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 20th fusion plasma physics

• First principle simulations

 Useful for detailed snapshot analysis

 Fluid model retaining important kinetic features (e.g. Landau damping, finite

• rbit 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

Gyrofluid model

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.

ci (ri

2 vti /Ln ) vs. time(a/ vti)

Potential fluctuation

Without ZF With ZF w/ ZF w/o ZF

Nonlinear simulations



Global nonlinear simulations using Beer model performed at fixed profile



Turbulence suppression by zonal flow observed



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 qmin position

• Turbulent eddies strongly sheared by ExB flow near qmin position
• Code collapse due to strong (1,0) mode generation  PS flow physics!

Ion temperature Potential fluctuation ExB shearing rate

ITB formation simulations

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

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-1

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=106 S=106

Small ELMs-2

Resistive ballooning modes as a possible candidate for small ELMs

2

2μ        B q dr dP R = α  BOUT++ simulation results for growth rate spectrum of RBMs (S=107)

• Resistivity destabilizes modes even when a < ac



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

Small ELMs-3

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  hH)

• 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 hH (background turbulence)  Te profile evolution will be a crucial factor!

• Time-varying hH shows reduction of ELM affected region.

Big ELMs-1

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
• Big ELMs-2

ELM Crash is NOT Filaments!!!

Self-consistent edge transport barrier simulations

LH-1  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

 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 1st order phase transition!!

Simulations shows formation of edge transport barrier

LH-2

 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 1st order phase transition?  origin of ZF triggering for LH?

Simulations reveal detailed dynamics during LH

LH-3

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,