X. Q. Xu Lawrence Livermore National Laboratory

1. Overview of recent BOUT++ Simulation and validation results X. Q. Xu Lawrence Livermore National Laboratory Acknowledgement: P.W.Xi1,2, C. H. Ma1,2 , T.Y.Xia1,3, B.Gui1,3, G.Q.Li1,3, J. F. Ma1,4, A.Dimits1, I.Joseph1, M.V.Umansky1, S.S.Kim5, T.Rhee5, G.Y.Park5, H.Jhang5, P.H.Diamond6,7, B.Dudson8, P.B.Snyder9 1Lawrence Livermore National Laboratory, Livermore, California 94551, USA 2School of Physics, Peking University, Beijing, China 3Institute of Plasma Physics, Chinese Academy of Sciences, Hefei, China 4Institute for fusion studies, University of Texas, Austin, TX 78712, USA 5WCI Center for Fusion Theory, National Fusion Research Institute, Daejon, South Korea 6CASS and Dept. of Physics, University of California, San Diego, La Jolla, CA, USA 7University of York, Heslington, York YO10 5DD, United Kingdom 8General Atomics, San Diego, California 92186, USA Presented at Institute of Plasma Physics, CASNovember 27, 2013, Hefei, China This work was performed under the auspices of the U.S. Department of Energy by Lawrence Livermore National Laboratory under Contract DE-AC52-07NA27344. LLNL-PRES-645770

2. Tokamak edge region encompasses boundary layer between hot core plasma and material walls • Complex geometry • Rich physics(plasma, atomic, material) • Sets key engineering constraints for fusion reactor • Sets global energy confinement Tokamak interior BOUT (BOUndary Turbulence) was originally developed at LLNL in late 1990s for modeling tokamak edge turbulence

3. BOUT++ is a successor to BOUT, developed in collaboration with Univ. York* Original BOUT, tokamak applications on boundary turbulence and ELMs with encouraging results BOUT-06: code refactoring using differential operator approach, high order FD, verification • Gyro-fluid extension • RMPs • Neutrals & impurities BOUT++: OOP, 2D parallelization, applications to tokamak ELMs and linear plasmas • Preconditioner • Computing on GPUs 2000 2005 2013 • X.Q. Xu and R.H. Cohen, Contrib. Plasma Phys. 38, 158 (1998) • Xu, Umansky, Dudson & Snyder, CiCP, V. 4, 949-979 (2008). • Umansky, Xu, Dudson, et al., , Comp. Phys. Comm. V. 180 , 887-903 (2008). • Dudson, Umansky, Xu et al., Comp. Phys. Comm. V.180 (2009) 1467. • Xu, Dudson, Snyder et al., PRL 105, 175005 (2010). B UT++ Boundary Plasma Turbulence Code

4. BOUT and BOUT++ have been products of broad international collaborations Lodestar Research Corporation Institute of plasma Physics Chinese Academy of Sciences Southwestern Institute of Physics

5. BOUT++ MAP

6. Principal Results • A suite of two-fluid models has been implemented in BOUT++ for • all ELM regimes and fluid turbulence • A suite of gyro-fluid models is under development for • pedestal turbulence and transport • Neutral models • Fluid neutral models are developed for • SMBI, GAS puffing, Recycling • Coupled to EIRENE Monte Carlo code to follow the neutral particles • A PIC module for impurity generation and transport • A framework for development of kinetic-fluid hybrid • A elm size dependence with density or collisionality for type-I ELMs mainly from edge bootstrap current and ion diamagnetic stabilization effects

7. BOUT++: A framework for nonlinear twofluid and gyrofluid simulations ELMs and turbulence • Different twofluid and gyrofluid models are developed under BOUT++ framework for ELM and turbulence simulations

8. A good agreement between BOUT++, ELITE and GATO for both peeling and ballooning modes • As edge current increases, the difference between BOUT++ and GATO/ELITE results becomes large • This difference is due to the vacuum treatment For the real “vacuum” model, the effect of resistivity should be included cbm18_dens8 A D n

9. 4-field model agrees well with 3-field for both ideal and resistive ballooning modes • ac value from eigenvalue solver agrees with BOUT simulation. • Non-ideal effects are consistent in both models • diamagnetic stabilization • resistive mode with a<ac • increase n of maximum growth rate with decrease of a

10. The onset of ELMs is shifted to due to P-B turbulence, which may explain those unknown questions observed in experiments • The occurrence of ELMs depends sensitively on the nonlinear dynamics of P-B turbulence; • The evolution of relative phase between P-B mode potential and the pressure perturbations is a key to ELMs • Phase coherence time determines the growing time of an instability by extraction of expansion free energy. • Nonlinear criterion sets the onset of ELMs P. W. Xi, X.Q. Xu, P. H. Diamond, submitted to PRL, 2013

11. BOUT++ global GLF model agrees well with gyrokinetic results • BOUT++ using Beer’s 3+1 model agrees well with gyrokinetic results. • Non-Fourier method for Landau damping shows good agreement with Fourier method. • Cyclone base case • Implemented in the BOUT++ • Padé approximation for the modified Bessel functions • Landau damping • Toroidal resonance • Zonal flow closure in progress • Nonlinear benchmark underway • Developing the GLF models • to behave well at large perturbations • for second-order-accurate closures • Conducting global nonlinear kinetic ITG/KBM simulations at pedestal and collisional drift ballooning mode across the separatrix in the SOL SS Kim, et al.

12. Development of flux-driven edge simulation Edge Transport Barrier formation with external sheared flow • Heat source inside the separatrix and sink outside the separatrix • ETB is formed by the externally applied sheared flow, but sometimes triggered by turbulence driven flow when external flow is zero SOL diffusion coefficient = 10-6 ExB shearing rate T=200 T=100 Time T=0 normalized poloidal flux normalized poloidal flux

13. Six-filed simulations show that Ion perturbation has a large initial crash and electron perturbation only has turbulence spreading due to inward ExB convection Te Ti

14. 6-field module has the capability to simulate the heat flux in divertor geometry Left: electron temperature perturbation Bottom: heat flux structures on toroidal direction. Toroidal direction (m) Toroidal direction (m) Toroidal direction (m) Six-field (ϖ, ni, Ti, Te, A||, V||): based on Braginskii equations, the density, momentum and energy of ions and electrons are described in drift ordering [1,2]. R (m) R (m) R (m) [1]X. Q. Xu et al., Commun. Comput. Phys. 4, 949 (2008). [2]T. Y. Xia et al., Nucl. Fusion53, 073009 (2013). Inner target Outer mid-plane Outer target

16. A set of equilibrium with different density profiles are generated Pressure profile is fixed Collisionality at peak gradient radial position:

17. As the edge density (collisionality) increases, the growth rate of the P-B mode increases for high n but decreases for low n (1<n<5) • S=10^8, SH=10^15, with ion diamagnetic effects and gyro-viscosity. • As the ballooning term dominates the high n modes, the stabilization effects of the ion diamagnetic drifts become less important when density is increased. • The kink term dominates the low n modes. Therefore, as the density increases, the edge current decreases and growth rate decreases. • As the edge collisionality increases, the dominant P-B mode shifts to higher n and the width of the dispersion relation increases. • The relation between ELM size and collisionality has been shown to have the same trend as the scaling law.

18. SMBI particle fueling models has been implementedPhysical model – plasmas, atom, molecule Quasi-neutral SMBI LCFS Local Const. Flux Boundary Simulation qualitatively consistent with Expts.

19. Ongoing validation of MHD instability data from EAST BOUT++ simulations show that the stripes from EAST visible cameramatch ELM filamentary structures Z (m) BOUT++ simulation shows that the ELM stripe are filamentary structures* EAST#41019@3034ms Visible camera shows bright ELM structure$ Z.X.Liu, et al., POSTER SESSION I 0 -0.5 2 2.25 • Pitch angle match! • Mode number match! T. Y. Xia, X.Q. Xu, Z. X. Liu, et al,TH/5-2Ra, 24th IEAE FEC, San Diego, CA, USA, 2012 $Photo by J. H. Yang *Figure by W.H. Meyer Major radius R (m)

20. Ongoing validation of MHD instability data from KSTAR The synthetic images from interpretive BOUT++ simulations show the similar patterns as ECEI H Park, et al., APS DPP invited talk, Nov., 2013 M. Kim, et al., POSTER SESSION I

21. Principal Results • A suite of two-fluid models has been implemented in BOUT++ for • all ELM regimes and fluid turbulence • A suite of gyro-fluid models is under development for • pedestal turbulence and transport • Neutral models • Fluid neutral models are developed for • SMBI, GAS puffing, Recycling • Coupled to EIRENE Monte Carlo code to follow the neutral particles • A PIC module for impurity generation and transport • A framework for development of kinetic-fluid hybrid • A elm size dependence with density or collisionality for type-I ELMs mainly from edge bootstrap current and ion diamagnetic stabilization effects

22. BOUT++ background information & websites • The 2013 BOUT++ workshop website, • https://bout2013.llnl.gov  • BOUT++ background information and • continuing development on the following websites: • https://bout.llnl.gov • http://www-users.york.ac.uk/~bd512//bout • http://boutproject.github.io