1. 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

2. Chalmers University of Technology 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

3. Chalmers University of Technology 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 α MHD = β/β c, β c =L p /(Rq 2 ), where L p is the pressure scale length and α d = V /(γ id L) where L is a characteristic turbulence scale length going as q(R ρ s ν ei /Ω ce ) 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 α d diagram in Fig 1.

4. Chalmers University of Technology α MHD – α d diagram

5. Chalmers University of Technology 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.

6. Chalmers University of Technology Transport model The main features of our transport model are: Saturation level: Reactive fluid closure

7. Chalmers University of Technology 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 (1b) Electromagnetic toroidal (parallel) momentum equation including curvature effects from the stress tensor (caused by the Coriolis pinch in gyrokinetics) (2) (1a)

8. Chalmers University of Technology Saturation level 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)

9. Chalmers University of Technology Edge barrier with basic data from JET69454 ____________ Start profile ……………… Simulation Experimental T i at r/a = 0.9 was around 1.5 KeV. B p =0.2T Fig 2

10. Chalmers University of Technology 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

11. Chalmers University of Technology 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.

12. Chalmers University of Technology 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.

13. Chalmers University of Technology 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.

14. Chalmers University of Technology 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 4dFig 4e

15. Chalmers University of Technology 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)

16. Chalmers University of Technology Feedback loop Increased heating -> increased δP due to temp grad. -> increased Γ p -> increased V p through Fick’s law -> increased E r 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

17. Chalmers University of Technology 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 Which is in agreement with the experiment Fig 5a Fig 5b

18. Chalmers University of Technology 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

19. Chalmers University of Technology High field cont Fig 6b Electron temperature with 50% increased magnetic field and 30 % increased power

20. Chalmers University of Technology Increased B cont Fig6c, poloidal and 6d toroidal momentum with 50% increased field

21. Chalmers University of Technology 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

22. Chalmers University of Technology 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

23. Chalmers University of Technology 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.

24. Chalmers University of Technology α MHD – α d 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 (q 95 = 2.28)

25. Chalmers University of Technology α MHD – α d diagram

26. Chalmers University of Technology 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.

27. Chalmers University of Technology 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.

28. Chalmers University of Technology 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.

29. Chalmers University of Technology 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

30. Chalmers University of Technology Summary cont The transition is triggered by the ion temperature gradient in combination with the diamagnetic part of the Reynolds stress