21 July, 2011
Y. Tanaka (Kanazawa Univ.),
A.Yu.Pigarov, R.D.Smirnov, S.I.Krasheninnikov (UCSD),
N.Asakura, H.Takenaga (JAEA),
N.Ohno (Nagoya Univ.), Y. Uesugi (Kanazawa Univ.)• Dust in fusion devices is one of the most critical issues, mainlyrelated to the safety hazard.
– Enhancement of the tritium inventory– Risk of explosion at an accidental air or coolant leakage• Dust may be an important contributor of impurities
in the main and SOL plasmas in some devices( The impurities may increase radiation loss )Numerical simulation is a powerful tool nowadays
for basic understanding of dust particle formationand its transport in edge plasma condition offusion devices.!
-Ion drag force & dust potential, etc-Electron emission-Improved to treat various materials

DUSTT code has been developed by Dr.A.Pigarov, UCSD
cooperating UEDGE code (Dr.T.Rognlien, LLNL)

Calculation of behaviors of C dust particles in a plasma
in JT-60U configuration with DUSTT code-Behavior of individual dust launchedfrom different wall positions with different initial radii anddifferent initial velocities.
1-100 micron-Statistical analysis of dust particles
with different initial velocities.
-Calculation of trajectories, temporal evolution intemperature, mass, electronic charge, velocity etc of dust
particles in a plasma in JT-60U.
Behavior of ablating particles in plasmas

Other examples:-Spallation particle flight from polymer bulk irradiated by plasmas-Evaporation simulation of polymer particle

-Equation of motion of dust particle:-Ion friction forces-Neutral particle friction forces-Shape factor(=1.0 for sphere)

Spinning effectis neglected-Gravity-Electric field force
due to charging of the dust

-Equation of mass of dust particle:-Mass flux due tophysical & chemical
sputtering, RES,
thermal evaporation/sublimation

Γs Uniform mass loss
in radial direction
 Dust shape is always sphere.

-Equation of energy (uniform temperature profile
assumption inside a dust particle):Rad.

ΓsFluxes;
e,i,a-Liquid fraction

For melting process-Heating power transfer -Cooling power due tofrom ions, electrons
thermal radiaiton,& neutrals in a plasma physical & chemical
sputtering, RES,
thermal evaporation,-Latent heat for melting
electron emission

-Quasi-equilibrium condition for dust:i, e(Floating potential of dust)

For negative floating potential of dust
-Electron flux from thermoionic emission(Richardson-Dushman’s equation):

Relative drift velocity:-Electron flux from plasma:-Ion flux from plasma:

If ΓeTE or ΓeSEE is high,the floating potentialof dust can be positive.

-Quasi-equilibrium condition for dust:
For positive floating potential of dust
-Electron flux from thermoionic emission(Richardson-Dushman’s equation):-Electron flux from plasma:-Ion flux from plasma:

Relative drift velocity:Parameters of background plasma calculated with UEDGE codelog10 Te [eV]log10 ni [m-3]2.5log10 Ti [eV]

2.5

2.0

2.0

1.5

1.5

1.0

1.0

0.5

0.5

Ion parallel velocity vpi [m/s] [x104]
20198
4018
17-4-8Calculated by Dr. Pigarov, UCSD

Outer-divertor

j=48(i,j)=(74,1) j=1

Trajectories of the dust from outer region for different initial dust velocities -#O1

Trajectories of the dust from outer region for different initial dust radii -#O3

-Initially, electrostatic force is dominant,and then is ion drag force-Dominant force is ion dragforce, and atomic drag force.

Inner-divertor

j=48(i,j)=(1,1)
j=1Trajectories of the dust from inner region for different initial dust radii -#I3

-Initially, electrostatic force is dominant,and then is ion drag force

AC-Dominant force is ion dragforce, and atomic drag force.

Dome

i=1
(i,j)=(1,1)

i=19
i=56
i=74

Trajectories of the dust from private region for different initial dust velocities -#P1

-Near the strike point, a dust particle is rapidly heated and sublimated,which causes short penetration length.
-A dust particle from private zone is slowly heated.

-Near the outer strike point and outer wall, a dust particle isaccelerated in toroidal direction counter-clockwise.
This arises from ion drag force due to ion flow.
-Near the inner strike point, clockwise acceleration occurs
on a dust particle.

Fundamental study on dust particle behavior
Using polymer spallation particles.
-Polymer Ablation for Application to Arc Quenching実験条件，実験装置及び対象バルク材料
Ar gasPlasmaPolymer bulk

RF coil

15 mmφ	5 mm	

Sample holder

実験条件
入力電力8.54 kW
Ar シースガス流量 30 slpm
トーチ内圧力760 Torr

Cooling water
Polymer bulk
Observation window
High-speed color video

測定条件
フレームレート 1000 fps
実験系	 ・ 電力用遮断器
PTFE
SUS holder

・ 配線用遮断器
・ アークホーン	・ 宇宙分野（熱遮蔽）対象ポリマー材料
PTFE（テフロン）[-C2F4-]nPE（ポリエチレン） [-C2H4-]nPOM（デルリン）[-CH2O-]nPMMA（アクリル） [-C5H8O2-]n
PA66（ナイロン66） [-C12H22O2N2-]n
PA6（ナイロン6）[-C6H11ON-]nPF（フェノール樹脂）[-C7H6-]n	高速度カラービデオカメラ撮影結果(a) PTFE[-C2F4-]n(b) PE(c) POM[-C2H4-]n[-CH2O-]n(d) PMMA[-C5H8O2-]nSpallation
particles
Polymer bulk(e) PA66[-C12H22O2N2-]n(f) PA6[-C6H11ON-]n(g) PF[-C7H6-]nsample＊露光時間50µs（POMとPFは250µs）	 *再生速度は15 fps フレームレート 1000 fps

高速度カラービデオカメラ撮影結果	
25 mm
5 mm0 mm(a) PTFE[-C2F4-]n25 mm(b) PE(c) POM[-C2H4-]n[-CH2O-]n(d) PMMA[-C5H8O2-]nSpallation
particles

5 mm
0 mm

Polymer bulk

初速度 約2.5 m/s(e) PA66[-C12H22O2N2-]n(f) PA6[-C6H11ON-]n(g) PF[-C7H6-]nsample＊露光時間50µs（POMとPFは250µs）	 *再生速度は15 fps フレームレート 1000 fps

スポレーション粒子の飛翔の様相⇒ 100枚（0.1秒間）の連続した画像⇒ 各ピクセルでの輝度の最大値 	
飛翔粒子が辿った軌跡 	
飛翔粒子がプラズマ内部まで侵入，溶発 	ポリマー表面からの最大飛翔高さ（3〜25 mm） 	
100枚 	(a) PTFE[-C2F4-]n(b) PA66[-C12H22O2N2-]n(c) PA6[-C6H11ON-]nスポレーション粒子飛翔軌跡の数値解析
運動方程式
粒子に加わる力 ⇒ ドラッグ力

エネルギー保存式
Innershells

重力

熱プラズマ流体の抗力

Outershell

質量保存式⇒ Next
背景プラズマ場の計算手法

径方向の温度分布： 径方向位置： 粒子の速度： プラズマの速度： 粒子の半径： プラズマの質量密度： 粒子の質量密度： ドラッグ係数： 重力加速度： 粒子の温度： 粒子の液化率： ポリマーの定圧比熱： ポリマーの融点の潜熱： ポリマーの沸点の潜熱： ポリマーの熱伝導率： 熱伝達係数 	計算空間と各計算条件

ポリマーバルク材の端から放出

ポリマー表面の径方向温度 	

スポレーション粒子の初期条件
対象ポリマー材料 PA66
初期温度

500 K

初期直径0.5 mm

初期速度

1.5 m/s

計算終了条件
熱プラズマの温度場と流速ベクトル

初期直径の1/100以下⇒ 蒸発して消滅した

スポレーション粒子の飛翔軌跡

Axial position [mm]250-25250
Radial position [mm]PA66の飛翔様相
軸方向に近い方向角⇒ ほぼ同様な軌跡

飛翔軌跡の撮影結果と計算結果との比較	

3〜25 mm範囲内 	

3〜25 mm範囲外 	
2.5
スポレーション粒子が飛翔時に持つ初期エネルギー

1〜100 nJ程度

高速度ビデオカメラ撮影 ⇒ 初期速さ 約2.5 m/s直径約0.15 mm

Ar thermal plasma flow
at atmospheric pressure
T=10000 K
u=100 m/s

Rapidablation

Ablated vapor cloud

Polyethylene (PE) sphere particle
with d=300 µm
The physics to be considered:-Heat transfer-Rapid ablation  Rapid pressure rise  Strong gas flow
-Rapid ablation  Energy loss
-Change in properties of the surrounding plasma-Transport of ablated vapor-Shielding due to the ablated vapor from Ar plasmas

Governing Equations-Mass equation:These equations are solved by the CIP-CUP
method developed by Prof. Yabe.
The CIP-CUP method is an unified algorithm-Momentum equation:
to solve incompressible and compressible flow,
and thus it can simulate multiphase flow.
Qheat-Energy equation:-Mass fraction of ablated vapor:f : the volume of fraction-VOF function:-Equation of state (EOS):

f =1: Solid0< f <1: containing solid surface
f =0: Gas or plasma

Thermodynamic and transport properties of Ar andablated vapor
Equilibrium composition of Ar, and ablated vapor
Thermodynamic properties

The first order approximationof Chapman-Enskog method
Transport properties
Thermal conductivity

99%Ar+1%PE vapor

Calculation space
2D-cylindrical coordinate

u=100 m/s
T=10000 K

Δz=Δr=7.5 µm
d=300 µmrz

4.0x106 µm = 4.0 m-Kundsen number: Ku~0.03-Reynolds number: Re~0.65

Gas flow velocity and temperature fields
t=0.000 µs

Initial temperature: T=10000 K for Ar plasma, T=300 K for PE particle
Initial gas flow field was calculated without ablation

Gas flow velocity and temperature fields
t=3002500

1.371 µs

50007500

[K]
10000

Gas flow velocity and temperature fields
t= 3.185 µs

3002500

50007500[K]10000Gas flow velocity and temperature fields
t= 8.736 µs

300

2500

5000

7500

[K]
10000

Gas flow velocity and temperature fields
t= 17.56 µs

300

2500

5000

7500

[K]
10000

Gas flow velocity and temperature fields
t= 35.71 µs

300

2500

5000

7500

[K]
10000

Gas flow velocity and temperature fields
t= 91.25 µs

300

2500

5000

7500

[K]
10000

Gas flow velocity and temperature fields
t= 183.0 µs

300

2500

5000

7500

[K]
10000

Gas flow velocity and temperature fields
t= 344.7 µs

300

2500

5000

7500

[K]
10000

Gas flow velocity and temperature fields
t= 430.7 µs

300

2500

50007500

[K]
10000

Gas flow velocity and temperature fields
t= 523.4 µs

300

2500

50007500[K]10000Gas flow velocity and temperature fields
t= 616.51 µs

300

2500

5000

7500

[K]
10000

Gas flow velocity and temperature fields
t= 709.89 µs

300

2500

5000

7500

[K]
10000

Gas flow velocity and temperature fields
t= 803.33 µs

300

2500

50007500

[K]
10000

Time evolution in gas flow and temperature fields-Rapid ablation occurs
especially at upstream surfaceof the solid particle, whichproduces gas flow.
-Temperature around the particle
is decreased because of thermal
conduction and convection by
low temperature ablated vapor.
-The ablated vapor shields
the solid particle from directinteraction with the Ar plasma.

t=0 µst=17.56 µs

t=709.9 µs

Mass fraction of ablated vapor and VOF function
t=0.000 µs

The VOF function. If f >0.5, the color is gray

Mass fraction of ablated vapor
t=10-310-21.371 µs

10-1100

Mass fraction of ablated vapor
t=10-310-23.185 µs

10-1100

Mass fraction of ablated vaport=10-310-2

8.736 µs

10-1100

Mass fraction of ablated vaport=10-310-2

17.56 µs

10-1100

Mass fraction of ablated vapor
t= 35.71 µs

10-310-210-1100

Mass fraction of ablated vapor
t= 91.25 µs

10-310-210-1100

Mass fraction of ablated vaport=10-310-2

183.0 µs

10-1100

Mass fraction of ablated vapor
t= 344.7 µs

10-310-210-1100

Mass fraction of ablated vapor
t= 430.7 µs

10-310-210-1100

Mass fraction of ablated vapor
t= 523.4 µs

10-310-210-1100

Mass fraction of ablated vapor
t= 616.51 µs

10-310-210-1100

Mass fraction of ablated vapor
t= 709.89 µs

10-310-210-1100

Mass fraction of ablated vapor
t= 803.31 µs

10-310-2

10-1100

Transport of ablated vapor and shape change of the particle-Ablated vapor is transported
by diffusion, and by also
convection due to the external
Ar gas flow and the gas flow
produced by the ablation.
-Rapid ablation especially around
upstream of the particle decreases
the upstream radius of the particle.
-Lifetime of dust particle
was estimated to be
6 times longer thanthe conventional method
without considering temperature
decrease around the particle.

-The DUSTT code was adopted to a dust particle in plasmaof JT-60U configuration.
-Behaviors of carbon dust particles with radiiof 1-100 µm from different walls
were calculated by solving mass, motion and energy equations.

-Behavior of dust particle is dominated by ion drag force.
-Dust radius is reduced mainly by thermal sublimation.
Future work
-Comparison with experimental data
-Statistical analysis of dust particles with other radii