chalmers university of technology the l-h transition on east jan weiland and c.s. liu chalmers...

Chalmers University of Technology

The L-H transition on EAST

Jan Weiland and C.S. LiuChalmers University of Technoloy and EURATOM_VR

Association, S-41296 Göteborg, Sweden

Seminar,

SWIP April 2014

ASIPP May 2014


Outline

• 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


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.


αMHD – αd diagram


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.


Transport modelThe main features of our transport model are:

Saturation level:

kkk Evk

nrerse LkkckT

e 1

nrerse LkkckT

e 1

nrerse LkkckT

e 1

nrerse LkkckT

e 1

Reactive fluid closure

)(2

5Txe

m

P

c

qq


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

Poloidal spinup due to Reynolds stress

The radial flux of poloidal momentum

ccPkkD irBp .1

2

1vv 2

Er

(1b)

)/)1(

(u200

Ack

enpT

UmUeUnmuU

tnm ee

iii

DiEiiDiii

i

Electromagnetic toroidal (parallel) momentum equation including curvature effects from the stress tensor (caused by the Coriolis pinch in gyrokinetics)

(2)

vp Srt

U

(1a)


Saturation level

22

23

)()35

(

/)()

9

10

3

2(

1

ExBDir

rExBni

ii

k

For reference we show our ion thermal conductivity for the simple pure ITG mode

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)]

(3)


Edge barrier with basic data from JET69454

____________ Start profile

……………… Simulation

Experimental Ti at r/a = 0.9 was around 1.5 KeV. Bp =0.2T

Fig 2


Flowshear

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.

Fig 3a,b


Simulations of EAST 38300We 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.


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.


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 the 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.


Simulation of EAST 38300 cont

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.

Fig 4d Fig 4e


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)


Feedback loop

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

Γ

Fig 5 Temp profile with heating and flux

ccPkkD irBp .1

2

1vv 2

Er


Scaling studiesIt 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 BTsep

BPthres Which is in agreement with the experiment

Fig 5a

Fig 5b


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


High field cont

Fig 6b Electron temperature with 50% increased magnetic field and 30 % increased power


Increased B cont

• Fig6c, poloidal and 6d toroidal momentum with 50% increased field


High field

We will now show a case with 50 % increased magnetic field

Fig 6a Ion temperature with 50% increasedmagnetic field and 30 % increase power

Fig 6b Electron temperature with 50% increased magnetic field and 30 % increase power


High field

Fig 6c Poloidal rot. with 50% increasedmagnetic field and 30 % increased power

Fig 6d Toroidal rot. with 50% increasedmagnetic field and 30 % increased power


High field

Fig 6e density with 50% increasedmagnetic 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.



• 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)


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.


Discussion As mentioned above, Rogers et. al. have sometimes obtained a L-

H 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.


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.


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


Summary cont

• The transition is triggered by the ion temperature gradient in combination with the diamagnetic part of the Reynolds stress

chalmers university of technology the l-h transition on east jan weiland and c.s. liu chalmers...

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