1. 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 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 Model under Tokamak Discharge Conditions (6 th Japan-Korea Workshop on Theory and Simulation of Magnetic Fusion Plasmas, NIFS) A Dust Charging Model under Tokamak Discharge Conditions (6 th Japan-Korea Workshop on Theory and Simulation of Magnetic Fusion Plasmas, NIFS)

2. Nam-Sik Yoon, Chungbuk National University, Dust Transport Simulation in KSTAR 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. 2 1. Dusts in Tokamaks

3. 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.

4. Nam-Sik Yoon, Chungbuk National University, Dust Transport Simulation in KSTAR 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 4 But, dust physics modeling & simulation are not complete. There are many problems to be solved.

5. Nam-Sik Yoon (Chungbuk National University of Korea) A Dust Charging Model under Tokamak Discharge Conditions 5 Electron bombardment Thermionic emission Secondary electron emission Ion bombardment 2. Dust Charge & Temperature Models Ion bombardment Ion backscattering N recombination Electron bombardment Thermionic emission Secondary electron emission Radiation Charging Mechanism Energy Balance

6. Nam-Sik Yoon (Chungbuk National University of Korea) A Dust Charging Model under Tokamak Discharge Conditions 6 Charging Model Total emitted electron yieldwhere Electron bombardment Thermionic emission Secondary electron emission Ion bombardment 2-a. Dust Charging Model

7. Nam-Sik Yoon (Chungbuk National University of Korea) A Dust Charging Model under Tokamak Discharge Conditions 7 For a repulsive pot. The OML(Orbit Motion Limited) Theory (Drifted Maxwellian) For an attractive pot.

8. Nam-Sik Yoon (Chungbuk National University of Korea) A Dust Charging Model under Tokamak Discharge Conditions 8 Q>0 Q<0 Maxwellian approximation & analytic solutions Lambert W-function

9. Nam-Sik Yoon (Chungbuk National University of Korea) A Dust Charging Model under Tokamak Discharge Conditions 9 For Maxwellian electrons * Numerical fit in DTOKS [10] C W C0 -1.341 -1.4755 C10.74280.724 C20.11490.1521 C3 -0.0849 -0.0765 Secondary Electron Emission Traditional Modified Richardson Equation

10. 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 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 electron emission Radiation Heating & Cooling Mechanisms 2-b. Dust Temperature Model

11. Nam-Sik Yoon (Chungbuk National University of Korea) A Dust Charging Model under Tokamak Discharge Conditions 11 Ion & Electron Bombardment K: heat flux Neutral Bombardment neglected in DTOKS

12. Nam-Sik Yoon (Chungbuk National University of Korea) A Dust Charging Model under Tokamak Discharge Conditions 12 Ion Backscattering Thomas-Fermi reduced energy Neutral recombination Electron emissionThermal radiation  : emissivity(1 for black body, 0.8 for C, 1 for W  : Stefan-Boltzmann constant

13. Nam-Sik Yoon (Chungbuk National University of Korea) A Dust Charging Model under Tokamak Discharge Conditions 13 For a negatively charged dust For a positively charged dust Particle extinction process (melting/evaporation/sublimation) Radius Mass variation

14. 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)

15. 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) 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 model Method 2: Time varying charging model Method 1 Method 2 Method 1 Method 2 Method 1 Method 2 3. Simulation Results

16. Nam-Sik Yoon (Chungbuk National University of Korea) A Dust Charging Model under Tokamak Discharge Conditions 16 Evaporation of carbon Charge number of dust Potential of dust (V) Temperature (eV) of dust 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

17. 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) 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

18. 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) 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. Nam-Sik Yoon (Chungbuk National University of Korea) A Dust Charging Model under Tokamak Discharge Conditions 19 Charge number of dust Potential of dust (V) Temperature (eV) of dust 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

20. 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)

21. Nam-Sik Yoon (Chungbuk National University of Korea) A Dust Charging Model under Tokamak Discharge Conditions 21 TE-Model in DUSTT-code: A Modified Rechardson Equation TE-Model in DTOKS-code: The Original Rechardson Equation An Extended Model of TE (for spherical dust including the image force) O. W. Rechardson and S. Dushman (1923) M. S. Sodha and S. Srivastava (2010) M. S. Sodha and S. Guha (1971) 4.

22. Nam-Sik Yoon (Chungbuk National University of Korea) A Dust Charging Model under Tokamak Discharge Conditions 22 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)

23. Nam-Sik Yoon (Chungbuk National University of Korea) A Dust Charging Model under Tokamak Discharge Conditions 23 Work function of metal sphere with Debye shielding

24. Nam-Sik Yoon (Chungbuk National University of Korea) A Dust Charging Model under Tokamak Discharge Conditions 24 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) 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

25. Nam-Sik Yoon (Chungbuk National University of Korea) A Dust Charging Model under Tokamak Discharge Conditions 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. 25 5. Summary