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ELM fluxes to ITER surfaces – issues in extrapolation. GF Counsell, UKAEA. Geometry transport // transport Radiation Asymmetry. Material properties. Erosion Damage. ELM fluxes.

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  • transport

// transport







ELM fluxes

Reality – predictions for ELM fluxes in ITER are not the point. We are actually specifying the degree of ELM mitigation required


Laboratory tests have helped set limits on energy density for ITER targets

Eden < 0.5MJ/m2 consistent with planned operations

  • Limits may be determined by melting or ‘structural damage’
  • Both total energy density and its evolution may be important

A. Zhitlukhin et al

JNM 363 (2007) 301

ELM heat pulse dynamics not well simulated  possible consequences for estimated limits?








in existing devices are small –

< 40% AUG, <20% in MAST

fR: Radiated power fractions

J.C. Fuchs, AUG

‘Steady-state’ radiated power fraction in ITER 70% - 80%

ELM volumetric power densities are much higher -


fLFS: in-out asymmetry

T.Eich, AUG

fLFS (=Ein/Etot) < 2/3 in AUG data but broad scatter

Empirical approach only, no theoretical understanding. Risk of systematic errors?

Difficult to reconcile results with // transport and total energy balance

MAST cDND results:

- consistent with B drift

Could fLFS = 2/3 be too conservative?

T.Eich (A. Kirk)


lH & fELM : heat flux widths

A. Herrmann, AUG

A. Kirk, MAST

AUG: 1 < fELM (= ELM/i-ELM) < 3

MAST: fELM ~ 1


Div I

Div II

D. Whyte

A. Kallenbach

lH & fELM : heat flux widths

Inter-ELM SOL heat-flux width – biggest uncertainty

Multi-variate scalings traditionally have little success

Divertor can affect scalings - even on a single device

Herrmann, AUG

  • Perhaps some success with Te
  • But:
  • Scatter still large
  • Extrapolation to target uncertain
  • Doesn’t encompass ions

Alternative/complementary picture of  transport (i,e)

Filamentary structures are ubiquitous in MAST edge

In ALL regimes


Filaments dominate the particle flux to mid-plane reciprocating probe across SOL

R. Scannell, MAST


No first wall interactions in MAST

Filament energy deposited at target


ELM filaments have 2 phases:

  • ‘Connected’ to separatrix for
  • t ~ tMHD
  • Separated and moving radially

measured in MAST & AUG

Simple model –

determined by // losses from connected filament

A. Kirk, AUG

Good fit to near-SOL l

A. Kirk, MAST


ELM fluxes to the wall

Heat flux in far SOL determined by radial motion of filament and // losses

Starting point follows connected phase – ~25% DWELM remaining

A. Herrmann, AUG

Typical mode number –

8 < n < 12  ~2.5% DWELM per filament


A. Kirk, MAST

increases with Tped (hence Tfil)

But at high Tped, nfil should decrease more quickly  shorter l

Unless filament is accelerating ….

Analysis of individual ELM filament motion clearly suggests acceleration -


A. Kirk, MAST

Acceleration increases with DW/Wped

Best fitted by –

ar (DW/Wped)0.25(dashed red)

MAST data doesn’t support model with constant vr/cs, increasing with DW/Wped


// currents limited by jsat at divertor plates

Unable to ‘short-circuit’ B driven current in filaments

Only  component of jpol of ambient plasma contributes to short-circuiting

Magnetic shear amplifies this, near X-point strong E formed

Result – ar= 2(Ti,f+ Te,f)/miR

Predicts for MAST ar~2.5x108m/s2 (1.8x108m/s2 measured)

ITER (filament from 1MJ ELM) predicts


Rozhansky, PPCF 08


A. Kirk, MAST

Model clearly not exact -

ar= ainitial + 2(Ti,f+ Te,f)/miR

ainitial~ 1.3x108 m/s2

- Could be associated with initial ‘explosive’ non-linear growth phase of filament?


Simple Monte-Carlo model of filament to predict ITER fall of lengths in nf and Ti,f

Models evolution of particle distribution function with // losses and evolving ar



Extrapolating to ITER power/energy loads

Must ‘launch’ filaments with energy after ‘connected’ phase losses

Upper target heat flux profile/evolution needs careful modelling of magnetic geometry, v, ar and // losses

Radial motion stops after contact with significant limiting surface

Very high q// on edges during t ~ d///cs ~ 200 ms



  • Max DWELM estimates are pretty robust
  • Issues – ELM heat pulse dynamics in lab simulations
  • Basis for heat flux width
  • In-out ELM energy distribution
  • Alternative assumptions give range 1MJ – 2.5MJ. Still very small
  • ELM wall deposition less robust
  • Issues – Initial ELM conditions at separation
    • Mode number & dimensions
  • Model for radial expulsion – hence vr, ar
  • Need for accurate modelling of upper target loads (helical stripes) and limiter interactions
  • Very probably Eden not an issue, even for 2.5MJ ELMs. Impurity influx could be an issue? (ions still hot)