Transcript Laser-produced plasma for EUV lithography

page 1 of 9
ELM loading conditions and
component responses
C. Kessel and M. S. Tillack
ARIES Project Meeting
4-5 April 2011
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The basics of the ELM process for our analysis

An ELM is a burst of energy from the plasma, ~ 90% goes to the
divertor and ~10% goes to the first wall

The energy that goes to the divertor is toroidally symmetric in the
higher heat flux region of the divertor plate

Time scale of energy burst arriving at divertor plate and first wall is τ
~ 2πRq95/cs,ped

A triangular waveform is a reasonable representation for ELM power
versus time, say with 0.5 ms rise, and 1.5 ms drop

Assuming all power from the ELM burst goes to the outboard side –
for double null is this true, DIII-D results?

The area on the divertor plate for estimating the peak heat flux is the
same for the ELM as it is for the steady heat flux

On the first wall there is a peaking of 2-4 based on the fact that the
energy burst is like helical filaments launched off the plasma surface
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ELM heat flux specification
ΔWELM x fELM ~ constant = 0.2-0.4 x (Palpha+Paux-Pbrem-Pcycl-Pline)
Using point from Lane’s latest systems run….
Pbrem = 51 MW
Pcycl = 10 MW
Pline = 31 MW
Palpha = 354 MW
Paux = 45 MW

PSOL = 306 MW (comparison ITER’s value is about 100 MW)
ΔWELM x fELM = 61-122 MJ/s
If fELM = 1 Hz, ΔWELM = 61-122 MJ (ITER’s value is 20 MJ)
τELM,rise ~ 2 x 2πRq95/cs,ped ~ 0.6 ms
τELM,drop ~ 4-6 x 2πRq95/cs,ped ~ 1.5 ms
Using 61 MJ,
24.5 MJ arrives in 0.6 ms, and 30.5 MJ arrives in 1.5 ms
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ELM heat flux specification in divertor
Assume 100% of 90% of ELM energy goes to outboard
Each divertor must handle ~ 65%, since we don’t know the up-down balance
Case 1: No radiation
pow ~ 0.005 m
Adiv,ELM = 2π(R-a/2) x λpow x fexp = 1.44 m2
1) power scrape-off width is uncertain
2) expansion factor is a combination of divertor plate
angle and poloidal flux expansion, fexpflux/sin(αdiv)
For a single outboard divertor, ~ 40 MJ gives ~ 28 MJ/m2
(For comparison, ITER assumes 17 MJ/m2 inboard and 8.5 MJ/m2 outboard)
Power over the ELM pulse (2.1 ms) is 19 GW, or 13.2 GW/m2
Heat flux factor (P x sqrt(Δt)) is 604 MW/m2s1/2
Case 2: ELM power distribution same as steady-state
Power peaking factor = 19 GW (peak) / 153 MW (normal) ~125
Nominal peak divertor heat flux is 8-10 MW/m2
Peak heat flux during ELM = 1250 MW/m2
Heat flux factor is 57 MW/m2s1/2
There is a huge difference! We need to know how ELM power deposits.
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The ELM energy burst and radiated power
vs. conducted power in the divertor
“The split of power in the divertor between radiated and conducted during an
ELM is not an easy issue”…A. Loarte (IO)
For large ELMs it appears that most of the power reaches the divertor.
A radiation spike is expected, but this actually follows the ELM pulse.
For small ELMs, ITER is assuming that all the power gets to the divertor plate
to be conservative….but experiments show that small ELMs do not disturb the
detachment of the divertor, and so radiation could in fact relieve some of the
power from reaching the plate (simulations indicate ~50% of ELM power could
be radiated).
The attachment or detachment of the divertor is related to our high radiating
regime in the divertor, although the connection is not simple…..so losing
detachment during an ELM (which is the ITER assumption) implies that
radiation is compromised.
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ELM heat flux limits from ITER
ITER says that they must have an ELM frequency of 33-67 Hz and a
corresponding ΔWELM of 0.6 MJ for their divertors to survive
A factor of 30-60 reduction in ΔWELM might make us OK too?
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Peak divertor temperature from ELM’s
x 2  q" x
 x 
2q" (t /  )1/ 2
T  To 
exp
erfc


k
4

t
k

2 t 


at x=0,

2q" (t /  )1/ 2
T  To 
k
q”
•
13.2
 GW/m2 over 2.1 ms
t
o ΔT = 37,800 K
o d = 536 mm
•
1250
MW/m2
Penetration depth:
over 2.1 ms
d  (4t)1/ 2
o ΔT = 3580 K
o d = 536 mm

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Transient ELM heat loads to the FW
o ΔWELM to FW = 5% for small ELMs and 10~20% for largest ELMs
o
Same rise time as divertor, 50% shorter decay: 1.35 ms total
o All of the energy lands outboard
o Peaking of 2-4x associated with filaments expanding off the plasma.
o Filaments do not land in the same place all of the time: random location.
o 268 m2 OB FW area, 3x peaking, 10% of ELM power to FW
o Pmax~ 51 MW/m2
o Heat flux factor is Pmax~ 2 (MW/m2)-s1/2
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Peak first wall temperature from ELM’s
at x=0,
•
2q" (t /  )1/ 2
T  To 
k
Steel 
first wall, 51 MW/m2 over 1.35 ms
o ΔT = 159 K
o d = 182 mm
•
W-pin first wall, 51
MW/m2
q”
over 1.35 ms
t
o ΔT = 116 K
o d = 429 mm
Penetration depth:
d  (4t)1/ 2

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High cycle fatigue is an additional concern
• Much work was performed in HAPL (e.g. by UW, UCSD) to
characterize fatigue cracking in armor for DT~500–1000 K.
• This is a current topic of R&D in the MFE materials program
(e.g., PISCES, UCLA modeling e.g. Crosby & Ghoniem, “Thermomechanical damage of tungsten surfaces exposed to rapid
transient plasma heat loads,” Fusion Reactor Materials Program
Semi-Annual Progress Report, DOE/ER-0313/49, Dec 31, 2010.)
• Fatigue to a steel first wall is less studied.
J. Nucl. Mater. 386 (2009) 127.
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Summary and future directions
• Unmitigated ELM’s (w/o radiation) will vaporize the divertor.
A factor of 30-60 reduction is needed.
• Unmitigated ELM’s (w/ radiation) will melt the divertor.
A factor of 3-6 reduction is needed.
• Should ARIES invest in detailed edge simulations? If LLNL
can do a transient calculation this would be good: we could see
if the power pulse changes the detachment and radiative
regime.
• Crack growth will be an issue. Some R&D is underway in the
material program. Should we do more in ARIES?
• The new first wall concept is more tolerant toward ELM’s, but
pure steel may be OK (especially if ELM freq is increased).
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Summary and Future, cont’d

The expansion factor that we use in the systems code is input as 10….
how should we refine this number, poloidal flux expansion from
equilibrium, while divertor tilt angle relative to the flux line is limited
by precision…. how much can this affect the ELM power picture?

The assessment of ELMs on the divertor, including radiation (at
varying fractions) or not, is an interesting trade-off, in spite of
experimental results. Should we generate a parametric examination
of this, and then isolate regions where there may be credible
solutions? How can LLNL analysis help us here?
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ΔWELM
fELM
frad,div (radiation assumption, examined by LLNL analysis)
TW < 0.85 TW,melt what can this be, can we have melting (NO, says Mark)
Tungsten properties, material modification
Other parameters that characterize the operating space for viable
solutions