Annika K. Eriksson

Toroidal and poloidal momentum transport studies in JET

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 τE/τφ=1 except for the low density discharges where the ratio is τE/τφ=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 χφ/χi�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 pedes- tal is weaker than that of ion temperature. Another observation is that while the Ti has a threshold in R/LTi and profiles are stiff, the gradient in vφ increases with increasing torque and no threshold is found. Predictive trans- port simulations also confirm that χφ/χi�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 or- der 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 gen- eration of the anomalous poloidal velocity is the turbulence driven flow through the Reynolds 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 Reynolds stress.

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 Reynolds 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.

Electromagnetic effects on toroidal momentum transport

A parametric study of electromagnetic effects on toroidal momentum transport has been performed. The work is based on a new version of the Weiland model where symmetry breaking toroidicity effects derived from the stress tensor have been taken into account. The model includes a self-consistent calculation of the toroidal momentum diffusivity, which contains both diagonal and off-diagonal contributions to the momentum flux. It is found that electromagnetic effects considerably increase the toroidal momentum pinch. They are sometimes strong enough to make the total toroidal momentum flux inward.

Predictive simulations of toroidal momentum transport at JET

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) 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 (χi) to be larger than the momentum diffusivity and it gives Prandtl numbers (Pr = χ/χi) 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.

Electromagnetic Effects on quasilinear turbulent particle transport

It is well known that a nonadiabatic part of the electron density response is needed for particle transport in tokamaks. Such main reactive effects are electron trapping and electromagnetic induction. Although electron trapping has been studied rather extensively, electromagnetic effects have hardly been studied at all although they are already included in transport codes. Here the electromagnetic effects have been analyzed and parameter studies have been performed, showing that an electromagnetic particle pinch may appear in the flat density regime, just as for the case of electron trapping although the conditions are more restrictive. The particle pinch is particularly sensitive to the direction of propagation of the eigenmode. The electromagnetic particle flux is found to be outward for modes propagating in the ion drift direction and inward for modes propagating in the electron drift direction. A pinch may be obtained rather close to the axis for International Thermonuclear Experimental Reactor simulation data.

Progress on anomalous transport in tokamaks, drift waves and nonlinear structures

Fluid and kinetic theory of drift wave turbulence and zonal flows are compared. The result from particle in cell codes that transport is reduced and zonal flows become stronger when the parallel nonlinearity is included is interpreted in terms of removing dissipative kinetic resonances from a fluid model. Also a kinetic derivation is given of the excitation of zonal flows and recent results on momentum transport are discussed. The recent results on particle pinches in fluid and kinetic codes are also interpreted in a similar way. General aspects of different fluid closures are discussed.

Influence of iron addition on the oxygen-deficient Sr{sub 0.85}Bi{sub 0.15}Co{sub 1-x}Fe{sub x}O{sub 3-{delta}} (0.0{<=}x{<=}1.0) perovskites

A series of oxygen-deficient Sr{sub 0.85}Bi{sub 0.15}Co{sub 1-x}Fe{sub x}O{sub 3-{delta}} (0.0{ =}0.8. Evidence of weak superstructures, reflecting local oxygen ordering, is also obtained from electron diffraction. For all oxygen-annealed phases the average structure reverts to cubic Pm3-bar m. The as-prepared samples show G-type antiferromagnetic order at room temperature. The oxygen annealed x=0.10, 0.25 and 1.0 samples display low-temperature spin-glass transitions. - Graphical abstract: Evolving crystal structures of the as-prepared Sr{sub 0.85}Bi{sub 0.15}Co{sub 1-x}Fe{sub x}O{sub 3-{delta}} perovskites as a function of iron content for the compositional range 0.1{<=}x{<=}1.0.

Influence of iron addition on the oxygen-deficient Sr0.85Bi0.15Co1−xFexO3−δ (0.0⩽x⩽1.0) perovskites

A series of oxygen-deficient Sr{sub 0.85}Bi{sub 0.15}Co{sub 1-x}Fe{sub x}O{sub 3-{delta}} (0.0{ =}0.8. Evidence of weak superstructures, reflecting local oxygen ordering, is also obtained from electron diffraction. For all oxygen-annealed phases the average structure reverts to cubic Pm3-bar m. The as-prepared samples show G-type antiferromagnetic order at room temperature. The oxygen annealed x=0.10, 0.25 and 1.0 samples display low-temperature spin-glass transitions. - Graphical abstract: Evolving crystal structures of the as-prepared Sr{sub 0.85}Bi{sub 0.15}Co{sub 1-x}Fe{sub x}O{sub 3-{delta}} perovskites as a function of iron content for the compositional range 0.1{<=}x{<=}1.0.

Anomalous particle transport in D–T plasmas

A study of turbulent particle transport and drift mode stability in deuterium-tritium plasmas is presented. The study is based on an extended implementation of the Weiland transport model for ion temperature gradient (ITG-) modes and trapped electron (TE-) modes. The dependence of the transport fluxes on the tritium density gradient and the tritium concentration is investigated. Particle pinches are demonstrated for general parameter values and an asymmetry is found in the deuterium and tritium transport fluxes.

Effects of A-site substitution on the structure and magnetic properties of Bi0.15Sr0.85−yAeyCo1−xFexO3−δ perovskites

The effects of partial substitution of Sr2+ by Ca2+ and Ba2+ on the A-site of oxygen-deficient perovskites, Bi(0.15)Sr(0.85-y)Ae(y)Co(1-x)FeO(3-delta), where y = 0.28 for Ae = Ba and y = 0.17 for Ae = Ca, and 0.0 = 0.25. The samples were studied with PXRD, NPD, TGA, electron microscopy and magnetic susceptibility measurements. All as-prepared samples exhibited long range G-type antiferromagnetic ordering. The effect of oxygen annealing was dramatic for the Bi0.15Sr0.68Ca0.17Co1-xFexO3-delta series, with a disappearance of magnetic order for x >= 0.25 linked to increasing spin-glass properties. The oxygen content of the Bi0.15Sr0.57Ba0.28Co1-xFexO3-delta as-prepared materials was generally higher than their Ca substituted counterparts, and the long range antiferromagnetic order was more resistant to oxygen annealing.