Edge-SOL Plasma Transport Sim-ulation for the KSTAR

Seung Bo Shima, Jin-Woo Parkb, Hyunsun Hanc,

Hae June Leea, Yong-Su Nab, Jin Yong Kimc

aPusan National University, Busan, KoreabSeoul National University, Seoul, Korea

cNational Fusion Research Institute, Daejon, Korea

The 6th Japan-Korea Workshop on Theory and Simulation of Magnetic

Fusion Plasmas28~29 July 2011

2

Contents

• Introduction to KTRAN

• Simulation Results– Comparison between carbon and tungsten divertor.– Gas puffing effects– Validation with experimental results

• Summary

Advent of KTRAN

3

Steady state two-dimensional coupled transport code for plasma, neutral and impurity particles

< Schematic diagram of a lower half of the edge region of a D-shaped tokamak >

• Consists of three major modules that cal-culate plasma, neutral and impurity trans-ports, respectively

• Self-consistent description in transport phenomena in the edge region

• Atomic interactions included (ionization, charge-exchange, recombina-

tion, elastic collision)

• Realistic wall configuration adaptable

• Empirical formula for surface reflection and reaction rate coefficients

Introduction of KTRAN

4

NTRAN

MC

Neutral densityNeutral velocityNeutral energyIonization rate

Charge exchange rateExcitation rate

PTRAN

FVM

Plasma density

Plasma velocity

Electron temperature

Particle flux

Heat flux

ITRAN

MC

Impurity density

Impurity velocity

Impurity energy

Radiation power

: Two-dimensional coupled edge transport code

* Deok-Kyu Kim, Phys. Plasma, 12, 062504 (2005)

KTRAN*

Governing Equations

5

( )nnt nu S

( ) ( ) pt nmu nmuu p j B S

�

3 52 2[ ] [ ] e e

e e e e c Et nkT nkT u q u p Q S

Γ⊥=−D⊥𝛻⊥𝑛 𝑛𝑣 =−D⊥

h𝑝

𝜕𝑛𝜕 𝜌

)+)=

)+)=-+

)+)=-+

Continuity Equation

Parallel Momentum equation

Perpendicular diffusion equation

Electron Temperature Equa-tion

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 .

Rate coefficients of electron impactionization of carbon in various ionization

Rate coefficients of radiative recombination of carbon in various ionization

Radiation rate coefficient of carbon depending on the electron temperature.

Impurity data for Tungsten

101 102 103 104 105 10610-2

10-1

100

101

102

W to W D to W

Energy of incident Particle [eV]

Sput

terin

g Yi

eld

(W

to W

)

10-4

10-3

10-2

10-1

Sput

terin

g Yi

eld

(D

to W

)10-2 10-1 100 101 102 103 104 105 106

10-27

10-25

10-23

10-21

10-19

10-17

10-15

10-13

Ioni

zatio

n Ra

te C

oeffi

cient

[m-3

sec

-1]

Electron Temperature [eV]

W0 W1+ W2+ W3+ W4+ W5+ W6+ W7+ W8+ W9+ W10+ W11+ W12+ W13+ W14+ W15+ W16+ W17+ W18+ W19+ W20+

10-1 100 101 102 103 104 105 10610-27

10-25

10-23

10-21

10-19

10-17

10-15

Reco

mbi

natio

n Ra

te C

oeffi

cient

[m-3

sec

-1]

Electron Temperature [eV]

10-3 10-1 101 103 10510-3

10-2

10-1

100

Refle

ctio

n Co

efficie

nts

Incident Energy [eV]

RN

RE

RE/R

N

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 impactionization of tungsten in various ionization

Rate coefficients of radiative recombination of tungsten in various ionization

100 101 102 103 104 105

10-32

10-31

10-30

Radi

atio

n Ra

te C

oeffi

cient

[W m

3 sec

-1]

Electron Temperature [eV]

Radiation Rate Coefficient

Computational parameters

8

SOL plasma

Divertor

Computational Domain

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 m2/s

Recycling ratio 1.0

Input Parameter

< KSTAR baseline operation mode >

( 35 x 9 ) grid

Results of KTRAN

[m-3] [m-3]

[eV][eV]

Plasma density

Plasma Tempera-

ture

TungstenCarbon

Results of KTRAN

Neutral density

Neutral Tempera-

ture

TungstenCarbon[m-3] [m-3]

[eV][eV]

Results of KTRAN

Max :1.5e18Max :8.69e18[m-3] [m-3]

[W/m2] [W/m2]

Impurity density

Power Radiation

TungstenCarbon

12

Heat flux on the divertor

• 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.

0.00 0.01 0.02 0.03 0.04 0.05 0.06 0.070

4

8

12

16

20

Hea

t Flu

x [M

W/m

2 ]Distance from strike point [m]

W / 4MW W / 6MW W / 8MW W / 10MW W / 12MW W / 14MW W / 16MW

0.00 0.01 0.02 0.03 0.04 0.05 0.06 0.070

4

8

12

16

20

Hea

t Flu

x [M

W/m

2 ]

Distance from strike point [m]

C / 4MW C / 6MW C / 8MW C / 10MW C / 12MW C / 14MW C / 16MW

TungstenCarbon

Reduction of Heat Flux by Gas Puffing

13

Puffing gas: Deuterium and Argon

Argon gases are transported by friction and thermal gradient force.

Puffing gas energy: Maxwellian distribution at thermal energy (0.026eV)

Deuterium gases are transported by collision with other particles and finally ionized or leaked out.

Puffing

D Ar

Puffing

14

Reduction of Heat Flux by Gas Puffing

As puffing gas flux density increases, heat flux is reduced and the location of peak heat flux point moves outward.

Considerable reduction of peak heat flux at the divertor target plates was found to oc-cur 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).

Deuterium puffing Argon puffing

15

Transition of Carbon Impurity Distribution

No puffing 6.4 x 1020 /s

The amount of carbon density is decreased as deuterium gas is increased.

The decreased carbon impurity in SOL and divertor region will be expected to en-hance the performance of steady state operation.

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.

Simulation Conditions for NSTX

Computational Domain

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

Input Parameter and assumption

( 31 x 17 ) grid

<NSTX shot 128797, 543 ms>

* B.J.Lee et al.,Fusion Sci.Technol.. 37,110, 2000

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.

Computational Results for NSTX

Electron Density Profile at Midplane

With D⊥ = 1 m2/s, ce,⊥ = 1 m2/s, it agrees well with the experimental

one.

For the density at separatrix, nsep = 6.79 x 1018 m-3, is set by interpola-

tion between the diagnostic points.: Error bar

19

Results of B2 code

• Ready to compare the KTRAN results with B2 and SOLPS.

Comparison with SOLPSPlasma den-

sityElectron Tempera-

tureTungsten 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)

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.

21