Predicting time evolution of hydrogen co-deposition in ITER based on self consistent global impurity transport modeling

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1 Max-Planck-Institut für Plasmaphysik Predicting time evolution of hydrogen co-deposition in ITER based on self consistent global impurity transport modeling K. Schmid M. Reinelt, K. Krieger

2 Outline Motivation Model description Input data Results Surface composition evolution Be influx onto targets Impurity influx into SOL D co-deposition Summary

3 Motivation Current predictions for co-deposition in ITER are based on local simulations at the CFC targets Requires ad-hoc assumption about Be influx No global flux or material balance Ignores co-deposition at other locations in the divertor Use WallDYN[1] to perform self consistent, global erosion deposition modeling of Be, C and W in ITER Self consistently calculates impurity fluxes (Be, C, W) onto the wall and erosion fluxes back to the plasma. Calculates the time evolution of the surface composition Maintains a global material and flux balance Calculates deposition of Be, C and W over the entire poloidal circumference of the ITER first wall [1] K. Schmid et Al An integrated model of impurity migration and wall composition dynamics for tokamaks PSI-19

4 Model description Subdivide the first wall into N-tiles Wall tiles Be, C, W, D, He Be, C, W Reaction zone Bulk Plasma ~Ion range Plasma model: Time scale of plasma transport is short compared to time scale of wall evolution Impurity concentrations in the plasma are low enough not to disturb the plasma Plasma transport can be characterized by a re-deposition matrix: r m,q i, j Surface model: from tile Fraction of j that ends eroded flux of up on tile i element m at charge state Reaction zone composition is variable, Bulk composition is constant All erosion & deposition is assumed to occur homogeneously in the reaction zone Total areal density of the reaction zone is kept constant via exchange with Bulk q

5 Model description Influx from plasma transport Defines an algebraic equation system for the incident fluxes Redistribution matrix from plasma transport code e.g DIVIMP = Fraction of element ei eroded at wr that ends up on ws at charge state qi

6 Model description Change in areal density [1] of element ei on wall wr For non depositing species e.g D no surface composition is calculated Additional material loss losschannels and and sources can canbe beadded addedhere Simulate chemical reactions (see (seem. M. Reinelt PSI-19) total areal density: NElem δ TOT = δ, wr ei= 1 ei, wr In net erosion cases material has to be moved from the bulk to the reaction zone to keep the total areal density constant In net deposition cases material has to be moved to the bulk from the reaction zone to keep the total areal density constant [1] K. Schmid et al., Nuclear Technology, 159, No. 3, (2007) 238

7 Z (m) Input data High power & high density ITER case [1]: iter812 WallDYN wall and B2/E grid boundary R (m) Wall B2/E grid edge Wall grid distance (m) Grid Grid wall wall distance up up to to cm! cm!? Extrapolation of of plasma plasma to to wall wall? Te, Te, Ti Ti D, D, He, He, C fluxes fluxes Main Wall Grid-Wall distance Outer baffle Outer strike PFR Inner strike Inner baffle 1E Wall element index [1] A. S. Kukushkin et al. Journal of Nuclear Materials (2005) 50 54

8 Input data Ion fluxes and plasma parameters at the wall 100 Main Wall Flat extrapolation from B2/E calculation grid to wall Outer baffle Outer strike PFR Inner strike Inner baffle Main Wall Outer baffle Outer strike PFR Inner strike Inner baffle Temperature (ev) 10 Te Ti D ion flux 1020 m-2 s Wall element index Wall element index Very high Te, Ti at W baffles and main chamber Strong physical sputtering Gap between grid and wall ~ 5 cm at baffles and ~ 20 cm at main wall Significant decay decay of of flux flux & temperatures is is likely likely

9 Input data Decay of ion fluxes and plasma temperatures towards the wall Flux decays exponentially with a decay length λ λ = D c s l l 180 m 2 10 m D s λ 5 c 10 m s s Drop by factor ½ on average 0.1m Temperature decay is more complicated, depends on χ parallel Ti ~ constant due to fast transport in gap (blobs) Te drops due to parallel heat loss (high χ parallel for e - ) By By how how much much?

10 Input data Drop in Te from grid to wall based on radial Te evolution in the B2/E solution Te Exp-fit Temperature (ev) λ Te = m Distance from separatrix (m) Radial Te, evolution well represented by exponential decay Use this λ values to extrapolate Te across the gap [1] A. S. Kukushkin et al. Journal of Nuclear Materials (2005) 50 54

11 Input data Resulting plasma parameters at wall due to Te decay 100 Main Wall Exp. decay of plasma parameters from B2/E calculation grid to wall Outer baffle Outer strike PFR Inner strike Inner baffle Main Wall Outer baffle Outer strike PFR Inner strike Inner baffle Temperature (ev) 10 Te Exp. decay Te Flat extrap. Ti D ion flux 1020 m-2 s Flux decay Flat extrapolation Wall element index Wall element index Decay affects main wall, divertor dome and baffle Lower Be source at main wall Less mitigation of C erosion

12 Input data New ITER design case [1]: F57_Series 1511 Flat plasma extrapolation Wall B2/E grid edge 17 Temperature (ev) Main Wall Te Ti D+1-Flux Outer baffle Outer strike Wall element index Similar D ion fluxes but plasma temperatures are lower by factor ~3 (Grid extends farther outward) Smaller difference between flat extrapolation and plasma decay [1] H.D. Pacher, A.S. Kukushkin et Al, J. Nucl. Mat (2009) p. 259 PFR Inner tgt Inner baffle Main Wall 1.0x x x x x103 D-Flux 1020 m-2 s-1

13 Input data Plasma model input data the redistribution matrix calculated by DIVIMP Destination wall index Launch impurities at a poloidal position Record impact position and charge state Be r i, j Be charge state integrated Inner baffle Inner strike Divertor dome Outer strike Outer baffle Main Wall Charge state resolved re-deposition matrix Strong diagonal Transport is step wise Most material ends up in inner divertor Source wall index

14 Input data Given the redistribution matrices, where is eroded material qualitatively transported to Material is transported in small steps and generally ends up at: But that does not mean it stays there! In the divertor material is recycling

15 Input data Surface model input data Erosion yields as function energy and surface composition Reflection yields as function energy and surface composition? 20 Years of MD, TRIM & Experimental data yield a solid basis for a scaling law based parameterization of the required yields Current approach: Fit TRIDYN data with scaling law Composition dependence Energy dependence (Bohdansky formula) Similar approach also for reflection yield

16 Results Calculations produce huge amount of information difficult to visualize Only excerpts & averages are shown Old and new ITER design B2/E backgrounds yield qualitatively the same results Not ever result will be shown for every case Only examples of observed effects will be shown Main influence on results comes from different extrapolation of main wall plasma Comparison of flat extrapolation with plasma decay case High Te, Ti & flux Strong Be source Low Te, Ti & flux Weak Be source

17 Surface composition evolution Erosion fluxes of Be, C & W vary with time due to changes surface composition Impurity influx varies with time There is no constant set of fluxes to be used in a local simulation Equilibrium state can only be found in a global simulation Old ITER design flat extrapolation Main Wall Outer baffle Outer target Dome Inner target Inner baffle

18 Be influx onto targets Be influx onto divertor targets as function of time Be flux fraction E-3 1E-4 1E-5 1E-6 Outer target 1E Wall element index Inner target Self consisten model at time (s) Old, local simulations Old calculations Be flux fraction varies by orders of magnitude vs. time and position Old ITER design flat extrapolation Old predictions based on constant Be flux fraction overestimate Be flux overestimate Be deposition overestimate co-deposition by Be underestimate co-deposition by C Self consistent calculations yield less Be deposition More C erosion C co-deposition dominates

19 Impurity influx into SOL Erosion fluxes of Be, C & W for the equilibrium surface composition Erosion flux #/m-tor s 1E20 1E19 1E18 Be (flat extrapolation) Be (Plasma decay) C (flat extrapolation) C (Plasma decay) C erosion flux depends on Be source Old ITER design 1E17 Outer wall Outer baffle Outer target Dome Inner target Inner baffle Inner wall Poloidal location For flat extrapolation the main wall Be erosion is higher by an order of magnitude. C erosion is more mitigated by Be deposition in flat extrapolation case Divertor region is still C erosion flux dominated in both cases W Sputtering is low in both cases and limited to the outer baffle

20 D co-deposition Calculated deposition of Be, C and W Growth rate #/m-tor s 1E21 1E20 1E19 1E18 1E17 Be (flat extrapolation) Be (plasma decay) C (flat extrapolation) C (plasma decay) New ITER design 1E16 1E15 Outer wall Outer baffle Outer target Dome Inner target Inner baffle Inner wall Poloidal position Be deposition mainly in inner divertor C deposition at divertor floor (dome) and outer main chamber Amount of C deposition depends on C erosion mitigation by Be i.e on the Be source C dominates deposition in all cases

21 Input data Based on net deposition rates (m -2 s -1 ) at each poloidal position + D/C, D/W and D/Be ratios [1] the D accumulation rate can be calculated D/C, D/W and D/Be ratios as functions of D/x flux ratio, T(K) and D-energy D x = New ITER design (Plasma decay) D/C ~ 0.2 D/Be ~ 5E-2 D/W ~5E-3 α Γ E + D D + e ΓBe Poloidal location Inner wall Inner baffle Inner target Dome Outer target Outer baffle β γ T D/W D/C D/Be D/x flux ratio, T(K) and D-energy were clamped to validity range Assumed temperatures Pos. Inner strikep. Outer strikep. Dome T(K) Outer wall D/x ratio [1] R.P. Doerner et. Al, Nucl. Fusion 49 (2009) Baffles Main wall

22 D co-deposition D co-deposition rate #/s D co-deposition rates from D/x ratios (D/s) 1E22 1E21 1E20 1E19 1E18 1E17 D co-deposition rate with Be (Flat extrapolation) Be (Plasma decay) C (Flat extrapolation) C (Plasma decay) New ITER design 1E16 Outer wall Outer baffle Outer target Dome Inner target Inner baffle Inner wall Poloidal position Highest D co-deposition rate located at divertor floor next to targets due chemical sputtering at target plates below strike C dominates total D co-deposition A high Be source partially mitigates C erosion and thus D co-deposition

23 D co-deposition Time to T-accumulation limit due to co-deposition Different C erosion mitigation by Be deposition Flux and Te decay Iter812 (old design) F57_1511 (new design) Flat plasma extrapolation Iter812 (old design) F57_1511 (new design) J. Roth et. al, J. Nucl. Mat (2009) p. 1 Self Self consistent model model of of Be Be flux flux drops drops # of of ITER ITER shots shots by by up up to to factor factor ~10! ~10! Most Most retention now now due due to to C Divertor floor floor should should be be kept kept HOT HOT New New ITER ITER design design yields yields same same result result as as old old design design

24 Summary The WallDYN code allows to calculate the evolution of the first tiles coupled via plasma transport Maintaining material and flux balance it self consistently calculates erosion and redeposition and the impurity influx into the plasma Based on the calculated deposition rates and D/x ratios from literature the D inventory due to co-deposition can be calculated Compared to previous estimates most of the co-deposition is due to C not due to Be. (Old local simulations overestimated Be influx) The deposition of Be eroded from the main chamber leads to a strong reduction of C erosion in the inner and partly also in the outer divertor. A high Be source mitigates C erosion and thus D co-deposition The calculation was performed both for the old and the new ITER design yielding essentially the same results: Co-deposition with C instead of Be reduces # of ITER discharges to reach T limit A lot of assumptions about the fluxes and plasma temperatures at the wall have to be made. More experiments are required to improve modeling main wall erosion