Korean Modeling Effort : C2 Code

1. Korean Modeling Effort : C2 Code J.M. Park NFRC/ORNL In collaboration with Sun Hee Kim, Ki Min Kim, Hyun-Sun Han, Sang Hee Hong Seoul National University presented at ITPA CDBM TG Meeting Princeton, NJ April 25, 2006

2. Current Status of KSTAR Project • The KSTAR main structures are almost completed. • The significant progresses, especially on the manufacture and test of TF and PF superconducting magnets, have been achieved. (16 TF coils encased, 4 CS coils completed, 4 Large PF coilds ready for assembly) • Machine assembly has to be finished by Aug. of 2007, then commisioning for integration will follow. • If the SCMS are commisioned successfully, the first plasma shot is expected in June of 2998. • KSTAR will open to the fusion research society not only domestically, but also internationally.

3. Integrated Discharge Simulation Code for KSTAR

4. C2 : Coupled 2-Dimensional A 2-D multi-fluid model extending the previous formulations of 1-D core and 2-D edge/divertor transports: Valid not only in the collisional edge/divertor regions but also in the high temperature core region. 1 Plasma continuity 2 Parallel momentum balance 3 Electron/Ion energy 4 Current continuity 5 Magnetic field diffusion * ExB drift * Diamagnetic drift Aparallel transient 2-D numericalmethod 1 Finite volume method in unstructured multi-block grid2 All-speed compressible pressure-correction algorithm 3Fully implicit time advancing 4 BiCGStab solver with physics-base preconditioner 5 Parallel computing: domain decomposition

5. C2 Equations • Self-consistent ExB and diamagnetic drifts • Parallel viscous force • local form • with neoclassical viscosity coefficients • valid in all collisional regimes, ij •  standard neoclassical expression if flux-surface averaged Normalized poloidal velocity • 1-Dmagnetic field diffusion equation (flux-surface averaged)

6. C2 Parallel Computation Domain Decomposition Method with MPI Sub-Domain

7. Temperature evolution at magnetic axis Radial profile of electron & ion temperatures C2 Validation: Core Region Benchmark with ASTRA* : Ohmic Discharge, Ip = 2 MA (C2 run with prescribed boundary conditions at core-edge interface) * ASTRA : Automated System for Transport Analysis in a Tokamak (1.5-D core transport code)

8. C2 Validation: Edge/SOL Region Benchmark with B2SOLPS : Te = Ti = 100 eV, ni = 2 x 10 19 m-3 (C2 run with prescribed boundary conditions at core-edge interface) C2 C2 B2SOLPS C2 B2SOLPS B2SOLPS B2SOLPS C2

9. C1 : Coupled 1-Dimensional 1.5D transport Code with 1D SOL model Assume boundary T* Advance core transport equations with boundary condition T* Calculate qu* Advance Edge-SOL transport equations with boundary condition qu* Calculate T** Check T*=T** Next time step

10. Integrated Computational Modules Module Code Feature Remark NBI NUBEAM Monte-Carlo NTCC* NBEAMS Semi-Analytic NTCC SINBI Semi-Analytic SNU ICRF/FWCD TORIC Full wave IPP CURRAY Ray-tracing NTCC ICRAY Ray-tracing NTCC FWCDSC Full wave SNU LH LSC Ray-tracing NTCC ECCD TORAY** Ray-tracing NTCC MHD EQ FEQ Free boundary/FDM SNU ROTEQ Fixed boundary/FEM SNU ESC Fixed boundary/Moment NTCC Neutral GTNEUT TEP NTCC NTRANS** Monte-Carlo SNU Transport MMM95 Multi-Mode Mode NTCC NCLASS Neoclassical Model NTCC * NTCC : National Transport Code Collaboration Libraries (http://w3.pppl.gov/ntcc) ** Coupling algorithm under development

11. Predictive Hybrid Scenario Modeling Ip = 1.0 MA, B = 2.0 T, PNBI = 8MW, <n>/nGW = 0.5 • Current ramp-up rates of KSTAR superconducting coils are too slow to adopt a conventional fast ramp-up method. • Current ramp-up rate of KSTAR : ~ 0.5 MA/sec • Necessary NBI preheating power : ~ 4 MW at t = 0.5 sec •  unrealistic scenario for KSTAR Pre-heating L-H transition

12. Predictive Hybrid Scenario Modeling Ip = 1.0 MA, B = 2.0 T, PNBI = 8MW, PLH = 1.5 MW, <n>/nGW = 0.5 • The desired q-profiles can be obtained with the baseline heating and current drive systems of KSTAR by earlier central heating and subsequent off-axis current drive during the current rise phase. • Lower hybrid power for off-axis current drive : 1.5 MW • Necessary NBI preheating power : ~ 2 MW at t = 0.5 sec Off-axis current drive Pre-heating

13. Electron temperature Te : keV Ion temperature Ti : keV Self-consistent 2-D Profiles in the Entire Region of KSTAR B = 3.5 T, Ip = 2 MA, <n> = 5.0x1019 m-3, Pnbi = 6 MW Neutral density Log(nn) x1019 Ion density ni

14. 1 3 2 Self-consistent 2-D Profiles in the Entire Region of KSTAR 1 2 3

15. Edge Pedestal Temperature during ELMs Edge Pedestal Temperature Tped: Limited by ELM (B = 3.5 T, Ip = 2 MA, <n> = 5.0x1019 m-3, Pnbi = 8 MW) Temporal evolution of ion pedestal temperature during ELM Temporal evolution of radial ion temperature profile during ELM Simplified ELM model (Ballooning)

16. Divertor Heat load during ELMs Rapid Emissions of Plasma Energy and Particles during ELM Large transient heat loads onto divertor plates Temporal evolution of maximumHeat flux onto outer divertor Temporal evolution of electrontemperature

17. Summary • A newly developed integrated simulation code C2 has been applied to predict high performance discharges of hybrid and standard H-mode scenario in the KSTAR tokamak. • The simulations have focused on • finding optimum operation scenarios to establish and sustain a broad current profiles with q0  1. • estimating edge pedestal parameters and divertor heat load • The desired q-profiles can be obtained with the baseline heating and current drive systems of KSTAR by earlier central heating and subsequent off-axis current drive during the current rise phase, although the current ramp-up rates of KSTAR superconducting coils are too slow to adopt a conventional fast ramp-up method. • Both the temperatures at the top of the edge pedestal and divertor heat load are estimated self-consistently during ELMs in the main heating phase.