Chalmers University of Technology

Simulations of the formation of transport barriers including the generation of poloidal

spinup due to turbulence

J. Weiland1,, T. Tala2 , V. Naulin3 , K. Crombe4 and P. Mantica5

and the JET-EFDA contributors

1. Department of Radio and Space Science, Chalmers. University of Technology and Euratom-VR Association, S41296 Gothenburg, Sweden2 Association Euratom-Tekes, VTT, P.O. Box 1000, FIN-02044 VTT, Finland3. Association Euratom-Risø DTU, Denmark4. Association Euratom-Belgian State Department of Applied Physics, Ghent University, Rozier 44 B-9000 Ghent Belgium5 .Istituto di Fisica del Plasma CNR-EURATOM, via Cozzi 53, 20125 Milano, Italy

ITPA Transport and Confinement meeting Culham March 22 – 25 2010

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Contents We have simulated the formation of a transport barrier in four channels , Ion and Electron

temperatures and Toroidal and Poloidal momentum simultaneously.

The transport barrier is formed due to simultaneous pinches in toroidal and poloidal momenta

A spinup in the poloidal momentum with the same location and approximate magnitude as in the experiment is generated

Density is kept fixed as experimental. However there are no traces of barrier in the density profile.

Poloidal spinup is due to Zonal flows. The q dependence of these is changed by the parallel perturbed heatflow now added to the model

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New fluid model for convective toroidal momentum transport (J. Weiland, R. Singh, H. Nordman. P.K. Kaw, A. Peeters and D. Strintzi Nuclear Fusion 49, 065033

(2009))

• We use the ExB flux of this quantity

• The poloidal flux is as before

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Inclusion of reactive parallel heatflow

• This is a purely reactive term which modifies the effects of parallel ion motion in the model. Thus it influences the q scaling. It is usually somewhat stabilizing but can sometimes be destabilizing. We continue to use one parameter dependent correlation length. It is different for ITG and TE modes. The most recent is that for the TE mode which is:

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where is the trapped fraction tf

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Simulation of JET69454

• As seen in the initial profiles there was no initial trace of a barrier. The density was kept fixed and did not show any sign of barrier.

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Simulation of JET69454 without initial barrier without parallel heatflow

____________ Start profile

………………… Simulation

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Simulation of JET69454 without initial barrier and without parallel heatflow

___________Initial condition

…….……….. Simulation

-- -- -- -- -- -- -- -- -- -- -- Neoclassical

16

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Simulation of JET69454 with parallel heatflow

____________ Start profile

………………… Simulation

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Simulation of JET69454 cont

___________Initial condition

…….……….. Simulation

-- -- -- -- -- -- -- -- -- -- -- Neoclassical

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What determines the location of the barrier?

The barrier is formed where the heatflux is large and the magnetic shear still is small

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Simulation of JET69454 with increased qminimum q = 3

Zonal flow increases with q!

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Mechanism of poloidal spinup

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Electrostatic model

No poloidal spinup Almost no barrier in Vtor but the toroidal momentum pinch leads to strong central rotation

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Electrostatic model

No well defined barrier. However still high central Ti due to toroidal momentum pinch

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Electrostatic model without trapping

Electrostatic model without trapping Here transport is reduced so much that we can see a tendency for an edge barrier in Vtor

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Electrostatic model without trapping

No sharp barrier without poloidal spinup but high central Ti due to toroidal rotation

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Simulation of JET72746

The almost flat q profile does not give a well defined location of a barrier

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JET72746 Exp. prof.

T=45.05 After increase in Vpol but before barrier

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Simulation of JET72746 including parallel heatflow

____________ Start profile

………………… Simulation

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Simulation of JET72746 contNo data for Vpol but graph as a function of R indicates a barrier

around r/a = 0.4

___________Initial condition Vtor reversed!

…….……….. Simulation

-- -- -- -- -- -- -- -- -- -- -- Neoclassical

0)( LD

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Directions of rotation

• The poloidal and toroidal rotations shown here are for the main ion species (Deuterium) while the rotation is measured for impurities. Since the Reynolds stress is symmetric with respect to direction of rotation it is actually the neoclassical rotation that gives the initial ”push” and thus determines the direction of rotation. The neoclassical rotation usually has opposite signs for deuterium and impurities, thus the measured poloidal rotation is usually in the opposite direction to the simulated. The toroidal rotation is not directly influenced by neoclassical effects and here the measured and simulated rotations are generally in the same direction. This is, however, not so for 72746. Of course the rotation is still measured for impurities and the only apparent reason for reversal would be the symmetry breaking effect of the gradient of the poloidal rotation on the average K_parallel.

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SummaryPrevious results on the formation of a transport barriere have been confirmed using a refined model

Tests of convergence with up to 99 gridpoints have been performed

The q dependence has changed when the parallel heatflow was included. The poloidal spinup increases with higher q.

Good agreement with experiment also in steady state

A poloidal spinup occurs only in transport barriers. However, sometimes the toroidal momentum pinch alone can give a transport barrier.arriers

The ITG mode is stable and the TE mode marginally unstable in

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Summary cont• The poloidal spinup seems to require both electron

trapping and electromagnetic effects.• The location of the barrier is due to a combination of

small shear large flux