Korean Modeling Effort : C2 Code
J.M. ParkNFRC/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
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.
Current Status of KSTAR Project
Integrated Discharge Simulation Code for KSTAR
Neutral- GTNEUT- NTRANS
Neutral- GTNEUT- NTRANS
LHCD- LSC
LHCD- LSC
NBI- NUBEAM- NBEAMS- SNBI
NBI- NUBEAM- NBEAMS- SNBI
ICRH- TORIC- CURRAY
ICRH- TORIC- CURRAY
MHD Eq- ESC- ROTEQ - FEQ
MHD Eq- ESC- ROTEQ - FEQ
Transport- MMM95- GLF23- IFS/PPPL- NCLASS
Transport- MMM95- GLF23- IFS/PPPL- NCLASS
EdgeTurbulence
- ETB3D*
EdgeTurbulence
- ETB3D*
ELM- Ballooning
ELM- Ballooning
Coupled Core-Edge-SOL2-D Transport Code
C2 (Coupled 2-D)*
Coupled Core-Edge-SOL2-D Transport Code
C2 (Coupled 2-D)*
1 Plasma continuity2 Parallel momentum balance 3 Electron/Ion energy4 Current continuity5 Magnetic field diffusion
C2 : Coupled 2-Dimensional
1 Finite volume methodFinite volume method in unstructured multi-block grid2 All-speed compressible pressure-correctionpressure-correction algorithm3 Fully implicitFully implicit time advancing4 BiCGStab solver with physics-base preconditionerphysics-base preconditioner5 Parallel computing: domain decompositiondomain decomposition
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.
A parallel transient 2-D numerical method
* ExB drift* Diamagnetic drift
C2 Equations
Self-consistent ExB and diamagnetic drifts
Parallel viscous forceo local form
with neoclassical viscosity coefficients valid in all collisional regimes, ij
standard neoclassical expression if flux-surface averaged
211 12
ˆ2ˆ
5 i
qB u
p
B
3/ 2 1// // //2
4
3B B u V
B
b
2
1 112
1
3
B
B
b
2
2 122
1
3
B
B
b
1-D magnetic field diffusion equation (flux-surface averaged)
3/ 2 2// // //2
4 2 2
3 5 5 ii
B B q pVB p
Normalized minor radius0.1 0.2 0.3 0.4 0.5-5000
-2500
0
2500
5000
C2NCLASS
Normalized poloidal velocity
C2 Parallel Computation
Sub-Domain
Domain Decomposition Method with MPI
Number of Processor
Sp
eed
Up
0 5 10 15 20 250
5
10
15
20
25
Minor radius (m)
Tem
per
atu
re(k
eV)
0 0.1 0.2 0.3 0.4 0.5 0.60
1
2
3
4
5
Ti
Te
broken line : ASTRAsolid line : C2
Radial profile of electron & ion temperatures
Benchmark with ASTRA* : Ohmic Discharge, Ip = 2 MA
* ASTRA : Automated System for Transport Analysis in a Tokamak (1.5-D core transport code)
(C2 run with prescribed boundary conditions at core-edge interface)
C2 Validation: Core Region
Time (sec)
Tem
per
atu
re(k
eV)
0 0.5 1 1.5 20
1
2
3
4
5
Ti
Te
broken line : ASTRAsolid line : C2
Temperature evolution at magnetic axis
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 Validation: Edge/SOL Region
C2
B2SOLPS
C2
B2SOLPS
C2
B2SOLPS
B2SOLPS
C2
C1 : Coupled 1-Dimensional
SOL Region
Core Region
divertor
X-point
midplane
SOL Region
Core Region
divertor
X-point
midplane
MidplaneX-point
DivertorPlate
Heat Source Region
0 a L
MidplaneX-point
DivertorPlate
Heat Source Region
0 a L
Assume boundary T*
Advance core transport equations with boundary condition T*
Calculate qu*
Advance Edge-SOL transport equationswith boundary condition qu*
Check T*=T**
Next time step
Calculate T**
1.5D transport Code with 1D SOL model
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
LH LSC Ray-tracing NTCC
MHD EQ FEQ Free boundary/FDM SNU ROTEQ Fixed boundary/FEM SNU
Transport MMM95 Multi-Mode Mode NTCC NCLASS Neoclassical Model NTCC
ECCD TORAY** Ray-tracing NTCC
ESC Fixed boundary/Moment NTCC
ICRAY Ray-tracing NTCC FWCDSC Full wave SNU
Neutral GTNEUT TEP NTCC NTRANS** Monte-Carlo SNU
Integrated Computational Modules
* NTCC : National Transport Code Collaboration Libraries (http://w3.pppl.gov/ntcc)** Coupling algorithm under development
0 1 2 3 4 5 60
1
2
<n>/nGW
H89
betaN
0 1 2 3 4 5 60
1
2
3
Ip
PNBI/4
0 1 2 3 4 5 60
1
2
3
4
5
q95
q0
Predictive Hybrid Scenario Modeling
Pre-heating L-H transition
Ip = 1.0 MA, B = 2.0 T, PNBI = 8MW, <n>/nGW = 0.5
0 1 2 3 4 5 60
1
2
<n>/nGW
H89
betaN
Current ramp-up rates of KSTAR superconducting coils are too slow to adopt a conventional fast ramp-up method.
o Current ramp-up rate of KSTAR : ~ 0.5 MA/seco Necessary NBI preheating power : ~ 4 MW at t = 0.5 sec unrealistic scenario for KSTAR
Predictive Hybrid Scenario Modeling
Pre-heatingOff-axis current drive
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.
o Lower hybrid power for off-axis current drive : 1.5 MWo Necessary NBI preheating power : ~ 2 MW at t = 0.5 sec
0 1 2 3 4 5 60
1
2
3
Ip
PNBI/4
PLH/4
0 1 2 3 4 5 60
1
2
3
4
5
q95
q0
0 1 2 3 4 5 60
1
2
<n>/nGW
H89
betaN
0 1 2 3 4 5 60
1
2
3
4
5
q95
q0
0 1 2 3 4 5 60
1
2
<n>/nGW
H89
betaN
R (m)
Z(m
)
1 1.5 2 2.5-1.5
-1
-0.5
0
0.5
1
1.5
400 eVContour spacing 500 eV
50 eV
75 eV
100 eV
Electron temperatureTe : keV
R (m)
Z(m
)
1 1.5 2 2.5-1.5
-1
-0.5
0
0.5
1
1.5
400 eVContour spacing 500 eV
50 eV75 eV
125 eV100 eV
Ion temperatureTi : keV
Ion densityni
Neutral densityLog(nn)
x1019
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
11
22
33
11 22
33
Self-consistent 2-D Profiles in the Entire Region of KSTAR
Edge Pedestal Temperature during ELMs
minor radius (m)Io
nT
emp
erat
ure
(keV
)
2 2.1 2.2 2.3
1
2
3
4
5
6
7
8
Time (sec)
Ion
Ped
esta
lTem
per
atu
re(e
V)
0.2 0.4 0.6 0.8 1
0
500
1000
1500
2000
H-mode transition
Pedestaltemperature
(B = 3.5 T, Ip = 2 MA, <n> = 5.0x1019 m-3, Pnbi = 8 MW)
Edge Pedestal Temperature Tped : Limited by ELM
Temporal evolution of ion pedestal temperature during ELM
Temporal evolution of radial ion temperature profile during ELM
Simplified ELM model (Ballooning)
Divertor Heat load during ELMs
Time (sec)
Max
imu
mH
eatF
lux
(MW
/m2)
0.2 0.4 0.6 0.8 1
5
10
15
20
25
Ou
ter
Div
erto
rRapid Emissions of Plasma Energy and Particles during ELM
R (m)
Z(m
)
1 1.5 2-1.4
-1.2
-1
-0.8
-0.6
-0.4
-0.2
0
189168147126105846342210
Large transient heat loads onto divertor plates
Temporal evolution of maximumHeat flux onto outer divertor
Temporal evolution of electrontemperature
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 ono finding optimum operation scenarios to establish and sustain a broad current profiles with q0 1.o 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.
Summary
