# Status of Continuum Edge Gyrokinetic Code Physics Development

## Abstract

We are developing an edge gyro-kinetic continuum simulation code to study the boundary plasma over a region extending from inside the H-mode pedestal across the separatrix to the divertor plates. A 4-D ({psi}, {theta}, {epsilon}, {mu}) version of this code is presently being implemented, en route to a full 5-D version. A set of gyrokinetic equations[1] are discretized on computational grid which incorporates X-point divertor geometry. The present implementation is a Method of Lines approach where the phase-space derivatives are discretized with finite differences and implicit backwards differencing formulas are used to advance the system in time. A fourth order upwinding algorithm is used for particle cross-field drifts, parallel streaming, and acceleration. Boundary conditions at conducting material surfaces are implemented on the plasma side of the sheath. The Poisson-like equation is solved using GMRES with multi-grid preconditioner from HYPRE. A nonlinear Fokker-Planck collision operator from STELLA[2] in ({nu}{sub {parallel}},{nu}{sub {perpendicular}}) has been streamlined and integrated into the gyro-kinetic package using the same implicit Newton-Krylov solver and interpolating F and dF/dt|{sub coll} to/from ({epsilon}, {mu}) space. With our 4D code we compute the ion thermal flux, ion parallel velocity, self-consistent electric field, and geo-acoustic oscillations, which we compare with standard neoclassicalmore »

- Authors:

- Publication Date:

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

- Sponsoring Org.:
- USDOE

- OSTI Identifier:
- 878209

- Report Number(s):
- UCRL-PROC-212647

TRN: US0602303

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

- Resource Type:
- Conference

- Resource Relation:
- Conference: Presented at: 10th IAEA Technical Meeting on "H-Mode Physics and Transport Barriers", St. Petersburg, Russia, Sep 28 - Sep 30, 2005

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 70 PLASMA PHYSICS AND FUSION TECHNOLOGY; ACCELERATION; ALGORITHMS; BOUNDARY CONDITIONS; DIVERTORS; ELECTRIC FIELDS; GEOMETRY; IAEA; IMPLEMENTATION; KINETICS; OSCILLATIONS; PHASE SPACE; PHYSICS; SIMULATION; SOLS; VELOCITY

### Citation Formats

```
Xu, X Q, Xiong, Z, Dorr, M R, Hittinger, J A, Kerbel, G D, Nevins, W M, Cohen, B I, and Cohen, R H.
```*Status of Continuum Edge Gyrokinetic Code Physics Development*. United States: N. p., 2005.
Web.

```
Xu, X Q, Xiong, Z, Dorr, M R, Hittinger, J A, Kerbel, G D, Nevins, W M, Cohen, B I, & Cohen, R H.
```*Status of Continuum Edge Gyrokinetic Code Physics Development*. United States.

```
Xu, X Q, Xiong, Z, Dorr, M R, Hittinger, J A, Kerbel, G D, Nevins, W M, Cohen, B I, and Cohen, R H. Tue .
"Status of Continuum Edge Gyrokinetic Code Physics Development". United States. https://www.osti.gov/servlets/purl/878209.
```

```
@article{osti_878209,
```

title = {Status of Continuum Edge Gyrokinetic Code Physics Development},

author = {Xu, X Q and Xiong, Z and Dorr, M R and Hittinger, J A and Kerbel, G D and Nevins, W M and Cohen, B I and Cohen, R H},

abstractNote = {We are developing an edge gyro-kinetic continuum simulation code to study the boundary plasma over a region extending from inside the H-mode pedestal across the separatrix to the divertor plates. A 4-D ({psi}, {theta}, {epsilon}, {mu}) version of this code is presently being implemented, en route to a full 5-D version. A set of gyrokinetic equations[1] are discretized on computational grid which incorporates X-point divertor geometry. The present implementation is a Method of Lines approach where the phase-space derivatives are discretized with finite differences and implicit backwards differencing formulas are used to advance the system in time. A fourth order upwinding algorithm is used for particle cross-field drifts, parallel streaming, and acceleration. Boundary conditions at conducting material surfaces are implemented on the plasma side of the sheath. The Poisson-like equation is solved using GMRES with multi-grid preconditioner from HYPRE. A nonlinear Fokker-Planck collision operator from STELLA[2] in ({nu}{sub {parallel}},{nu}{sub {perpendicular}}) has been streamlined and integrated into the gyro-kinetic package using the same implicit Newton-Krylov solver and interpolating F and dF/dt|{sub coll} to/from ({epsilon}, {mu}) space. With our 4D code we compute the ion thermal flux, ion parallel velocity, self-consistent electric field, and geo-acoustic oscillations, which we compare with standard neoclassical theory for core plasma parameters; and we study the transition from collisional to collisionless end-loss. In the real X-point geometry, we find that the particles are trapped near outside midplane and in the X-point regions due to the magnetic configurations. The sizes of banana orbits are comparable to the pedestal width and/or the SOL width for energetic trapped particles. The effect of the real X-point geometry and edge plasma conditions on standard neoclassical theory will be evaluated, including a comparison of our 4D code with other kinetic neoclassical codes (such as NCLASS[3] and XGC[4]) and experiments.},

doi = {},

url = {https://www.osti.gov/biblio/878209},
journal = {},

number = ,

volume = ,

place = {United States},

year = {2005},

month = {5}

}