More on Pedestal and ELMs
C. Kessel
Princeton Plasma Physics Laboratory
ARIES Project meeting, Gaithersburg, MD, July 2728, 2011
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 0.15-0.2 times
the pedestal energy
Pedestal pressure and energy
There exists a pedestal database and scaling law developed for ITER
 M 
 2410

n

 ped ,20 
0.33
p ped
0.06
I p2
R1.33
3.2 3.62 2.94  Ptot 
1   A  
a 4 1  2 2.33
PL H 


 2 
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
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 ~ 20-27 MJ
This can be contrasted with ΔWELM ~ 61-122 MJ based on a fraction of the input
power, when we assume fELM is similar to ITER (1 Hz)
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 ~ 0.05-0.12
This gives ΔWELM of 7-16 MJ
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
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 60100% of the energy released by the ELM
The remaining energy is expected to be deposited on the FW
2 limiting cases of ELM energy, convective and
conductive
Conductive
Convective
ΔWELM = 20% Wped
ΔWELM = 7% Wped
ΔWELMdiv = 50% ΔWELM
ΔWELMdiv = 80% ΔWELM
ΔWELMdiv(t < 2 x τ||front) = 40% ΔWELMdiv
ΔWELMdiv(t < 2 x τ||front) = 20% ΔWELMdiv
ΔWELMFW = 50% ΔWELM
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*
Analysis of ELM impact on divertor
ΔWELM x fELM ~ constant = 0.2-0.4 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 ~ 20 - 27 MJ
From ΔWELM/Wped vs τ||front we get ΔWELM ~ 7 - 16 MJ
With DN, we have 65% to either divertor, ΔWELM ~ 4.6 - 17.6 MJ
ΔWELMdiv ~ 3.7 – 8.8 MJ
ΔWELMdiv, τrise ~ 0.75 – 3.5 MJ
Adiv,ELM = 1.44 m2
(2α/πk) ΔWELMdiv, τrise
ΔTrise = --------------------------------- = 1522 –7242 oK for W
Adiv,ELM (2 τ||front)1/2
Analysis of ELM impact on FW
From ΔWELM/Wped vs υ* we get ΔWELM ~ 20 - 27 MJ
From ΔWELM/Wped vs τ||front we get ΔWELM ~ 7 - 16 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
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
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