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

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

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

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)

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)

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)

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

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

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

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)

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

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

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

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

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

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

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. )

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)

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])

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)

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

Max-Planck-Institut für Plasmaphysik, EURATOM Association Results