1. Edge-SOL Plasma Transport Simulation for the KSTAR
The 6th Japan-Korea Workshop on Theory and Simulation of Magnetic Fusion Plasmas
28~29 July 2011
Edge-SOL Plasma Transport Simulation for the KSTAR
Seung Bo Shima, Jin-Woo Parkb, Hyunsun Hanc,
Hae June Leea, Yong-Su Nab, Jin Yong Kimc
aPusan National University, Busan, Korea
bSeoul National University, Seoul, Korea
cNational Fusion Research Institute, Daejon, Korea

2. Contents Introduction to KTRAN Simulation Results Summary
Comparison between carbon and tungsten divertor.
Gas puffing effects
Validation with experimental results
Summary

3. Advent of KTRAN
Steady state two-dimensional coupled transport code for plasma, neutral and impurity particles
Consists of three major modules that calculate plasma, neutral and impurity transports, respectively
Self-consistent description in transport phenomena in the edge region
Atomic interactions included
(ionization, charge-exchange, recombination, elastic collision)
Realistic wall configuration adaptable
Empirical formula for surface reflection and reaction rate coefficients
< Schematic diagram of a lower half of the edge region of a D-shaped tokamak >

4. * Deok-Kyu Kim, Phys. Plasma, 12, 062504 (2005)
Introduction of KTRAN
KTRAN*
: Two-dimensional coupled
edge transport code
NTRAN MC
Neutral density
Neutral velocity
Neutral energy
Ionization rate
Charge exchange rate
Excitation rate
PTRAN
FVM
Plasma density
Plasma velocity
Electron temperature
Particle flux
Heat flux
ITRAN
Impurity density
Impurity velocity
Impurity energy
Radiation power
* Deok-Kyu Kim, Phys. Plasma, 12, (2005)

5. Governing Equations Continuity Equation Parallel Momentum equation
1 𝐽 𝜕 𝜕𝑠 ( 𝐽 ℎ 𝑆 𝑛𝑢)+ 1 𝐽 𝜕 𝜕𝜌 ( 𝐽 ℎ 𝜌 𝑛𝑣)= 𝑆 𝑛
Parallel Momentum equation
1 𝐽 𝜕 𝜕𝑠 ( 𝐽 ℎ 𝑆 𝑛𝑚𝑢 𝑢 ∥ − 𝐽 ℎ 𝑠 2 𝜇 𝑠 𝜕 𝑢 ∥ 𝜕𝑠 )+ 1 𝐽 𝜕 𝜕𝜌 ( 𝐽 ℎ 𝜌 𝑛𝑚𝑢 𝑢 ∥ − 𝐽 ℎ 𝜌 2 𝜇 𝜌 𝜕 𝑢 ∥ 𝜕𝜌 )=- 𝐵 𝜃 𝐵 1 ℎ 𝑠 𝜕𝜌 𝜕𝑠 + 𝑆 𝑢 ∥
Perpendicular diffusion equation
𝑛𝑣=− D ⊥ ℎ 𝑝 𝜕𝑛 𝜕𝜌
Γ ⊥ =− D ⊥ 𝛻 ⊥ 𝑛
Electron Temperature Equation
1 𝐽 𝜕 𝜕𝑠 ( 𝐽 ℎ 𝑆 𝑛𝑢𝑘 𝑇 𝑒 − 𝐽 ℎ 𝑠 2 𝜒 𝑠 𝜕𝑘 𝑇 𝑒 𝜕𝑠 )+ 1 𝐽 𝜕 𝜕𝜌 ( 𝐽 ℎ 𝜌 𝑛𝑣𝑘 𝑇 𝑒 − 𝐽 ℎ 𝜌 2 𝜒 𝜌 𝜕𝑘 𝑇 𝑒 𝜕𝜌 )=- 𝑢 ℎ 𝑠 𝜕 𝑝 𝑒 𝜕𝑠 + 𝑆 𝐸

6. Impurity data for Carbon
Reflection rate coefficients of deuterium ion
incident on the carbon target .
Physical sputtering yields by the impact of
deuterium and carbon on the graphite target .
Radiation rate coefficient of
carbon depending on the electron temperature.
Rate coefficients of electron impact
ionization of carbon in various ionization
Rate coefficients of radiative recombination
of carbon in various ionization

7. Impurity data for Tungsten
Reflection rate coefficients of deuterium ion
incident on the tungsten target .
Physical sputtering yields by the impact of
deuterium and tungsten on the tungsten target .
Radiation rate coefficient of
tungsten depending on the electron temperature.
Rate coefficients of electron impact
ionization of tungsten in various ionization
Rate coefficients of radiative recombination
of tungsten in various ionization

8. Computational parameters
Computational Domain
Input Parameter
Total heating power (PNBI) 8 MW
Radiation loss ratio in the core plasma 40 %
Out/in power split
3/1
Plasma density at the core boundary 3
1019 m-3
Electron thermal diffusivity
1.0
m2/s
Radial diffusion coefficient
0.5
Recycling ratio
SOL plasma
Divertor
< KSTAR baseline operation mode >
( 35 x 9 ) grid

9. Results of KTRAN Carbon Tungsten Plasma density Plasma Temperature
[eV]
[eV]
Plasma
Temperature
These figures show the plasma density and plasma temperature in the carbon and tungsten divertor. Plasma density increased along the strike point until meet the divertor. Plasma density decreased when dirvertor is changed to the tungsten. Near the separatrix, 16% is reduced. In case of temperature, it decreased as wall is closer. And temperature increased slightly along the strike point.
Radiation 증가로 인한 power loss가 증가하여 탄소의 경우와 비교하여 온도가 약간 떨어지게 되고 이는 plasma flux가 줄어들게 된다. 이는 recycled neutral양도 줄어들게 되고 이같은 과정이 반복되면서 plasma density도 낮아지게 된다.

10. Results of KTRAN Carbon Tungsten Neutral density Neutral Temperature
[eV]
[eV]
Neutral Temperature
These figures show the neutral density and temperature. Near the divertor neutral density is higher, especially between strikepoint and divertor like a plasma density. Compared with carbon and tungsten divertor case, neutral density of tungsten divertor case is lower than carbon case along the strike point. .

11. Results of KTRAN Carbon Tungsten Impurity density Power Radiation
Max :8.69e18
Max :1.5e18
[m-3]
[m-3]
Impurity density
[W/m2]
[W/m2]
Power Radiation
As seen in the sputtering yield figure, tungsten sputtering is lower very much. Peak density is alomost 1/6 compare with carbon divertor. Low valent ion exist near the divertor and high valent ion exist near the separatrix. In case of carbon, it has sputtering very much and mono or di valent ion is dominant. In case of tungsten, it doesn’t occur much sputtering. So, density is lower, and multi valent ion increased compared with carbon divertor. So, impurity density is higher near the separatrix in case of tungsten divertor. And Power radiation is very lager in case of tungsten divertor.
Tungsten의 sputtering이 줄어들어 불순물 농도가 줄어든 것을 볼 수 있다. Radiation은 일단 rate coefficient가 탄소의 경우에 비하여 아주 높고 charge가 큰 이온일수록 멀리 떨어져 나가서 radiation을 내놓아서 넓은 영역에서 많은 radiation이 일어난다.

12. Heat flux on the divertor
Carbon
Tungsten
Heat flux on the tungsten divertor decreased slightly compared with carbon divertor..
As input power increased, increase of Heat flux on the carbon divertor is bigger than tungsten divertor.

13. Reduction of Heat Flux by Gas Puffing
Puffing gas: Deuterium and Argon
Puffing gas energy: Maxwellian distribution at thermal energy (0.026eV) D Ar
Puffing
Puffing
Deuterium gases are transported by collision with other particles and finally ionized or leaked out.
Argon gases are transported by friction and thermal gradient force.

14. Reduction of Heat Flux by Gas Puffing
Deuterium puffing
Argon puffing
Considerable reduction of peak heat flux at the divertor target plates was found to occur when the both gas puffing rate exceeds a certain threshold value
(~ 1.0 x 1020 /s for deuterium and ~ 5.0 x 1018 /s for argon).
As puffing gas flux density increases, heat flux is reduced and the location of peak heat flux point moves outward.

15. Transition of Carbon Impurity Distribution
No puffing
6.4 x /s
The amount of carbon density is decreased as deuterium gas is increased.
When the puffing rate is reached 6.4 x 1020 /s, the peak heat flux is about 5 MW/m2 (engineering limit), carbon peak density is lowered by 25 % compared to the one without puffing.
The decreased carbon impurity in SOL and divertor region will be expected to enhance the performance of steady state operation.

16. Simulation Conditions for NSTX
Computational Domain
Input Parameter and assumption
Total heating power (PNBI) 6 MW
Beam ion loss 15 %
Radiation loss ratio in the core plasma* 40
Out/in power split
4/1
Plasma density at the separatrix
6.79
1018m-3
Plasma temperature at the separatrix
110 eV
Plasma surface area 42 m2
<NSTX shot , 543 ms>
* B.J.Lee et al.,Fusion Sci.Technol.. 37,110, 2000
( 31 x 17 ) grid

17. Computational Results for NSTX
Plasma Density
Neutral Density
Plasma Temperature
Neutral Temperature
Plasma density is accumulated in front of the divertor target due to the neutral-plasma recycling effect.
Resulting mainly from charge-exchange reaction with the background plasma,
neutrals could have high energy about 160 eV.

18. Electron Density Profile at Midplane
For the density at separatrix,
nsep = 6.79 x 1018 m-3, is set by interpolation between the diagnostic points.
: Error bar
With D⊥ = 1 m2/s, ce,⊥ = 1 m2/s,
it agrees well with the experimental one.

19. Results of B2 code
Ready to compare the KTRAN results with B2 and SOLPS.

20. Comparison with SOLPS Plasma density Electron Temperature
Tungsten density
M.Toma et al.”First steps towards the coupling of the IMPGYRO and SOLPS Codes
to Analyze Tokamak Plasmas with Tungsten Impurities”, contrib. plasma phys. 50,392(2010)

21. Summary
The 2-D modeling of SOL and divertor region in KSTAR is performed with the KTRAN code.
In case of tungsten divertor, plasma and impurity density lowered than carbon divertor. But, power radiation increased which emitted from impurity.
As the puffing gas flux density increases more than a certain value (~ 1.0 x 1020 /s for deuterium and ~ 5.0 x 1018 /s for argon), peak heat flux is significantly reduced and the location of the peak heat flux moves outward from the strike point.
The density profile and peak heat flux of NSTX experiments is well-reproduced.
I plan to compare the KTRAN result with B2 and SOLPS.