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 bulk
qELM 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 ΔWELMΔT/(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 ΔtELM1/2) / 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 gaps
100 pulses with 0.5-2.0 MJ/m2, or 5 pulses with >2.5 MJ/m2, pulses are 0.5
ms
Plasma is 8cm half width, usually inclined 30o with respect to material
surface
For sintered tungsten
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
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
ΔWELMΔT) 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
What is different between
ITER and ARIES (reactor)?
MJ/m2, Δtpulse, ΔT
Plasma pulse length
# pulses to replacement
PFC lifetime requirements
Base temperature (under steady heat load)
Smaller geometrically
qSS is momentarily replaced by qELM
Lower Ip
(Tlimit – TSS), what is Tlimit
Collisionality of pedestal
(Tmelt – TDBTT) after neutron exposure
Plasma shaping
Very close FW PFCs