Modelling Erosion and Redeposition on Plasma Facing Walls: Basics and Recent progress

Joint ICTP-IAEA Workshop on Fusion Plasma Modelling Using Atomic and Molecular Data, Trieste, Italy, 23-27 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

Joint ICTP-IAEA Workshop on Fusion Plasma Modeling Using Atomic and Molecular Data, Trieste, Italy, 23-27 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) Re-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 in tungsten divertor targets 2

Joint ICTP-IAEA Workshop on Fusion Plasma Modeling Using Atomic and Molecular Data, Trieste, Italy, 23-27 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 impurities, simultaneously receiving (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

Joint ICTP-IAEA Workshop on Fusion Plasma Modeling Using Atomic and Molecular Data, Trieste, Italy, 23-27 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. 363-365(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 e =.9x 2 cm -3. 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

poloidal direction (mm) Joint ICTP-IAEA Workshop on Fusion Plasma Modeling Using Atomic and Molecular Data, Trieste, Italy, 23-27 January 22 A-) Local deposition of impurities on plasma facing materials 2D patterns of 3 C deposition 3 CH 4 Injection hole Kreter et al. (27) Standard condition: S=.5 and Y chem =3% Calculated: ~5% depsoition efficiency, and a factor of larger than in experiment 3 2 - Observed pattern Calculated 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.5 patterns still too much peaked.4 S=.3(or small) &.2 Enhanced erosion -2-3 -5-4 -3-2 - 2 3 4 5 toroidal direction (mm). K.Ohya & A.Kirschner; Phys.Scr.T38(29)4. 5

Joint ICTP-IAEA Workshop on Fusion Plasma Modeling Using Atomic and Molecular Data, Trieste, Italy, 23-27 January 22 A-) Local deposition of impurities on plasma facing materials Deposition efficiency strongly changes with injection time. 3 C deposition efficiency (%) S=.5 S=. S=.5 S=. S=. EDDY Steady state value from ERO-HMM. 2 3 4 5 6 3 CH 4 injection time (s) Deposition efficiency in steady state is in fair agreement with the efficiency calculated by ERO-HMM, not only for S= but also for S=.-.5. 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 33. 5. 2.2.5*.* ERO 32. 5. 2..5 ~. *averaged between 5.29 s and 5.88 s K.Ohya & A.Kirschner; Phys.Scr.T38(29)4. 6

SOL/ Divertor plasma Joint ICTP-IAEA Workshop on Fusion Plasma Modeling Using Atomic and Molecular Data, Trieste, Italy, 23-27 January 22 B-) Particle-in-Cell simulation of plasma sheath electrostatic potential Debye Sheath E Plasmas in the fusion devices are usually contacting with walls. Sheath layer is formed in front of wall. ion electron collisional presheath x plasma B j Magnetic Presheath PIC simulation y Magnetic Presheath H e + - Trajectory simulation of plasma ions and electrons with numerical solution of the equation of motion in three dimensions Solution of the Poisson s equation in one or two dimensions to obtain the selfconsistent electric field, acting plasma particles. Debye Sheath PIC code solves the equations of motion and Poisson 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 z wall

Joint ICTP-IAEA Workshop on Fusion Plasma Modeling Using Atomic and Molecular Data, Trieste, Italy, 23-27 January 22 x Ion Electron y - z j B-) Particle-in-Cell simulation of plasma sheath 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. -2-3 2 j = (H) o 45 o 7 o 85.5 o x (mm) n e = 8 m -3 T e =3eV.5 Coupling of PIC with secondary electron Emission (SEE) e / T e -.5 -. -.5-2. (a) =9 deg =45 deg = 5 deg K.Ohya; JNM45(2)S. -2.5 with SEE from W w/o SEE - j = 85 o -3. 2 5 Distance from surface (/ D ) 5-2 -3 2 H D T.5 x (mm) n e = 8 m -3 T e =3eV.5 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.

Joint ICTP-IAEA Workshop on Fusion Plasma Modeling Using Atomic and Molecular Data, Trieste, Italy, 23-27 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..3.2 j = 85 o H D T n e = 8 m -3 T e =3eV.4.3.2 H j = 2 o 85 o 45 o 7 o.. 5 5 2 25 3 Incident energy (ev) 3 6 9 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

Vertical distance (/ D) Vertical distance (/ D) Vertical distance (/ D) Vertical distance (/ D) Joint ICTP-IAEA Workshop on Fusion Plasma Modeling Using Atomic and Molecular Data, Trieste, Italy, 23-27 January 22 Poloidal 2 4 6 8 B--) Carbon deposition in the gaps of castellated tiles 9 Toroidal W T =5deg B T W G Magnetic field line Poloidal gap 2 4 6 8 ) Poloidal distance (/ D ) 2 4 6 8 ) Poloidal distance (/ D ) 2 4 6 8 =2deg B T T e =T i =ev, n = 8 m -3 W G =.5 mm V p [V] 5 Tile Poloidal 2 4 6 8 Toroidal W T =5deg Magnetic field line Toroidal 9 gap W G Tile 8 2 4 6 8 2 4 6 8 ) Toroidal distance (/ D ) Poloidal distance (/ D ) 2 4 6 =2deg Plasma Plasma Plasma Plasma Plasma density and potential are strongly asymmetric between poloidal and toroidal gaps. Plasma distribution around the gaps, in particular, toroidal gap, depends on the magnetic field angle. K.Ohya; JNM45(2)S. -5 - -5-2 -25-3 -35

Vertical distance (/ D) Vertical distance (/ D) Vertical distance (/ D) Joint ICTP-IAEA Workshop on Fusion Plasma Modeling Using Atomic and Molecular Data, Trieste, Italy, 23-27 January 22 Poloidal 2 4 6 8 B--) Carbon deposition in the gaps of castellated tiles Toroidal W T Toroidal 9 gap W G Magnetic field line W G = mm =5deg W G =.5 mm =5deg W G =.2 mm =5deg 2 4 6 8 2 4 6 8 Toroidal distance (/ D ) Toroidal distance (/ D ) plasma particles can penetrate into a wide gap of mm. 2 4 6 8 Magnetic field line is only inclined by 5 o with respect to the toroidal direction. Gap width is changed. ExB drift 2 4 6 8 K.Ohya; JNM45(2)S. T e =T i =ev, n = 8 m -3 2 4 6 8 Toroloidal distance (/ D ) H ion with gyro radius of.mm cannot penetrate into a narrow gap of.2mm. When the gap width is.5mm, H ion cannot deeply penetrate due to E x B drift. V p [V] 5-5 - -5-2 -25-3 -35

Joint ICTP-IAEA Workshop on Fusion Plasma Modeling Using Atomic and Molecular Data, Trieste, Italy, 23-27 January 22 B--) Carbon deposition in the gaps of castellated tiles Penetration depth of hydrocarbons in the toroidal gap Tile side Bottom -2 =5 deg. = deg. Toroidal gap Gap width, W G Poloidal Magnetic field line Toroidal 9 gap -3 mm.5 mm.2 mm Toroidal W T W G -4 5 5 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 localized at the gap edge. 2

Effect of reflection Joint ICTP-IAEA Workshop on Fusion Plasma Modeling Using Atomic and Molecular Data, Trieste, Italy, 23-27 January 22 B--) Carbon deposition in the gaps of castellated tiles - 3 (d) TFTR bumper limiter ref. bottom side -2 Toroidal gap n e = 9 m -3 T e =3 ev S gap = S gap = (MD data) 2-3 - -2-3 -4 Tanabe et al. 5 5 2 25 3 distance from tile surface (mm) Species dependence Toroidal gap T e,i =3 ev n e = 9 m -3 no thermal force S gap = (MD data) ion species neutral species 5 5 2 25 3 distance from tile surface (mm) -4 5 5 2 25 3 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

Redeposition rate Redeposition rate Redeposition rate Joint ICTP-IAEA Workshop on Fusion Plasma Modeling Using Atomic and Molecular Data, Trieste, Italy, 23-27 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 B=5 T - -2-3 -4 5 mm (a) 2 mm D=5mm mm Un-tilted (=deg) observed 2 W G =mm Bottom 5 5 2 25 3 Distance along the gap (mm) 9 8 7 6 C at./ cm -2 The redeposition layer is re-eroded by the bombardment of background plasma, therefore, C deposition is reduced at the gap edge of plasma-open side. - -2-3 -4 (b) Tilt angle, =5deg The calculated redeosition profiles reproduce the experimental profiles of C deposition. 4 The redeposition on plasma-open side is suppressed due to the tilt of top surface of the cell D=5mm 2 W G =mm 5 5 2 25 3 Distance along the gap (mm) Bottom - -2-3 -4 K.Ohya; JNM45(2)S. (c) Tilt angle, =2deg observed D=5mm 2 Bottom 5 5 2 25 3 Distance along the gap (mm) W G =mm 9 8 7 6 C at. / cm -2

Joint ICTP-IAEA Workshop on Fusion Plasma Modeling Using Atomic and Molecular Data, Trieste, Italy, 23-27 January 22 B-2) Molecular Dynamics simulation of plasma wall interaction Integrating equation of motions of constituent atoms t 2 Fj ( t) Verlet algorithm: rj ( t t) rj ( t) tr j ( t) 2m : Small cell containing 3-7 atoms The force on each atom calculated from the analytical derivation of appropriate interaction potential form. bij b c R ji A V fij ( rij ) V ij ( rij ) Vij ( rij ) : Empirical bond order potential i j 2 Attractive term: Cutoff-function: t r k ( t t) r k ( t) F k ( t t) Fk ( t) 2m D V R ( r) exp 2S r r S SD V ( ) exp 2 S r r A r S, r R D, f c ( r) r R D 2 2 sin 2, R r D,, r R D Repulsive term: 2 Bond-order function: Many-body term: Fusion-related parameter sets for C-C, C-H : Brenner (99, 992), REBO (22) and AIREBO (2) W-W, W-C, W-H : Juslin et al. (25) Be-Be, Be-C, Be-H, Be-W : Bjorkas et al. (29, 2) ij b ij f ( r ) g ( ) exp 2 r r c ik k( i, j) 2 2 c c Angular function:g( ) 2 2 2 d d h cos ik ik ijk ij ijk ik ij ik

Joint ICTP-IAEA Workshop on Fusion Plasma Modeling Using Atomic and Molecular Data, Trieste, Italy, 23-27 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 t:time 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 the space to form an infinite lattice. If an atom leaves the simulation cell, one of its images will enter through the opposite face. Simulation cell:should be large More realistic, but time-consuming. Simulation cell 6

Joint ICTP-IAEA Workshop on Fusion Plasma Modeling Using Atomic and Molecular Data, Trieste, Italy, 23-27 January 22 B-2) Molecular Dynamics simulation of plasma wall interaction W C φ C = 2 m -2 (N=) E=eV incident number 3 2 m -2 (N=3) 5 2 m -2 (N=5) incident energy E=eV E=keV 7

Joint ICTP-IAEA Workshop on Fusion Plasma Modeling Using Atomic and Molecular Data, Trieste, Italy, 23-27 January 22 B-2) Molecular Dynamics Simulation of plasma wall interaction C W C reflection coefficient, R C, C and W sputtering yields, Y C and Y W.8.6.4.2.8.6.4.2 MD.8 MD.8 MD R C.6.6 R C Y C.4 Y.4 C Y W Y W R W(pure) (a) 3eV Y W(pure) R C Y C Y W Y R C(pure) C(pure) 2 3 4 5 C fluence, C ( 6 cm -2 ).2.8.6.4.2 R W(pure) Y W(pure) (b) ev @ Changes in C and W sputtering yields are in good agreement with those between MD and dynamic MC code, EDDY. @ For C reflection coefficients, it is different from each other at low energy. Y W R C Y C R C(pure) Y W Y C(pure) 2 3 4 5 C fluence, C ( 6 cm -2 ).2.8.6.4.2 Y C R W(pure) Y W(pure) (c) kev Dynamic BCA Dynamic BCA Dynamic BCA R C R C Y C Y W Y C(pure) R C(pure) 2 3 4 5 C fluence, C ( 6 cm -2 ) 8

Joint ICTP-IAEA Workshop on Fusion Plasma Modeling Using Atomic and Molecular Data, Trieste, Italy, 23-27 January 22 B-2-) Reflection/sticking coefficient of deposited materials Preparation of Realistic PFW Surfaces W crystal Bombardment with ev-c Bombardment with ev-c W-C mixed layer Simultaneous bombardment with.-3ev-h and.25ev-c C deposition layer (amorphous carbon) Hydrogenated/ amorphous carbon (H/C:.4) The W surface is bombarded with C atoms at the temperature of ev and ev. At low plasma temperature, the W is covered by deposited C and at higher temperature W-C mixed layer is formed. 9 The a-c:h layer with different H/C is formed when a-c is bombarded with H atom.

Reflection coefficient Joint ICTP-IAEA Workshop on Fusion Plasma Modeling Using Atomic and Molecular Data, Trieste, Italy, 23-27 January 22 B-2-) Reflection/sticking coefficient of deposited materials Emission probability of reflected species CH 4 CH 4 CH4.8.6.4.2 amorphous carbon C CH CH2 CH3 CH4 particle energy (ev).8.6.4.2 CH 4 impact hydrogenated/ amorphized carbon CH4 CH3 CH2 CH C a-c:h H:C.4 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..8.6.4.2 W-C mixed layer CH 4 CH 3 CH 2 CH C CH 4 impact W-C mixed layer particle energy (ev)

CH y reflection coefficient C 2 H y reflection coefficient Joint ICTP-IAEA Workshop on Fusion Plasma Modeling Using Atomic and Molecular Data, Trieste, Italy, 23-27 January 22 B-2-) Reflection/sticking coefficient of deposited materials Incident species dependence of reflection coefficient Incident at CH y (y=~4) Incident at C 2 H y (y=~6).8.8.6.4 C CH CH 2 CH 3.6.4 C 2 C 2 H C 2 H 2 C 2 H 3.2 CH 4 on a-c:h(.42).. Incident energy (ev) More hydrogen contents C 2 H 4.2 C 2 H 5 on C 2 H 6 a-c:h(.42).. Incident energy (ev) Higher reflection coefficients 2

Joint ICTP-IAEA Workshop on Fusion Plasma Modeling Using Atomic and Molecular Data, Trieste, Italy, 23-27 January 22 B-2-2) Re-erosion of deposited impurities on plasma facing walls Be coverage effect on C has been recently demonstrated in the experiments. Be seeding on a plasma in contact with a C target decreases to negligible levels the CD light emission above C target even at Be concentration of ~.% in the plasma. J.M.Baldwin, R.P.Doerner; Nucl.Fusion 46(26)444. Norm. CD Band strength (Arb. units)..4% Be.6% Be.4 % Be. % Be.3 % Be.3 % Be.8 % Be. Surface carbon concentration 5 5 2 Time (s) Mitigation of chemical carbon erosion by Be deposition Plasma divertor simulator PISCES-B 22

Areal density ( 5 cm -2 ) Be coverage (%) Areal density ( 5 cm -2 ) Areal density ( 5 cm -2 ) Joint ICTP-IAEA Workshop on Fusion Plasma Modeling Using Atomic and Molecular Data, Trieste, Italy, 23-27 January 22 B-2-2) Re-erosion of deposited impurities on plasma facing walls Deposition of Beryllium on hydrogenated carbon Be coverage % 2% 2..5..5 (a) C Number of D or Be 3 6 8 2..5..5 (b) D C (w/o Be) Number of D 3 6 8 5% -2. -.. Depth (nm) 2. C (w/o Be).5 (c) Be -2. -.. Depth (nm) 8 (d) 92%..5 Number of Be 3 6 8 6 4 2-2. -.. Depth (nm) 2 4 6 8 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

Probability of traveling at a depth C areal density ( 5 cm -2 ) Joint ICTP-IAEA Workshop on Fusion Plasma Modeling Using Atomic and Molecular Data, Trieste, Italy, 23-27 January 22 B-2-2) Re-erosion of deposited impurities on plasma facing walls.25.2.5..5 (a) E i =5 ev Be coverage C % 7% 5% 82% (w/o Be) 2..5..5 Interaction depth in C and Be deposition Noncumulative bombardments with D atoms with energies of ev are performed and the same initial surface is used for each simulation..25.2.5..5 (b) Be coverage: 5% ev ev 5 ev ev -2. -.5 -. -.5.5..5 Depth (nm) C (w/o Be) E i 2..5..5 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

Emission yield C emission yield Emission yield Emission yield Joint ICTP-IAEA Workshop on Fusion Plasma Modeling Using Atomic and Molecular Data, Trieste, Italy, 23-27 January 22 B-2-2) Re-erosion of deposited impurities on plasma facing walls (a) Hydrogenated carbon........ C CD CD2 CD3 T=2 K D/(C+D)=.3 T=3 K T=8 K D/(C+D)=.3 D/(C+D)=.3 (b) (c) C CD CD2 CD3 CD4. Incident D energy, E i (ev) C CD CD2 CD3 At 3 K, dominant emission species are small molecules. Larger molecules (CD 2 and CD 3 ) are emitted with increasing D/(C+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 for physical sputtering... C T= 3 K T= 8 K T=2 K (d) D/(C+D)=. Incident D energy, E i (ev) 25

Normalized CD y yield Joint ICTP-IAEA Workshop on Fusion Plasma Modeling Using Atomic and Molecular Data, Trieste, Italy, 23-27 January 22 B-2-2) Re-erosion of deposited impurities on plasma facing walls Hydrogenated C with beryllium deposition..8.6.4.2..8.6.4.2 T=8 K E i = ev Ei= Ei= (a) ev 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 2 4 6 8 Be coverage (%) (b) Decrease in the emission yield is much faster than an increase in Be coverage on the surface. 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. 363-365(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

Joint ICTP-IAEA Workshop on Fusion Plasma Modeling Using Atomic and Molecular Data, Trieste, Italy, 23-27 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 H Vertical Target (C) Chemical erosion C x H y H Carbon tile C deposition (a-c:h ) C x H y Codeposition Be + Be first wall 27

Joint ICTP-IAEA Workshop on Fusion Plasma Modeling Using Atomic and Molecular Data, Trieste, Italy, 23-27 January 22 C-) Long-distance transport of carbon and beryllium in plasmas Model geometry of edge plasma and walls (Be) 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.29-293(2)26. Aside from sputtering by plasma ions, sputtering by charge exchange (CX) neutrals is taken into account at the first wall. (CFC) (W) (CFC) 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. Chemical sputtering of C target is calculated using Roth formulae [3]. Only CD 4 molecules are released from the target. [3] J.Roth et al., J.Nucl.Mater. 266-269(999)/337-339(25)97. 28

Ion and neutral energy (ev) Surface temperature, T s (K) Ion and neutral fluxes (m -2 s - ) Joint ICTP-IAEA Workshop on Fusion Plasma Modeling Using Atomic and Molecular Data, Trieste, Italy, 23-27 January 22 C-) Long-distance transport of carbon and beryllium in plasmas Dome Target Inner region First wall Outer region First wall Target Dome 25 D + (L=cm) D + 2 (L=3cm) D + (L=cm) DCX 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. 33-36(23)338. 7 3 9 5 7 6 5 4 3 2 D + DCX Ts (a) (b) 2 8 6 Angular distribution of ions is influenced by gyro-motion of the ions; most probable angles of the distribution are 2 o ~8 o, which are much larger than the magnetic angles intersecting the wall. Average angle of magnetic field lines intersecting the first wall equipped with blanket modules is chosen to be 5 o, which results in an incident 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. 5 5 2 Poloidal distance (m) 4 29

Sputtering fluxes (m -2 s - ) Joint ICTP-IAEA Workshop on Fusion Plasma Modeling Using Atomic and Molecular Data, Trieste, Italy, 23-27 January 22 C-) Long-distance transport of carbon and beryllium in plasmas Dome Target 23 2 Inner region First wall C CD4 Be(ion,L=cm) Outer region First wall Be(ion,L=3cm) Be(ion,L=cm) Be(neutral) 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. 9 7 5 3 5 5 2 Poloidal distance (m) 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

Vertical distance (m) Flight time integral Joint ICTP-IAEA Workshop on Fusion Plasma Modeling Using Atomic and Molecular Data, Trieste, Italy, 23-27 January 22 C-) Long-distance transport of carbon and beryllium in plasmas 4 2-2 -4 C, CD y and Be distributions in edge plasma Physical sputtering (a) (b) (c) C CD y Be Chemical sputtering Physical sputtering 4 6 8 4 6 8 4 6 8 Radial distance (m) Radial distance (m) Radial distance (m) 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. 28 26 24 22 2 The color represents the sum of the flight time of all particles traveling in each grid cell, per unit area in the poloidal crosssection. 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

Net erosion/deposition flux ( 2 m -2 s - ) Joint ICTP-IAEA Workshop on Fusion Plasma Modeling Using Atomic and Molecular Data, Trieste, Italy, 23-27 January 22 C-) Long-distance transport of carbon and beryllium in plasmas Dome Target 4 2 Net erosion and deposition profile on walls Inner region (a) First wall C Outer region First wall 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. -2-4.4.2 (b) Be L=cm L=3cm L=cm C deposits in the inner divertor are strongly reeroded 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. -.2 -.4 5 5 2 Poloidal distance (m) 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

T codeposition flux ( 9 m -2 s - ) Joint ICTP-IAEA Workshop on Fusion Plasma Modeling Using Atomic and Molecular Data, Trieste, Italy, 23-27 January 22 C-) Long-distance transport of carbon and beryllium in plasmas Dome Target 4 3 2 8 6 4 2 Inner region (a) First wall C, CD y (b) Be Tritium codeposition profile on walls Outer region First wall L=cm L=3cm L=cm Target Dome 5 5 2 Poloidal distance (m) Empirical formulae recently proposed 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. Finally, assuming toroidal symmetry, total retention rate can be estimated from the calculated T codeposition profile. 33

Joint ICTP-IAEA Workshop on Fusion Plasma Modeling Using Atomic and Molecular Data, Trieste, Italy, 23-27 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.6.3.48.58 3.6.4.6.7.3.4.48.65 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 standard 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 295 395 discharges, depending on the decay length. 34

Joint ICTP-IAEA Workshop on Fusion Plasma Modelling Using Atomic and Molecular Data, Trieste, Italy, 23-27 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 T arget ( W ) Local collision and thermal processes: Codeposition Implantation, with diffusion, C and Be trapping/ detrapping and surface recombination Be first wall Be + 35

Joint ICTP-IAEA Workshop on Fusion Plasma Modelling Using Atomic and Molecular Data, Trieste, Italy, 23-27 January 22 Fick s law with source and trapping terms n i c j x, t c Tj x, t D j c j x, t G j x, t t t c i Tj i C j ( x, t ) : j th solute concentration, D j : Diffussion coefficient for j th solute G j x,t : source term (range profile) ( x, t ) : concentration of j th solute trapped I th trapping site c i Tj Rate equation for trapping and detrapping i Te i x, t D c x, tc x, t t j j i x, t CTex, t C f c ( x, t) :jump distance, i j i x, t exp( E / ) Te i c 2 Tj T kt j i j i Tj : detrapping attempt frequency f i E T : the inverse trap saturability of j th solute fot the I th trapping site : detrapping energy of I th trap Boundary condition e.g., recombination limited c x C-2) Local tritium retention in tungsten divertor targets Thermal Processes after a Collision Process K 2 j r 2 J K c x rc j x D j j K r : recombination coefficient t= t t t DIFFUSE Vacuum Sputtered atom E el ( )-E sb Solid Recoiled atom E el ( 2 ) DIFFUSE DIFFUSE DIFFUSE BCA BCA BCA BCA BCA L =-ln (E ) E =E -E inel (L )-E el ( ) L 2 =-ln (E ) Projectile ion E E 2 =E -E inel (L 2 )-E el ( 2 ) Time / Time N H 36

Areal D density (cm -2 ) Released D flux (cm -2 s - ) Joint ICTP-IAEA Workshop on Fusion Plasma Modeling Using Atomic and Molecular Data, Trieste, Italy, 23-27 January 22 6 5 4 3 7 6 5 4 3 2 C-2) Local tritium retention in tungsten divertor targets Parameter Fitting with a TDS experiment Implantation (3K) Outgass (3K) TDS (5K/s) (a) (b) Total Mobile Trap Trap 2 ref + rec rec exp. Ttar 2 3 4 5 6 7 8 Time (s) 8 6 4 2 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 2.5 5 cm -2 s -. [] C.Garcia-Rosales et al., J.Nucl.Mater.233-237(996)83. (a) Diffusion (b) Surface recombination D (cm 2 s - ) E D (ev) E r (ev) K r (cm 4 K /2 s - ).39 2.5-7 -.59.2-25 (c) Trapping E T (ev) D trap /W E T2 (ev) D tarp2 /W.85..5. 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

E (ev), (deg), Ttar (x K) (cm -2 s - ) (cm -2 s - ) Joint ICTP-IAEA Workshop on Fusion Plasma Modeling Using Atomic and Molecular Data, Trieste, Italy, 23-27 January 22 5 5 5 5 C-2) Local tritium retention in tungsten divertor targets Plasma Parameters used for calculation Ttar Ttar E Outer target (a) Inner target -...2.3.4.5.6 Distance from strike point (m) 2 9 8 7 6 5 2 9 8 7 6 5 Incident energy (T), angle () and flux () and target temperature (T tar ) as a function of the position on the inner and outer target. E (b) 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.29-293(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 material and additional traps may be produced in the near-surface region due to high D fluxes to the target, resulting in a depth-dependent concentration. 38

Areal density of retained D atoms (cm -2 ) Areal density of retained D atoms (cm -2 ) Joint ICTP-IAEA Workshop on Fusion Plasma Modeling Using Atomic and Molecular Data, Trieste, Italy, 23-27 January 22 C-2) Local tritium retention in tungsten divertor targets Time evolution of retained D distribution 8 During plasma exposure (a) 7 6 5 4 3 2 8 7 6 5 s Inner target 4 s After plasma exposure s Dtrap/W=. 4 s 3 3 (b) 8 4 s (a) 7 6 5 4 3 2 8 7 6 5 s Outer target s During plasma exposure Dtrap/W=. After plasma exposure 4 s 3 3 (b) 4 3 Inner target Dtrap/W=. 4 3 Outer target Dtrap/W=. 2 -...2.3.4.5.6 Distance from strike point (m) 2 -...2.3.4.5.6 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

Tritium retention (mg) Joint ICTP-IAEA Workshop on Fusion Plasma Modeling Using Atomic and Molecular Data, Trieste, Italy, 23-27 January 22 C-2) Local tritium retention of in tungsten divertor targets 2 - -2-3 -4-5 -6 2 - -2-3 -4-5 -6 (a) Time evolution of Tritium Retention in Targets Total Trap 2 Mobile During discharge Trap Total Mobile Trap 2 Trap During discharge (b) Inner target Dtrap/W=. After discharge After discharge Outer target Dtrap/W=. 2 4 6 8 Time (s) In case of the inner target, dominant retention mechanism is the trapping in the deep trap (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

Tritium retention (mg) Joint ICTP-IAEA Workshop on Fusion Plasma Modeling Using Atomic and Molecular Data, Trieste, Italy, 23-27 January 22 5 4 3 2 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...... Trap concentration, Ttrap/W Tritium retention (mgt) after a discharge (4 s) in tunsgten. Trap concentration T trap /W Inner target Outer target (a) Just after discharge (4 s) Divertor 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. Total..8 47.3 58.. 2.6 3. 33.7.. 28.5 29.6 (b) Subsequently after discharge ( s). 8.5 23.4 3.9. 2. 2.8 4.9..6..7 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

Joint ICTP-IAEA Workshop on Fusion Plasma Modeling Using Atomic and Molecular Data, Trieste, Italy, 23-27 January 22 Acknowledgements THANK YOU for your attention and for collaboration and discussion with The Grant-in-Aid for Scientific Research on Priority Areas Tritium Science and Technology for Fusion Reactor of the Ministry of Education, Culture, Science and Technology in Japan Prof. T. Tanabe, Kyushu Univ., Japan Drs. Y. Tomita, H. Nakamura, A. Ito, G. Kawamura, NIFS, Japan Drs. K. Shimizu, T. Takizuka, K. Hoshino, JAEA, Japan Prof. A. Hatayama, Mr. M. Toma, Keio Univ., Japan Prof. Ono, Okayama Univ. Sci., Dr. T. Kenmotsu, Doshisha Uni., Japan Dr. A. Kirschner, FZJ, Germany 42