1. More on Pedestal and ELMs
C. Kessel
Princeton Plasma Physics Laboratory
ARIES Project meeting, Gaithersburg, MD, July 27-28, 2011

2. Pedestal parameters and another way to estimate the energy released in ELMs
One approach to estimating the energy released in an ELM is from a database from several existing tokamaks, showing ΔWELM/Wpedestal versus the collisionality in the pedestal
Estimate the pedestal collisionality to be 0.088
T = 5.2 keV
n = 1.25x1020 /m3
q = 4.5
R = 5.5, a = 1.38, κ = 2.2
This indicates something around times the pedestal energy

3. Pedestal pressure and energy
There exists a pedestal database and scaling law developed for ITER
The formula gives for our parameters
M=2.5
nped ~ 1.25 x 1020 /m3
R = 5.5
a = 1.38
Ip = 11 MA
κ = 2.2
δ = 0.75
A = 4
Ptot = 430 MW
PLH = 160 MW
I get ~ 150 kPa, or 210 kPa for ARIES-AT which is similar to EPED1 estimates for ARIES-AT

4. Pedestal and ELM, cont’d
Keep in mind that the pressure is the sum of electrons and ions
pped = k(neTe + niTi), but the ions are often not measured accurately at the plasma edge, so this approximated as ~2kneTe
The energy in the pedestal can be estimated from Wped = (3/2)ppedVplasma
Vplasma is the total plasma volume, not the volume associated with the pedestal region or affected by the pedestal crash
Vplasma = 454 m3 for the whole plasma
Then the pedestal energy is Wped ~ 136 MJ, this infers a ΔWELM ~ MJ
This can be contrasted with ΔWELM ~ MJ based on a fraction of the input power, when we assume fELM is similar to ITER (1 Hz)

5. Using the ion parallel flow time as scaling for ELM energy
The experimental data of energy released in an ELM, normalized to the pedestal energy, has also been correlated to the ion parallel flow time τ||front = 2πRq95/cs,ped
cs,ped = [ k (Te,ped+Ti,ped)/mDT]1/2
We get τ||front ~ 220 μs which infers that ΔWELM/Wped ~
This gives ΔWELM of 7-16 MJ

6. ELM energy loss and its breakup into density and temperature parts
ΔWELM = Wplasmabefore ELM – Wplasmaafter ELM
= 3 (<nped>ΔTe,ped, ELM + <Tped>Δne,ped, ELM) VELM
ΔTe,ped, ELM is the conductive ELM loss, decreases with increasing density or collisionality from ~ 20% to near zero
Δne,ped, ELM is the convective ELM loss, typically stays constant at ~ 7% of ne,ped as the density is increased
VELM is the ELM affected volume, usually from r ~ 0.8a to a, even though the pedestal only occupies the region of r ~ 0.95a to a
Consequently, the ΔWELM decreases with increasing density or collisionality, and so the normalized parameter ΔWELM/Wped varies from ~ 15-20% at low density to 5-7% at high density

7. Power reaching the divertor, in the early phase and overall
The fraction of the energy released by an ELM that arrives in the divertor over the 2 x τ||front rise phase is about about 40% for our collisionalities
More power arrives after this in the 2nd phase, 4 x τ||front, delivering a total of % of the energy released by the ELM
The remaining energy is expected to be deposited on the FW

8. 2 limiting cases of ELM energy, convective and conductive
ΔWELM = 20% Wped
ΔWELMdiv = 50% ΔWELM
ΔWELMdiv(t < 2 x τ||front) = 40% ΔWELMdiv
ΔWELMFW = 50% ΔWELM
Convective
ΔWELM = 7% Wped
ΔWELMdiv = 80% ΔWELM
ΔWELMdiv(t < 2 x τ||front) = 20% ΔWELMdiv
ΔWELMFW = 20% ΔWELM
It is not presently possible to determine for sure which type we would have, but the convective ELMs are usually associated with higher densities and collisionalities, while the conductive are associated with the opposite regime
On present tokamaks, the convective ELMs are obtained for 1) high density/collisionality (υ* ~ 1), 2) high triangularity and q95 > 4, with low υ*

9. Analysis of ELM impact on divertor
ΔWELM x fELM ~ constant = x (Palpha+Paux-Pbrem-Pcycl-Pline) is used to get fELM, we use another approach to get ΔWELM
From ΔWELM/Wped vs υ* we get ΔWELM ~ MJ
From ΔWELM/Wped vs τ||front we get ΔWELM ~ MJ
With DN, we have 65% to either divertor, ΔWELM ~ MJ
ΔWELMdiv ~ 3.7 – 8.8 MJ
ΔWELMdiv, τrise ~ 0.75 – 3.5 MJ
Adiv,ELM = 1.44 m2
(2α/πk) ΔWELMdiv, τrise
ΔTrise = = –7242 oK for W
Adiv,ELM (2 τ||front)1/2

10. Analysis of ELM impact on FW
From ΔWELM/Wped vs υ* we get ΔWELM ~ MJ
From ΔWELM/Wped vs τ||front we get ΔWELM ~ MJ
ΔWELMFW ~ 1.4 – 13.5 MJ all energy goes to outboard
AFW is 268 m2, take 4x peaking
(2α/πk) ΔWELMFW
ΔTrise = = 62 – 600oK for W, 84 – 815oK for Fe
AFW,ELM (2 τ||front)1/2

11. Particle loss during an ELM
Not much data on this, but what there is shows little variation as a function of collisionality or density
Nped = ne,pedVplasma
Data also shows that the density change in the plasma during an ELM is pretty constant over a wide range supports the idea that this does not vary

12. Other ELM things
In terms of radiation helping us with the ELM power deposition to the divertor, it appears that it does not help for large ELMs, but does for small ELM……recent expts show lots of radiated power, but this seems to follow the ELM as inferred by Loarte
New expts have show that the footprint on the divertor actually does get bigger during an ELM, ~ 1.4x for small ELMs and 4x for large ELMs………this could be a win for us since it would make the Adiv,ELM larger, and make our worst ELM case have a ΔTrise ~ 1800oK
SS power width
ELM power width