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M. Reinelt, K. Schmid, K. Krieger SEWG High-Z Ljubljana 01.10.2009 Max-Planck-Institut für Plasmaphysik EURATOM Association, Garching b. München, Germany.

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Presentation on theme: "M. Reinelt, K. Schmid, K. Krieger SEWG High-Z Ljubljana 01.10.2009 Max-Planck-Institut für Plasmaphysik EURATOM Association, Garching b. München, Germany."— Presentation transcript:

1 M. Reinelt, K. Schmid, K. Krieger SEWG High-Z Ljubljana Max-Planck-Institut für Plasmaphysik EURATOM Association, Garching b. München, Germany Extended grid DIVIMP erosion deposition modelling

2 Outline Question: Steady state surface composition of the ITER first wall ? Our conceptual approach & strategy Standard and extended grids for DIVIMP Modeling of material mixing Modeling of plasma impurity generation Modeling of chemical phase formations "Work in progress" Question: Steady state surface composition of the ITER first wall ? Our conceptual approach & strategy Standard and extended grids for DIVIMP Modeling of material mixing Modeling of plasma impurity generation Modeling of chemical phase formations "Work in progress"

3 Motivation What are the steady state surface concentrations of the ITER first wall ? Initial surface composition Initial surface composition Plasma impurity concentration Plasma impurity concentration Erosion by hydrogen Bulk material Bulk material Temperature Re-deposition Erosion by impurities and self sputtering Deposition Plasma transport Sublimation Diffusion Phase formations Layer growth Dynamic surface composition Dynamic surface composition Steady state surface: Total flux balance Steady state surface: Total flux balance

4 Simplifications Assumption 1: Plasma transport is instantaneous Erosion by hydrogen Re-deposition Erosion by impurities and self sputtering Deposition INSTANT Plasma transport Sublimation Dynamic surface composition Dynamic surface composition Bulk material Bulk material Temperature Diffusion Phase formations Layer growth

5 Simplifications Erosion by hydrogen Temperature Re-deposition Erosion by impurities and self sputtering Deposition INSTANT Plasma transport Sublimation Diffusion Phase formations Layer growth CONSTANT bulk composition Dynamic surface composition Dynamic surface composition Assumption 1: Plasma transport is instantaneous Assumption 2: Bulk composition is constant All processes depend primarily on the concentrations in the near surface region. All processes depend primarily on the concentrations in the near surface region.

6 Conceptual approach DIVIMP Plasma transport of impurities Expected results: * Steady state wall concentrations & erosion fluxes * Plasma impurity concentrations Benchmark results with JET experiments Extrapolate to ITER ERODEPDIF: Flux balances ERODEPDIF: Flux balances Background plasma OEDGE (OSM) OEDGE (OSM) SOLPS (B2+Eirene) SOLPS (B2+Eirene) CARRE, recent codes CARRE, recent codes Grid Diffusion Sublimation Chemical phase formation Impurity generation SDTrim Materials properties Materials properties

7 Conceptual approach DIVIMP Plasma transport of impurities ERODEPDIF: Flux balances ERODEPDIF: Flux balances Background plasma OEDGE (OSM) OEDGE (OSM) SOLPS (B2+Eirene) SOLPS (B2+Eirene) CARRE, recent codes CARRE, recent codes Grid Diffusion Sublimation Chemical phase formation Impurity generation SDTrim Materials properties Materials properties

8 Conceptual approach DIVIMP Plasma transport of impurities ERODEPDIF: Flux balances ERODEPDIF: Flux balances Background plasma OEDGE (OSM) OEDGE (OSM) SOLPS (B2+Eirene) SOLPS (B2+Eirene) CARRE, recent codes CARRE, recent codes Grid Diffusion Sublimation Chemical phase formation Impurity generation SDTrim Materials properties Materials properties

9 Extended grid (EG) JET SG (Standard grid) JET SG (Standard grid) JET EG [1] (Extended grid) JET EG [1] (Extended grid) [1] By S. Lisgo

10 Extended grid (EG)... to be filled with plasma

11 Conceptual approach DIVIMP Plasma transport of impurities ERODEPDIF: Flux balances ERODEPDIF: Flux balances Background plasma OEDGE (OSM) OEDGE (OSM) SOLPS (B2+Eirene) SOLPS (B2+Eirene) CARRE, recent codes CARRE, recent codes Grid Diffusion Sublimation Chemical phase formation Impurity generation SDTrim Materials properties Materials properties Material mixing model

12 Material mixing Plasma Each tile receives a flux due to erosion & re-deposition from other tiles Plasma transport is characterized by a re-deposition matrix: Flux of material m on tile i: Result: Set of n coupled differential / algebraic equations Concept: The first wall is divided into n tiles

13 Mixed material formation Plasma BulkReaction zone Background plasma Concept: Each tile is composed of a thin reaction zone and a bulk material Allows layer growth and erosion, sublimation and simplified chemistry. No diffusion! * Constant thickness Collision cascades: < 50 nm * Variable composition * Constant source / sink * Constant composition

14 Mixed material formation Bulk For n-tiles and k-chemical phases: kn coupled differential equations First tests with Mathematica: Works for >1000 coupled equations For n-tiles and k-chemical phases: kn coupled differential equations First tests with Mathematica: Works for >1000 coupled equations dσ X / dt = Plasma +Influx (by re-deposition matrix) – Erosion flux (by hydrogen and impurities) – Flux of sublimation (from vapor pressure of the chemical phase) ± Balancing flux (with bulk material) k Chemical phases or elements [X] [Y] [Z]... Chemical reactions +Flux of formation reactions (X is Product) – Flux of dissociation reactions (X is Reactant) Concept: Each tile is composed of a thin reaction zone and a bulk material

15 Prove-Of-Principle (w/o chemical reactions) Numerical solution for 69 tiles, re-deposition matrix and C wall + Be evaporation Initial Be coverage Re-deposition of Be

16 Prove-Of-Principle (w/o chemical reactions) Numerical solution for 69 tiles, re-deposition matrix and C wall + Be evaporation Initial Be coverage Re-deposition of Be Be is covered by C

17 Prove-Of-Principle (w/o chemical reactions) Numerical solution for 69 tiles, re-deposition matrix and C wall + Be evaporation [Be / Ǻ 2 ] Time [s] Tiles with Be at surface Tiles with C at surface All Be is covered by C

18 Conceptual approach DIVIMP Plasma transport of impurities ERODEPDIF: Flux balances ERODEPDIF: Flux balances Background plasma OEDGE (OSM) OEDGE (OSM) SOLPS (B2+Eirene) SOLPS (B2+Eirene) CARRE, recent codes CARRE, recent codes Grid Diffusion Sublimation Chemical phase formation Impurity generation SDTrim Materials properties Materials properties Model of surface chemistry

19 ITER first wall He Be W W C C O O H H N N Elements

20 ITER first wall He Nitrides: WN Be 3 N 2 Nitrides: WN Be 3 N 2 Hydrides: BeH 2 C X H Y OH 2 Hydrides: BeH 2 C X H Y OH 2 Carbides: WC, W 2 C Be 2 C Carbides: WC, W 2 C Be 2 C Beryllides: Be 2 W, Be 12 W Beryllides: Be 2 W, Be 12 W Oxides: WO 3 BeO CO 2 Oxides: WO 3 BeO CO 2 Be W W C C O O H H N N Elements Binary phases

21 ITER first wall He Nitrides: WN Be 3 N 2 Nitrides: WN Be 3 N 2 Hydrides: BeH 2 C X H Y OH 2 Hydrides: BeH 2 C X H Y OH 2 Carbides: WC, W 2 C Be 2 C Carbides: WC, W 2 C Be 2 C Beryllides: Be 2 W, Be 12 W Beryllides: Be 2 W, Be 12 W Oxides: WO 3 BeO CO 2 Oxides: WO 3 BeO CO 2 Be W W C C O O H H N N Tungstates: BeWO 3, BeWO 4 Hydroxides: Be(OH) 2, W(OH) X … Tungstates: BeWO 3, BeWO 4 Hydroxides: Be(OH) 2, W(OH) X … Elements Binary phases Ternary phases

22 Simplified description of ITERs first wall chemistry Be W C Be 2 C W 2 C WC Be 2 W Be 12 W Be gas BeO O ads WO 3 WO 3,gas Chemical phases Chemical phases 2 Be + C Be 2 C Be 2 C 2 Be + C W + C WC WC W + C 2 W + C W 2 C W 2 C 2 W + C W + 2 Be Be 2 W Be 2 W W + 2 Be W 2 C WC + W WC + W W 2 C Be + O BeO BeO Be + O W + 3 O WO 3 WO 3 W + 3 O Sublimation: Be Be gas WO 3 WO 3,gas O-Adsorption: O 2,gas O ads O ads O 2,gas Elementary reactions Elementary reactions … Equations for reaction fluxes Reaction balances Change of areal density of chemical phase = + all formation reaction fluxes – all dissociation reaction fluxes Couple to plasma transport code

23 Benchmarking example: W/Be/O XPS XPS experimental data 2.1 nm Be on W (Substrate,pc) mbar O 2 Layered system XPS experimental data 2.1 nm Be on W (Substrate,pc) mbar O 2 Layered system Model Model of coupled reaction equations Elementary processes: O adsorption Be and W oxidation BeO and WO 3 dissociation Be and WO 3 sublimation Be 2 W formation and dissociation Not included: Depth profiles (Homogeneous distributed phases) Model of coupled reaction equations Elementary processes: O adsorption Be and W oxidation BeO and WO 3 dissociation Be and WO 3 sublimation Be 2 W formation and dissociation Not included: Depth profiles (Homogeneous distributed phases)

24 Summary Set up a scalable model for JET (and ITER) that describes the first wall material evolution as a combination of: + Dynamic impurity generation (Parametrised TRIDYN) + Plasma transport via a static background (DIVIMP) + Some temperature dependent processes (Chemical phase formations, sublimation, directly benchmarked by XPS data) Method: Numerical solution of a set of coupled algebraic differential equations (Mathematica) Result: Time evolution of Surface concentrations (incl. layer growth) Plasma impurity concentrations Erosion and re-erosion fluxes Benchmark the results with JET experiments (e.g. post-mortem analysis of layers, spectroscopy of erosion fluxes)

25

26 Erosion and re-erosion by impurities Assumption: Individual sputteryields Y j of a mixture of elements scales linearily with the surface concentration Assumption: Individual sputteryields Y j of a mixture of elements scales linearily with the surface concentration Works well for Be / C but only fairly good for W / C, W / Be 50 eV D eV Be on C (Precalculated Yields)

27 Re-deposition matrix (JET SG) Promt re-deposition... Simple (unverified) OSM plasma background

28 Re-deposition matrix by DIVIMP Lauch flux of Be impurity ions and map points of re-deposition (Charge resolved) Re-deposition matrix, n ~ 70 static BGP Bin static BGP, standard grid


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