- Publisher:
- American Institute of Physics (AIP)

- Country of Publication:
- United States

- Language:
- English

### Citation Formats

```
Rogers, Barrett N., Zhu, Ben, and Francisquez, Manaure. Gyrokinetic theory of slab universal modes and the non-existence of the gradient drift coupling (GDC) instability. United States: N. p., 2018.
Web. doi:10.1063/1.5024748.
```

```
Rogers, Barrett N., Zhu, Ben, & Francisquez, Manaure. Gyrokinetic theory of slab universal modes and the non-existence of the gradient drift coupling (GDC) instability. United States. doi:10.1063/1.5024748.
```

```
Rogers, Barrett N., Zhu, Ben, and Francisquez, Manaure. Wed .
"Gyrokinetic theory of slab universal modes and the non-existence of the gradient drift coupling (GDC) instability". United States. doi:10.1063/1.5024748. https://www.osti.gov/servlets/purl/1540179.
```

```
@article{osti_1540179,
```

title = {Gyrokinetic theory of slab universal modes and the non-existence of the gradient drift coupling (GDC) instability},

author = {Rogers, Barrett N. and Zhu, Ben and Francisquez, Manaure},

abstractNote = {A gyrokinetic linear stability analysis of a collisionless slab geometry in the local approximation is introduced. We focus on k∥=0 universal (or entropy) modes driven by plasma gradients at small and large plasma β. These are small scale non-MHD instabilities with growth rates that typically peak near k⊥ρi~1 and vanish in the long wavelength k⊥→0 limit. This report also discusses a mode known as the Gradient Drift Coupling (GDC) instability previously reported in the gyrokinetic literature, which has a finite growth rate γ= $\sqrt{β/[2(1+β)]C_{s}/|L_{p}|}$ with C$^{2}_{s}$ =p0/ρ0 for k⊥→0 and is universally unstable for 1/Lp≠0. Here, we show that the GDC instability is a spurious, unphysical artifact that erroneously arises due to the failure to respect the total equilibrium pressure balance p0+B$^{2}_{0}$ /(8π)=constant, which renders the assumption B$^{\prime}_{0}$ 0 =0 inconsistent if p$^{\prime}_{0}$ ≠0.},

doi = {10.1063/1.5024748},

journal = {Physics of Plasmas},

number = 5,

volume = 25,

place = {United States},

year = {2018},

month = {5}

}

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