Edge Two Fluids and Gyrokinetic Continuum Simulations Xueqiao Xu Presented at ITER Fusion Simulation Workshop May 16, 2006, Peking University Diverted tokamak magnetic fusion device and its poloidal Cross Section After R. Waltz et al, 2002 SnowMass Mtg. The Edge Transport Barrier is Critical to ITERs Performance Transport barriers form spontaneously at plasma edge Studies of core turbulence show Turbulent transport constrains gradient scale lengths T central ~ proportional to T ped T ped is the largest source of uncertainty in projecting ITERs performance Fusion gain = P fusion /P aux Projection of ITERs Fusion Gain Edge codes (BOUT and TEMPEST ) are aimed at reducing uncertainty in projections of ITERs fusion gain 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 BOUT is 3D EM Boundary Plasma Turbulence Code 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 a parallelized 3D nonlocal electromagnetic turbulence code using MPI A suite of the codes work together to make BOUT simulation results similar to real experiments A simple analytical neutral mode added In BOUT simulations turbulence is found in divertor leg region Cross-correlation plot shows that divertor turbulence is not correlated with upstream turbulence Plot of spatial distribution of RMS fluctuations amplitude shows that fluctuations grow in regions of unfavorable curvature BOUT simulations for C-Mod are consistent with experimental amplitude and spatial spectra of N i 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 Results show that strong spatial dependence of transport must be included a) Typical previous model b) Our new coupled results Poloidal variation understood from curvature instability Experiment (DIII-D, C-Mod) Radial distance (cm) 0.1 Results consistent with expt. Open - DIII-D Filled - C-Mod A kinetic edge code is required to model both todays tokamaks and ITER Fluid approximation requires: Not satisfied on DIII-D today Wont be satisfied on ITER Need to move beyond fluid codes DIII-D Edge Barrier or Describe each species with a kinetic distribution function, F ( ) ( , , , E 0, ,) Orbit width Tempest is a 5D Continuum Edge Gyrokinetic Plasma Code Gyrokinetic equations Valid for edge ordering Nonlinear Fokker-Planck collision Realistic X-point geometry open+closed flux surfaces Simulate neoclassical transport, turbulence and plasma-Surface interactions Fully Nonlinear Ion gyrokinetic equations We have designed and implemented a 4D edge simulation framework pyMPI (parallel Python) Gyrokinetic module Gyrokinetic module pyUEDGE module pyUEDGE module Visualization module (pyGist) Collisions Advection Acceleration Streaming Radial Drift Advection Acceleration Streaming Radial Drift Field solve SUNDIALS Distribution Function module Data Manager SAMRAI Hypre We have implemented a gyrokinetic Poisson equation field solver Discretized in - 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 N e = e e /Te / Simulation results agree very well with neoclassical theory in Ring geometry Radial Position R(m) Ion distribution function F(R,Z,E 0 in DIII-D geometry with endloss at plates in the SOL looks as expected V || Tempest recovers theoretical U || inside separatrix and increases as expected in SOL Tempest exhibits collisionless damping of GAMs and zonal Flow 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 s /L x Dirichlet radial boundary conditions GAMs provide opportunity to verify TEMPEST physics Rosenbluth-Hinton residual Frequency Time(v ti /R 0 ) Rosenbluth-Hinton Residual zonal flow Collisionless damping of zonal flow and GAM (t)/ t ) GAM sim / GAM th =1.06 Tempest exhibits collisionless damping of GAMs and zonal Flow Time(v ti /R 0 ) Rosenbluth-Hinton Residual zonal flow Collisionless damping of zonal flow and GAM (t)/ t ) GAM sim / GAM th =1.06 GAMs simulations converge with n v, n , and K Emax K Emax =15 rtol=10 -7, atol= r/R=0.02 q=2.23 n =30, n =50, n E =30, n =15 n =30, n =50, n E =60, n =30 n =30, n =50, n E =100, n =50 n =30, n =100, n E =60, n =30 n =30, n =50, n E =30, n =15, K Emax =10 Rosenbluth-Hinton Residual zonal flow Maximum kinetic energy has to be 10x thermal energy n =30, n =50, n E =30, n =15 rtol=10 -7, atol= r/R=0.02,q=2.2 K Emax =15 K Emax =10 K Emax =5 Contour plot of distribution function Time=0 Time=75 resonance Summary Edge simulation and modeling are critical to ITERs 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!