Toroidal and poloidal momentum transport studies in tokamaks

The present status of understanding of toroidal and poloidal momentum transport in tokamaks is presented in this paper. Similar energy confinement and momentum confinement times, i.e. tau(E)/tau(phi)approximate to 1 have been reported on several tokamaks. It is more important though, to study the local transport both in the core and edge plasma separately as, for example, in the core plasma, a large scatter in the ratio of the local effective momentum diffusivity to the ion heat diffusivity chi(phi eff)/chi(i.eff) among different tokamaks can be found. For example, the value of effective Prandtl number is typically around chi(phi eff)/chi(i.eff)approximate to 0.2 on JET while still tau(E)/tau(phi)approximate to 1 holds. Perturbative NBI modulation experiments on JET have shown, however, that a Prandtl number chi(phi)/chi(i) of around 1 is valid if there is an additional, significant inward momentum pinch which is required to explain the amplitude and phase behaviour of the momentum perturbation. The experimental results, i.e. the high Prandtl number and pinch, are in good qualitative and to some extent also in quantitative agreement with linear gyro-kinetic simulations. In contrast to the toroidal momentum transport which is clearly anomalous, the poloidal velocity is usually believed to be neo-classical. However, experimental measurements on JET show that the carbon poloidal velocity can be an order of magnitude above the predicted value by the neo-classical theory within the ITB. These large measured poloidal velocities, employed for example in transport simulations, significantly affect the calculated radial electric field and therefore the E x B flow shear and hence modify and can significantly improve the simulation predictions. Several fluid turbulence codes have been used to identify the mechanism driving the poloidal velocity to such high values. CUTIE and TRB turbulence codes and also the Weiland model predict the existence of an anomalous poloidal velocity, peaking in the vicinity of the ITB and driven dominantly by the flow due to the Reynold's stress. It is worth noting that these codes and models treat the equilibrium in a simplified way and this affects the geodesic curvature effects and geodesic acoustic modes. The neo-classical equilibrium is calculated more accurately in the GEM code and the simulations suggest that the spin-up of poloidal velocity is a consequence of the plasma profiles steepening when the ITB grows, following in particular the growth of the toroidal velocity within the ITB.