Nam-Sik Yoon (Chungbuk National University of Korea) A Dust Charging Model under Tokamak Discharge Conditions 6 th Japan-Korea Workshop on Theory and Simulation

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


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.


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


Thermionic emission


Radiation dT

Charging Mechanism Energy Balance

dR


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


Thermionic emission


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


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


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


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


• 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


Thermionic emission


Radiation

Heating & Cooling Mechanisms

dT

2-b. Dust Temperature Model2-b. Dust Temperature Model


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


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


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


Various data for C & W (from J. D. Martin, 2006)


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


Evaporation of carbon

19 3

8

10

300

10

i e

i e

d

n n m

T T eV

R m



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


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




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


19 3

8

2 10

500

10

i e

i e

d

n n m

T T eV

R m



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


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)


, 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)


, 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


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)


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)



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

Documents

Nam-Sik Yoon (Chungbuk National University of Korea) A Dust Charging Model under Tokamak Discharge Conditions 6 th Japan-Korea Workshop on Theory and Simulation