Plasma wall interaction

IPP-Teilinstitut Greifswald, EURATOM Association, Wendelsteinstraße 1, D-17491 Greifswald, 

Germany 

Max-Planck-Institut für Plasmaphysik, EURATOM Association 

Plasma wall interaction – 

a bridge between several disciplines 

Ralf Schneider 

Ralf Schneider


Fusion 

good energy 

confinement without 

too large radiation 

losses and helium 

ash removal 

necessary


Magnetic confinement 

strongly non-linear parallel heat 

conduction by Coulomb collisions: 

extreme anisotropy: 

4 

κ 

|| 

∝10 

→10 

κ 

|| 

∝ T 

7 

κ 

⊥ 

5 

2


Plasma-wall interaction 

challenge: extremely high power loads 

requirement: pure plasma core


Basic question 

Can we manage the power load at the 

plates? 

Development of computational tools to 

model this power loading. 

Estimate of power load: 

Q 

⊥ 

= 

2n 

X 

Pheat 

× 2πR 

× Δ 

E 

Q 

! 

−2 

W 

≈ 35MWm 

7− X


Multi-scales 

sputtered and backscattered species and fluxes 

Plasma-wall interaction 

Molecular 

dynamics 

Binary collision 

approximation 

Kinetic 

Monte Carlo 

Kinetic 

model 

Fluid 

model 

impinging particle and energy fluxes


Hydrocarbon-codeposition 

Hydrogen 

G F Counsell, Plasma Sources Sci. Technol. 11 (2002) A80–A85 

• Chemical Erosion of carbon by hydrogen produces hydrocarbon 

species (C x H y ) 

• Dissociation & Recombination's leads to amorphous hydrocarbon 

layer formation 

• Carbon acts as sponge for hydrogen 

• Tritium is retained by co-deposition with carbon, on the plasma 

facing sides or on remote areas.


Radiation instability


Other options 

ITER 

ASDEX-Upgrade 

• Problems with Carbon have motivated to opt for other materials 

• Tungsten 

• Beryllium 

• W erosion and interaction with H and He is still a challenge 

• Mixed materials!

ITER 

• Mission: 

‣ “Burning plasma” Q=10 

• Reactor level fusion 

power 

‣ P fusion ~ 400 MW for 500 

s 

‣ Heating = 40 MW 

‣ 20% duty cycle 

• Size R~6 m + 

Field B~6 T 

= 5 Billion dollars 

‣ 1000 m 3 plasma 

‣ 1000 m 2 plasma-facing 

wall 

16

Divertor magnetic topology 

is used in ITER (and probably a 

reactor) 

• ITER Magnetic Field- 

Line Geometry in SOL: 

‣ B poloidal / B φ ~ 1/10 

‣ SOL: L // ~ 100 m 

‣ 2 π R ~ 50 m 

~ 1m 

ITER Divertor Cross-section 

17

Constant heat removal at divertor surfaces 

is daunting: #1 priority in edge “design” 

⎛ 

q target 

= q // ⎜ 

⎝ 

B p 

B φ 

⎞ 

⎟ 

⎠ 

divertor 

≅ q // 

0.02≈ 40 MW 

m 2 

Melts 10 cm of tungsten in ~20 seconds ! 

Field lines 

Conforming divertor surface 

2 π R 

≈ 50 MW 

m 2 

Distorted surface “proud” to the 

field line receives q // ~ 1 GW/m 2 

and is immediately 

melted/ablated. 

Field lines 

Distorted divertor surface 

20

q 

plasma 

Heat exhaust, T melt , material stress 

and heat conductivity set armour 

thickness 

d 

Coolant 

substrate 

coolant 

• Limits material choices to 

refractory metals (W, Mo) or 

graphite. 

d tile 

= κ plate 

(T max, surface 

− T coolant 

) 

q target 

Tungsten 

CFC 

carbon 

κ (W/m/K) 150 300 

T melt (K) 3700 3700 

d tile ~ 1 cm ~ 2 cm 

21

W & C bonding technology capable 

of exhausting ~ 25 MW/m 2 

castellations 

ITER 

prototype 

divertor 

module 

~ 1m 

22

Plasma-Facing Components for ITER 

First wall and limiter: beryllium 

•Low Z, getters oxygen 

•Retains T, but releases T at lower 

temperature than carbon 

Separatrix hit point: CFC 

• withstands a wide range of plasma 

parameters 

• T retention problem 

Divertor dome and baffle: W 

The divertor has a modular structure, 

replaceable within 4 months 

The final selection of 1st divertor 

PFC will be made in 2010

Tritium inventory 

• Assumption of in-vessel 

mobilisable tritium = 1kg 

• Extrapolation from exp. 

Is highly uncertain 

• Use of CFC is limited in 

ITER 

• small addition of Be 

reduces T retention


Plasma edge physics

Radial transport: turbulence 

Better heat insulation by sheared flows (H-mode)


Molecular physics 

Franck-Condon atoms: low plasma temperature -> mostly molecules reflected from 

saturated walls


MAR


MAD and MAI

Spatial variation of the electric potential, ion velocity and the 

ion and electron densities across the plasma sheath 

Potential; note the 

presheath potential 

Ion velocity; the ions 

are accelerated into 

the sheath 

Ion and electron 

Density; the electrons 

are depleted due to 

the negative potential

Very strong SEE (ion thruster dielectrics) 

Plasma density: 

electrons 

ions 

Plasma potential 

Irregular surface: 0

Plasma density: 

electrons 

ions 

Plasma potential 

Flat surface: 0

Max-Planck Institut für Plasmaphysik, EURATOM Association, 17491 Greifswald, Germany 

PIC modeling of arcing: DC discharge 

L = 20 μm 

U a = +10 kV 

Species included: e - , Cu + ,Cu 

• electrodes material is Copper. 

• constant electron thermo-emission current I eth = 

2.35*10 6 A/cm 2 from the cathode is assumed. 

• the constant flux of evaporated copper atoms from 

the cathode I Cu = 0.01I eth /e is assumed



Start-up phase of the discharge (the first 0.7 ns )



Simulated time 18 ns



Discharge current to anode 

• Cu atoms evaporated from cathode 

are ionized by the electrons 

accelerated in the gap, creating e - , 

Cu + plasma 

• flux of the plasma particles to the 

electrodes enhances the sputtering, 

increasing the concentration of the 

Cu atoms in the gap 

• plasma space charge start to 

influence the external electric field in 

the gap when the Debye length 

becomes smaller then the electrode 

spacing. 

• electric field is concentrated in 

sheath



Cu + flux energy composition at the cathode 

Cu flux energy composition at the cathode 

Maximum energy corresponds to sheath 

potential drop 

Lower enrery part is populated by 

collisions with neutrals 

High energy neutrals due to charge 

exchange

non-thermal: 

splashing 

thermal: 

no splashing


TRIM, TRIDYN: much faster than MD (simplified physics: 

binary collision approximation) 

- very good match of physical sputtering 

- dynamical changes of surface composition


2D-TRIDYN


2D-TRIDYN

2-point model

low recycling

high recycling


TRIM, TRIDYN: much faster than MD (simplified physics: 

binary collision approximation) 

- very good match of physical sputtering 

- dynamical changes of surface composition

Energy threshold 

• Because an atom leaving the surface has 

to overcome the surface binding energy 

E s there is a threshold energy E T for 

sputtering. This is given by 

• Where 

E T 

= 

E S 

γ sp 

(1 − γ sp 

) 

γ = 4m m /( m + m ) 2 

sp 1 2 1 2

Sputter yields for Be, C and W 

by D and self ions 

Note the 

increasing 

threshold 

energy with 

target mass. 

Using D + ions 

yield is ~ same 

for Be, C and W 

W Eckstein PMI, Garching, Report PP9/8 (1993)

High energy sputtering 

• The maximum in the yield and the 

decrease at high energies is due to the 

collision cascade occurring deeper and 

deeper in the solid. 

• The surface atoms have less chance of 

receiving sufficient energy to be sputtered

Uncertainty in yields 

• There is an variation in yields measured 

experimentally ~ 2. 

• This is not experimental error but genuine 

variations which depend on surface 

conditions which can affect the binding 

energy 

• Examples are variation in the structure, 

surface roughness or impurity levels

Effect of incident angle 

• The sputter yield increases as the angle (θ) 

increase from normal (θ =0) 

• This is due to the increased probability of the 

incident ion being backscattered 

• At energies


Tore Supra deposits 

Toroidal pumped limiter 

Cross-section of Tore-Supra 

Neutraliser 

No signs of wall saturation (50 % hydrogen is retained) 

Where is the hydrogen going ? 

Flux ~10 17 -10 18 H m -2 s -1 

Temperatures up to 1500 K


Structure of Tore Supra deposits 

TS deposits analyzed: Adsorption isotherm measurements 

Electron microscopy 

SEM 

Parallel network of 

slit-shaped pores 

Multi-scale porosity 

• Micropores 

( < 2 nm, ~ 11 %) 

• Mesopores 

( < 50 nm, ~ 5%) 

• Macropores 

( > 50 nm, ~ 10%) 

TEM 

TEM 

Parallel to oval axis 

Perpendicular to oval axis


Diffusion in graphite 

Real structure of the material 

needs to be included 

Internal Structure of Graphite 

Granule sizes ~ microns 

Void sizes ~ 0.1 microns 

Crystallite sizes ~ 50-100 Ångstroms 

Micro-void sizes ~ 5-10 Ångstroms 

Multi-scale problem in space (1cm to 

Ångstroms) and time (pico-seconds to 

seconds)


Multi-scale approach 

´Intelligent´ coupling necessary 

Macroscales 

KMC and Monte Carlo 

Diffusion (MCD) 

Mesoscales 

Kinetic Monte Carlo (KMC) 

Microscales 

Molecular Dynamics (MD)


Molecular dynamics - HCParcas 

- Hydrogen in perfect crystal graphite – 

960 atoms 

- Brenner potential, Nordlund long range 

interaction 

- Berendsen thermostat, 150K to 900K 

for 100ps 

- Periodic boundary conditions 

Developed by Kai Nordlund, Accelarator laboratory, University of Helsinki


MD - results 

150K 

900K


MD – results 

Non-Arrhenius temperature dependence


Kinetic Monte Carlo 

ω 0 = jump attempt frequency (s -1 ) 

E m = migration energy (eV) 

T = trapped species temperature (K) 

Assumptions: 

- Poisson process (assigns real time to the jumps) 

- jumps are not correlated


MD – results (II) 

two diffusion channels 

no diffusion across graphene layers (150K – 900K) 

Lévy flights?


Macroscales 

Trapping - detrapping (2.7 eV) 

Desorption (1.9 eV) 

Surface diffusion (0.9 eV) 

KMC with 

Jump lengths depend on the process 

Monte Carlo Diffusion (MCD) 

used to simulate TGD 

ζ


Multi-scale approach 

´Intelligent´ coupling necessary 

Macroscales 

KMC and Monte Carlo 

Diffusion (MCD) 

Mesoscales 

Kinetic Monte Carlo (KMC) 

Microscales 

Molecular Dynamics (MD)


Effect of voids 

A: 10 % voids B: 20 % voids C: 20 % voids 

Larger voids Longer jumps Higher diffusion 

Large variation in observed diffusion coefficients (4 orders of 

magnitude at 1000 K due to different structures) 

Diffusion coefficients without knowledge of 

structure are meaningless


Results at macroscales 

adsorptiondesorption 

1.9 eV 

variation of 

3D structure 

surface 

diffusion 

0.9 eV 

Different processes dominate at different temperatures 

Diffusion in voids dominates 

Diffusion coefficients without knowledge of structure are meaningless


Chemical erosion of graphite 

Mechanism of molecule formation: 

• CH 3 molecule formation only within the implantation zone 

(local chemistry, sticking) 

• H 2 molecule formation even beyond the implantation zone 

(diffusion through voids)


Flux dependence of chemical erosion 

Experiment: Flux dependence of chemical erosion 

J. Roth et. al., Nucl. Fusion 44 (2004) L21 – L25 

? 

Need for a better understanding of chemical erosion (quantitatively) 

• Quantifying co-deposition 

• Can we still use carbon as PFM ?


Flux dependence of chemical erosion 

• Release probability determined by geometrical constraints 

• Erosion yield from 3D KMC model 

Only few surface layers accessible by incoming hydrogen atom 

Upper limit of the released carbon flux

Oxygen ionization state distribution in 

coronal equilibrium 

Calculated charge states in equilibrium conditions as a function 

of electron temperature (Carolyn and Piotrowitz 1983)


Divertor optimization 

ASDEX Upgrade 

B2-Eirene code package: 

coupled multi-species plasma fluid and 

kinetic neutral MC code (used for many machines, 

including ITER) 

reflection of neutrals towards separatrix


Radiation instability


PIC application 

Parasitic plasma below divertor roof baffle in ASDEX 

Upgrade Div IIb from photoionisation or photoeffect 

Typical parameters: 

4*10 8 < ne < 7*10 11 cm -3 

5 < Te < 15 eV 

Scaling: ne ~ Radiation 2.7 *Particle_flux 0.7


Divertor structures 

Divertor 

Plasma


3D transport 

ergodic 

region 

plasma 

core 

(nonergodic) 

ϕ = 0° 

island 

(nonergodic) 

Divertors


Transport in an ergodic region 

Radial direction 

Wall 

Scrape Off 

Layer 

Ergodic 

region 

r 

Enhancement of 

radial transport 

due to 

contribution from 

parallel transport 

χ 

r 

∝ 

D 

χ 

fl || 

Plasma 

core 

Parallel direction 

Electron 

temperature 

Rechester Rosenbluth, Physical Review Letters, 

1978


Kolmogorov length 

Kolmogorov length L K is a measure of field line ergodicity 

δ 0 

S 

exponential divergence 

δ 1 

L K 

= 

S 

⎛ δ 

log ⎜ 1 

⎝ δ 

0 

⎞ 

⎟ 

⎠ 

Typical value in W7-X : L K = 10 – 30 m


Local magnetic coordinates 

x 3 

forward cut 

x 2 

x 1 

Local system shorter than Kolmogorov 

length to handle ergodicity 

One coordinate aligned with the magnetic 

field to minimize numerical diffusion 

central cut 

backward cut 

g ij 

Area is conserved 

Use a full metric tensor 

⎡g 

⎢ 

= ⎢g 

⎢ 

⎣g 

11 

21 

31 

g 

g 

g 

12 

22 

32 

g 

g 

g 

13 

23 

33 

⎤ 

⎥ ⎥⎥ ⎦


Computational process 

Magnetic field 

Fieldline tracing 

Triangulation 

Mesh 

optimization 

Metric coefficients 

Grid 

Neighborhoods 

g ij 

⎡g 

⎢ 

= ⎢g 

⎢ 

⎣g 

11 

21 

31 

g 

g 

g 

12 

22 

32 

g 

g 

g 

13 

23 

33 

⎤ 

⎥ 

⎥ 

⎥ 

⎦ 

Transport code 

Linearization matrix 

Temperature solution


Effect of higher plasma pressure 

vacuum 

finite-β 

Island structures smeared 

out


Ergodic effects in W7-X 

T (eV) 

Normalized field line length 

Ergodic effects lead to 3D modulation 

of long open field lines 

Cascading of energy from 

ergodic to open field lines


Power loading on divertor 

Heat flux density (MW/m 2 ) 

Vacuum case 

finite-β case 

Fieldline length (m) 

No power-load problem for W7-X

Components of SOL ion flows 

Determine transport of impurities from source to destination 

in a tokamak – material migration – T-retention 

E r xB, ∇pxB 

E θ xB 

Pfirsch- 

Schlüter 

Divertor 

sink 

Poloidal 

Ballooning 

B ϕ 

Bx∇B 

B ϕ 

Bx∇B 

Parallel 

FWD-B ϕ 

REV-B ϕ

Parallel ion SOL flow in JET – comparison with EDGE2D 

[S.K.Erents et al., PPCF 2000 & 2004] 

reciprocating 

probe 

ballooning 

Parallel flow: ballooning + drift 

Bt-independent 

(Average flow) 

Bt-dependent 

Measured flows 

are consistent with 

P-S formula, when 

p i , E r … are taken 

from experiment


Turbulence 

Study and understanding of turbulence under simplified conditions 

as a pre-requisite for understanding turbulence in tokamaks or 

stellarators 

Far scrape off layer (in fusion devices): blobs 

S. I. Krasheninnikov, Phys. Lett. A. (2001) 

Blobs also exist in devices with linear magnetic geometry 

G. Y. Antar et. al., PRL (2001), G. Y. Antar et. al., POP (2003) 

Radial movement of blobs in PISCES experiments was explained by 

the concept of ‘neutral wind’ 

S.I. Krasheninnikov at al., POP (2003) 

Net force: F 

Ni 

= μ n 

Ni 

( NV) ( K − K ) 

fast 

fast 

Net force to wall replaces curvature 

slow


VINETA 

VINETA with its four modules: 

total length is 4.5 m and the diameter 0.4 m). 

n 

≤ 

19 

10 

m 

−3 

p Ar 

≈ 0. 1Pa 

T e 

≈ 3eV 

B ≤ 0. 1T 

T i 

≈ 0. 2eV 

blobs observed in VINETA experiments 

T. Windisch et al. Physica Scripta (2005)

Gyrofluid modeling 

Time scan of squared 

amplitude of density 

Electron density 

Time scan of squared 

amplitude of potential


Results 


Potential 

Simulation: drift-wave instability m=6 

Experiment: drift-wave instability m=1-8 (C. Schröder at al. )


Results 

Turbulence 


Potential 

Simulation: no radial movement of blobs 

Experiment: no radial movement of blobs (T. Windisch at al. 2005)

IFMIF - International Fusion Materials Irradiation Facility 

creep testing

Plasma wall interaction

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