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 q SS, q ELM q SS sets our average PFC temperature at the surface and in the bulk q ELM provides a periodic rise and fall only near the PFC surface with short timescale T PFC (x=0) = T SS,PFC (x=0) + ΔT ELM,PFC (x=0) ΔT ELM,PFC (depending on pulse model) = 2 q ELM (αt/π) 1/2 /k* = C material ΔW ELM ΔT /(A ELM Δt ELM 1/2 ) ΔW ELM ΔT is filtered value from W ped *solution to semi-infinite region heat conduction at x=0

The ELMs are transient….cont’d T SS + ΔT ELM must be less than T melt or any other limit (allowing melting and erosion or T limit < T melt )? ΔW ELM ΔT < (T melt –T SS ) (A ELM Δt ELM 1/2 ) / C material Then we have the relationship f ELM x ΔW ELM ~ x P SOL (P α + P aux – P rad ) Given ΔW ELM, we derive f ELM and can assess the cycling issues using ΔW ELM ΔT such as micro-cracking or thermal fatigue….. Using ΔW ELM (from 7/27/11 presentation) = 7-27 MJ, giving f ELM = /s which is x 10 8 cycles in a year Is there any ΔW ELM ΔT that can be tolerated for ~ 10 8 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 500 o C, macro-brush W 1x1 cm 2, 0.5 mm gaps 100 pulses with MJ/m 2, or 5 pulses with >2.5 MJ/m 2, pulses are 0.5 ms Plasma is 8cm half width, usually inclined 30 o with respect to material surface 1) Negligible erosion for < 0.4 MJ/m 2 2) Melting of brush edges 0.4 < Q < 0.9 MJ/m 2 3) Melting of edges and surface 0.9 < Q < 1.3 MJ/m 2 (bridges form between brush after 50 pulses) 4) Droplet ejection observed for > 1.3 MJ/m 2 5) Average erosion < 0.04 μm/pulse for < 1.5 MJ/m 2 6) For Q < 1.6 MJ/m 2 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/m 2 For 0.6 < Q < 1.0 MJ/m 2 2 types of cracks are observed, one type 500 μm and the other 50 μm For Q > 1.0 MJ/m 2 cracks form a grid with cell sizes ~ 50 μm, and these are remelted each pulse Preheating to above the DBTT (650 o C) 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/m 2 as the maximum energy flux (interpreted to mean ΔW ELM ΔT ) to avoid erosion (and cracking?), which corresponds to our lowest possible Type I ELM energy This is 24 MJ/m 2 -s 1/2, ΔT ~ 1430 o C……expts were at ~ 500 o C

What is our operating space? Or what is ARIES going to add to this story? ΔW ELM, A ELM, f ELM MJ/m 2, Δt pulse, ΔT # pulses to replacement Base temperature (under steady heat load) q SS is momentarily replaced by q ELM (T limit – T SS ), what is T limit (T melt – T DBTT ) 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