# Analytical and numerical study of the transverse Kelvin-Helmholtz instability in tokamak edge plasmas

## Abstract

Sheared flows perpendicular to the magnetic field can be driven by the Reynolds stress or ion pressure gradient effects and can potentially influence the stability and turbulent saturation level of edge plasma modes. On the other hand, such flows are subject to the transverse Kelvin–Helmholtz (KH) instability. Here, the linear theory of KH instabilities is first addressed with an analytic model in the asymptotic limit of long wavelengths compared with the flow scale length. The analytic model treats sheared $$\boldsymbol{E}\times \boldsymbol{B}$$ flows, ion diamagnetism (including gyro-viscous terms), density gradients and parallel currents in a slab geometry, enabling a unified summary that encompasses and extends previous results. In particular, while ion diamagnetism, density gradients and parallel currents each individually reduce KH growth rates, the combined effect of density and ion pressure gradients is more complicated and partially counteracting. Secondly, the important role of realistic toroidal geometry is explored numerically using an invariant scaling analysis together with the 2DX eigenvalue code to examine KH modes in both closed and open field line regions. For a typical spherical torus magnetic geometry, it is found that KH modes are more unstable at, and just outside of, the separatrix as a result of the distribution of magnetic shear. Finally implications for reduced edge turbulence modelling codes are discussed.

- Authors:

- Lodestar Research Corp., Boulder, CO (United States)
- Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States)

- Publication Date:

- Research Org.:
- Lodestar Research Corp., Boulder, CO (United States); Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States)

- Sponsoring Org.:
- USDOE Office of Science (SC), Fusion Energy Sciences (FES) (SC-24); USDOE National Nuclear Security Administration (NNSA)

- Contributing Org.:
- Lodestar Research Corporation Lawrence Livermore National Lab.

- OSTI Identifier:
- 1463839

- Alternate Identifier(s):
- OSTI ID: 1248339

- Report Number(s):
- LRC-16-164; LLNL-JRNL-737835

Journal ID: ISSN 0022-3778

- Grant/Contract Number:
- FG02-97ER54392; AC52-07NA27344

- Resource Type:
- Journal Article: Accepted Manuscript

- Journal Name:
- Journal of Plasma Physics

- Additional Journal Information:
- Journal Volume: 82; Journal Issue: 02; Journal ID: ISSN 0022-3778

- Publisher:
- Cambridge University Press

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 70 PLASMA PHYSICS AND FUSION TECHNOLOGY; plasma instabilities; Kelvin-Helmholtz; spherical torus

### Citation Formats

```
Myra, James R., D'Ippolito, Daniel A., Russell, David A., Umansky, Maxim V., and Baver, Derek A.
```*Analytical and numerical study of the transverse Kelvin-Helmholtz instability in tokamak edge plasmas*. United States: N. p., 2016.
Web. doi:10.1017/S0022377816000301.

```
Myra, James R., D'Ippolito, Daniel A., Russell, David A., Umansky, Maxim V., & Baver, Derek A.
```*Analytical and numerical study of the transverse Kelvin-Helmholtz instability in tokamak edge plasmas*. United States. doi:10.1017/S0022377816000301.

```
Myra, James R., D'Ippolito, Daniel A., Russell, David A., Umansky, Maxim V., and Baver, Derek A. Mon .
"Analytical and numerical study of the transverse Kelvin-Helmholtz instability in tokamak edge plasmas". United States. doi:10.1017/S0022377816000301. https://www.osti.gov/servlets/purl/1463839.
```

```
@article{osti_1463839,
```

title = {Analytical and numerical study of the transverse Kelvin-Helmholtz instability in tokamak edge plasmas},

author = {Myra, James R. and D'Ippolito, Daniel A. and Russell, David A. and Umansky, Maxim V. and Baver, Derek A.},

abstractNote = {Sheared flows perpendicular to the magnetic field can be driven by the Reynolds stress or ion pressure gradient effects and can potentially influence the stability and turbulent saturation level of edge plasma modes. On the other hand, such flows are subject to the transverse Kelvin–Helmholtz (KH) instability. Here, the linear theory of KH instabilities is first addressed with an analytic model in the asymptotic limit of long wavelengths compared with the flow scale length. The analytic model treats sheared $\boldsymbol{E}\times \boldsymbol{B}$ flows, ion diamagnetism (including gyro-viscous terms), density gradients and parallel currents in a slab geometry, enabling a unified summary that encompasses and extends previous results. In particular, while ion diamagnetism, density gradients and parallel currents each individually reduce KH growth rates, the combined effect of density and ion pressure gradients is more complicated and partially counteracting. Secondly, the important role of realistic toroidal geometry is explored numerically using an invariant scaling analysis together with the 2DX eigenvalue code to examine KH modes in both closed and open field line regions. For a typical spherical torus magnetic geometry, it is found that KH modes are more unstable at, and just outside of, the separatrix as a result of the distribution of magnetic shear. Finally implications for reduced edge turbulence modelling codes are discussed.},

doi = {10.1017/S0022377816000301},

journal = {Journal of Plasma Physics},

issn = {0022-3778},

number = 02,

volume = 82,

place = {United States},

year = {2016},

month = {4}

}

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