# Theory and Fluid Simulations of Boundary Plasma Fluctuations

## Abstract

Theoretical and computational investigations are presented of boundary plasma microturbulence that take into account important effects of the geometry of diverted tokamaks--in particular, the effect of x-point magnetic shear and the termination of field lines on divertor plates. We first generalize our previous 'heuristic boundary condition' which describes, in a lumped model, the closure of currents in the vicinity of the x-point region to encompass three current-closure mechanisms. We then use this boundary condition to derive the dispersion relation for low-beta flute-like modes in the divertor-leg region under the combined drives of curvature, sheath impedance, and divertor tilt effects. The results indicate the possibility of strongly growing instabilities, driven by sheath boundary conditions, and localized in either the private or common flux region of the divertor leg depending on the radial tilt of divertor plates. We re-visit the issue of x-point effects on blobs, examining the transition from blobs terminated by x-point shear to blobs that extend over both the main SOL and divertor legs. We find that, for a main-SOL blob, this transition occurs without a free-acceleration period as previously thought, with x-point termination conditions applying until the blob has expanded to reach the divertor plate. We also derivemore »

- Authors:

- Publication Date:

- Research Org.:
- Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States)

- Sponsoring Org.:
- USDOE

- OSTI Identifier:
- 936982

- Report Number(s):
- UCRL-JRNL-227892

TRN: US0806151

- DOE Contract Number:
- W-7405-ENG-48

- Resource Type:
- Journal Article

- Resource Relation:
- Journal Name: Nuclear Fusion, vol. 47, July 2007, July 1, 2007, pp. 612; Journal Volume: 47

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 70 PLASMA PHYSICS AND FUSION; BOUNDARY CONDITIONS; CLOSURES; DISPERSION RELATIONS; DIVERTORS; FLUCTUATIONS; GEOMETRY; IMPEDANCE; PLASMA; PLATES; SHEAR; SOLS; TURBULENCE

### Citation Formats

```
Cohen, R H, LaBombard, B, LoDestro, L L, Rognlien, T D, Ryutov, D D, Terry, J L, Umansky, M V, Xu, X Q, and Zweben, S.
```*Theory and Fluid Simulations of Boundary Plasma Fluctuations*. United States: N. p., 2007.
Web. doi:10.1088/0029-5515/47/7/012.

```
Cohen, R H, LaBombard, B, LoDestro, L L, Rognlien, T D, Ryutov, D D, Terry, J L, Umansky, M V, Xu, X Q, & Zweben, S.
```*Theory and Fluid Simulations of Boundary Plasma Fluctuations*. United States. doi:10.1088/0029-5515/47/7/012.

```
Cohen, R H, LaBombard, B, LoDestro, L L, Rognlien, T D, Ryutov, D D, Terry, J L, Umansky, M V, Xu, X Q, and Zweben, S. Tue .
"Theory and Fluid Simulations of Boundary Plasma Fluctuations". United States.
doi:10.1088/0029-5515/47/7/012. https://www.osti.gov/servlets/purl/936982.
```

```
@article{osti_936982,
```

title = {Theory and Fluid Simulations of Boundary Plasma Fluctuations},

author = {Cohen, R H and LaBombard, B and LoDestro, L L and Rognlien, T D and Ryutov, D D and Terry, J L and Umansky, M V and Xu, X Q and Zweben, S},

abstractNote = {Theoretical and computational investigations are presented of boundary plasma microturbulence that take into account important effects of the geometry of diverted tokamaks--in particular, the effect of x-point magnetic shear and the termination of field lines on divertor plates. We first generalize our previous 'heuristic boundary condition' which describes, in a lumped model, the closure of currents in the vicinity of the x-point region to encompass three current-closure mechanisms. We then use this boundary condition to derive the dispersion relation for low-beta flute-like modes in the divertor-leg region under the combined drives of curvature, sheath impedance, and divertor tilt effects. The results indicate the possibility of strongly growing instabilities, driven by sheath boundary conditions, and localized in either the private or common flux region of the divertor leg depending on the radial tilt of divertor plates. We re-visit the issue of x-point effects on blobs, examining the transition from blobs terminated by x-point shear to blobs that extend over both the main SOL and divertor legs. We find that, for a main-SOL blob, this transition occurs without a free-acceleration period as previously thought, with x-point termination conditions applying until the blob has expanded to reach the divertor plate. We also derive propagation speeds for divertor-leg blobs. Finally, we present fluid simulations of the C-Mod tokamak from the BOUT edge fluid turbulence code, which show main-SOL blob structures with similar spatial characteristics to those observed in the experiment, and also simulations which illustrate the possibility of fluctuations confined to divertor legs.},

doi = {10.1088/0029-5515/47/7/012},

journal = {Nuclear Fusion, vol. 47, July 2007, July 1, 2007, pp. 612},

number = ,

volume = 47,

place = {United States},

year = {Tue Jan 09 00:00:00 EST 2007},

month = {Tue Jan 09 00:00:00 EST 2007}

}