Edge Two Fluids and Gyrokinetic Continuum Simulations

1. Edge Two Fluids and Gyrokinetic Continuum Simulations Xueqiao Xu Presented at ITER Fusion Simulation Workshop May 16, 2006, Peking University

2. Diverted tokamak magnetic fusion device and its poloidal Cross Section

3. The Edge Transport Barrier isCritical to ITER’s Performance • Transport barriers form spontaneously at plasma edge • Studies of core turbulence show • Turbulent transport constrains gradient scale lengths • Tcentral ~ proportional to Tped • Tped is the largest source of uncertainty in projecting ITER’s performance • Fusion gain = Pfusion/Paux Projection of ITER’s Fusion Gain Edge codes (BOUT and TEMPEST… ) are aimed at reducing uncertainty in projections of ITER’s fusion gain After R. Waltz et al, 2002 SnowMass Mtg.

4. Edge simulation models/codes • Two fluid model • Transport; • UEDGE, B2 • Turbulence • BOUT • BDM • DALF3 • Gyrokinetic model • Continuum methods • Tempest, FEFI • Particle-in-cell methods • XGC, ASCOT, ELMFIRE • Mont-Carlo Model • Degas, Eirene

5. Braginskii --- collisional, two-fluids electromagnetic equations Realistic X-point geometry open+closed flux surfaces BOUT is being applied to DIII-D, C-mod, NSTX, MAST, ITER (for Snowmass), ... LOTS of edge fluctuation data! BES, GPI, PCI, Probe, and Reflectometer Provide excellent opportunity for validating BOUT against experiments. BOUT is 3D EM Boundary Plasma Turbulence Code

6. BOUT is a parallelized 3D nonlocal electromagnetic turbulence code using MPI

7. A suite of the codes work together to make BOUT simulation results similar to real experiments

8. A simple analytical neutral mode added

9. Plot of spatial distribution of RMS fluctuations amplitude shows that fluctuations grow in regions of unfavorable curvature In BOUT simulations turbulence is found in divertor leg region Cross-correlation plot shows that divertor turbulence is not correlated with upstream turbulence

10. BOUT simulations for C-Mod are consistent with experimental amplitude and spatial spectra of Ni

11. BOUT simulations yield filamentary structures as experiments for edge localized modes (ELMs) • Ingredients of an ELM simulation • Nonlinear with “fast” explosive nonlinearities • Produces fine scale fingers/blobs/ etc • Fast transport along the field line and turbulent transport across the field line • Allow for magnetic reconnection • BOUT simulations • Early structure & growth similar to linear pressure-/current-gradient driven modes • Radially propagating filamentary structures grow explosively (as seen in MAST, DIII-D) • Filaments acting as conduits to pedestal, provide mechanisms for ELM losses • Not able to simulate complete bursting event at present; mesh alignment is a problem PRL 2004 A. Kirk et al. BOUT simulations, Snyder et al, PoP 2005

12. Experiment (DIII-D, C-Mod) 0.1 0 2 4 Radial distance (cm) Results show that strong spatial dependence of transport must be included Results consistent with expt. a) Typical previous model b) Our new coupled results • Poloidal variation understood from curvature instability Open - DIII-D Filled - C-Mod

13. Orbit width A kinetic edge code is required to model both today’s tokamaks and ITER • Fluid approximation requires: • Not satisfied on DIII-D todayWon’t be satisfied on ITER • Need to move beyond fluid codes DIII-D Edge Barrier or  Describe each species with akinetic distribution function, F(a)(y, , ,E0, ,)

14. Gyrokinetic equations Valid for edge ordering Nonlinear Fokker-Planck collision Realistic X-point geometry open+closed flux surfaces Tempest is a 5D Continuum Edge Gyrokinetic Plasma Code Simulate neoclassical transport, turbulence and plasma-Surface interactions

15. Fully Nonlinear Ion gyrokinetic equations

16. We have designed and implemented a 4D edge simulation framework pyMPI (parallel Python) Visualization module (pyGist) Gyrokinetic module pyUEDGE module SUNDIALS Data Manager Advection Acceleration Streaming Radial Drift Hypre Field solve Collisions SAMRAI Distribution Function module

17. We have implemented a gyrokinetic Poisson equation field solver Ne=<Ni0 >eeF/Te/< eeF/Te> • Discretized in y-q coordinates using standard finite differencing • Uses Hypre library of parallel linear algebra solvers and preconditioners • Solvers: • Conjugate Gradient (CG) • Generalized Minimum Residual (GMRES) • Stabilized BiConjugate Gradient (BiCGSTAB) • Preconditioners • Diagonal scaling • Block Gauss-Seidel with PFMG or SMG in each block • BoomerAMG • Currently implemented with Boltzmann electron model

18. Radial Position R(m) Simulation results agree very well with neoclassical theory in Ring geometry

19. V|| V|| V|| V|| Ion distribution function F(R,Z,E0,m) in DIII-D geometry with endloss at plates in the SOL looks as expected

20. Tempest recovers theoretical U|| inside separatrix and increases as expected in SOL

21. Tempest exhibits collisionless damping of GAMs and zonal Flow f(t)/f(t=0) • Axis-symmetric mode (no toroidal variation) – Parallel ion dynamics – Magnetic curvature  TEMPEST should see GAMs • Tempest model • Drift kinetic ions with radial drift, streaming, and acceleration • Boltzmann electron • Gyrokinetic Poisson equation in limit small rs/Lx • Dirichlet radial boundary conditions • GAMs provide opportunity to “verify” TEMPEST physics • Rosenbluth-Hinton residual • Frequency Rosenbluth-Hinton Residual zonal flow Collisionless damping of zonal flow and GAM wGAMsim/wGAMth=1.06 Time(vti/R0)

22. Tempest exhibits collisionless damping of GAMs and zonal Flow f(t)/f(t=0) Rosenbluth-Hinton Residual zonal flow Collisionless damping of zonal flow and GAM wGAMsim/wGAMth=1.06 Time(vti/R0)

23. GAMs simulations converge with nv, nq, and KEmax ny=30, nq=50, nE=30, nm=15 ny=30, nq=50, nE=60, nm=30 ny=30, nq=50, nE=100, nm=50 ny=30, nq=100, nE=60, nvy=30 ny=30, nq=50, nE=30, nm=15, KEmax=10 KEmax=15 rtol=10-7, atol=10-12 r/R=0.02 q=2.23 Rosenbluth-Hinton Residual zonal flow

24. Maximum kinetic energy has to be 10x thermal energy KEmax=15 KEmax=10 KEmax=5 ny=30, nq=50, nE=30, nm=15 rtol=10-7, atol=10-12 r/R=0.02,q=2.2

25. Contour plot of distribution function Time=75 Time=0 resonance

26. Summary • Edge simulation and modeling are critical to ITER’s Performance • Two fluid turbulence code BOUT yields simulation results consistent with experiments for present day tokamaks • Edge gyrokinetic continuum code TEMPEST is under development • A lot of scientific phenomenon remain to be discovered via advanced computing!