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Max-Planck-Institut für Plasmaphysik. Prediction of wall fluxes and implications for ITER limiters. Arne Kallenbach, ASDEX Upgrade Team. Topics of this talk: guidelines on load specifications.  steady state particle main chamber fluxes from spectroscopy

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Max-Planck-Institut für Plasmaphysik

Prediction of wall fluxes and implications for ITER limiters

Arne Kallenbach, ASDEX Upgrade Team


Topics of this talk: guidelines on load specifications

  •  steady state particle main chamber fluxes from spectroscopy
  • estimates of connected power fluxes and decay lengths
  • contribution due to ELMs (enhancement factor)

Current ITER Guidelines (PID V3.0):

Only radiation and CX load to first wall, 0.5 MW/m2

transport and drifts lead to

parallel heat fluxes in far SOL

diffusive transport between ELMs

blobby transport between ELMs

(radial outward convection)

ELM SOL transport (like large blobs)

- parallel drift towards high-field side

- strong recycling around inner X-point

additional players in particle transport:


Innner and outer wall plasma-surface interaction in AUG

from CII spectroscopy: very sensitive on in-out alignment

R lim

8 m2

0.3 m2

  • inner heat shield major recycling region except plasma close to outer limiter
  • lower inner wall flux dominated from inner divertor
  • upper inner wall flux has radial e-folding length ~ 2-3 cm

How to estimate the stationary power flows on the limiters

  • estimate the total radial ion outflux*
  • estimate the deposited energy per electron-ion pair
  • estimate the effective wetted area
  • or peak load and decay length

average value from different models,

be conservative and use upper end

 limiter power flux density

*IO calculates in terms of parallel power fluxes and decay lengths


1) Total radial ion wall flux in ITER

[i] scaling like diffusive transport

Radial SOL particle flux in ITER

ansatz with effective D:


 = D dn/dr



D = 3 m2/s this value typical for

SOL wing in many devices

dn/dr = 21019 m-3 / 0.05 m


can be larger

 = 1.21021 m-2 s-1

AUG edge density profiles from Li-beam

Transport balloons around outer midplane:

total main chamber ion influx: multiply  with 1/3 of plasma surface area

F ITER = 680 m21/3  ~ 31023 s-1


Total radial ion wall flux in ITER

[ii] some alternative ways of estimation

  • Same flux density as in AUG discharge with high similar fGreen, P/R,
  • and absolute density, scaled with area

ITER: 100 MW/6 m, not possible in AUG, scale P0.24[NF 42 (2002) 1184]

AUG 21015/17, 7.5 MW, ne=1020 m-3, =21022 1/s, drXP=3 cm

4.41023 s-1

b) Same flux density as in AUG discharge with high similar fGreen, P/R2

and absolute density, scaled with area  16

ITER: 100 MW/36 m2, 7.5 MW in AUG, AUG # as above

3.21023 s-1

c) Same flux density as in JET discharge with high similar fGreen, P/R2

and absolute density, scaled with area (best use 4 MA, 25 MW discharge)

JET 70054, 3.5 MA, 24 MW, 1e20, midplane H2072 m2  main=7.21022 s-1

2.91023 s-1

Over all, 3(1-5)1023 s-1

seems reasonable estimate


Energy per electron ion pair

Te in the SOL wing of a high density H-mode discharge is typically 5-10 eV,

Ti tends to be moderately higher

We assume for ITER Te= 10 eV, Ti= 20 eV

standard model for sheath power deposition (negl. secondary el. emission)

P= ei (2Ti + 3Te + Erec) + ee 2Te  100 e

per 11023 part/s

100 eV per e-i pair  1.6 MW


3) effective wetted area and resulting loads

The wetted area depends on actual wall design !

wetted width depends on decay length in limiter shadow

ITER quick guess: 18 protruding ribs, height 5 m, 0.05 m wetted width  4.5 m2 for HFS and LFS each (good alignment required !)

3 1023 ions/s  4.8 MW

  • charge exchange is expected to increase this number by 10-20 %

 ELMs contribute to recycling fux by factor 1.5

  • radiation is expected to contribute < 0.2 MW/m2
  • some contrib. by fast ion losses on LFS

overall, expected peak loads about 1 MW/m2

not problematic, but safely  1 MW/m2 would allow to avoid active cooling

Of course, the upper X-point region takes more power and must be strengthened


ELM contributions to average particle influxes:

small for D, C, dominnat for W

Outer limiter

ELM-cycle averaged,

D and C fluxes increased

by ~ 1.5

but: 70 % of the W influx

due to ELMs

(increased yield)

R. Dux


Decay length depends on connection length to limiters

Increasing the number of limiters can reduce the power load.

However: the decay length shortens with reduced connection length

and more precise alignment will be required

measurements in

AUG limiter shadow

by H.W. Müller


ITER expects negligible loads on inner wall

- does the existence of a 2nd sep. shield the inner wall ?

No !

further investigations needed on inner wall load close DN

dRXP= 3 mm


Comparison to previous estimate based on JET-AUG

Recycling scaling (Tarragona meeting, July 2005)

new insight: predominantly HFS recycling  multiply with S/4 only: Rtot= 1024 s-1

(ne,sol= 4.7 1019)

Strong dependence of total recycling on ne,line-av (power 4) 

If pellets are needed to reach 1020 m-3 in ITER, this number comes down:

If ITER produces ne= 7.5 1019 by recycling only, Rtot= 3 1023, ne,sol= 2.6 1019



  •  Main chamber recycling occurs predominantly on the high field side
  • and on wall structures touching the innermost flux surfaces
  •  Effect supposed to be connected to strong drifts towards HFS
  • Strong plasma wall interaction with the inner wall close to DN

operation is not understood:

fluxes close to the separatrix or ExB drifts around upper X-point ?

 Expected total particle fluxes 3 2 1023 part/s, power fluxes ~ 5 MW

  • How will the ITER FW will look like ?


Simple size scaling and effect to wall materials

  • Size scaling based on empirical findings:
  • natural type-I ELM size ~ 10 % of pedestal energy, 3.5 % of plasma energy
  • ELMs carry 30 % of the power flux
  • simple algebra: PELM= 0.3 Ploss = 0.3 Wtot/tE = 0.035 fELM Wtot = fELMWELM
  • fELM = 8.6/tE
  • ITER Sc. 1: Wtot = 353 MJ, tE=3.4 sAUG typ.: 0.8 MJ, 0.1 s
  •  fELM = 2.5 Hz, WELM= 12 MJ80 Hz, 28 kJ
  • controlled ELMs: if fELM is changed, WELM scales ~ 1/fELM


uncontrolled ELMs fELM = 1 Hz, WELM= 15-20 MJ

controlled ELMs fELM = 5 Hz, WELM= 3-4 MJ




Simple size scaling and effect to wall materials

Material properties:

1556 K 3683 K 3640 K (subl.)

melting/ablation limits: Be 20, W 60, CFC 60-70 [MJ m-2s-0.5]

example: ELM 1 MJ/m2, 0.5 ms duration  45 MJ m-2s-0.5

recent lab exps. (Russian-EU collab.) suggest limit below

0.7 MJ/m2 both for W and CFC (fatigue, crack formation)

 reduce peak load by factor 0.5

Divertor peak power load:

ITER PID assumed effective wetted divertor area of 7.5 m2 (w= 0.1 m along targets)

resulting maximum loads were 2.7 MJ/m2 (uncontr.), 0.5 MJ/m2 (contr.)

the maximum allowed ELM was controlled to 4 MJ

latest changes: no ELM power broadening lp  5 mm (fact 2/3)

in-out asymmetry 2:1 – (fact ¾), recover factor 2 safety margin 0.5  0.25 MJ/m2 ?

 maximum “ELM” ~ 1 MJ

too pessimistic – ignores large lp inner div


Open points = possible AUG contributions

1) midplane inter-ELM power width

midplane Te decay length scales ~ machine size

A. Kallenbach et al.,

ITPA SOL&Div Topical Group,

PSI 2004

expected power width 2/7  Te

AUG: 1.3 mm omp

considerably broader widths observed in divertor (mapped to omp)

good topic for future AUG / inter-machine exps (L. Horton)