1. page 1 of 9 ELM loading conditions and component responses C. Kessel and M. S. Tillack ARIES Project Meeting 4-5 April 2011

2. page 2 of 9 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 ~ 2πRq 95 /c s,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

3. page 3 of 9 ELM heat flux specification ΔW ELM x f ELM ~ constant = 0.2-0.4 x (P alpha +P aux -P brem -P cycl -P line ) Using point from Lane’s latest systems run…. P brem = 51 MW P cycl = 10 MW P line = 31 MW P alpha = 354 MW P aux = 45 MW  P SOL = 306 MW (comparison ITER’s value is about 100 MW) ΔW ELM x f ELM = 61-122 MJ/s If f ELM = 1 Hz, ΔW ELM = 61-122 MJ (ITER’s value is 20 MJ) τ ELM,rise ~ 2 x 2πRq 95 /c s,ped ~ 0.6 ms τ ELM,drop ~ 4-6 x 2πRq 95 /c s,ped ~ 1.5 ms Using 61 MJ, 24.5 MJ arrives in 0.6 ms, and 30.5 MJ arrives in 1.5 ms

4. page 4 of 9 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 A div,ELM = 2π(R-a/2) x λ pow x f exp = 1.44 m 2 For a single outboard divertor, ~ 40 MJ gives ~ 28 MJ/m 2 (For comparison, ITER assumes 17 MJ/m 2 inboard and 8.5 MJ/m 2 outboard) Power over the ELM pulse (2.1 ms) is 19 GW, or 13.2 GW/m 2 Heat flux factor (P x sqrt(Δt)) is 604 MW/m 2  s 1/2 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/m 2 Peak heat flux during ELM = 1250 MW/m 2 Heat flux factor is 57 MW/m 2  s 1/2 There is a huge difference! We need to know how ELM power deposits. 1)power scrape-off width is uncertain 2)expansion factor is a combination of divertor plate angle and poloidal flux expansion, f exp flux /sin(α div )

5. page 5 of 9 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.

6. page 6 of 9 ELM heat flux limits from ITER ITER says that they must have an ELM frequency of 33-67 Hz and a corresponding ΔW ELM of 0.6 MJ for their divertors to survive A factor of 30-60 reduction in ΔW ELM might make us OK too?

7. page 7 of 9 Peak divertor temperature from ELM’s 13.2 GW/m 2 over 2.1 ms o ΔT = 37,800 K o  = 536  m 1250 MW/m 2 over 2.1 ms o ΔT = 3580 K o  = 536  m q” t at x=0, Penetration depth:

8. page 8 of 9 Transient ELM heat loads to the FW o ΔW ELM 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 m 2 OB FW area, 3x peaking, 10% of ELM power to FW o P max ~ 51 MW/m 2 o Heat flux factor is P max ~ 2 (MW/m 2 )-s 1/2

9. page 9 of 9 Peak first wall temperature from ELM’s Steel first wall, 51 MW/m 2 over 1.35 ms o ΔT = 159 K o  = 182  m W-pin first wall, 51 MW/m 2 over 1.35 ms o ΔT = 116 K o  = 429  m q” t at x=0, Penetration depth:

10. page 10 of 9 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  T~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, “Thermo- mechanical 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.

11. page 11 of 9 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).

12. page 12 of 9 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?  ΔW ELM  f ELM  f rad,div (radiation assumption, examined by LLNL analysis)  T W < 0.85 T W,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