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

M. Reinelt, K. Schmid, K. Krieger

SEWG High-Z Ljubljana 01.10.2009

Max-Planck-Institut für PlasmaphysikEURATOM Association, Garching b. München, Germany

Extended grid DIVIMP erosion deposition modelling

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"

Motivation

What are the steady state surface concentrations of the ITER first wall ?

Initial surface composition

Initial surface composition

Plasma impurityconcentration

Plasma impurityconcentration

Erosion by hydrogen

Bulk material

Bulk material

Temperature

Re-deposition

Erosion by impuritiesand self sputtering

Deposition

Plasma transport

Sublimation Diffusion

Phase formations

Layer growth

Dynamic surface composition


Steady state surface:Total flux balance

Steady state surface:Total flux balance

Simplifications

Assumption 1: Plasma transport is instantaneous

Erosion by hydrogen

Re-deposition


Deposition

INSTANTPlasma transport

Sublimation



Bulk material

Bulk material

Temperature

Diffusion

Phase formations

Layer growth

Simplifications

Erosion by hydrogen Temperature

Re-deposition


Deposition

INSTANTPlasma transport

Sublimation Diffusion

Phase formations

Layer growth

CONSTANTbulk composition



Assumption 1: Plasma transport is instantaneousAssumption 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.

Conceptual approach

DIVIMPDIVIMP

Plasma transport ofimpurities

Expected results:

* Steady state wall concentrations & erosion fluxes* Plasma impurity concentrations

Benchmark results with JET experiments Extrapolate to ITER

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

SDTrimSDTrim

Materials properties


Conceptual approach

DIVIMPDIVIMP




Background plasma

OEDGE(OSM)

OEDGE(OSM)

SOLPS(B2+Eirene)

SOLPS(B2+Eirene)

CARRE,recent codes

CARRE,recent codes

Grid


Impurity generation

SDTrimSDTrim



Conceptual approach

DIVIMPDIVIMP




Background plasma

OEDGE(OSM)

OEDGE(OSM)

SOLPS(B2+Eirene)

SOLPS(B2+Eirene)

CARRE,recent codes

CARRE,recent codes

Grid


Impurity generation

SDTrimSDTrim



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)

... to be filled with plasma

Conceptual approach

DIVIMPDIVIMP




Background plasma

OEDGE(OSM)

OEDGE(OSM)

SOLPS(B2+Eirene)

SOLPS(B2+Eirene)

CARRE,recent codes

CARRE,recent codes

Grid


Impurity generation

SDTrimSDTrim



Material mixing model

Material mixing

Plasma

Each tile receives a flux due to erosion & re-deposition from other tilesPlasma transport is characterized by a re-deposition matrix:

i on tile up ends that j tilefrom melement offlux eroded ofFraction , mjir

Flux of material m on tile i:

n

j

mji

Dj

mj

mjm

i rYxN

tt

1,

Result: Set of n coupled differential / algebraic equationsResult: Set of n coupled differential / algebraic equations

Concept: The first wall is divided into n tilesConcept: The first wall is divided into n tiles

Mixed material formation

Plasma

BulkReactionzone

Backgroundplasma

Concept: Each tile is composed of a thin reaction zone and a bulk materialConcept: Each tile is composed of a thin reaction zone and a bulk material

Allows layer growth and erosion, sublimation and simplified chemistry. No diffusion!Allows layer growth and erosion, sublimation and simplified chemistry. No diffusion!

* Constant thickness Collision cascades:

< 50 nm* Variable composition

* Constant source / sink

* Constant composition

Mixed material formation

Bulk

For n-tiles and k-chemical phases: kn coupled differential equationsFirst tests with Mathematica: Works for >1000 coupled equations

For n-tiles and k-chemical phases: kn coupled differential equationsFirst tests with Mathematica: Works for >1000 coupled equations

dσX / 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 materialConcept: Each tile is composed of a thin reaction zone and a bulk material

Prove-Of-Principle (w/o chemical reactions)

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

Numerical solution for 69 tiles, re-deposition matrix and C wall + Be evaporationNumerical solution for 69 tiles, re-deposition matrix and C wall + Be evaporation

Initial Be coverage Re-deposition of Be


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


Initial Be coverage Re-deposition of BeBe is covered by C



[Be

/ Ǻ2 ]

Time [s]

Tiles with Be at surface

Tiles with C at surface

All Be is covered by C

Conceptual approach

DIVIMPDIVIMP




Background plasma

OEDGE(OSM)

OEDGE(OSM)

SOLPS(B2+Eirene)

SOLPS(B2+Eirene)

CARRE,recent codes

CARRE,recent codes

Grid


Impurity generation

SDTrimSDTrim



Model of surface chemistry

ITER first wall

HeHe BeBeWW

CC

OO

HH

NNElementsElements

ITER first wall

HeHe

Nitrides:WNBe3N2

Nitrides:WNBe3N2

Hydrides:BeH2

CXHY

OH2

Hydrides:BeH2

CXHY

OH2

Carbides:WC, W2CBe2C


Beryllides:Be2W, Be12W


Oxides:WO3

BeOCO2

Oxides:WO3

BeOCO2

BeBeWW

CC

OO

HH

NNElementsElements

Binary phasesBinary phases

ITER first wall

HeHe

Nitrides:WNBe3N2

Nitrides:WNBe3N2

Hydrides:BeH2

CXHY

OH2

Hydrides:BeH2

CXHY

OH2





Oxides:WO3

BeOCO2

Oxides:WO3

BeOCO2

BeBeWW

CC

OO

HH

NN

Tungstates:BeWO3, BeWO4

Hydroxides:Be(OH)2, W(OH)X

…

Tungstates:BeWO3, BeWO4

Hydroxides:Be(OH)2, W(OH)X

…

ElementsElements

Binary phasesBinary phases

Ternary phasesTernary phases

Simplified description of ITERs first wall chemistry

Be W C Be2C W2C WC Be2W Be12WBegas BeO Oads

WO3 WO3,gas

Chemical phases

Chemical phases

2 Be + C → Be2CBe2C → 2 Be + CW + C → WCWC → W + C2 W + C → W2CW2C → 2 W + CW + 2 Be → Be2WBe2W → W + 2 BeW2C → WC + WWC + W → W2CBe + O → BeOBeO → Be + OW + 3 O → WO3

WO3 → W + 3 O

Sublimation:Be → Begas

WO3 → WO3,gas

O-Adsorption:O2,gas → Oads

Oads → O2,gas

Elementary reactions

Elementary reactions

sm

smk

kT

EkCW

4

2 11

121

1 withexp][][

ssmk

kT

EkCW 1

22

221

2 withexp][2

…

Equations for reaction fluxesEquations for reaction fluxes

...][

212

dt

CWd...22

][21

dt

Wd

Reaction balancesReaction balances

Change of areal density of chemical phase = + all formation reaction fluxes – all dissociation reaction fluxes

Couple to plasma transport code Couple to plasma transport code

Benchmarking example: W/Be/O

XPS

XPS experimental data• 2.1 nm Be on • W (Substrate,pc)• 10-10 mbar O2

Layered system

XPS experimental data• 2.1 nm Be on • W (Substrate,pc)• 10-10 mbar O2

Layered system

Model

Model of coupled reaction equations

Elementary processes:• O adsorption• Be and W oxidation• BeO and WO3 dissociation• Be and WO3 sublimation• Be2W 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 WO3 dissociation• Be and WO3 sublimation• Be2W formation and dissociation

Not included: Depth profiles (Homogeneous distributed phases)

SummarySet 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)

Erosion and re-erosion by impurities

Assumption: Individual sputteryields Yj of a mixture of elements scales linearily with the surface concentration

Assumption: Individual sputteryields Yj of a mixture of elements scales linearily with the surface concentration

Works well for Be / C but only fairly good for W / C, W / BeWorks well for Be / C but only fairly good for W / C, W / Be

0 200 400 600 800 10000.0

0.2

0.4

0.6

0.8

1.0

Be

su

rfa

ce

co

nc

en

tra

tio

n

Fluence (#/A2)

TRIDYN Analytical model

50 eV D + 100 eV Be on C(Precalculated Yields)

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

Re-deposition matrix (JET SG)

Promtre-deposition

... ... ...

Simple (unverified) OSM plasma background

Re-deposition matrix by DIVIMP

2 3 4

-2

-1

0

1

2

Outer plasma grid cells Projection of the grid to the vessel wall Areas for homogeneous

impurity launch

Z [

m]

R [m]

Lauch flux of Be impurity ionsand map points of re-deposition (Charge resolved)

Re-deposition matrix, n ~ 70

static BGP

Bin

static BGP,standard grid

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

Documents

plasma slide

flux of material

tiles plasma transport

impurities flux of sublimation

constant composition

flux balances erodepdif

deposition matrix erosion

chemical phase balancing