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Benchmarking DIVIMP-ERODEPDIF ITER predictions on material mixing using JET results
M. Reinelt, K. Schmid, K. Krieger
SEWG Meeting JET 07.07.2009
Max-Planck-Institut für PlasmaphysikEURATOM Association, Garching b. München, Germany
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
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
• 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
• 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
DIVIMPDIVIMP
Materials properties databases
Materials properties databases
OEDGE(OSM)
OEDGE(OSM)
ERODEPDIF /Analytical models
ERODEPDIF /Analytical models
SOLPS(B2+Eirene)
SOLPS(B2+Eirene)
CARRE,recent codes
CARRE,recent codes
FluxCalcProbCalc
FluxCalcProbCalc
SDTrimSDTrim
Codes for "material side"
Codes for "plasma side"
Conceptual approach
DIVIMPDIVIMP
Materials properties databases
Materials properties databases
Expected results:* Steady state wall concentrations & erosion fluxes
* Plasma impurity concentrations
Re-deposition matrixfor each element
Background plasma
• Diffusion• Sublimation
OEDGE(OSM)
OEDGE(OSM)
ERODEPDIF /Analytical models
ERODEPDIF /Analytical models
SOLPS(B2+Eirene)
SOLPS(B2+Eirene)
CARRE,recent codes
CARRE,recent codes
Grid
FluxCalcProbCalc
FluxCalcProbCalc
Impurity generation
SDTrimSDTrim
Phys. sputtering
Conceptual approach
DIVIMPDIVIMP
Materials properties databases
Materials properties databases
Re-deposition matrixfor each element
Background plasma
• Diffusion• Sublimation
OEDGE(OSM)
OEDGE(OSM)
ERODEPDIF /Analytical models
ERODEPDIF /Analytical models
SOLPS(B2+Eirene)
SOLPS(B2+Eirene)
CARRE,recent codes
CARRE,recent codes
Grid
FluxCalcProbCalc
FluxCalcProbCalc
Impurity generation
SDTrimSDTrim
Phys. sputtering
Conceptual approach
DIVIMPDIVIMP
Materials properties databases
Materials properties databases
Re-deposition matrixfor each element
Background plasma
• Diffusion• Sublimation
OEDGE(OSM)
OEDGE(OSM)
ERODEPDIF /Analytical models
ERODEPDIF /Analytical models
SOLPS(B2+Eirene)
SOLPS(B2+Eirene)
CARRE,recent codes
CARRE,recent codes
Grid
FluxCalcProbCalc
FluxCalcProbCalc
Impurity generation
SDTrimSDTrim
Phys. sputtering
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
Extended grid (EG)
Conceptual approach
DIVIMPDIVIMP
Materials properties databases
Materials properties databases
Re-deposition matrixfor each element
Background plasma
• Diffusion• Sublimation
OEDGE(SOL22 option)
OEDGE(SOL22 option)
ERODEPDIF /Analytical models
ERODEPDIF /Analytical models
SOLPS(B2+Eirene)
SOLPS(B2+Eirene)
CARRE,recent codes
CARRE,recent codes
Grid
FluxCalcProbCalc
FluxCalcProbCalc
Impurity generation
SDTrimSDTrim
Phys. sputtering
ERODEPDIF
[2] K. Schmid, Nucl. Fusion 48 (2008) p. 105004
ERODEPDIF [2]:Looks iteratively for a flux balance solutionNo time evolution
Treat komplex plasma-wall interactions and material evolution in a simplified wayTreat komplex plasma-wall interactions and material evolution in a simplified way
ERODEPDIF
[2] K. Schmid, Nucl. Fusion 48 (2008) p. 105004[3] K. Krieger et al, J. Nucl. Mat. 390–391 (2009) p. 110
ERODEPDIF [2]:Looks iteratively for a flux balance solutionNo time evolution
Be-evaporation
wall gap L-mode high L-mode low H-mode low
JET experimental data [3]:Integrated Be flux from e.g. outer divertor from Be II (527nm)
JET experimental data [3]:Integrated Be flux from e.g. outer divertor from Be II (527nm)
Treat komplex plasma-wall interactions and material evolution in a simplified wayTreat komplex plasma-wall interactions and material evolution in a simplified way
New analytical model
BulkReactionzone
Backgroundplasma
Treat komplex plasma-wall interactions and material evolution in a simplified wayTreat komplex plasma-wall interactions and material evolution in a simplified way
Newly developed analytical model [4]:
[4] Concept and implementation by K. Schmid, Nucl. Techn., 159/3, 2007, p. 238
New analytical model
Bulk, z.B. CReactionzone
BGPD, He, Ar
Be, C, D, He, Ar
Be, C
Be, C
C
* Constant thickness* Variable composition (but homogeneous distribution)
* Variable thickness* Constant composition
Net deposition:Layer growth
Net erosion
[4] Concept and implementation by K. Schmid, Nucl. Techn., 159/3, 2007, p. 238
Treat komplex plasma-wall interactions and material evolution in a simplified wayTreat komplex plasma-wall interactions and material evolution in a simplified way
New analytical model
Bulk, z.B. CReactionzone
BGPD, He, Ar
Be, C, D, He, Ar
Be, C
Be, C
C
Net deposition:Layer growth
Net erosion
positionerosion/de Be and C
throughchange thickness toDueD toDue transportPlasma
Bulk from / oTransfer tfluxErosion -Influx dtd Be
k
[4] Concept and implementation by K. Schmid, Nucl. Techn., 159/3, 2007, p. 238
Treat komplex plasma-wall interactions and material evolution in a simplified wayTreat komplex plasma-wall interactions and material evolution in a simplified way
Applicable to “simple” systems like Be & C
YPartial ~ C*YTotal
Applicable to “simple” systems like Be & C
YPartial ~ C*YTotal
* Constant thickness* Variable composition (but homogeneous distribution)
* Variable thickness* Constant composition
Plasma
Each tile receives a flux due to erosion & re-deposition from other tilesPlasma transport is characterized by a re-deposition matrix:
BeC,m
i on tile up ends that j tilefrom melement offlux eroded ofFraction ,
mjir
Flux of material m on tile i:
Solved as a 4n coupled differential equation system in Mathematica
BulkReactionzone
RESULT: Time evolution of the first wall !RESULT: Time evolution of the first wall !
First wall is subdivided into n-tilesFirst wall is subdivided into n-tiles
n
j
mji
Dj
mj
mjm
i rYxN
tt
1,
New analytical model
[4] Concept and implementation by K. Schmid, Nucl. Techn., 159/3, 2007, p. 238
1
2
3 4
5
6
7
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)
# 4
Initi
ally
pur
e B
e Be buried by re-dep. C
Be re-deposition
#4 eroded
Prove Of Principle of solver
Initially pure C
Conceptual approach
DIVIMPDIVIMP
Materials properties databases
Materials properties databases
Re-deposition matrixfor each element
Background plasma
• Diffusion• Sublimation
OEDGE(SOL22 option)
OEDGE(SOL22 option)
ERODEPDIF /Analytical models
ERODEPDIF /Analytical models
SOLPS(B2+Eirene)
SOLPS(B2+Eirene)
CARRE,recent codes
CARRE,recent codes
Grid
FluxCalcProbCalc
FluxCalcProbCalc
Impurity generation
SDTrimSDTrim
Phys. sputtering
Concept: Re-deposition matrix by DIVIMP
2 3 4
-2
-1
0
1
2
Neutral wall Areas for homogeneous
impurity launch Ion wall
Z [
m]
R [m]
Lauch flux of Be impurity ionsand map points of re-deposition (Charge resolved)
Re-deposition matrix
static BGPstatic BGP
Bin
Re-deposition matrix (JET SG)
10 20 30 40 50 60 70
10
20
30
40
50
60
70
Destination bin
So
urc
e b
in
1.00E-4
6.31E-4
3.98E-3
2.51E-2
1.58E-1
1.00E0
Flux fraction (LOG scale)
BeTotal
10 20 30 40 50 60 70
10
20
30
40
50
60
70
Destination bin
So
urc
e b
in
1.00E-4
6.31E-4
3.98E-3
2.51E-2
1.58E-1
1.00E0
Flux fraction (LOG scale)
BeTotal
Re-deposition matrix (JET SG)
Promtre-deposition
... ... ...
Re-deposition matrix (JET SG)
10 20 30 40 50 60 70
10
20
30
40
50
60
70
Outer target
Destination bin
So
urc
e b
in
1.00E-4
6.31E-4
3.98E-3
2.51E-2
1.58E-1
1.00E0
Flux fraction (LOG scale)
Inner Target
BeTotal
Re-deposition matrix (JET SG)
10 20 30 40 50 60 70
10
20
30
40
50
60
70
Outer target
Destination bin
So
urc
e b
in
1.00E-4
6.31E-4
3.98E-3
2.51E-2
1.58E-1
1.00E0
Flux fraction (LOG scale)
Inner Target
BeTotal
0 20 40 60 80 100 120 140 160
Tot
al B
e re
-de
posi
tion
flux
Neutral wall element index
Most Be is re-deposited at the inner taget
Short term plans
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
JET SG + EG (Partly done) Be + C Background plasma: OEDGE, Experimental + Extrapolation
JET SG + EG (Partly done) Be + C Background plasma: OEDGE, Experimental + Extrapolation
ITER SG (Previously done) + EG Be migration (+ W Divertor) Background plasma: OEDGE
ITER SG (Previously done) + EG Be migration (+ W Divertor) Background plasma: OEDGE
Experimental data (K. Krieger)Experimental data (K. Krieger)
Validation
Extrapolation
What is DIVIMP ?
CARRE (SONNET)2D Grid generator: Plasma current Magnetic field
B2 (B2.5)Fluid codeB. Braams, NY
DIVIMP (MC):Impurity transport(Stangeby, Toronto)
SOLPS 4.0 (5.0)
OEDGEOnion skin model
EDGE2D NIMBUS
Modelling framework:
EIRENE (MC)Neutral transport (Reiter, FZJ)
EIRENE (MC)Neutral transport (Reiter, FZJ)
Grid
?
Free gird (w/o cut with neutral wall) is modified by DIVIMP (requires a lot of manual input,automatic generation in progress)
Grid extension to match the vessel geometry,so far manually customized
Grid extension to match the vessel geometry,so far manually customized
Standard grid (SG)directly from B2/Eirene:
+ PWI Interpolation of plasmaparameters to the wall (lack of physics: linear)
Overestimation of flux into divertor !
Standard grid (SG)directly from B2/Eirene:
+ PWI Interpolation of plasmaparameters to the wall (lack of physics: linear)
Overestimation of flux into divertor !
Standard grids : ITER (Divertor)
Core PlasmaCore Plasma
SOLSOL Flux SurfacesFlux Surfaces
SeparatrixSeparatrix
Div
erto
rD
iver
tor
Div
erto
rD
iver
tor
Unrolled data structure:
Core Plasma
Core Plasma
Flux Surfaces
Flux Surfaces
Div
erto
rD
iver
tor
Div
erto
r
Div
erto
r
Separatrix
Separatrix
SOLSOL
Background plasma
Background plasma
Standard grids : ITER (Divertor)
Background plasma
Background plasma
Core PlasmaCore Plasma
SOLSOL Flux SurfacesFlux Surfaces
SeparatrixSeparatrix
Div
erto
rD
iver
tor
Div
erto
rD
iver
tor
Unrolled data structure (B2-EIRENE):
Impurity transport
IonisationRecombinationThermalisation
IonisationRecombinationThermalisation
Classic transport || B(gyro center motion)• Friction force• Thermal gradient force• Electric force
Classic transport || B(gyro center motion)• Friction force• Thermal gradient force• Electric force
Ano
mal
diff
usio
n ┴
BA
nom
al d
iffus
ion
┴ B
Wal
l / D
iver
tor:
R
efle
ctio
n, D
epos
ition
Wal
l / D
iver
tor:
R
efle
ctio
n, D
epos
ition
What is FluxCalc / ProbCalc ?
Problem: Impurity generation by impurities (Self sputtering of W !)Problem: Impurity generation by impurities (Self sputtering of W !)
• Background plasma• Grid• Ion fluxes at grid edge• CX-Flux at grid edge• Neutral wall
FluxCalcFluxCalc
ProbCalcProbCalc
For every wall element:• Te, Ti• Ion flux (D, He, C)• CX-flux (Energy & angle resolved)
SDTrim (parameterized)SDTrim (parameterized) Sputteryields
For every wall element:• Erosion flux• Absolute wall launch probabilities of impurities
ERODEPDIV +Redeposiotionmatrix
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