How do we deal with the power/energy fluxes we have derived for ELMs, disruptions or others

C. Kessel, PPPL

ARIES Project Meeting, Jan 23-24, 2012, UCSD

The ELMs are transient loads, while the disruptions are off-normal events

If we have ELMs, they are expected, and the heat flux on the divertor is composed of a steady state and a transient term

qSS, qELM

qSS sets our average PFC temperature at the surface and in the bulkqELM provides a periodic rise and fall only near the PFC surface with short timescale

TPFC (x=0) = TSS,PFC(x=0) + ΔTELM,PFC(x=0)

ΔTELM,PFC (depending on pulse model) = 2 qELM (αt/π)1/2/k* = Cmaterial ΔWELM

ΔT/(AELM ΔtELM1/2)

ΔWELMΔT is filtered value from Wped

*solution to semi-infinite region heat conduction at x=0

The ELMs are transient….cont’d

TSS + ΔTELM must be less than Tmelt or any other limit (allowing melting and erosion or Tlimit < Tmelt)?

ΔWELMΔT < (Tmelt –TSS) (AELM ΔtELM

1/2) / Cmaterial

Then we have the relationship

fELM x ΔWELM ~ 0.2-0.4 x PSOL (Pα + Paux – Prad)

Given ΔWELM, we derive fELM and can assess the cycling issues using ΔWELMΔT

such as micro-cracking or thermal fatigue…..

Using ΔWELM (from 7/27/11 presentation) = 7-27 MJ, giving fELM = 3.5-13.5 /s which is 1.1-4.3 x 108 cycles in a year

Is there any ΔWELMΔT that can be tolerated for ~ 108 cycles or more

Apart from desiring no ELMs, what is the operating space assuming we do have a bursty transient heat flux like ELMs

There is both analysis and experiments done with facilities at Karlsruhe, Julich, ???, trying to close the loop on these loading conditions

What is observed (these facilities used plasma guns or, other and generally are not directly applicable to

the ITER conditions*)Simulation codes are used to reproduce the experiments and then applied to ITER specific conditions

Pre-heat to 500oC, macro-brush W 1x1 cm2, 0.5 mm gaps100 pulses with 0.5-2.0 MJ/m2, or 5 pulses with >2.5 MJ/m2, pulses are 0.5 msPlasma is 8cm half width, usually inclined 30o with respect to material surface

1) Negligible erosion for < 0.4 MJ/m2

2) Melting of brush edges 0.4 < Q < 0.9 MJ/m2

3) Melting of edges and surface 0.9 < Q < 1.3 MJ/m2 (bridges form between brush after 50 pulses)4) Droplet ejection observed for > 1.3 MJ/m2

5) Average erosion < 0.04 μm/pulse for < 1.5 MJ/m2

6) For Q < 1.6 MJ/m2 mass loss is due to evaporation, mass loss from droplet formation is small

* These facilities create a much larger plasma pressure than ITER, the codes are needed to remove this effect

For sintered tungsten

More…..Crack formation on tungsten surfaces has been observed for > 0.6 MJ/m2

For 0.6 < Q < 1.0 MJ/m2 2 types of cracks are observed, one type 500 μm and the other 50 μm

For Q > 1.0 MJ/m2 cracks form a grid with cell sizes ~ 50 μm, and these are remelted each pulse

Preheating to above the DBTT (650oC) only removes the 500 μm cracks, not the other type

It will take some interpretation to understand these results…..but assuming we take 0.5 MJ/m2 as the maximum energy flux (interpreted to mean ΔWELM

ΔT) to avoid erosion (and cracking?), which corresponds to our lowest possible Type I ELM energy

This is 24 MJ/m2-s1/2, ΔT ~ 1430oC……expts were at ~ 500oC

What is our operating space? Or what is ARIES going to add to this story?

ΔWELM, AELM, fELM

MJ/m2, Δtpulse, ΔT

# pulses to replacement

Base temperature (under steady heat load)

qSS is momentarily replaced by qELM

(Tlimit – TSS), what is Tlimit

(Tmelt – TDBTT) after neutron exposure

What is different between ITER and ARIES (reactor)?

Plasma pulse length

PFC lifetime requirements

Smaller geometrically

Lower Ip

Collisionality of pedestal

Plasma shaping

Very close FW PFCs