27.03.2017 Benchmarking DIVIMP-ERODEPDIF ITER predictions on material mixing using JET results M. Reinelt, K. Schmid, K. Krieger Max-Planck-Institut für Plasmaphysik EURATOM Association, Garching b. München, Germany SEWG Meeting JET 07.07.2009

Outline Concepts and status of modeling of 27.03.2017 Outline Concepts and status of modeling of PWI with DIVIMP (Work in progress!) Limits and extensions of DIVIMP Standard and extended grids Modeling of material mixing Status of Be / C calculations for JET Short term plans

27.03.2017 What is DIVIMP ? DIVIMP : "DIVertor IMPurities" developed by P.Stangeby / D. Elder (1992) Designed for impurity transport in divertor and SOL of tokamaks Simulates (erosion) and impurity transport in plasma boundary Monte Carlo modeling ... of particle trajectories through plasma background based on forces on impurity atoms ... of reactions in the plasma (ionisation, neutralisation, chemistry)

What is DIVIMP ? Limitations Improvements 27.03.2017 What is DIVIMP ? Limitations Improvements 2D Model (poloidal X-section) -----  Toroidal symmetry ! Static plasma background -----  Impurities are traces ! Outer most flux surface from target to target Extended grids  Gaps between grid and wall (S. Lisgo) Impurity generation FluxCalc/ProbCalc  No sputtering by multiple plasma species (K. Schmid)  No sputtering at walls (only target) Plasma facing wall ERODEPDIF  No multiple wall elements (K. Schmid)  No wall material mixing  No T-dep. effects (Sublimation...)  No re-deposition

What is DIVIMP ? Limitations Improvements 27.03.2017 What is DIVIMP ? Limitations Improvements 2D Model (poloidal X-section) -----  Toroidal symmetry ! Static plasma background -----  Impurities are traces ! Outer most flux surface from target to target Extended grids  Gaps between grid and wall (S. Lisgo) Impurity generation FluxCalc/ProbCalc  No sputtering by multiple plasma species (K. Schmid)  No sputtering at walls (only target) Plasma facing wall ERODEPDIF  No multiple wall elements (K. Schmid)  No wall material mixing  No T-dep. effects (Sublimation...)  No re-deposition

Conceptual approach Codes for "plasma side" Codes for "material side" properties databases OEDGE (OSM) SOLPS (B2+Eirene) CARRE, recent codes Codes for "plasma side" DIVIMP ERODEPDIF / Analytical models Codes for "material side" SDTrim FluxCalc ProbCalc

Conceptual approach Materials properties databases OEDGE (OSM) SOLPS (B2+Eirene) CARRE, recent codes Grid Background plasma DIVIMP Diffusion Sublimation Expected results: * Steady state wall concentrations & erosion fluxes * Plasma impurity concentrations Re-deposition matrix for each element ERODEPDIF / Analytical models Phys. sputtering Impurity generation SDTrim FluxCalc ProbCalc

Conceptual approach Materials properties databases OEDGE (OSM) SOLPS (B2+Eirene) CARRE, recent codes Grid Background plasma DIVIMP Diffusion Sublimation Re-deposition matrix for each element ERODEPDIF / Analytical models Phys. sputtering Impurity generation SDTrim FluxCalc ProbCalc

Conceptual approach Materials properties databases OEDGE (OSM) SOLPS (B2+Eirene) CARRE, recent codes Grid Background plasma DIVIMP Diffusion Sublimation Re-deposition matrix for each element ERODEPDIF / Analytical models Phys. sputtering Impurity generation SDTrim FluxCalc ProbCalc

Extended grid (EG) JET SG (Standard grid) JET EG [1] (Extended grid) 27.03.2017 Extended grid (EG) JET SG (Standard grid) JET EG [1] (Extended grid) [1] By S. Lisgo

27.03.2017 Extended grid (EG)

Conceptual approach Materials properties databases OEDGE (SOL22 option) SOLPS (B2+Eirene) CARRE, recent codes Grid Background plasma DIVIMP Diffusion Sublimation Re-deposition matrix for each element ERODEPDIF / Analytical models Phys. sputtering Impurity generation SDTrim FluxCalc ProbCalc

ERODEPDIF Treat komplex plasma-wall interactions and material evolution in a simplified way ERODEPDIF [2]: Looks iteratively for a flux balance solution No time evolution [2] K. Schmid, Nucl. Fusion 48 (2008) p. 105004

ERODEPDIF Treat komplex plasma-wall interactions and material evolution in a simplified way ERODEPDIF [2]: Looks iteratively for a flux balance solution No time evolution Be-evaporation JET experimental data [3]: Integrated Be flux from e.g. outer divertor from Be II (527nm) wall gap  L-mode high  L-mode low  H-mode low [2] K. Schmid, Nucl. Fusion 48 (2008) p. 105004 [3] K. Krieger et al, J. Nucl. Mat. 390–391 (2009) p. 110

New analytical model Treat komplex plasma-wall interactions and material evolution in a simplified way Newly developed analytical model [4]: Reaction zone Bulk Background plasma [4] Concept and implementation by K. Schmid, Nucl. Techn., 159/3, 2007, p. 238

New analytical model Treat komplex plasma-wall interactions and material evolution in a simplified way Net deposition: Layer growth BGP D, He, Ar Reaction zone Be, C Bulk, z.B. C Be, C, D, He, Ar C Be, C Net erosion * Constant thickness * Variable composition (but homogeneous distribution) * Variable thickness * Constant composition [4] Concept and implementation by K. Schmid, Nucl. Techn., 159/3, 2007, p. 238

Applicable to “simple” New analytical model Treat komplex plasma-wall interactions and material evolution in a simplified way Net deposition: Layer growth BGP D, He, Ar Reaction zone Be, C Bulk, z.B. C Be, C, D, He, Ar C Be, C Net erosion Applicable to “simple” systems like Be & C YPartial ~ C*YTotal * Constant thickness * Variable composition (but homogeneous distribution) * Variable thickness * Constant composition [4] Concept and implementation by K. Schmid, Nucl. Techn., 159/3, 2007, p. 238

New analytical model Reaction Bulk zone Plasma Bulk First wall is subdivided into n-tiles 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: Solved as a 4n coupled differential equation system in Mathematica RESULT: Time evolution of the first wall ! [4] Concept and implementation by K. Schmid, Nucl. Techn., 159/3, 2007, p. 238

Prove Of Principle of solver First (simple) test case: 7 Wall tiles Constant D plasma flux in the range of 1022 m-2 s-1 Be & C erosion yields in % range Very simplified plasma transport (exp. distance decay) Initially pure C #4 eroded Be buried by re-dep. C # 4 Initially pure Be Be re-deposition

Conceptual approach Materials properties databases OEDGE (SOL22 option) SOLPS (B2+Eirene) CARRE, recent codes Grid Background plasma DIVIMP Diffusion Sublimation Re-deposition matrix for each element ERODEPDIF / Analytical models Phys. sputtering Impurity generation SDTrim FluxCalc ProbCalc

Concept: Re-deposition matrix by DIVIMP static BGP Lauch flux of Be impurity ions and map points of re-deposition (Charge resolved) static BGP Bin  Re-deposition matrix

Re-deposition matrix (JET SG)

Re-deposition matrix (JET SG) Promt re-deposition ... ... ...

Re-deposition matrix (JET SG)

Re-deposition matrix (JET SG) Most Be is re-deposited at the inner taget

Short term plans 1) Get EG and OEDGE running for both JET and ITER Experimental data (K. Krieger) Validation JET SG + EG (Partly done) Be + C Background plasma: OEDGE, Experimental + Extrapolation ITER SG (Previously done) + EG Be migration (+ W Divertor) Background plasma: OEDGE Extrapolation 1) Get EG and OEDGE running for both JET and ITER 2) Obtain re-deposition matrices for JET: Be, C ITER: Be, W 3) Compare SG and EG based calculations 4) Investigate the steady state wall compositions and impurity plasma concentrations

What is DIVIMP ? Modelling framework: SOLPS 4.0 (5.0) CARRE (SONNET) 27.03.2017 What is DIVIMP ? Modelling framework: SOLPS 4.0 (5.0) CARRE (SONNET) 2D Grid generator: Plasma current Magnetic field B2 (B2.5) Fluid code B. Braams, NY EIRENE (MC) Neutral transport (Reiter, FZJ) OEDGE Onion skin model EIRENE (MC) Neutral transport (Reiter, FZJ) DIVIMP (MC): Impurity transport (Stangeby, Toronto) CARRE: Spulen, * Plasmastrom  Magnetfeld  Plasmastrom *  Magnetfeld  Cut with wall  Gitter dass die magnet. Flussflächen abbildet B2/Eirene : Grid  NeutralTeilchen  Ionisation  B2 fluid  z.B.Collision mit Wand Neutralisation  Generation von neuen Neutralen Eirene: Neutralteilchentransport  Ionisation  ... Selbstkonsistente Lösung unter Energie und Massenerhalt EDGE2D NIMBUS

? Grid Standard grid (SG) directly from B2/Eirene: 27.03.2017 Grid Standard grid (SG) directly from B2/Eirene: + PWI  Interpolation of plasma parameters to the wall (lack of physics: linear) Overestimation of flux into divertor ! Grid extension to match the vessel geometry, so far manually customized ? Free gird (w/o cut with neutral wall) is modified by DIVIMP (requires a lot of manual input, automatic generation in progress)

Standard grids : ITER (Divertor) 27.03.2017 Standard grids : ITER (Divertor) Unrolled data structure: Background plasma SOL Flux Surfaces Divertor Separatrix Divertor Core Plasma Separatrix Core Plasma Flux Surfaces SOL Divertor Divertor

Standard grids : ITER (Divertor) 27.03.2017 Standard grids : ITER (Divertor) Core Plasma SOL Flux Surfaces Separatrix Divertor Unrolled data structure (B2-EIRENE): Background plasma

Impurity transport Anomal diffusion ┴ B Classic transport || B 27.03.2017 Impurity transport Reflection, Deposition Wall / Divertor: Ionisation Recombination Thermalisation Anomal diffusion ┴ B Classic transport || B (gyro center motion) Friction force Thermal gradient force Electric force

What is FluxCalc / ProbCalc ? Problem: Impurity generation by impurities (Self sputtering of W !) Background plasma Grid Ion fluxes at grid edge CX-Flux at grid edge Neutral wall For every wall element: Te, Ti Ion flux (D, He, C) CX-flux (Energy & angle resolved) FluxCalc SDTrim (parameterized) ProbCalc Sputteryields For every wall element: Erosion flux Absolute wall launch probabilities of impurities ERODEPDIV + Redeposiotionmatrix

Summary Latest DIVIMP version (6 revision 41) working Modifications for coupling with ERODEPDIF Ability to calculate re-distribution matrices (Be for JET SG) Analytical solution for Be/C JET cases