1.
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

2. Outline Concepts and status of modeling of
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

3.
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)

4. What is DIVIMP ? Limitations Improvements
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

5. What is DIVIMP ? Limitations Improvements
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

6. 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

7. 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

8. 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

9. 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

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

11.
Extended grid (EG)

12. 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

13. 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

14. 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
[3] K. Krieger et al, J. Nucl. Mat. 390–391 (2009) p. 110

15. 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

16. 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

17. 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

18. 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

19. 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

20. 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

21. 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

22. Re-deposition matrix (JET SG)

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

24. Re-deposition matrix (JET SG)

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

26. 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

32. What is DIVIMP ? Modelling framework: SOLPS 4.0 (5.0) CARRE (SONNET)
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

33. ? Grid Standard grid (SG) directly from B2/Eirene:
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)

34. Standard grids : ITER (Divertor)
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

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

36. Impurity transport Anomal diffusion ┴ B Classic transport || B
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

37. 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

38. 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