This paper reports on recent studies of toroidal and poloidal momentum transport in tokamaks. The ratio of the global energy confinement time to the momentum confinement is found to be close to τ E /τ φ = 1 among several tokamaks. On the other hand, local transport analysis in the core plasma shows a larger scatter in the ratio of the local effective momentum diffusivity to the ion heat diffusivity χ φ,eff / χ i,eff among different tokamaks, for example the value of effective Prandtl number being typically around χ φ,eff / χ i,eff ≈ 0.2 on JET. Perturbative NBI modulation experiments on JET have indicated, however, that the Prandtl number (calculated only with diffusive terms) χ φ / χ i is around 1, and in addition, a significant inward momentum pinch is needed 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. Concerning the poloidal velocity, the experimental measurements on JET show that the carbon poloidal velocity can be an order of magnitude above the neo-classical estimate within the ITB. This significantly affects the calculated radial electric field and therefore, the E×B flow shear used for example in transport simulations. Several fluid turbulence codes have been used to identify the mechanism driving the poloidal velocity to such high values. CUTIE and TRB turbulence codes predict the existence of an anomalous poloidal velocity, peaking in the vicinity of the ITB and being dominantly caused by flow due to the Reynold's stress. It is important to note that both codes treat the equilibrium in a simplified way and this affects the geodesic curvature effects and Geodesic Acoustic Modes (GAMs). The neo-classical equilibrium is calculated more accurately in the GEM code and interestingly, the simulations suggest that the spin-up of poloidal velocity is a consequence of the plasma profiles steepening when the ITB grows, with poloidal velocity tight to the 2D neo-classical equilibrium and following in particular the growth of the toroidal velocity within the ITB.
This paper reports on the recent studies of toroidal and poloidal momentum transport in JET. The ratio of the global energy confinement time to the momentum confinement is found to be close to τ E /τ φ =1 except for the low density discharges where the ratio is τ E /τ φ =2-3. On the other hand, local transport analysis of tens of discharges shows that the ratio of the local effective momentum diffusivity to the ion heat diffusivity is χ φ /χ i 0.1-0.4 rather than unity, as expected from the global confinement times and used in ITER predictions. The apparent discrepancy in the global and local momentum versus ion heat transport is explained by the fact that momentum confinement within edge pedestal is worse than that of the ion heat and thus, momentum pedestal is weaker than that of ion temperature. Another observation is that while the T i has a threshold in R/L Ti and profiles are stiff, the gradient in v φ increases with increasing torque and no threshold is found. Predictive transport simulations also confirm that χ φ /χ i 0.1-0.4 reproduce the core toroidal velocity profiles well. Concerning poloidal velocities on JET, the experimental measurements show that the carbon poloidal velocity can be an order of magnitude above the neo-classical estimate within the ITB. This significantly affects the calculated radial electric field and therefore, the E×B flow shear used for example in transport simulations. The Weiland model reproduces the onset, location and strength of the ITB well when the experimental poloidal rotation is used while it does not predict an ITB using the neo-classical poloidal velocity. The most plausible explanation for the generation of the anomalous poloidal velocity is the turbulence driven flow through the Reynold's stress. Both TRB and CUTIE turbulence codes show the existence of an anomalous poloidal velocity, being significantly larger than the neo-classical values. And similarly to experiments, the poloidal velocity profiles peak in the vicinity of the ITB and is caused by flow due to the Reynold's stress.
Since the installation of an ITER-like wall, the JET programme has focused on the consolidation of ITER design choices and the preparation for ITER operation, with a specific emphasis given to the bulk tungsten melt experiment, which has been crucial for the final decision on the material choice for the day-one tungsten divertor in ITER. Integrated scenarios have been progressed with the re-establishment of long-pulse, high-confinement H-modes by optimizing the magnetic configuration and the use of ICRH to avoid tungsten impurity accumulation. Stationary discharges with detached divertor conditions and small edge localized modes have been demonstrated by nitrogen seeding. The differences in confinement and pedestal behaviour before and after the ITER-like wall installation have been better characterized towards the development of high fusion yield scenarios in DT. Post-mortem analyses of the plasma-facing components have confirmed the previously reported low fuel retention obtained by gas balance and shown that the pattern of deposition within the divertor has changed significantly with respect to the JET carbon wall campaigns due to the absence of thermally activated chemical erosion of beryllium in contrast to carbon. Transport to remote areas is almost absent and two orders of magnitude less material is found in the divertor.
A new version of the Weiland model has been used in predictive JETTO simulations of toroidal rotation. The model includes a self-consistent calculation of the toroidal momentum diffusivity ( χ φ ) which contains both diagonal and non-diagonal (pinch) contributions to the momentum flux.Predictive transport simulations of JET H-mode, L-mode and hybrid discharges are presented.It is shown that experimental temperatures and toroidal velocity were well reproduced by the simulations. The model predicts the ion heat diffusivity ( χ i ) to be larger than the momentum diffusivity and it gives Prandtl numbers (Pr = χ φ / χ i ) between 0.1 and 1. The Prandtl numbers are often, depending on the plasma conditions, predicted to be significantly smaller than unity. This is in accordance with experimental findings.
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