Joint ICTP-IAEA Workshop on Fusion Plasma Modelling using Atomic and Molecular Data January 2012

Transcription

1 2327- Joint ICTP-IAEA Workshop on Fusion Plasma Modelling using Atomic and Molecular Data January 22 Modelling Basics of Erosion and Redeposition Kaoru OHYA Instit. of Tech.& Science, The University of Tokushima, 2- Minamijyosanjima-cho, Tokushimna JAPAN

2 Joint ICTP-IAEA Workshop on Fusion Plasma Modelling Using Atomic and Molecular Data, Trieste, Italy, January 22 Modelling Erosion and Redeposition on Plasma Facing Walls: Basics and Recent progress (II) Recent progress and integrated modelling Kaoru Ohya Institute of Technology and Science, The University of Tokushima, Japan

3 Joint ICTP-IAEA Workshop on Fusion Plasma Modeling Using Atomic and Molecular Data, Trieste, Italy, January 22 Outline of Lecture (A) INTEGRATED MODELLING OF EROSION/DEPOSITION A-) Local deposition of impurities on plasma facing materials (B) MODELLING USING PLASMA AND MATERIAL CODES B-) Particle-in-Cell simulation of plasma sheath B--) Carbon deposition in the gaps of castellated tiles B-2) Molecular dynamics simulation of plasma wall interaction B-2-) Reflection/sticking coefficient of deposited materials B-2-2) 2) Re-erosion erosion of deposited impurities on plasma facing walls (C) TRITIUM RETENTION IN ITER WALL MATERIALS C-) Long-distance transport of carbon and beryllium in plasmas C-2) Local tritium retention ti in tungsten t divertor targets t 2

4 Joint ICTP-IAEA Workshop on Fusion Plasma Modeling Using Atomic and Molecular Data, Trieste, Italy, January 22 Dynamic plasma wall interaction code, EDDY Plasma ion bombardment of Material Surfaces () Simultaneous bombardment with hydrogen and impurity ions ; H + +C q+ +Be q+ +W q+ (2) Maxwellian velocity distribution and sheath acceleration (PIC simulation of plasma density and potential) Dynamic Erosion and Deposition Processes (3) Physical sputter erosion and plasma impurities deposition (dynamic BCA) (4) Chemical sputter erosion due to hydrocarbons formation (Roth formulae) (5) Collisional mixing and thermal diffusion materials mixing Impurity Transport in Plasma above Surfaces (6) Multiple ionizations and dissociations of sputtered and reflected impurities, including CH 4 and higher hydrocarbons a set of rate coefficients from Janev/Reiter (7) Gyromotion of the ionized i impurities, iti simultaneously l receiving i (a) collisional friction force, (b) temperature gradient thermal force, (c) crossed field diffusion, (d) sheath and presheath electric field, and (e) elastic collision with neutral hydrogen. (Also, PIC simulation) Local Redeposition of Impurities on Surfaces (8) Reflection or sticking of carbon and hydrocarbons (MD simulation) particle species-, impact energy- and material-dependent. (9) Re-erosion of deposited and mixed materials (MD simulation) 3

5 Joint ICTP-IAEA Workshop on Fusion Plasma Modeling Using Atomic and Molecular Data, Trieste, Italy, January 22 A-) Local deposition of impurities on plasma facing materials 3 CH 4 injection experiments at TEXTOR A.Kreter et al.; J.Nucl.Mater (27)79. Top of the limiter was positioned at LCFS, the radial position of which is r=46 cm. At LCFS, T e =54 ev, T i =.5T e and n -3 e =.9x 2 cm. Radial decay of the plasma parameter: l Te =l Ti =4 mm, and l ne =22 mm 3 CH 4 was injected into the plasma through a hole in the limiter surface. roof-like test limiter exposed to SOL plasma of TEXTOR 2 C concentration of the background plasma was taken to be 3%. (Assumption) Most unexpected observation was the very low local deposition of 3 C on the limiter surface (~.2%). 4

6 Joint ICTP-IAEA Workshop on Fusion Plasma Modeling Using Atomic and Molecular Data, Trieste, Italy, January 22 A-) Local deposition of impurities on plasma facing materials 2D patterns of 3 C deposition Kreter et al. (27) 3 Standard condition: S=.5 and Y CH chem =3% 4 Injection hole Calculated: ~5% depsoition efficiency, and a factor of larger than in experiment poloidal direc ction (mm) Observed pattern Calculated l pattern (EDDY) ExB S= Injection cell S=.5, but enhanced erosion of redeposited carbon atoms, Y enh =3% Calculated: 33% 3 C depsoition Still too large 3 C depsoition and patterns still too much peaked S= (or small) & Enhanced erosion toroidal direction (mm) K.Ohya & A.Kirschner; Phys.Scr.T38(29)4. 5

7 Joint ICTP-IAEA Workshop on Fusion Plasma Modeling Using Atomic and Molecular Data, Trieste, Italy, January 22 A-) Local deposition of impurities on plasma facing materials 3 C deposit tion efficie ncy (%) Deposition efficiency strongly changes with injection time. Deposition efficiency in steady state is in fair agreement with the efficiency S=. calculated by ERO-HMM, not only for S= but also for S=.-.5. S=.5 S=.5 S=. S=. EDDY Steady state value from ERO-HMM CH 4 injection time (s) Sticking probability of hydrocarbons and re-erosion of redeposited carbon are still unknown parameters, which determine erosion and deposition of plasma facing materials. Sticking probability S=.5 S=. S=.5 S=. S= 3 C deposition efficiency (%) EDDY *.* ERO ~. *averaged between 5.29 s and 5.88 s K.Ohya & A.Kirschner; Phys.Scr.T38(29)4. 6

8 Joint ICTP-IAEA Workshop on Fusion Plasma Modeling Using Atomic and Molecular Data, Trieste, Italy, January 22 B-) Particle-in-Cell simulation of plasma sheath SOL/ Div vertor pla asma electrostatic potential Solution of the Poisson s equation in one or two dimensions to obtain the self- consistent electric field, acting plasma particles. ion electron collisional presheath x plasma B Magnetic Presheath Debye Sheath E PIC simulation y Magnetic Presheath H e + - ehe Plasmas in the fusion devices are usually contacting with walls. Sheath layer is formed in front of wall. Trajectory simulation of plasma ions and electrons with numerical solution of the equation of motion in three dimensions z Debye Sheath PIC code solves the equations of motion and Poisson s s equation self-consistently. The plasma particles with Maxwellian velocity distribution are generated at the edge region. The sheath potential vary with the charging of the wall. 7 wall

9 Joint ICTP-IAEA Workshop on Fusion Plasma Modeling Using Atomic and Molecular Data, Trieste, Italy, January 22 Ion Electron x y - B-) Particle-in-Cell simulation of plasma sheath z B wall Potential Profiles with Oblique Magnetic Field The magnetic presheath is formed due to the polarization between ions and electrons. When the magnetic field is almost parallel to the surface, the width of MP increases. The heavier hydrogen isotopes have larger Larmor radius, the width of MP increases o = (H) o 45 o 7 o 85.5 x(mm) n e = 8 m -3 T e =3eV.5 Coupling of PIC with secondary electron Emission (SEE) K.Ohya; JNM45(2)S. e/ T e = 85 o 2 H D T.5 x (mm) n e = 8 m -3 T e =3eV (a) =9 deg =45 deg = 5 deg with SEE from W w/o SEE 5 Distance from surface (/ D With an oblique magnetic field, some of SEs are reabsorbed at the wall within a gyrocircle, the net SE yield decreases. Mizoshita et al. (995), Inai el al. (29) Potential drop of the sheath is independent of the magnetic angle, but SE emission from W causes a decrease 8 in the potential drop. 5

10 Joint ICTP-IAEA Workshop on Fusion Plasma Modeling Using Atomic and Molecular Data, Trieste, Italy, January 22 B-) Particle-in-Cell simulation of plasma sheath Energy and angular distributions of ions incident on walls.4.5 K.Ohya; JNM45(2)S..3 = 85 o H D T.2 n e = 8 m H 85 o = 2 o 45 o o 7 o T e =3eV Incident energy (ev) Incident angle (degree) The impact energy does not depend on angle of magnetic field because potential drop is same. The energy distribution of heavier hydrogen isotopes is shifted to higher energy. The most probably angle is smaller than the angle of the magnetic field except for the case of the nearly normal magnetic field to the surface. The energy and angular distributions affect the sputtering and the reflection from the wall 9

11 Joint ICTP-IAEA Workshop on Fusion Plasma Modeling Using Atomic and Molecular Data, Trieste, Italy, January 22 Poloidal ance (/ D) Vertical dist B--) Carbon deposition in the gaps of castellated tiles Toroidal W W T =5degg B T W G Magnetic field line nce (/ D) 2 4 Poloidal gap =2degg B T T e =T i =ev, n = 8 m -3 W G =.5 mm V p [V] ance (/ D) Poloidal 2 4 Toroidal W T =5deg Magnetic field line Toroidal gap W G ance (/ D) 2 4 =2deg Plasma Plasma Plasma Plasma Poloidal distance (/ D ) Vertical dista Poloidal distance (/ D ) Vertical dist 6 Tile 8 Vertical dist 6 Tile Toroidal distance (/ D) D ) Poloidal distance (/ D ) Plasma density an potential are strongly asymmetric between poroidal and toroidal gaps. Plasma distribution ib ti around the gaps, in particular, toroidal gap, depends d on the magnetic field angle. K.Ohya; JNM45(2)S.

12 Joint ICTP-IAEA Workshop on Fusion Plasma Modeling Using Atomic and Molecular Data, Trieste, Italy, January 22 / D) Vertical distance ( Poloidal B--) Carbon deposition in the gaps of castellated tiles Toroidal W T Magnetic field line Toroidal gap W G Magnetic field line is only inclined by 5 o with respect to the toroidal direction. Gap width is changed. K.Ohya; JNM45(2)S. T e =T i =ev, n = 8 m -3 W G = mm =5deg W G =.5 5mm =5deg W G =.2 2mm =5deg / D) Vertical distance ( ExB drift Toroidal distance (/ D ) Toroidal distance (/ D ) plasma particles can penetrate into a wide gap of mm. / D) Vertical distance ( Toroloidal distance (/ D ) Hi ion with gyro radius of f.mm cannot penetrate t into a narrow gap of f2.2mm. When the gap width is.5mm, H ion cannot deeply penetrate due to E x B drift. V p [V]

13 Joint ICTP-IAEA Workshop on Fusion Plasma Modeling Using Atomic and Molecular Data, Trieste, Italy, January 22 B--) Carbon deposition in the gaps of castellated tiles Penetration depth of hydrocarbons in the toroidal gap Bottom Tile side Poloidal Magnetic field line Toroidal gap -2 =5 deg. Toroidal gap -3 = deg. Gap width, W G mm.5 mm.2 mm Toroidal W W T W G Distance from the top surface (mm) When the gap width is.5 mm or more, the redeposition can be found at the bottom of the gap. Very narrow gap (<.2 mm) causes the redeposition is localizedli at the gap edge. 2

14 Joint ICTP-IAEA Workshop on Fusion Plasma Modeling Using Atomic and Molecular Data, Trieste, Italy, January 22 B--) Carbon deposition in the gaps of castellated tiles (d) TFTR bumper limiter Tanabe et al. ref. bottom side Effect of re eflectio on -2-3 Toroidal gap n = 9 m -3 e T =3 ev e S gap = S gap = (MD data) distance from tile surface (mm) Species dependence -2 Toroidal gap T e,i =3 ev n e = 9 m -3 no thermal force S gap = (MD data) -3 ion species neutral species distance from tile surface (mm) distance from tile surface (mm) Using sticking coefficient calculated by MD, low energy hydrocarbons are reflected repeatedly. The neutral species are liberated from a magnetic constrain, they are redeposited deeply. Since the ionized particles are confined by the magnetic field and have high sticking coefficient due to sheath acceleration, they are redeposited in the gap edge. 3

15 Joint ICTP-IAEA Workshop on Fusion Plasma Modeling Using Atomic and Molecular Data, Trieste, Italy, January 22 B--) Carbon deposition in the gaps of castellated tiles PIC EDDY Experiment (A.Litnovsky et al.:jnm39-39(29)556.) Magnetic field line Shadowed area Red deposition rat te B=5 T 5 mm - (a) 2-2 The redeposition layer is re-eroded by the bombardment mm of background plasma, therefore, C deposition is reduced at mm Un-tilted (=deg) observed Bottom 6 C at./ cm -2 eposition rate Red the gap edge of plasma-open side (b) Tilt angle, =5deg Bottom Rede eposition rate - -2 K.Ohya; JNM45(2)S. (c) Tilt angle, =2deg observed Bottom C at. / cm Distance along the gap (mm) Distance along the gap (mm) Distance along the gap (mm) The calculated redeosition profiles reproduce the experimental profiles of C deposition. The redeposition on plasma-open side is suppressed due to the tilt of top surface of the cell 4

16 Joint ICTP-IAEA Workshop on Fusion Plasma Modeling Using Atomic and Molecular Data, Trieste, Italy, January 22 B-2) Molecular Dynamics simulation of plasma wall interaction Integrating equation of motions of constituent atoms : Small cell containing 3-7 atoms t 2 Fj ( t) Verlet algorithm r t t r t tr j ( ) j ( ) j ( t ) 2m r k t ( t t) r k ( t) F k ( t t) Fk ( t) 2m The force on each atom calculated from the analytical derivation of appropriate interaction potential form. b b c R ij ji A V fij ( rij ) Vij ( rij ) Vij ( rij ) : Empirical i bond order potential ti i j 2 D V ( ) exp 2S r r R Repulsive term r Bond-order function bij ij 2 S SD V ( r) exp 2 S r r A c Attractive term f ( r ) g ( ) exp2 r r Cutoff-function S, f c r) 2 2 sin, ( 2 r R D, Many-body term ij ik k ( i, j) 2 2 r R D, R r D, c c Angular functiong( ) r R D d d h cos Fusion-related parameter sets for C-C, C-H : Brenner (99, 992), REBO (22) and AIREBO (2) W-W, W, W-C, W-H : Juslin et al. (25) Be-Be, Be-C, Be-H, Be-W : Bjorkas et al. (29, 2) ik ik ijk ijk ik ij ik

17 Joint ICTP-IAEA Workshop on Fusion Plasma Modeling Using Atomic and Molecular Data, Trieste, Italy, January 22 B-2) Molecular Dynamics simulation of plasma wall interaction Coupling to an external bath (Langevin equation) : Excess heat dissipation in collisions with energetic atom. HJC.Brendsen et al.: JCP8(984)3684. t T T T ttime step, T time constant T temperature of the system, T fixed reference temperature It represents a proportional scaling of the velocities per time step. Periodic boundary condition : Topmost atoms are free, but bottommost atoms are fixed. The simulation cell is replicated throughout h t the space to Simulation cell form an infinite lattice. If an atom leaves the simulation cell, one of its images will enter through h the opposite face. Simulation cellshould be large More realistic, but time consuming. 6

18 Joint ICTP-IAEA Workshop on Fusion Plasma Modeling Using Atomic and Molecular Data, Trieste, Italy, January 22 B-2) Molecular Dynamics simulation of plasma wall interaction C W E=eV N= incident number N=3 N=5 incid dent en nergy E=eV E=keV 7

19 Joint ICTP-IAEA Workshop on Fusion Plasma Modeling Using Atomic and Molecular Data, Trieste, Italy, January 22 B-2) Molecular Dynamics Simulation of plasma wall interaction C W R C, Y C and Y W oefficient, g yields, Y eflection co sputtering C re C and W (a)) 3eVV (b) ev WMD MD 8.8 MD R C C Y C R C 4 Y W R C Y C Y W.4 Y C Y W R C Y W Y C (c) kev Dynamic BCA Dynamic BCA Dynamic BCA R W(pure) Y W(pure) Y R C(pure) C(pure) C fluence, C ( 6 cm -2 ).4.2 R W(pure) Y W(pure) Y C Y W Y C(pure) R C(pure) C fluence, C ( 6 cm -2 ).4.2 R W(pure) Y W(pure) R C R C Y C Y W Y C(pure) R C(pure) C fluence, C ( 6 cm -2 Changes in C and W sputtering yields are in good agreement with those between MD and dynamic MC code, For C reflection coefficients, it is different from each other at low energy. 8

20 Joint ICTP-IAEA Workshop on Fusion Plasma Modeling Using Atomic and Molecular Data, Trieste, Italy, January 22 B-2-) Reflection/sticking coefficient of deposited materials Preparation of Realistic PFW Surfaces Bombardment W crystal with ev-c W-C mixed layer Bombardment with ev-c Simultaneous bombardment with.-3ev-h and.25ev-c C deposition layer Hydrogenated/ d/ (amorphous carbon) amorphous carbon (H/C:.4) The W surface is bombarded with C atoms at the temperature of ev and ev. At low plasma temperature, t the W is covered by deposited d C and at higher h temperature t W-C mixed layer is formed. The a-c:h layer with different H/C is formed when a-c is bombarded with H atom. 9

21 Joint ICTP-IAEA Workshop on Fusion Plasma Modeling Using Atomic and Molecular Data, Trieste, Italy, January 22 B-2-) Reflection/sticking coefficient of deposited materials Emission probability of reflected species CH 4 CH 4 CH4 Reflection co oefficient amorphous carbon a-c:h C CH CH2 CH3 CH4 particle energy (ev) CH 4 impact hydrogenated/ amorphized carbon CH4 CH3 CH2 CH C H:C.4 particle energy (ev) W-C mixed layer CH 4 CH 3 CH 2 CH C CH 4 impact W-C mixed layer particle energy (ev) Most of incident methane reflect at thermal energy and break up at higher energy (>ev). Increase of hydrogen in amorphous carbon increases the reflection coefficients. 2 The W surface increases the reflection coefficients and there reflected much more C atoms.

22 Joint ICTP-IAEA Workshop on Fusion Plasma Modeling Using Atomic and Molecular Data, Trieste, Italy, January 22 B-2-) Reflection/sticking coefficient of deposited materials Incident species dependence of reflection coefficient ent eflection coeffici CH y r Incident at CH y (y=4) C CH CH 2 CH CH 4 on a-c:h(.42).. Incident energy (ev) More hydrogen contents ient C 2 H y reflection coeffic Incident at C 2 H y (y=6) C 2 C 2 H C 2 H 2 C 2 H 3 C H 2 4 C 2 H 5 on. C 2 H 6 a-c:h(.42). Incident energy (ev) Higher reflection coefficients 2

23 Joint ICTP-IAEA Workshop on Fusion Plasma Modeling Using Atomic and Molecular Data, Trieste, Italy, January 22 B-2-2) Re-erosion of deposited impurities on plasma facing walls Thermocouple Be coverage effect of plasma impurities on C has been recently demonstrated in the experiments. J.M.Baldwin, R.P.Doerner; Nucl.Fusion 46(26)444. Cooled target holder Target 2 mm 53 mm High temperature MBE effusion cell used to seed plasma with evaporated Be Axial spectroscopic field of view 76 mm Deposition 45 o probe sample 2 Beryllium impurity seeding PISCES-B Plasma 95 mm Be seeding on a plasma in contact with a C target decreases to negligible g levels the chemical sputtering yield of carbon even at Be concentration of ~.% in the plasma. its) Norm. CD Band stren ngth (Arb. un..6% Be.4 % Be.4% Be. % Be.3 % Be.3 % Be.8 % Be Time (s) Radial transport Water cooled Mo guard heat dump Mitigation of chemical carbon Heatable deposition probe Resistive heating assembly Thermocouple coils erosion by Bedeposition Plasma divertor simulator PISCES-B 22 Surfa ace carbon co oncentration

24 Joint ICTP-IAEA Workshop on Fusion Plasma Modeling Using Atomic and Molecular Data, Trieste, Italy, January 22 B-2-2) Re-erosion of deposited impurities on plasma facing walls Deposition of Beryllium on hd hydrogenated tdcarbon Be coverage % 5 cm -2 ) l density ( % 5.5 Areal (a) C Number of D or Be cm -2 ) l density ( Areal (b) D C (w/o Be) Number of D % 92% Areal density y ( 5 cm -2 ) Depth (nm) Depth (nm) 2 2. C (w/o Be).5 (c) Be Number of Be Be cover rage (%) (d) Depth (nm) Number of incident Be atoms Be atoms are deposited on a hydrogenated C layer by simultaneous bombardment with ev Be and ev D atoms. The Be deposition grows up with increasing number of incident Be atoms, where incident D atoms are codeposited as well. The percent coverage of Be is increased with increasing number of incidence, up to 92 %. 23

25 Joint ICTP-IAEA Workshop on Fusion Plasma Modeling Using Atomic and Molecular Data, Trieste, Italy, January 22 B-2-2) Re-erosion of deposited impurities on plasma facing walls Probab bility of tr raveling at a depth (a) E i =5 ev (b) Be coverage C % 7% 5% 82% (w/o Be) Be coverage: 5% C (w/o Be) E i ev ev 5 ev ev Depth (nm) Interaction depth in C and Be deposition 5 cm -2 C areal de ensity ( ) Noncumulative bombardments with D atoms with energies of ev are performed and the same initial surface is used for each simulation. Incident atoms hit the top surface at random positions. Incident polar angle is 45 o, whereas the azimuthal angle is randomly selected from o 8 o. Target temperature is changed from 3 K to 2 K. Dominant interaction occurs within a hydrogenated C layer and Be deposition. Interaction layer tends to move from the C layer to the Be deposition layer with increasing Be coverage and decreasing D impact energy. 24

26 Joint ICTP-IAEA Workshop on Fusion Plasma Modeling Using Atomic and Molecular Data, Trieste, Italy, January 22 B-2-2) Re-erosion of deposited impurities on plasma facing walls ion yield Emissi ion yield Emiss Emiss sion yield..... C CD CD2 CD3 T=3 K T=8 K D/(C+D)=.3 D/(C+D)=.3 (a) (b). C CD CD2 CD3 CD4.. T=2 K D/(C+D)=.3 (c). Incident D energy, E i (ev) C CD CD2 CD3 Hydrogenated carbon At 3 K, dominant emission species are small molecules. Larger molecules l (CD 2 and CD 3 ) are emitted with increasing i D/(C+D) D) ratio. C atoms are emitted through physical sputtering mechanism. With increasing temperature, CD y emission is strongly enhanced. At 8 K, a maximum value of the emission yield is observed in the energy range of ev, where CD y s are more emitted with decreasing D impact energy. Clearly, D uptake in the C layer induces sputtering of C atoms at energies much less than the threshold energy for physical sputtering. At 2 K, the numbers of emitted C and CD y increase monotonously with increasing D energy. If there is no uptake of D in the layer (D/(C+D)=), hydrocarbon emission is very rare and sputtering of C atoms shows a clear threshold h ldfor physical sputtering. C emission yield.. C T= 3 K T= 8 K T=2 K (d) D/(C+D)=. Incident D energy, E i (ev) 25

27 Joint ICTP-IAEA Workshop on Fusion Plasma Modeling Using Atomic and Molecular Data, Trieste, Italy, January 22 B-2-2) Re-erosion of deposited impurities on plasma facing walls Hydrogenated C with beryllium deposition CD yield No ormalized (a) T=8 K Decrease in the emission yield is much faster than Ei= ev an increase in Be coverage on the surface. E i = ev Ei= 3 ev Ei= ev Ei= 3 ev Ei= ev PISCES-B T= 3 K T= 6 K T= 8 K T= K T=2 K (b) Be coverage (%) This result shows a good correlation with the mitigation of chemical erosion (i.e., the decrease in CD band light emission) of a C target exposed to a Be seeded plasma in PISCES B experiments [8]. [8] R.P.Doerner et al., Phys.Scr. T28(27)5. The reduction rate increases monotonically with decreasing D impact energy. This explain the ion energy dependence of decay time of chemical CD light emission observed [9]. [9] D.Nishijima et al., J.Nucl.Mater (27)26. The reduction rate changes in the different manner from the experiments with increasing surface temperature. The calculation indicates a maximum reduction rate at ~8 K where the CD y emission yield peaks. 26

28 Joint ICTP-IAEA Workshop on Fusion Plasma Modeling Using Atomic and Molecular Data, Trieste, Italy, January 22 C-) Long-distance transport of carbon and beryllium in plasmas Divertor Wing (W) Dome (W) Mutual contamination between C and W Be deposition on C and W Vertical Target (C) Chemical erosion C x H y H Carbon tile Cd deposition (a-c:h ) C x H y Codeposition Be + Be first wall 27

29 Joint ICTP-IAEA Workshop on Fusion Plasma Modeling Using Atomic and Molecular Data, Trieste, Italy, January 22 C-) Long-distance transport of carbon and beryllium in plasmas (m) Model geometry of edge plasma and walls Gas puff First wall Plasma parameters in an ITER edge plasma with D and impurities (C and He) are taken from a B2/Eirene calculation []. [] G.Federici et al., J.Nucl.Mater (2)26. (Be) Aside from sputtering by plasma ions, sputtering by charge exchange (CX) neutrals is taken into account at the first wall. Ve ertical distance (m) (m) Core plasma 4.9 (m) Physical sputtering yield of C target in the divertor and Be first wall is calculated by using EDDY [2]. [2] K.Ohya, Phys.Scr. T24 (26)7. Due to high threshold energy for physical sputtering by D ions, sputtering of W baffle and dome is not taken into account (CFC) Inner target.85 (m) (W) Dome Pump Outer target 2.85 (m) Divertor (CFC) Radial distance (m) Chemical sputtering of C target is calculated using Roth formulae [3]. Only CD 4 molecules l are released from the target. [3] J.Roth et al., J.Nucl.Mater (999)/ (25)97. 28

30 Joint ICTP-IAEA Workshop on Fusion Plasma Modeling Using Atomic and Molecular Data, Trieste, Italy, January 22 C-) Long-distance transport of carbon and beryllium in plasmas Dome Target Inner region First wall Outer region First wall Target Dome Io on and neutra al fluxes (m -2 s - ) Io on and neutr ral energy (ev V) 25 D + (L=cm) D + (L=cm) D + 2 (L=3cm) D (L=cm) DCX (a) D + DCX Ts (b) Poloidal distance (m) Surface temp perature, T s (K) Poloidal distributions of the flux of CX neutrals and of their mean energy along the grid edge are taken from ref. [5]. [5] R.Behrisch et al., J.Nucl.Mater (23)338. Angular distribution of ions is influenced by gyromotion of the ions; most probable angles of the distribution are 2 o ~8 o, which are much larger than the magnetic angles intersecting ti the wall. Average angle of magnetic field lines intersecting the first wall equipped with blanket modules is chosen to be 5 o, which h results in an incident id angle of ~2 o to the first wall. Ion flux at the first wall is assumed to decay exponentially from the grid edge to the wall. The decay length is taken to be cm, 3 cm and cm. 29

31 Joint ICTP-IAEA Workshop on Fusion Plasma Modeling Using Atomic and Molecular Data, Trieste, Italy, January 22 C-) Long-distance transport of carbon and beryllium in plasmas Sputter ring fluxe es (m -2 s - ) Dome Target Inner region First wall C CD4 Be(ion,L=cm) Outer region First wall Be(ion,L=3cm) Be(ion,L=cm) Be(neutral) Poloidal distance (m) Target Dome Dominant erosion mechanism at the outer divertor target is physical sputtering. Asymmetric erosion between the inner and outer targets is observed, depending on the incident ion energy. Erosion of the inner target is dominated by chemical sputtering, a maximum yield of which occurs at the strike point. Erosion of the first wall is at least by factors of smaller than that of the divertor targets. Localized gas puffing and recycling at the top of the first wall causes sputtering flux to be strongly decreased. If decay length of ion flux between the grid edge and the first wall is taken to be cm, the sputtering flux by ions is high enough to be comparable to the flux by CX neutrals. With decreasing length, the ion flux is strongly reduced, showing complicated profile closely related to the local distance between the grid edge and the first wall. 3

32 Joint ICTP-IAEA Workshop on Fusion Plasma Modeling Using Atomic and Molecular Data, Trieste, Italy, January 22 C-) Long-distance transport of carbon and beryllium in plasmas Vertic cal distanc ce (m) C, CD y and Be distributions ib ti in edge plasma 4 (a) (b) (c) C CD y Be Physical sputtering Chemical sputtering Physical sputtering Radial distance (m) Radial distance (m) Radial distance (m) Fligh ht time integ gral The color represents the sum of the flight time of all particles traveling in each grid cell, per unit area in the poloidal crosssection. A part of C atoms is promptly ionized and redeposit in the vicinity of the birthplace. The other part is transported away from it and some of them distribute out of the divertor. CD y is rather limited within the private flux region (PFR) of the divertor. Be atoms are ionized and subsequently transported along the magnetic field lines for a long distance, therefore, they distribute over the whole area of the machine. 3

33 Joint ICTP-IAEA Workshop on Fusion Plasma Modeling Using Atomic and Molecular Data, Trieste, Italy, January 22 C-) Long-distance transport of carbon and beryllium in plasmas Net erosion n/depositio on flux ( 2 m -2 s - ) Dome Target Net erosion and deposition profile on walls Inner region First wall (a) C (b) Be Outer region First wall L=cm L=3cm L=cm Poloidal distance (m) Target Dome Physical and chemical sputtering yields of original materials are used for the re-erosion yields for C (CD y ) and Be deposits. Net erosion and deposition profiles of C, CD y and Be, calculated as the flux difference between redeposition and re-erosion. C deposits in the inner divertor are strongly re- eroded except for the dome where sputtering is negligibly small. Position near the strike point, as well as the dome, is a deposition zone whereas the position far from it is an erosion zone. Be deposits on the inner and outer targets are strongly re-eroded due to low threshold energy for physical sputtering. The top of the first wall and the inner dome are deposition zones. 32

34 Joint ICTP-IAEA Workshop on Fusion Plasma Modeling Using Atomic and Molecular Data, Trieste, Italy, January 22 C-) Long-distance transport of carbon and beryllium in plasmas s - x ( 9 m -2 ) T codep position flu Dome Target Inner region (a) Tritium codeposition profile on walls First wall C, CD y (b) Be Outer region First wall L=cm L=3cm L=cm Target Dome Empirical formulae recently yproposed p by Doerner et al. [6] are used for atomic ratios of D to C and of D to Be. [6] R.P.Doerner et al., Nucl.Fusion 49(29)352. (The estimation of T retention, corresponding D data, are performed in this work.) Using surface temperature and D energy on the inner and outer targets and the first wall, D/C and D/Be values are calculated as a function of the position. Net redeposition flux profiles are multiplied with D/C and D/Be profiles to obtain T codeposition profile Poloidal distance (m) Finally, assuming toroidal symmetry, total retention rate can be estimated from the calculated T codeposition profile. 33

35 Joint ICTP-IAEA Workshop on Fusion Plasma Modeling Using Atomic and Molecular Data, Trieste, Italy, January 22 C-) Long-distance transport of carbon and beryllium in plasmas Tritium retention rate in C and Be deposits Decay length * Divertor *2 First wall Total (cm) Inner target dome Outer target (a) Carbon deposition.26 [mgt/s]. [mgt/s] 2.5 [mgt/s].2 [mgt/s] 3.89 [mgt/s] (b) Beryllium deposition Dominant T retention in C occurs at the inner and outer divertor target, whereas it occurs at the first wall. Retention rate in Be is strongly influenced by decay length of plasma parameters from the grid edge to the first wall. Using a discharge duration of 4 s, the number of discharge after which an in-vessel T safety limit of 7 g is reached are estimated from the sum of the T retention rate in C and Be deposits, if the retention rate in W is negligibly low. It is predicted to be discharges, depending on the decay length. 34

36 Joint ICTP-IAEA Workshop on Fusion Plasma Modelling Using Atomic and Molecular Data, Trieste, Italy, January 22 C-2) Local tritium retention in tungsten divertor targets Local plasma wall interaction related to Tritium Retention Divertor Wing(W) Dome(W) Vertical Target (W) Local collision and thermal processes: Codeposition Implantation, with diffusion, C and Be trapping/detrapping and surface recombination Be + Be first wall 35

37 Joint ICTP-IAEA Workshop on Fusion Plasma Modelling Using Atomic and Molecular Data, Trieste, Italy, January 22 C-2) Local tritium retention in tungsten divertor targets Thermal Processes after a Collision i Process Fick s law with source and trapping terms c n i j x, t ctj x, t D j c j x, t G j x, t t Vacuum Sputtered atom E el ( )-E sb Projectile ion E t i L C ( x, t ) j th solute concentration, D j : Diffussion coefficient =-ln (E ) j Solid for j th solute E =E -E inel (L )-E el ( ) G j x,t source term (range profile) c i Tj ( x, t ) : concentration of j th solute trapped I th trapping site Rate equation for trapping and detrapping i i ctj x, t D j c j x, t CTe x, t i i c x, t exp( E / kt 2 Tj T t i i i i C x t C x, t f c ( x, t) Te, Te jump distance, : detrapping attempt frequency i f : the inverse trap saturability of j th j solute fot the I th trapping site i E T j j Tj : detrapping energy of I th trap Boundary condition e.g., g, recombination limited c x K 2 j r 2 J K c x rc j x D j j Kr ) recombination coefficient Recoiled atom E el ( 2 ) el( 2 ) t= t t t DIFFUSE DIFFUSE DIFFUSE DIFFUSE L 2 =-ln (E ) BCA BCA BCA BCA BCA E 2 =E -E inel (L 2 )-E el ( 2 ) Time / Time N H 36

38 Joint ICTP-IAEA Workshop on Fusion Plasma Modeling Using Atomic and Molecular Data, Trieste, Italy, January 22 - ) Re eleased D flux (cm -2 s - Are eal D densit ty (cm -2 ) 6 3 C-2) Local tritium retention in tungsten divertor targets Parameter Fitting with a TDS experiment Implantation (3K) Outgass (3K) TDS (5K/s) ref + rec rec 5 exp. 8 Ttar 6 4 (a) Total Mobile Trap 3 Trap 2 2 (b) Time (s) Time evolution of the areal density of trapped D in W is shown along with that of the density retained as mobile atoms. Ttar (K) In the experiment [], a wrought W surface was irradiated by D 3+ ions with an energy of ev/d and a flux of cm -2 s -. [] C.Garcia-Rosales et al., J.Nucl.Mater (996)83. ()Diff (a) Diffusioni (b) Surface recombination i D (cm 2 s - ) E D (ev) E r (ev) K r (cm 4 K /2 s - ) (c) Trapping E T (ev) D trap /W E T2 (ev) D tarp2 /W Density of mobile and trapped D atoms increases successively during implantation. After implantation, a part of mobile D atoms are released due to surface recombination. Trapped D atoms are kept to be retained in the bulk. At the early stage of the TDS phase, D atoms in the Trap are released via mobile D atoms. At the delayed stage, D atoms in the deeper trap (Trap 2) are released. 37

39 Joint ICTP-IAEA Workshop on Fusion Plasma Modeling Using Atomic and Molecular Data, Trieste, Italy, January 22 (x K) (deg), Ttar E (ev), 5 5 C-2) Local tritium retention in tungsten divertor targets Plasma Parameters used for calculation l Ttar E (a) Inner target Ttar Outer target E (b) (cm -2 s - ) (cm -2 s - ) The plasma parameters in front of the targets are taken from a B2-EIRENE calculation [2], as a function of the distance from the strike point. [2] G.Federici et al., J.Nucl.Mater (2)26. The surface temperature depending on the position on the target is taken from [3], where the temperature were calculated assuming CFC, not W, with the thickness of mm. [3] G.Federici et al., Plasma Phys. Control.Fus.45(23)523. Typical duration of a discharge in ITER is 4 s. The surface temperature at each position is kept constant after discharge as well as during it. The trap concentration strongly depends on the 5 material and additional traps may be produced in the Distance from strike point (m) near-surface region due to high D fluxes to the target, resulting in a depth-dependent concentration. Incident energy (T), angle () and flux () and target temperature (T tar ) as a function of the position on the inner and outer target. 38

40 Joint ICTP-IAEA Workshop on Fusion Plasma Modeling Using Atomic and Molecular Data, Trieste, Italy, January 22 C-2) Local tritium retention in tungsten divertor targets 2 ) atoms (cm al density of retained D Are 7 Time evolution of retained dd distributionib i 8 During plasma exposure (a) s 4 s 3 Inner target Dtrap/W= After plasma exposure (b) 6 s Inner target 4 s Dtrap/W=. 2 ) atoms (cm al density of retained D Are 8 4 s (a) s During plasma exposure 3 Dtrap/W=. 7 Outer target After plasma exposure (b) 6 s s Outer target Dtrap/W= Distance from strike point (m) Distance from strike point (m) At the position where the temperature is high, the number of retained D atoms increases without any saturation. Most of D atoms are retained as mobile atoms. At the low temperature position, it tends to saturate where most of trap sites near the surface are occupied by implanted D atoms. After discharge (>4 s), most of D atoms are kept to be retained in the bulk, where they can diffuse deeper. 39

41 Joint ICTP-IAEA Workshop on Fusion Plasma Modeling Using Atomic and Molecular Data, Trieste, Italy, January 22 Tr ritium reten ntion (mg) C-2) Local tritium retention of in tungsten divertor targets Time evolution of Tritium Retention in Targets (a) Inner target Total Dtrap/W=. mechanism is the trapping in the deep trap Trap 2 Mobile During -3 discharge -4 Trap Total Mobile Trap 2 Trap During discharge (b) After discharge After discharge Outer target Dtrap/W= Time (s) In case of the inner target, dominant retention (Trap 2) during discharge and most of the T atoms are kept in the trap even after discharge. Mobile T atoms dominate the T retention in the outer target due to its high temperature leading to detrapping from the trap and subsequent diffusion inside the bulk. The T atoms are retained ten times more in the outer target than in the inner target during discharge, whereas sufficiently after discharge the T retention is reduced due to surface recombination of mobile atoms. From the distribution of retained D atoms during and after discharge, the T retention in the inner and outer targets are estimated by taking the atomic mass difference between D and T into account, and assuming toroidal symmetry. 4

42 Joint ICTP-IAEA Workshop on Fusion Plasma Modeling Using Atomic and Molecular Data, Trieste, Italy, January 22 tion (mg) ium reten Trit C-2) Local tritium retention in tungsten divertor targets Tritium Retention in Divertor Targets Just after discharge Inner target Mobile Trap Trap 2 Outer target Tritium retention (mgt) after a discharge (4 s) in tunsgten. Trap concentration ti Divertor Total T trap /W Inner target Outer target (a) Just after discharge (4 s) (b) Subsequently after discharge ( s) Trap concentration, Ttrap/W Finally, the number of discharges, after which an in-vessel T safety limit of 7 g is reached, is estimated from the sum of T retention of the inner and outer targets; T retention in other walls is not taken into account. The number of discharges is of the range between 2 and 24, depending on the trap concentration from. to.. It is increased to the values between 22 and 6, if the T retention sufficiently after discharge ( s) is used. 4