Chalmers University of Technology
The L-H transition on EAST
Jan Weiland and C.S. Liu
Chalmers University of Technoloy and EURATOM_VR
Association, S-41296 Göteborg, Sweden
Seminar,
SWIP April 2014
ASIPP May 2014
Chalmers University of Technology
Outline
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The turbulence simulations at Maryland
Comparison with C-mod
Fluid model
Previous JET simulations
Simulations of L-H transition on EAST
Comparison with the results of Rogers and Drake
Comparisons with C-mod, scaling studies
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The L-H transition found by Rogers,
Drake and Zeiler
Very detailed turbulence simulations of the L-H transition were made in
1998 by Rogers, Drake and Zeiler. (PRL 81, 4396 (1998)). In particular they
introduced the two parameters αMHD = β/βc , βc =Lp /(Rq2), where Lp is the
pressure scale length and αd = V⃰ /(γidL) where L is a characteristic
turbulence scale length going as q(R ρs νei/Ωce)0.5. These authors used an
electromagnetic fluid code in a radially localized flux tube domain,
including both pressure gradient and current gradient drives as well as
background flow. The results of Rogers, Drake and Zeiler can be
summarized by their own α αd diagram in Fig 1.
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αMHD – αd diagram
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Rogers Drake Zeiler
The H mode obtained by Rogers, Drake and Zeiler was usually
caused by rotation but could sometimes be due to Finite Larmor
Radius (FLR) stabilization. Clearly an H-mode has steep gradients
so it is not surprising that the H-mode regime is in the upper right
corner.
However for large collisionality (large L) they found very strong
transport. This regime is associated with high density and works as
a density limit.
e
Te


k c s k r 


1
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 e k r L n
Transport model
The main features of our transport model are:
Saturation level:
 k  k  k  v E k
e

Te

k c s k r 


1
 e k r L n
Reactive fluid closure
q  q 
5
P
2 m c
(e x T )
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Poloidal spinup due to Reynolds stress
The radial flux of poloidal momentum
U 
t


r
2
p  Sv
 p  v Er v    D B k r k 
(1a)
1    1  
   Pi   c .c
2
 

(1b)
We have obtained a spinup of poloidal momentum both at an internal and at an edge
transport barrier. In both cases the bifurcation seems to be closely related to this spinup
Electromagnetic toroidal (parallel) momentum equation including curvature effects from
the stress tensor (caused by the Coriolis pinch in gyrokinetics)


 
m i ni 
 2U Di    u
 t


  m i ni u E   U
0


 e   U

m iU D i
0
Ti
  ( p i  en i 
    e (1   e ) / 
k c
A )
(2)
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Saturation level
For reference we show our ion thermal conductivity for the simple
pure ITG mode
i 
1
i
( i 
2
3

10
9
(    ExB ) / k r
3
n)
( r 
5
3
2
 Di )  (    ExB )
2
(3)
2
We have here used a Non-Markovian mixing length rule [J.Weiland and
H. Nordman Theory of Fusion Plasmas, Chexbres 1988, A. Zagorodny and J. Weiland Phys.
Plasmas 6, 2359 (1999)] and the Waltz rule [R.E. Waltz et. al. Phys. Plasmas 1, 2229
(1994) (numerical) and A. Zagorodny and J. Weiland, Phys. Fluids 16, 052308 (2009)
(analytical)]
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Edge barrier with basic data from JET69454
Fig 2
____________
………………
Start profile
Simulation
Experimental Ti at r/a = 0.9 was around 1.5 KeV. Bp =0.2T
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Flowshear
Fig 3a,b
Ion temperature and Flowshear
profiles showing why we get
stabilization at the edge. Note that
this was obtained self-consistently
in a global simulation The
flowshear is driven primarily by
the poloidal nonlinear spinup of
rotation. Careful study of
simulation data shows that a mode
propagating in the electron drift
direction is unstable at the edge
point and at the first point inside
the edge.
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Simulations of EAST 38300
We will now show results of simulations of EAST 38300. A standard
case is shown in Fig 4a for ion temperature.
Fig 4a. Our standard case for East H-mode. The heating is the experimental and about 20%
over the powerthreshold. The full line is the initial profile and the dotted is the simulated. The
experimental temperature was slightly below the simulated.
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Sim of EAST 38300 cont
Fig 4b. The same case as in a but for electron temperature. The full line is the initial profile
and the dotted is the simulated. The experimental temperature was slightly below the
simulated.
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Simulation of EAST 38300 cont
Fig 4c. The same case as in a but for electron density. The full line is the initial profile and the
dotted is the simulated. The experimental temperature was slightly below the simulated while th
experimental density was above the simulated in the interior. However, we know that it takes a
long time for the particle pinch to build up the central density. We note that the H-mode density
is much flatter than in L-mode.
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Simulation of EAST 38300 cont
Fig 4d
Fig 4e
Fig 4 d,e. The same case as in a but for poloidal momentum d) and toroidal momentum e).
The full line is the initial profile and the dotted is the simulated. The poloidal rotation
triggered the L-H transition.
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Simulations of EAST 38300
• We have also rum this case with magnetic q reduced by 25%
• We find that the pdestal of the ion temperature has increased by
25% doe to the reduction of q (increase of current)
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Feedback loop
Γ
Fig 5 Temp profile with heating and flux
 p  v Er v    D B
2
1    1  
k r k     Pi   c .c
2
 

Increased heating -> increased δP due to temp grad. -> increased Γp -> increased Vp
through Fick’s law -> increased Er through force balance -> increased flow shear: ->
Reduced turbulence –increased temp grad .> increased δP and so on
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Scaling studies
It is now very interesting to compare with experimental scalings. This is
particalarly so since the gradients in our H-mode barriere, using a
nonlocal transport code, tends to agree with the H-mode region from local
turbulence simulations in Fig 1. In particular from Hubbard et. al, Phys
Plasmas 14, 056109, (2007) we find that the temperature at the separatrix
and the power threshold increase with the total magnetic field (Fig 2 and
abstract). As it turns out, the power threshold decreases with B if we keep
the edge temperature fixed while it increases with B if we take into
account the increase of the edge (separatrix) temperature. The edge
temperature was in Hubbard et. al found to scale as
Using this scaling we find
T sep  B
Pthres  B
Which is in agreement with the experiment
Fig 5a
Fig 5b
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High field
We will now show the case with 50% increased magnetic field
Fig 6a Ion temperature with 50% increased magnetic field and 30 % increased power
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High field cont
Fig 6b Electron temperature with 50% increased magnetic field and
30 % increased power
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Increased B cont
• Fig6c, poloidal and 6d toroidal momentum with 50% increased
field
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High field
We will now show a case with 50 % increased magnetic field
Fig 6a Ion temperature with 50% increased
magnetic field and 30 % increase power
Fig 6b Electron temperature with 50%
increased magnetic field and 30 % increase
power
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High field
Fig 6c Poloidal rot. with 50% increased
magnetic field and 30 % increased power
Fig 6d Toroidal rot. with 50% increased
magnetic field and 30 % increased power
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High field
Fig 6e density with 50% increased
magnetic field and 30 % increased power
We note that the temperstures and density become considerably increased with higher
magnetic field and power. Here we do not have any experimental data to compare
the profiles with, we just obtained the right scaling for the power threshold.
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αMHD – αd diagram
• As mentioned above our H-mode pedestals tend to give gradients in
the H- mode regime of the paper by Rogers, Drake annd Zeiler We
show this in Fig 7
• We have made some changes in the conditions. Thus the “best”
results (filled black dota) are with comparably high gas puffing rate.
• The ones in the L-mode regime but close to the H-mode regime
(actually some experimental points in H-modehave been here are
open rings whilke those for the high B case are just past the MHD
stability boundary. The crosses correspond to slightly decreased q
(q95= 2.28)
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αMHD – αd diagram
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Fluid closure aspects
• In our reactive fluid model the temperature perturbation has a
fluid resonance. Thus the temperature perturbation is stronger
than we would have if we added Landaudamping. On the other
hand the edge is usually so collisional that we have a closure
because of that. Thus this question may be more relevant for
internal barriers.
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Discussion
As mentioned above, Rogers et. al. have sometimes obtained a LH transition due to Finite Larmor (FLR) radius stabilization. We
can also get that. In fact, in my first book I compared flowshear
due to neoclassical rotation with FLR stabilisation and found that
FLR stabilization usually woul be more important. The reason
why flowshear is more important here is the poloidal spinup due
to zonal flows. However, when the barrier has been formed the
neoclassical rotation becomes comparable to that of zonal flows.
Since we are solving transport equations for the flows, the flows
remain also after the turbulence has been stabilized but, of
course, then there is no turbulence drive.
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Discussion cont.
This seems to be the first time that an L-H transition has been
obtained in a transport code where we do not help the
transition by putting in an tanhyp function where the pedestal
is expected. Thus our code relies heavily on the mechanisms
for stabilization of turbulence which we have already in the
code.
The fact that we have only a few (5 – 6) gridpoints in the
barrier might be of concern. However the fact that we recover
the gradients found by Rogers et. al,. in the barrier indicates
that we have, in fact, at least the right physics responsible gor
the barrier. Then there is a case where teo neighbouring
radial points are both in the H-mode regime.
This case behaves as all other cases, i.e. everything varies
continously and we thus conclude that we have captured the
right physics.
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Summary
• This is the first time that the global dynamics of the L-H
transition in a transport code has been connected to the local
dynamics, at the pedestal, in a turbulence code.
• We start from L-mode type initial conditions in temperatures,
density, poloidal and toroidal rotation and simulate the transition
to H-mode profiles in all 5 channels by just applying the
experimental heating.
• We use the same grid everywhere so there is no way of telling
where the barrier would be formed.
• The power threshold of the transition is about 20% below the
experimental power.
• The density profile is much flatter in H- mode than in L-mode.
• We recover the linear growth of the power threshold with total
B seen in C-mod
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Summary cont
• The transition is triggered by the ion
temperature gradient in combination with the
diamagnetic part of the Reynolds stress