K. Shimizu1), T. Takizuka1), K. Ohya2), K. Inai2), T. Nakano1),A. Takayama3), H. Kawashima1), K. Hoshino1)

Kinetic Modelling of Impurity Transport in Detached Plasmafor Integrated Divertor Simulation with SONIC

(SOLDOR/NEUT2D/IMPMC/EDDY)

22nd IAEA Fusion Energy ConferenceGeneva, Switzerland 13 - 18 October, 2008

TH/3-3

1) Japan Atomic Energy Agency2) The University of Tokushima

3) National Institute for Fusion Science

Integrated Divertor Code for Fusion Reactor 2a

To investigate the power and particle control in tokamakreactor, integrated divertor codes have been developed.

• Gyro-motion ==> Erosion • Neutrals ==> Methane breakup• Kinetic effect ==> Thermal force

The MC approach has an advantage to the flexibility of modelling.

Plasma: Fluid

Impurities: Fluid

prediction

Neutrals:Monte Carlo

Interpretation

Plasma: Fluid

Neutrals:Monte Carlo

Impurities: MC

(not fully self-consistent because of MC problems)

Integrated Divertor Code in JAEA 2b

Without solving inherent MC problems, we hardly perform the integrateddivertor simulations with impurity MC code self-consistently.

Impurity Transport is solved with Monte Carlo modelling.

Plasma: Fluid

Neutrals:Monte Carlo

Impurities: MC

IMPMC

SOLDOR

NEUT2D

SONIC

long CPU

MC noise

steady state

How did we attack?

1. Model Developments2. X-point MARFE in JT-60U3. Methane Breakup Process4. Effect of Kinetic Thermal Force on Helium Retention

Means to Solve MC Problems 3

Time step for scattering process in conventional MC code is restricted as t << s ( typically 10-8 sec in detached plasma).

Diffusion model using Langevin analytical solution

Time step is extend up to transit time (typically L/v//=10-6 sec).

(1) long computational time

(2) MC noise use many sample particles (typically 50000) and optimize MC calculation by MPI

(3) assumption of steady state extension toward time evolution code

encounter a serious problem to increase test particle number with time.

Particle reduction scheme which consists of three steps:sorting of weight, pairing and Russian roulette.

After these improvement, we succeeded in the self-consistent coupling with IMPMC.

SONIC simulations reproduced the formation of X-pointMARFE in JT-60U discharge with high heating NBI power.

JT-60U experiment (PNB=15~20MW)

SONIC simulation

(PNB=15MW)

PNBI

D2 puff

attached detached Xp MARFE

time

4 Simulation of X-point MARFE with SONIC

To reduce the high heat load onto the divertor plate, the control method for impurity retention in the divertor region should be established.

Hydrocarbons sputtered from the dome contribute to the enhanced radiation near the X-point.

attached plasma detached plasma X-point MARFE

MW/m3

0

10

20

dome

Further Integration of EDDY code 5

We are proceeding to include the effect of PWI by introducing EDDY code to the integrated code SONIC.

EDDY & MD simulation

Plasma: Fluid

Neutrals:Monte Carlo

Impurities: MC

IMPMC

SOLDOR

NEUT2D

SONIC

• erosion on the divertor target• dissociation processes of hydrocarbon

The EDDY is a 3D Monte Carlo Impurity code to evaluate erosion on divertor plates.

EDDY

Code development was half done.

6 EDDY/IMPMC Simulation

IMPMC

EDDY C +

Plasma ion irradiation on material surfacesDynamic erosion and deposition processesImpurity transport in near-surface plasmadissociation processes of hydrocarbons: 700 reactions!

CxHy,x=1,2,3 (R.K.Janev, D.Reiter, Rep.FZ-Juelich, Jul-3966 (2002); Jul-4005 (2003))

Comparison with the observed erosion distribution:a small sticking of hydrocarbons and erosion yield of 0.01–0.02 on the outer divertor plate.

To investigate migration of carbon in large scale and contamination process into the main plasma,

H

CxHy Cx’Hy’

Redeposited layer

CH4 EDDY

for Methane Breakup Model

number density

Comparison with Simple Methane Breakup 7

detached inner divertor

(ned = 4.2 1020 m-3, Ted = 1.7 eV) attached outer divertor (ned = 1.9 1020 m-3, Ted = 17 eV)

The dome with a small sticking coefficient enhances the contam- ination of carbon into the main plasma.

In attached plasma, the methane breakup can not be simplified

In detached plasma, simple model is relatively good approximation

C => C+

CD4 => C+CD4 => C+

C => C+

sticking coef. = 0.2

EDDY/IMPMC

simpleionization

1/16

[1/mm2]

8

Kinetic thermal force strongly depends on the impurity ion speed.

Its direction changes for impurities with a high velocity of the order of Vthi.

averaged thermal force (fluid type)

R Ti= mI

v C(fI, fi)d

v (1)

kinetic thermal force

Substituting fI(

v ) = (

v V0 ) into the eq. (1),

we calculated the force along the magnetic field (

b ) acting on a impurity with a velocity of

V 0

FTi (

V 0 ) d v fi (

v )mI { v // }i

= d v fi(

v )

4 e4Zi2ZI

2

mIi

u

b

u3

(2)

where

u =

V 0 v

ion distribution function (fi = fM + fi ) distorted by Ti gradient

Kinetic Thermal Force

Detached plasma in JT-60SA

flux = 5 x1021s-1 , Qtotal = 37 MW , puff = 5 x1021 s-1 , Spump = 50 m3/s

The kinetic thermal force (toward colder region) have an effect for impurity ions with

Usually, V0 << Vthi for C ions

Te (eV)~1

300He2+

When He ions with Ti in core region flow into the cold divertor region, V0 > Vthi.~

V0 > Vthi.

plasma flow

9 Simulations of He transport in JT-60SAto study effect of kinetic thermal force

The kinetic effect of the thermal force is found to increase the He density in thedivertor region by a factor of ~2, compared with the conventional (fluid) evaluation.

He Density Profile W/O Recycling 10

kinetic

factor 2 !

fluid

AB

DC

He flux onto inner target

AB

He flux onto outer target

D C

11

• The kinetic effect is masked by the recycling at the target plates.

He Flux onto the Target in Steady Sate

The recycling regionmoves to strike point.

• Total amounts of He particles in the inner and outer divertor region increase by 15 and 21 %, respectively

He+

He+

He+He0

He0

plasma flow

AB D C

to outer divertor plate

AB

DC

to inner divertor plate

Summary 12

We overcame the disadvantage of MC modelling

limitation of time step ==> new diffusion model

large MC noise ==> optimizing on the massively parallel computer

assumption of steady state ==> particle reduction scheme

A self-consistent coupling of the divertor code with MC impurity code has been accomplished. The integrated divertor code is now available for study of the kinetic effect and hydrocarbon dissociation processes.

SONIC (SOLDOR/NEUT2D/IMPMC) simulations reproduced the formation of X-point MARFE in JT-60U discharge with high heating NBI power.

The dome with a small sticking coef. enhances the contamination of carbon into the main plasma. The methane breakup cannot be simplified in the attached plasma.

Without the recycling, the kinetic thermal force increases He density in the divertor region by a factor of ~2. This kinetic effect is masked by the recycling. Further study is needed for various flow patterns.

Kinetic Effect on C-density in Attached Plasma

The kinetic effect of thermal force enhances impurity retention for C4+. This factor is relatively high.

1015

1016

1017

1018

0 20 40 60 80 100 120

wx87&88_it25

C4

+ densit

y (m

-3 )

poloidal mesh

1015

1016

1017

1018

0 20 40 60 80 100 120

wx87&88_it25

K-effect

fluid

C2

+ densit

y (m

-3 )

poloidal mesh

1.3~1.5 1.2~1.4

Understanding of Kinetic Thermal Force

The definition of kinetic thermal force : the momentum change by Coulomb collisionis integrated over ion distribution distorted due to ion temperature gradient.

divertor

T1 T2

T1 < T0 < T2T0 T0

mfp

f1f0

F1+ F0F0

+ F2

F1+> F0

Fnet > 0

V0 ~ 0

f2

f0F2 < F0

+

Fnet > 0

composite force

V0 ~ vthiF1+< F0 Fnet < 0 F2 > F0

+ Fnet < 0

FTi

(

V 0 ) d v fi(

v )mI { v// }i

F0++ F0 = Fvf