Towards Self-consistence Integrated Simulations of Tokamak Plasmas - PowerPoint PPT Presentation

Towards Self-consistence Integrated Simulations of Tokamak Plasmas Hogun Jhang [1] , S. S. Kim [1] , T. Rhee [1] , G. Y. Park [1] , R. Singh [1,2] , P. H. Diamond [1,3] In collaboration with X. Q. Xu [4] , M. Umansky [4] , A. Dimits [4] [1] National Fusion Research Institute (NFRI), Rep. of Korea [2] Institute of Plasma Research (IPR), India [3] CMTFO and CASS, Univ. of California, San Diego, USA [4] LLNL, Livermore, USA KSTAR Conference 2014 (2014. 02. 25)

Outline  Introduction  Core gyrofluid code development  Edge plasma simulations  Summary  Future plans

Introduction

Self-consistent simulations  Important to have self-consistent simulation tools in interpreting /predicting magnetic fusion plasma experiments  Understanding of physics of magnetically confined plasmas  Reliable prediction of fusion performance  reliable reactor design  Self-consistent fusion plasma simulations essential to address new challenges in fusion plasma physics – understanding multi-scale, integrated interactions  Traditional 1.5D transport simulations: not self-consistent  Legacy of 20 th fusion plasma physics  First principle simulations  Useful for detailed snapshot analysis

Gyrofluid model  Fluid model retaining important kinetic features (e.g. Landau damping, finite orbit effects etc.)  Retain relevant physics:  Self-consistently evolving profiles  Turbulence  Computationally attractive  long-term, flux-driven core-edge coupled simulation feasible  Framework has been developed (e.g. BOUT++)  easy to implement. Major efforts in WCI

Core Gyrofluid Module Development Using BOUT++  S. S. Kim in this conference

Linear benchmark done 3+1 ITG gyrofluid model [Beer and Hammett PoP ’96 ] implemented  BOUT++ using the Beer model agrees well with gyrokinetic results. 

Nonlinear simulations Global nonlinear simulations using Beer model performed at fixed profile  Turbulence suppression by zonal flow observed  c i ( r i 2 v ti /L n ) vs. time(a/ v ti ) With ZF Without ZF w/o ZF w/ ZF Potential fluctuation

ITB formation simulations Use a simpler model (3+0) with reversed shear configuration  Non-resonant modes are fully taken into account  Signature of ITB-like structure observed near q min position   Turbulent eddies strongly sheared by ExB flow near qmin position  Code collapse due to strong (1,0) mode generation  PS flow physics! ExB shearing rate Ion temperature Potential fluctuation

Edge Plasma Simulations

Main focus  Explore the physics of ELM crash  Origin of small ELMs?  four-field model  Dynamical processes leading to large ELMs?  three field model  T. Rhee, et. al. in this conference  Self-consistent edge transport barrier formation with RBM turbulence by implementing  Flux-driven capability  Zonal flow evolution  G. Y. Park, et. al. in this conference

Small ELMs-1 Stability islands as origin of small ELMs? Theory predicts the existence of instability island at high n ( Hastie et al. 2003 PoP)   Ion drift waves + electron drift-acoustic waves  a new instability island  Claimed consistent with JT-60U grassy ELM regime showing stability boundary near infinite-n ideal ballooning modes [Aiba et.al. 2012 NF]

Small ELMs-2 Linear stability analysis using BOUT++ Four-field reduced MHD equations [Hazeltine et. al. PR 1985] implemented to  BOUT++ to find stability islands predicted by Hastie et. al. Linear stability analysis shows that   Contribution from parallel compression is negligible  No stability islands in intermediate to high-n regions  ideal ballooning modes may not be a candidate for small ELMs S=10 6 S=10 6

Small ELMs-3 Resistive ballooning modes as a possible candidate for small ELMs  BOUT++ simulation results for growth rate spectrum of RBMs (S=10 7 )  Resistivity destabilizes modes even when a < a c 2   dP q  α 2 μ   = R 0   dr B Mode number for maximum growth  rate decreases as α increases  For low α , broad high n modes are excited  edge turbulence  For large α , intermediate-n modes are excited  ELM-like bursty behavior

Big ELMs-1 Stochastic fields and role of electron dynamics Detailed observations during an ELM crash (three-field model) show  Formation of a strong initial current sheet triggered by initial instability:  (magnetic energy  h H ) Strong reconnection followed by a rapid propagation of stochastic field front  ELM affected area determined by the region occupied by stochastic fields   depends on electron dynamics (i.e. electron temperature profile) through h H (background turbulence)  Te profile evolution will be a crucial factor! Time-varying h H shows reduction of ELM affected region. 

Big ELMs-2 ELM energy loss: parallel vs. filamentary Filamentary-like convection loss vs. Rechester-Rosenbluth-like parallel heat  flow  Use RR diffusion along stochastic field lines with a kinetic adjustment  Parallel energy loss dominant in fully developed ELM crash (3-10 times depending on the kinetic factor)  Filamentary loss saturates at later stage due to phase-mixing  ELM Crash is NOT Filaments!!!

LH-1 Self-consistent edge transport barrier simulations  L-H transition:  Experimentally known for ~30 years  Theory well established based on transport bifurcation and/or profile self-organization (predator-prey dynamics, feedback) BUT  Self-consistent LH transition simulations successfully performed only in a variety of simplified forms  Flux-tube simulations (RBM turbulence): Rogers et. al. 1998  Sandpifle model: Gurzinov et. al. 2002  Externally imposed ExB shear (RBM): Beyer et. al. 2005  1-D transport model: Miki et. al. 2012-2013  No successful self-consistent, flux driven LH transition simulations featuring steady state profiles.  Still issue in fusion plasma simulations  Focus of this work

LH-2 Simulations shows formation of edge transport barrier  Flux-driven simulations with zonal flow taking into account  ETB forms around x~0.95 when power exceeds threshold value  formation of strong Er shear layer  exhibits features of 1 st order phase transition!!

LH-3 Simulations reveal detailed dynamics during L  H  Existence of limit cycle oscillations (LCOs) before transition  Triggering of L  H by turbulence-driven flow  Transition by mean ExB shear-driven positive feedback  Prediction of ExB stagnation period  indispensible for 1 st order phase transition?  origin of ZF triggering for L  H? ExB stagnation ExB stagnation

Summary and future plans  WCI efforts focused on towards integrated simulations using BOUT++ framework  Core-edge integration  Spatio-temporal multi-scale physics (turbulence + MHD, electron + ion)  Core gyrofluid modules developed using BOUT++ framework  Verification procedure established linear benchmark done  Nonlinear simulations are underway to obtain ITB in reversed shear  Edge simulations have been performed extensively to elucidate physics of  Small ELM (linear calculation) and Big ELMs (nonlinear calculation)  Self-consistent LH transition  Future plans:  Three big milestones:  Flux-driven repetitive ELM simulations with ZF  ITB formation in reversed shear plasma  Core-edge coupling through EM model  KBM+ITG+RBM  Simpler applications : RMP with ZF,