Nam-Sik Yoon (Chungbuk National University of Korea) A Dust Charging Model under Tokamak Discharge Conditions
6th Japan-Korea Workshop on Theory and Simulation of Magnetic Fusion Plasmas 1
1. Dusts in Tokamaks
2. Dust Charge & Temperature Models
3. Simulation Results
4. New Formula of Thermionic Emission
5. Summary
1. Dusts in Tokamaks
2. Dust Charge & Temperature Models
3. Simulation Results
4. New Formula of Thermionic Emission
5. Summary
Nam-Sik Yoon
(Chungbuk National
University of Korea),
B. H. Park and J. Y. Kim
(NRFI)
A Dust Charging Modelunder Tokamak Discharge Conditions
(6th Japan-Korea Workshop on Theory and Simulationof Magnetic Fusion Plasmas, NIFS)
A Dust Charging Modelunder Tokamak Discharge Conditions
(6th Japan-Korea Workshop on Theory and Simulationof Magnetic Fusion Plasmas, NIFS)
Nam-Sik Yoon, Chungbuk National University, Dust Transport Simulation in KSTAR 2
Dust is produced by various processes in Tokamaks;
- Arcing & explosive ejection of hot plasma- Flaking, blistering & fracturing of deposited layers- Brittle destruction of surface imperfections- Coagulation of metal atoms on hot carbon surfaces- Nucleation/Agglomeration processes from supersaturated
vapor- Growth of dust in cold edge, e.g. in a detached divertor- Dust from carbon is much more pronounced than from
metals because of large erosion rates.
Dust can play an important role in the performance of fusion devices in 'standard' condition. [2008, Plasma Phys. Control. Fusion 50]
Dust problem will become more significant for future high power loadings and longer operation time fusion devices.
Dust is produced by various processes in Tokamaks;
- Arcing & explosive ejection of hot plasma- Flaking, blistering & fracturing of deposited layers- Brittle destruction of surface imperfections- Coagulation of metal atoms on hot carbon surfaces- Nucleation/Agglomeration processes from supersaturated
vapor- Growth of dust in cold edge, e.g. in a detached divertor- Dust from carbon is much more pronounced than from
metals because of large erosion rates.
Dust can play an important role in the performance of fusion devices in 'standard' condition. [2008, Plasma Phys. Control. Fusion 50]
Dust problem will become more significant for future high power loadings and longer operation time fusion devices.
1. Dusts in Tokamaks1. Dusts in Tokamaks
Nam-Sik Yoon, Chungbuk National University, Dust Transport Simulation in KSTAR 3
The issues surrounding the dust production include
- Issues on Plasma Performance:* Impurity transport around the Scrape-Off Layer (SOL). * Impurity can transport into the core.
- Engineering Issues:* Dust deposition blocking gaps
- Operation Issues: * Startup could be impeded.* Dust may disrupt the fusion plasma.
- Safety Issues: * Mobile dust containing tritium and beryllium which are
chemically reactive and/or toxic and/or radioactive.- Diagnostics Issues:
* Degradation of in-vessel diagnostic components by deposition
end erosion* Dust can be used for some kinds of diagnostics.
The issues surrounding the dust production include
- Issues on Plasma Performance:* Impurity transport around the Scrape-Off Layer (SOL). * Impurity can transport into the core.
- Engineering Issues:* Dust deposition blocking gaps
- Operation Issues: * Startup could be impeded.* Dust may disrupt the fusion plasma.
- Safety Issues: * Mobile dust containing tritium and beryllium which are
chemically reactive and/or toxic and/or radioactive.- Diagnostics Issues:
* Degradation of in-vessel diagnostic components by deposition
end erosion* Dust can be used for some kinds of diagnostics.
Nam-Sik Yoon, Chungbuk National University, Dust Transport Simulation in KSTAR 4
DUSTT & DTOKS codes DUSTT(Dust Transport) code:
- A. Y. Pigarov(2005), R. D. Smirov, S. I. Krasheninnikov (U. of Calif.) - Y. Tanaka (Kanazawa University): extends for various materials.
- 3D equation of motion of dust particles - Dust charging module is coupled. - Dust energy and mass balance model is included. - Ignore the perturbations of background plasma parameters by individual grains - Ignore grain-grain interactions
DUSTT(Dust Transport) code: - A. Y. Pigarov(2005), R. D. Smirov, S. I. Krasheninnikov (U. of Calif.) - Y. Tanaka (Kanazawa University): extends for various materials.
- 3D equation of motion of dust particles - Dust charging module is coupled. - Dust energy and mass balance model is included. - Ignore the perturbations of background plasma parameters by individual grains - Ignore grain-grain interactions DTOKS(Dust in Tokamaks) code: - J. D. Martin(2006, Max-Planck-Institute) - Employs a different charging developed as an extension of OML - Adopts, in some cases, a simpler approach to the modeling of plasma-dust grain interactions
DTOKS(Dust in Tokamaks) code: - J. D. Martin(2006, Max-Planck-Institute) - Employs a different charging developed as an extension of OML - Adopts, in some cases, a simpler approach to the modeling of plasma-dust grain interactions
But, dust physics modeling & simulation are not complete.There are many problems to be solved.
Nam-Sik Yoon (Chungbuk National University of Korea) A Dust Charging Model under Tokamak Discharge Conditions 5
Electron bombardment
Thermionic emission
Secondary electronemission
Ion bombardment
2. Dust Charge & Temperature Models2. Dust Charge & Temperature Models
Ion bombardment
Ion backscattering
N
recombination
Electron bombardment
Thermionic emission
Secondary electronemission
Radiation dT
Charging Mechanism Energy Balance
dR
Nam-Sik Yoon (Chungbuk National University of Korea) A Dust Charging Model under Tokamak Discharge Conditions 6
Charging Model
, , , , , ,1di OML e OML e th e se i OML tot e OML
dQI I I I I I
dt
,, ,
d OMLi OML e OML
dQI I
dt
tot se th Total emitted electron yield where,
,
e thth
e OML
I
I
1tot
1tot
Electron bombardment
Thermionic emission
Secondary electronemission
Ion bombardment
04d
dd
Q
R
,,
04d OMLd d
d d OMLd
QT T
e R e
00 ,
44 d d
d d d d OML
R TQ R Q
e
,d OML
dT
e
2-a. Dust Charging Model2-a. Dust Charging Model
Nam-Sik Yoon (Chungbuk National University of Korea) A Dust Charging Model under Tokamak Discharge Conditions 7
00
0 0
2 ( )
2t
qt t
U RI I
m
t 0
t 0
2
2 2
2 ( )
00
2 2m
t t
U R
mq
II I e e
2 20 0
2 2
0 0 00
0 0
0 0
( )
2 4
1 1 1
2
m m
t t
t m mq
t t t t
m m
U RI I erf erf
m
e e
t 00
2
2 2 ( )1q
t
I U RI
m
t 00
00 0
2 ( )
2t
qt t
U RI I
m
20
0 00
0 0
2 ( )
2
t
tq
t t t
e U RI I erf
m
For a repulsive pot. ( ) 0U r
( ) 0U r
The OML(Orbit Motion Limited) Theory (Drifted Maxwellian)
For an attractive pot.
2t
T
m 2
0 tI R qn
2 ( )m
U R
m
Nam-Sik Yoon (Chungbuk National University of Korea) A Dust Charging Model under Tokamak Discharge Conditions 8
0 0
21 1 0
q d
i
z e
T di e se th
e
Q eI e I I
t T
Q>0 Q<0
Maxwellian approximation & analytic solutions
Lambert W-function
0 0
21 1 0
d
e
eq d T
i e se thi
z eI I e I
T
0
0
21
2
q d
i
de e
e
z e
Ti i
eI I
T
I I e
20
20
e e et
i q i it
I R en
I R z en
0
0
2
21
d
e
e
Te e
q di i
i
I I e
z eI I
T
0
0
0
12 1
1
id
q
e qth
e se i
e se i
i e q
T ee W
z
T zI
I T
I T
I T z
0
0
0
12
1
d e
th i
i e q
e qi
e se i
ee T W
I T
I T z
T zI
I T
Nam-Sik Yoon (Chungbuk National University of Korea) A Dust Charging Model under Tokamak Discharge Conditions 9
3/22
2,
E
Tt
t
n Tf e
m
sec0
0
2
2e
se e
e
Ef E E dE
mT
Ef E dE
m
For Maxwellian electrons
* Numerical fit in DTOKS [10]
3 210 3 2 1 0log se e e e eT C T C T C T C
C WC0 -1.341 -1.4755 C1 0.7428 0.724C2 0.1149 0.1521C3 -0.0849 -0.0765
Secondary Electron Emission
2
3
1 04
expexp 1 , 0
d
ed d d d
d dd d
em WJ T T e e
h TT T
Traditional Modified
Richardson Equation
Nam-Sik Yoon (Chungbuk National University of Korea) A Dust Charging Model under Tokamak Discharge Conditions 10
• Heating Mechanisms− Ion Bombardment− Electron Bombardment− Neutral Bombardment
• Cooling Mechanisms− Ion Backscattering− Erosion Processes− Thermionic Emission− Secondary Electron Emission− Neutral Particle Emission− Radiative Cooling
Ion bombardment
Ion backscattering
N
recombination
Electron bombardment
Thermionic emission
Secondary electronemission
Radiation
Heating & Cooling Mechanisms
dT
2-b. Dust Temperature Model2-b. Dust Temperature Model
Nam-Sik Yoon (Chungbuk National University of Korea) A Dust Charging Model under Tokamak Discharge Conditions 11
Ion & Electron Bombardment
2i i d iK T e 0Q
0Q
2e e eK T K: heat flux
2i i d iK T e
2e e eK T
04d
dd
Q
R
04d d
dd
Q T
R e
Neutral Bombardment
12 ,
4n n d n n e eK T T n neglected in DTOKS
Nam-Sik Yoon (Chungbuk National University of Korea) A Dust Charging Model under Tokamak Discharge Conditions 12
Ion Backscattering
64
1 2,
3 5
2/3 2/3
ln,
1
0.0325
TFN E AA
TF TF
d iTF
i d i d i d
A A E eR
A E A E
M EE
m M Z Z Z Z
Thomas-Fermi reduced energy
2
22i i
i i d
mE T e
0dQ
0dQ 13.6 1.1rec d iK T
13.6 1.1 1rec d N iK T R
Neutral recombination
Electron emission
2 3emit d th se iK T W W
Thermal radiation
4 4rad d wK T T
a: emissivity(1 for black body, 0.8 for C, 1 for Ws: Stefan-Boltzmann constant
Nam-Sik Yoon (Chungbuk National University of Korea) A Dust Charging Model under Tokamak Discharge Conditions 13
4
2 1 13.6 1.1
2 3
net i i d E d
e e th se d
K T e R T
T W T
4
2 1 13.6 1.1 1
2
net i i d E d N
e e d
K T e R T R
T W T
For a negatively charged dust
For a positively charged dust
64
1 2,
3 5
2/3 2/3
ln,
1
0.0325
TFN E AA
TF TF
d iTF
i d i d i d
A A E eR
A E A E
M EE
m M Z Z Z Z
2 3 244 4 3
3B dd d d d d
d d d net d d d d B net netB
d k TdT R C eV dTM C R K R C R k K K
dt dt k dt
0Q
0Q
2
22i i
i i d
mE T e
Particle extinction process (melting/evaporation/sublimation)
24 d net
Mh R K
t
d
d net
Rh K
t
RadiusMass variation
Nam-Sik Yoon (Chungbuk National University of Korea) A Dust Charging Model under Tokamak Discharge Conditions 14
Various data for C & W (from J. D. Martin, 2006)
Nam-Sik Yoon (Chungbuk National University of Korea) A Dust Charging Model under Tokamak Discharge Conditions 15
Charge number of dust
Potential of dust (V) Temperature (eV) of dust
Time (m sec)
Time (m sec)Time (m sec)
18 3 610 , 40 , 10i e i e dn n m T T eV R m
Steady state temperature of carbon
-100000
-95000
-90000
-85000
-80000
-75000
0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6
-140
-135
-130
-125
-120
-115
-110
-105
0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 0
0.05
0.1
0.15
0.2
0.25
0.3
0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6
Method 1: Steady state charging modelMethod 2: Time varying charging model
Method 1
Method 2
Method 1
Method 2
Method 1
Method 2
3. Simulation Results3. Simulation Results
Nam-Sik Yoon (Chungbuk National University of Korea) A Dust Charging Model under Tokamak Discharge Conditions 16
Evaporation of carbon
19 3
8
10
300
10
i e
i e
d
n n m
T T eV
R m
Charge number of dust
Potential of dust (V) Temperature (eV) of dust
Time (m sec)
Time (m sec)Time (m sec)
-7500
-7000
-6500
-6000
-5500
-5000
-4500
-4000
-3500
-3000
-2500
0 2e-5 4e-5 6e-5 8e-5 0.0001 0.00012 0.00014 0.00016 0.00018 0.0002
-1100
-1000
-900
-800
-700
-600
-500
-400
-300
0 2e-005 4e-005 6e-005 8e-005 0.0001 0.00012 0.00014 0.00016 0.00018 0.0002
Method 1
Method 2
0
0.05
0.1
0.15
0.2
0.25
0.3
0.35
0 2e-005 4e-005 6e-005 8e-005 0.0001 0.00012 0.00014 0.00016 0.00018 0.0002
Method 1
Method 2 Method 1
Method 2
Nam-Sik Yoon (Chungbuk National University of Korea) A Dust Charging Model under Tokamak Discharge Conditions 17
Thermionic current
Electron OML current
Ion OML current
Time (m sec) Time (m sec)
Time (m sec)
Radius of dust
9.5e-009
9.55e-009
9.6e-009
9.65e-009
9.7e-009
9.75e-009
9.8e-009
9.85e-009
9.9e-009
9.95e-009
1e-008
0 2e-005 4e-005 6e-005 8e-005 0.0001 0.00012 0.00014 0.00016 0.00018 0.0002
Time (m sec)
-1.6e-009
-1.4e-009
-1.2e-009
-1e-009
-8e-010
-6e-010
-4e-010
-2e-010
0
0 2e-005 4e-005 6e-005 8e-005 0.0001 0.00012 0.00014 0.00016 0.00018 0.0002
-9e-009
-8e-009
-7e-009
-6e-009
-5e-009
-4e-009
-3e-009
-2e-009
-1e-009
0
0 2e-005 4e-005 6e-005 8e-005 0.0001 0.00012 0.00014 0.00016 0.00018 0.0002 9e-011
1e-010
1.1e-010
1.2e-010
1.3e-010
1.4e-010
1.5e-010
1.6e-010
1.7e-010
1.8e-010
0 2e-005 4e-005 6e-005 8e-005 0.0001 0.00012 0.00014 0.00016 0.00018 0.0002
Method 1
Method 2
Method 1
Method 2
Method 1
Method 2
Method 1
Method 2
Nam-Sik Yoon (Chungbuk National University of Korea) A Dust Charging Model under Tokamak Discharge Conditions 18
Charge number of dust
Potential of dust (V) Temperature (eV) of dust
Time (m sec)
Time (m sec)Time (m sec)
18 3
7
1 10
40
10
i e
i e
d
n n m
T T eV
R m
Steady state temperature of tungsten
-14000
-12000
-10000
-8000
-6000
-4000
-2000
0
0 0.5 1 1.5 2 2.5 3
Method 1
Method 2
-200
-180
-160
-140
-120
-100
-80
-60
-40
-20
0
0 0.5 1 1.5 2 2.5 3
Method 1
Method 2
0.1
0.12
0.14
0.16
0.18
0.2
0.22
0.24
0.26
0.28
0.3
0 0.5 1 1.5 2 2.5 3
Method 1
Method 2
Nam-Sik Yoon (Chungbuk National University of Korea) A Dust Charging Model under Tokamak Discharge Conditions 19
19 3
8
2 10
500
10
i e
i e
d
n n m
T T eV
R m
Charge number of dust
Potential of dust (V) Temperature (eV) of dust
Time (m sec)
Time (m sec)Time (m sec)
Melting & evaporation of tungsten
-7000
-6000
-5000
-4000
-3000
-2000
-1000
0
0 1e-006 2e-006 3e-006 4e-006 5e-006 6e-006
-12000
-10000
-8000
-6000
-4000
-2000
0
0 1e-006 2e-006 3e-006 4e-006 5e-006 6e-006 0.2
0.25
0.3
0.35
0.4
0.45
0.5
0.55
0 1e-006 2e-006 3e-006 4e-006 5e-006 6e-006
Method 1
Method 2
Method 1
Method 2
Method 1
Method 2
Nam-Sik Yoon (Chungbuk National University of Korea) A Dust Charging Model under Tokamak Discharge Conditions 20
0
1e-009
2e-009
3e-009
4e-009
5e-009
6e-009
7e-009
8e-009
9e-009
1e-008
0 1e-006 2e-006 3e-006 4e-006 5e-006 6e-006
Radius of tungsten dust
Time (m sec)
Nam-Sik Yoon (Chungbuk National University of Korea) A Dust Charging Model under Tokamak Discharge Conditions 22
, 1Q e Z
2 3 2 2
0 020 0
1 4 6 2 3 11 1
8 41 1 / 2R RZe E Ze E
W W WR d W R W
2
04
ed
W
2
R
eE
R, 1Q e Z
2 3 2
0 020
1 4 6 2 1 3
4 81 1 / 2R
m R R R
Ze EW U r W W ZE ZE E
R d W
2 2 6 2 24 exp , 1.20173 10d dd
WI T R AT A Am K
T
d
R
A New Work Function Formula for Spherical Dust (including Schottky Effect)
Modern Interpretation of the Nature of the Workfunction
- Debye(1910) & Langmuir(1916)'s image potential model (1910)- Schottky's concept of microscopic cutoff distance (1923) - Halas's metallic plasma model (1998)
Nam-Sik Yoon (Chungbuk National University of Korea) A Dust Charging Model under Tokamak Discharge Conditions 23
, 1Q e Z
2 3 2
0 2
00 0 0
1 4 6 2= 1 exp 1
1 1 / 2
3 1 1 1 1 1 1 1
8 4 4
D
R R RR
D
e dW W Z
R d
E E R EW E Z
W W W
Work function of metal sphere with Debye shielding
, 1Q e Z mW U r U R d 22 2
22 2
1exp
22 D
Z ee R e R R rU
r rr R
2
11
3 1
5
8
m
m
Z
eU r Z Z
R
Nam-Sik Yoon (Chungbuk National University of Korea) A Dust Charging Model under Tokamak Discharge Conditions 24
18 3
6
10
100
10
i e
i e
d
n n m
T T eV
R m
Calculation with new work function formula: carbon
0
0.05
0.1
0.15
0.2
0.25
0.3
0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 4.3
4.4
4.5
4.6
4.7
4.8
4.9
5
0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4
Work function (eV)Dust temperature (eV)
Time (m sec)Time (m sec)
result from new formula
-240000
-220000
-200000
-180000
-160000
-140000
0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4
Time (m sec)
Charge number of dust
Nam-Sik Yoon (Chungbuk National University of Korea) A Dust Charging Model under Tokamak Discharge Conditions 25
C & W dust particle charging mechanisms were simulated
based on the DUSTT & DTOKS physics models.
A dust charging model including a new thermionic electron emission formula is developed.
We have a plan to make a full dust code which includes
the particle dynamics.
C & W dust particle charging mechanisms were simulated
based on the DUSTT & DTOKS physics models.
A dust charging model including a new thermionic electron emission formula is developed.
We have a plan to make a full dust code which includes
the particle dynamics.
5. Summary5. Summary