Benchmarking DIVIMP-ERODEPDIF ITER predictions on material mixing using JET results M. Reinelt, K. Schmid, K. Krieger SEWG Meeting JET07.07.2009 Max-Planck-Institut

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


OEDGE(OSM)

OEDGE(OSM)

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



Expected results:* Steady state wall concentrations & erosion fluxes

* Plasma impurity concentrations

Re-deposition matrixfor each element

Background plasma

• Diffusion• Sublimation

OEDGE(OSM)

OEDGE(OSM)



SOLPS(B2+Eirene)

SOLPS(B2+Eirene)

CARRE,recent codes

CARRE,recent codes

Grid

FluxCalcProbCalc

FluxCalcProbCalc

Impurity generation

SDTrimSDTrim

Phys. sputtering

Conceptual approach

DIVIMPDIVIMP




Background plasma


OEDGE(OSM)

OEDGE(OSM)



SOLPS(B2+Eirene)

SOLPS(B2+Eirene)

CARRE,recent codes

CARRE,recent codes

Grid

FluxCalcProbCalc

FluxCalcProbCalc

Impurity generation

SDTrimSDTrim

Phys. sputtering

Conceptual approach

DIVIMPDIVIMP




Background plasma


OEDGE(OSM)

OEDGE(OSM)



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




Background plasma


OEDGE(SOL22 option)

OEDGE(SOL22 option)



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)


New analytical model

BulkReactionzone

Backgroundplasma


Newly developed analytical model [4]:

[4] Concept and implementation by K. Schmid, Nucl. Techn., 159/3, 2007, p. 238


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




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



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,



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




Background plasma


OEDGE(SOL22 option)

OEDGE(SOL22 option)



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


BeTotal


Promtre-deposition

... ... ...


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


Inner Target

BeTotal


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


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

Documents

Benchmarking DIVIMP-ERODEPDIF ITER predictions on material mixing using JET results M. Reinelt, K. Schmid, K. Krieger SEWG Meeting JET07.07.2009 Max-Planck-Institut