Study of Impurity Distribution and Transport Coefficients - PowerPoint PPT Presentation

Study of Impurity Distribution and Transport Coefficients Determination in ITER like Plasma Coefficients Determination in ITER-like Plasma Liping Zhu, Woochang Lee, Gunsu Yun, Hyeon K. Park Pohang University of Science and Technology, Pohang 790-784, Korea 85 th KPS Meeting 85 KPS Meeting (Changwon, October 21-23, 2009)

Contents � Introduction of MIST code Main plasma profiles and parameters used in this study � � Impurity distribution in ITER-like plasma � Steady state case Time dependent case � Determination of impurity transport coefficients in � ITER-like plasma

I. Introduction of MIST code (1) An impurity transport simulation code, Multiple Ionization State Transport (MIST), p y p , p p ( ), which is designed for circular cross-section plasma , has been used to study the radial distribution of impurities in various charge states in the standard ITER-like plasma parameters. The code solves for density of ions in each charge state of the impurity and their associated radiation rates using atomic physics appropriate for these low-density and high-temperature plasmas high-temperature plasmas. The expression governing the time evolution of a given impurity charge-state density in space and time has the form: in space and time has the form: ∂ ∂ n n 1 = − Γ + − + + − + q q ( r ) I n ( I R n ) R n S − − + + ∂ ∂ τ q q 1 q 1 q q q q 1 q 1 q t r r q Γ Γ where where is particle flux density, its general form is is particle flux density its general form is q ∂ n Γ = − + υ q D r ( ) ( ) r n ∂ q q q q r υ υ D r : particle diffusion coefficient, : particle diffusion coefficient : convective velocity : convective velocity D r ( ) ( ) q r ( ) ( ) r q τ , , and are functions of charge state, radius, and time. I R S q q q q

I. Introduction of MIST code (2) Assuming symmetry in all but the radial ssu g sy e y bu e d one zone coordinate (cylindrical geometry), the plasma has been divided into 50 radial a zones from the plasma center to the scrape off layer. o r R The impurity transport coefficients can be determined by ffi i t b d t i d b comparing the code results with measured local radiation power or spectral line intensities spectral line intensities .

II. Plasma profiles & main parameters used in this study ITER is a joint international research and development project that aims to emonstrate the scientific and technical feasibility of fusion power. 25 [ ] Major radius, R 620 cm 20 [ [ ] ] T e T Minor radius, a i di cm 200 [ ] Center 23.3 T e , T i (keV) 15 T keV T i e [ ] Edge keV 0.43 T e 10 [ [ ] ] T T Center Center 19.3 19.3 keV keV i i [ ] Electron & ion T Edge 2.4 keV 5 i temperature ⎡ ⎤ 10 m − n 19 3 Center 10.67 ⎣ ⎦ e 0 ⎡ 10 m − ⎤ n 19 3 Edge 0.55 ⎣ ⎦ 0.0 0.2 0.4 0.6 0.8 1.0 e Normalized minor radius (r/a) ( ) 8 12 7 10 6 or q 5 8 Safety facto -3 ) 13 cm 4 6 n e (x10 3 4 2 2 2 1 1 Electron density Safety factor q 0 0 0.0 0.2 0.4 0.6 0.8 1.0 0.0 0.2 0.4 0.6 0.8 1.0 Normalized minor radius (r/a) Normalized minor radius (r/a) Reference: ‘Design study for ITER High Resolution x-ray Spectroscopy Array’, Pobin Barnsley, EFDA-JET-CP(04)01/09

Impurity concentration determination for steady state case The main limitation to allowed impurity concentration is not the contribution to Zeff, but the impurity radiated power, there being a broad operating range between about 100kW and 10 MW. r = × 2 Reference: D D 0,2 D D =1 D =0.1~3.0m /s D(r)=D +D ( ) AREXP AR AC AREXP AC AC AR a r = = × − × (‘Power Radiated from ITER and CIT by Impurities’, J. Cummings, PPPL-2702) C 0 ~10 V r ( ) C [ 2 D(r) ] VR VR 2 a a r = × × = × We use : V r ( ) 0.1 [-2 D r a ( ) ] 4 2 D 1 10 cm / s 2 10 10 10 He He 9 Be 8 Be 9 10 C 7 C Cu Cu 6 8 Ar 10 Ar 5 wer(Watts) Kr Kr 7 10 4 Radiated pow 6 10 10 Z eff f 3 3 5 10 2 4 10 3 10 2 1 10 -5 -4 -3 -2 -1 -5 -4 -3 -2 -1 10 10 10 10 10 10 10 10 10 10 Impurity concentration (n imp /n e ) Impurity concentration (n imp /n e ) Total radiated power Z effective / / n n n n Maximum impurity concentration Maximum impurity concentration i imp e He Be C Cu Ar Kr 1.5 10 − 6 10 − 8 10 − × × × 4 5 4 25% 4% 1.5%

III. Impurity distribution in steady state case (1) 14 10 Impurity concentration He2+ He2+ 13 10 He Be C Cu e Density (cm -3 ) Be4+ 12 10 10% 1% 0.5% 2e-5 C6+ He2+ 11 10 He1+ The 4 impurity species are The 4 impurity species are Charge State Be4+ Be3+ Be2+ calculated respectively. 10 10 C6+ C5+ C4+ 9 C3+ 10 C2+ Radiated power (MW): p ( ) 8 10 0.0 0.2 0.4 0.6 0.8 1.0 He Be C Cu Normalized minor radius (r/a) Impurity charge state density (He, Be, C) 4.4 2.27 3.25 1.16 11 9x10 C 29 Cu29+ Cu29+ 9 Cu28+ 11 1.6x10 8x10 Cu28+ Cu27+ Cu27+ 2 /s) Cu26+ 11 7x10 Cu27+ 9 Cu26+ 1.4x10 Cu25+ particles/cm -3 ) Cu25+ Cu24+ 11 6x10 nsity (cm Cu23+ Cu24+ 9 1.2x10 11 Cu22+ 5x10 Cu23+ Cu29+ Cu21+ Cu22+ Cu28+ 11 Cu20+ 9 4x10 1.0x10 Cu21+ ansport flux density (p Charge State De Cu20+ 11 3x10 8 8.0x10 Cu28+ 11 2x10 Cu29+ 8 6.0x10 11 1x10 Cu26+ 0 8 4.0x10 Cu26+ 11 -1x10 Cu25+ 8 8 Tra 2 0 10 2.0x10 Cu27+ 11 -2x10 0.0 11 -3x10 0.0 0.2 0.4 0.6 0.8 1.0 0.0 0.2 0.4 0.6 0.8 1.0 Normalized minor radius (r/a) Normalized minor radius (r/a) Impurity charge state density (Cu) Transport flux density (Cu)

III. Impurity distribution in steady state case (2) -1 1.4 10 He He Be Be C C C C 1.3 Cu Cu n power(W/cm 3 ) 1.2 He -2 1.1 10 Z eff Local radiation Z 1.0 C Be 0.9 Cu -3 0.8 10 0.0 0.2 0.4 0.6 0.8 1.0 0.0 0.2 0.4 0.6 0.8 1.0 Normalized minor radius (r/a) Normalized minor radius (r/a) Effective atomic number Local radiation power 16 16 10 10 He1+ He1+ 15 C2+ 10 C3+ He1+ C4+ 14 2 /ion) 10 C5+ os/cm 3 /sec) C3+ 15 13 otos/s/cm 10 10 C2+ C2+ 12 C5+ 10 C5+ C3+ Line brightness (pho Line emission(photo 11 10 He1+ C4+ 14 10 10 10 C3+ 9 C4+ 10 C5+ C3+ C3+ 8 C3+ 10 C5+ C3+ 13 7 10 10 10 10 C5+ 6 10 0 50 100 150 200 250 300 350 400 1200 1600 0.0 0.2 0.4 0.6 0.8 1.0 Wavelength (Angstrom) Normalized minor radius (r/a) Line emission (photos/cm3/s) Line emission brightness (photos/s/cm2/ion)

IV. Impurity distribution in time dependent case (1) Impurity charge state density pu y c a ge s a e de s y Injected Krypton atom number: 5.3e17 jec ed yp o a o u be : 5.3e 7 10 3.0x10 9 2.4x10 Kr36+ Kr35+ Kr34+ Kr20+ Kr33+ 10 2.5x10 Kr1+ Kr32+ 9 2.0x10 Kr19+ Kr31+ Kr30+ Kr21+ m -3 ) m -3 ) Kr29+ rge state density (cm rge state density (cm Kr28+ Kr28+ 10 10 2.0x10 9 Kr27+ 1.6x10 Kr26+ Kr25+ Kr24+ 10 Kr23+ 1.5x10 9 1.2x10 Kr22+ Kr21+ Kr20+ Kr19+ 10 1.0x10 Kr18+ 8 8.0x10 Kr17+ Char Kr16+ Kr16+ Cha Kr15+ Kr14+ 9 8 5.0x10 time = 0.0 s time = 0.001 s 4.0x10 Kr13+ Kr12+ Kr11+ Kr10+ Kr9+ 0.0 0.0 0 40 80 120 160 200 0 40 80 120 160 200 Minor radius (cm) Minor radius (cm) ( ) 8 5x10 Kr36+ Kr36+ Kr35+ 8 Kr35+ 2.0x10 Kr34+ Kr34+ Kr26+ Kr33+ Kr34+ Kr33+ Kr32+ 8 Kr32+ 4x10 Kr31+ Kr31+ (cm -3 ) Kr30+ Kr25+ 8 cm -3 ) 1.6x10 Kr30+ Kr29+ Kr29+ Kr28+ Kr27+ harge state density (c Kr27 Kr27+ Kr28 Kr28+ Charge state density 8 Kr26+ Kr27+ 3x10 Kr25+ Kr26+ 8 Kr33+ 1.2x10 Kr24+ Kr25+ Kr23+ Kr24+ Kr22+ Kr23+ Kr21+ Kr22+ 8 Kr20+ 2x10 7 Kr21+ Kr32+ 8.0x10 Kr19+ Kr20+ Kr18+ Kr17+ Kr16+ Kr15+ Kr15+ Ch C 8 7 1x10 4.0x10 Kr14+ time = 0.05s Kr13+ time = 0.01s Kr12+ Kr11+ Kr10+ 0.0 Kr9+ 0 0 40 80 120 160 200 0 40 80 120 160 200 Minor radius (cm) Minor radius (cm)

IV. Impurity distribution in time dependent case (2) 8 7 1.2x10 5.0x10 Kr36+ Kr36+ Kr35+ Kr35+ 7 7 Kr35+ K 35+ 4.5x10 Kr34+ Kr34+ Kr34+ Kr34+ 8 1.0x10 Kr33+ Kr33+ 7 4.0x10 Kr32+ Kr32+ Kr31+ nsity (cm -3 ) Kr31+ nsity (cm -3 ) 7 3.5x10 Kr30+ Kr30+ 7 8.0x10 Kr29+ Kr29+ 7 3.0x10 Kr35+ 7 7 7 7 Charge state de 6.0x10 6 0 10 Charge state de 2.5x10 2 5 10 7 2.0x10 7 Kr33+ 4.0x10 7 1.5x10 Kr33+ 7 1.0x10 Kr35+ 7 Kr36+ 2.0x10 Kr32+ 6 6 Kr32+ Kr32+ 5 0 10 5.0x10 0.0 0.0 0 40 80 120 160 200 0 40 80 120 160 200 time = 0.15s Minor radius (cm) Minor radius (cm) time = 0.5s Kr36+ Kr36+ Kr36+ K 36+ 7 7 1.4x10 Kr35+ Kr35+ Kr34+ Kr34+ Kr34+ 6 2.0x10 Kr33+ Kr34+ Kr33+ 7 1.2x10 Kr32+ Kr32+ Kr31+ sity (cm -3 ) sity (cm -3 ) Kr31+ Kr30+ Kr30+ 7 1.0x10 Kr29+ Kr29+ 6 1.5x10 Kr35+ Kr35+ Kr35 Charge state dens Charge state dens 6 8.0x10 6 1.0x10 6 6.0x10 6 4.0x10 5 5.0x10 Kr36+ Kr36+ Kr33+ Kr33+ Kr33+ Kr33+ 6 2.0x10 Kr32+ Kr32+ 0.0 0.0 0 40 80 120 160 200 0 40 80 120 160 200 time = 1.5s time = 3.0s Minor radius (cm) Minor radius (cm)