1. Gyrofluid Turbulence Modeling of the Linear
Max-Planck-Institut für Plasmaphysik, EURATOM Association
Gyrofluid Turbulence Modeling of the Linear
Device VINETA
G. N. Kervalishvili, R. Kleiber, R. Schneider, B. D. Scott,
O. Grulke and T. Windisch

2. Max-Planck-Institut für Plasmaphysik, EURATOM Association
Outline
Motivation
Linear VINETA Device
Gyrofluid Code GEM3
Benchmarks
Results
Conclusions

3. Max-Planck-Institut für Plasmaphysik, EURATOM Association
Motivation
Study and understanding of turbulence under simplified conditions as a pre-requisite for understanding turbulence in tokamaks or stellarators
Far scrape off layer (in fusion devices): blobs
S. I. Krasheninnikov, Phys. Lett. A. (2001)
Blobs also exist in devices with linear magnetic geometry
G. Y. Antar et. al., PRL (2001), G. Y. Antar et. al., POP (2003)
Radial movement of blobs in PISCES experiments was explained by the concept of ‘neutral wind’
S.I. Krasheninnikov at al., POP (2003)
Net force:
Net force to wall replaces curvature

4. Max-Planck-Institut für Plasmaphysik, EURATOM Association
Motivation
Study and understanding of turbulence under simplified conditions as a pre-requisite for understanding turbulence in tokamaks or stellarators
Far scrape off layer (in fusion devices): blobs
S. I. Krasheninnikov, Phys. Lett. A. (2001)
Blobs also exist in devices with linear magnetic geometry
G. Y. Antar et. al., PRL (2001), G. Y. Antar et. al., POP (2003)
Interpretation of experiment: better diagnostics of VINETA
No radial movement of blobs observed in VINETA experiments
T. Windisch et al. Physica Scripta (2005)

5. Max-Planck-Institut für Plasmaphysik, EURATOM Association
Motivation
Study and understanding of turbulence under simplified conditions as a pre-requisite for understanding turbulence in tokamaks or stellarators
Far scrape off layer (in fusion devices): blobs
S. I. Krasheninnikov, Phys. Lett. A. (2001)
Blobs also exist in devices with linear magnetic geometry
G. Y. Antar et. al., PRL (2001), G. Y. Antar et. al., POP (2003)
Interpretation of experiment: better diagnostics of VINETA
No radial movement of blobs observed in VINETA experiments
T. Windisch et al. Physica Scripta (2005)
Turbulence modeling of linear VINETA device, using the gyrofluid 3D code GEM3
B. D. Scott, PPCF (2003)

6. Max-Planck-Institut für Plasmaphysik, EURATOM Association
Linear VINETA Device
Illustration of the VINETA device with its four modules (the total length is 4.5 m and the diameter 0.4 m).
C. Frank, O. Grulke, T. Klinger, POP (2002)

7. Max-Planck-Institut für Plasmaphysik, EURATOM Association
Gyrofluid Code GEM3
Electromagnetic gyrofluid model
Two-moment equations for each species: density, parallel velocity
VINETA case: no curvature, electrostatic, cylindrical annulus
Ion density and velocity moment equations
Electron density and velocity moment equations

8. Max-Planck-Institut für Plasmaphysik, EURATOM Association
Gyrofluid Code GEM3
Ions and electrons are connected by the polarization equation
is gyroaveraged potential
is approximated by
Dimensionless coordinates

9. Max-Planck-Institut für Plasmaphysik, EURATOM Association
Gyrofluid Code GEM3
Differential operators for cylindrical annulus
advection operators are given in terms of Poisson brackets
Parallel derivative is given by
Perpendicular parts of Laplacian are given by

10. Max-Planck-Institut für Plasmaphysik, EURATOM Association
Benchmarks
Slab case: estimation of the time for one turn
Cylinder case: diamagnetic estimate (time for one rotation)
Growth rate for slab case
Arakawa scheme for Poisson brackets (cylinder geometry)
2D Helmholtz solver (cylinder geometry)
Resolution study (cylinder geometry)
Computational dissipation study (cylinder geometry)

11. Max-Planck-Institut für Plasmaphysik, EURATOM Association
Benchmarks
Time = 500
Time = 250
Time = 0
Slab case: estimation of the time for one turn
Linearized 2D set of equations:
Fourier ansatz: simplification for small
Test case: ,
estimated time = 500 agrees with simulation result

12. Max-Planck-Institut für Plasmaphysik, EURATOM Association
Benchmarks
Time = 0
Time = 22
Time = 44
Cylinder case: estimation of the time for one rotation
Linear density profile:
Dimensionless variables:
Test case:
estimated time = 44 agrees with simulation result

13. Max-Planck-Institut für Plasmaphysik, EURATOM Association
Benchmarks
Estimation of growth rate in slab case
Linearized set of equations
Fourier ansatz: analytical dispersion relation

14. Max-Planck-Institut für Plasmaphysik, EURATOM Association
Benchmarks
Analytic result
Code result
Time scan of squared amplitude of
growth rate
growth rate

15. Max-Planck-Institut für Plasmaphysik, EURATOM Association
Results
Density profile from VINETA
Simulation parameters
Magnetic field
Electron temperature
Ion temperature
Drift scale
Sound speed
Radial dependent collisionality

16. Results Time scan of squared amplitude of density
Max-Planck-Institut für Plasmaphysik, EURATOM Association
Results
Time scan of squared amplitude of density
Time scan of squared amplitude of potential
Electron density

17. Max-Planck-Institut für Plasmaphysik, EURATOM Association
Results
Linear
Potential
Electron density
Simulation: drift-wave instability m=6
Experiment: drift-wave instability m=1-8 (C. Schröder at al. )

18. Max-Planck-Institut für Plasmaphysik, EURATOM Association
Results
Turbulence
Electron density
Potential
Simulation: no radial movement of blobs
Experiment: no radial movement of blobs (T. Windisch at al. 2005)

19. Max-Planck-Institut für Plasmaphysik, EURATOM Association
Conclusions
Adaption and checks of GEM3 for cylinder geometry
First simulations for VINETA parameters
No radial movement of blobs observed experimentally in VINETA (in contrast to previous results by PISCES) and in simulation
Future plans: complete physics and diagnostics in order to
compare quantitatively with experiment (also for
different operational regimes)
[C. Schröder at al. POP 2004])

24. Max-Planck-Institut für Plasmaphysik, EURATOM Association
Results
Linear
Potential
Electron density
Simulation: drift-wave instability m=6
Experiment: drift-wave instability m=1-8 (C. Schröder at al. 2004)

25. Max-Planck-Institut für Plasmaphysik, EURATOM Association
Benchmarks
Non-linear case
Time = 225
without dissipation
With dissipation

26. Max-Planck-Institut für Plasmaphysik, EURATOM Association
Results