C. Angioni

Linear gyrokinetic calculations of toroidal momentum transport in a tokamak due to the ion temperature gradient mode

It is shown from a symmetry in the gyrokinetic equation that for up–down symmetric tokamak equilibria and for uϕ⪢ρυthi∕r (where uϕ is the toroidal velocity, υthi is the thermal ion velocity, ρ is the Larmor radius, and r is the radius of the flux surface), the transport of parallel momentum can be written as the sum of a diffusive and a pinch contribution with no off-diagonal terms due to temperature and pressure gradients. The measured parallel velocity gradient in ASDEX Upgrade [O. Gruber, H.-S. Bosch, S. Gunter et al., Nucl. Fusion 39, 1321 (1999)] is insufficient to drive the parallel velocity shear instability. The parallel velocity is then transported by the ion temperature gradient mode. The diffusive contribution to the transport flux is investigated using a linear gyrokinetic approach, and it is found that the diffusion coefficient for parallel velocity transport divided by the ion heat conductivity coefficient is close to 1, and only weakly dependent on plasma parameters.

On the physics guidelines for a tokamak DEMO

The physics base for the ITER Physics Design Guidelines is reviewed in view of application to DEMO and areas are pointed out in which improvement is needed to arrive at a consistent set of DEMO Physics Design Guidelines. Amongst the proposed improvements, the area of power exhaust plays a crucial role since predictive capability of present-day models is low and this area is expected to play a major role in limiting DEMO designs due to the much larger value of Ptot/R in DEMO than in present-day devices and even ITER.

Overview of toroidal momentum transport

Toroidal momentum transport mechanisms are reviewed and put in a broader perspective. The generation of a finite momentum flux is closely related to the breaking of symmetry (parity) along the field. The symmetry argument allows for the systematic identification of possible transport mechanisms. Those that appear to lowest order in the normalized Larmor radius (the diagonal part, Coriolis pinch, E x B shearing, particle flux, and up-down asymmetric equilibria) are reasonably well understood. At higher order, expected to be of importance in the plasma edge, the theory is still under development.

Physics of transport in tokamaks

This paper is an overview of recent results relating to turbulent particle and heat transport, and to the triggering of internal transport barriers (ITBs). The dependence of the turbulent particle pinch velocity on plasma parameters has been clarified and compared with experiment. Magnetic shear and collisionality are found to play a central role. Analysis of heat transport has made progress along two directions: dimensionless scaling laws, which are found to agree with the prediction for electrostatic turbulence, and analysis of modulation experiments, which provide a stringent test of transport models. Finally the formation of ITBs has been addressed by analysing electron transport barriers. It is confirmed that negative magnetic shear, combined with the Shafranov shift, is a robust stabilizing mechanism. However, some well established features of internal barriers are not explained by theory.

Influence of the centrifugal force and parallel dynamics on the toroidal momentum transport due to small scale turbulence in a tokamak

The paper derives the gyro-kinetic equation in the comoving frame of a toroidally rotating plasma, including both the Coriolis drift effect [A. G. Peeters et al., Phys. Rev. Lett. 98, 265003 (2007)] as well as the centrifugal force. The relation with the laboratory frame is discussed. A low field side gyro-fluid model is derived from the gyro-kinetic equation and applied to the description of parallel momentum transport. The model includes the effects of the Coriolis and centrifugal force as well as the parallel dynamics. The latter physics effect allows for a consistent description of both the Coriolis drift effect as well as the ExB shear effect [R. R. Dominguez and G. M. Staebler, Phys. Fluids B 5, 3876 (1993)] on the momentum transport. Strong plasma rotation as well as parallel dynamics reduce the Coriolis (inward) pinch of momentum and can lead to a sign reversal generating an outward pinch velocity. Also, the ExB shear effect is, in a similar manner, reduced by the parallel dynamics and stronger rotation.

Density response to central electron heating: theoretical investigations and experimental observations in ASDEX Upgrade

Theory of ion temperature gradient (ITG) and trapped electron modes (TEMs) is applied to the study of particle transport in experimental conditions with central electron heating. It is shown that in the unstable domain of TEMs, the electron thermodiffusive flux is directed outwards. By means of such a flux, a mechanism is identified likely to account for density flattening with central electron heating. Theoretical predictions are compared with experimental observations in ASDEX Upgrade. A parameter domain (including L- and H-mode plasmas) is identified, in which flattening with central electron heating is observed in the experiments. In general, this domain turns out to be the same domain in which the dominant plasma instability is a TEM. On the contrary, the dominant instability is an ITG in plasmas whose density profile is not affected significantly by central electron heating. The flattening predicted by quasi-linear theory for low density L-mode plasmas is too small compared to the experimental observations. At very high density, even when the dominant instability is an ITG, electron heating can provide density flattening, via the coupling with the ion heat channel. In these conditions the anomalous diffusivity increases in response to the increased ion heat flux, while the large collisionality makes the anomalous pinch small and the Ware pinch important.

The effect of a metal wall on confinement in JET and ASDEX Upgrade

In both JET and ASDEX Upgrade (AUG) the plasma energy confinement has been affected by the presence of a metal wall by the requirement of increased gas fuelling to avoid tungsten pollution of the plasma. In JET with a beryllium/tungsten wall the high triangularity baseline H-mode scenario (i.e. similar to the ITER reference scenario) has been the strongest affected and the benefit of high shaping to give good normalized confinement of H98???1 at high Greenwald density fraction of fGW???0.8 has not been recovered to date. In AUG with a full tungsten wall, a good normalized confinement H98???1 could be achieved in the high triangularity baseline plasmas, albeit at elevated normalized pressure ?N?>?2. The confinement lost with respect to the carbon devices can be largely recovered by the seeding of nitrogen in both JET and AUG. This suggests that the absence of carbon in JET and AUG with a metal wall may have affected the achievable confinement. Three mechanisms have been tested that could explain the effect of carbon or nitrogen (and the absence thereof) on the plasma confinement. First it has been seen in experiments and by means of nonlinear gyrokinetic simulations (with the GENE code), that nitrogen seeding does not significantly change the core temperature profile peaking and does not affect the critical ion temperature gradient. Secondly, the dilution of the edge ion density by the injection of nitrogen is not sufficient to explain the plasma temperature and pressure rise. For this latter mechanism to explain the confinement improvement with nitrogen seeding, strongly hollow Zeff profiles would be required which is not supported by experimental observations. The confinement improvement with nitrogen seeding cannot be explained with these two mechanisms. Thirdly, detailed pedestal structure analysis in JET high triangularity baseline plasmas have shown that the fuelling of either deuterium or nitrogen widens the pressure pedestal. However, in JET-ILW this only leads to a confinement benefit in the case of nitrogen seeding where, as the pedestal widens, the obtained pedestal pressure gradient is conserved. In the case of deuterium fuelling in JET-ILW the pressure gradient is strongly degraded in the fuelling scan leading to no net confinement gain due to the pedestal widening. The pedestal code EPED correctly predicts the pedestal pressure of the unseeded plasmas in JET-ILW within ?5%, however it does not capture the complex variation of pedestal width and gradient with fuelling and impurity seeding. Also it does not predict the observed increase of pedestal pressure by nitrogen seeding in JET-ILW. Ideal peeling ballooning MHD stability analysis shows that the widening of the pedestal leads to a down shift of the marginal stability boundary by only 10?20%. However, the variations in the pressure gradient observed in the JET-ILW fuelling experiment is much larger and spans a factor of more than two. As a result the experimental points move from deeply unstable to deeply stable on the stability diagram in a deuterium fuelling scan. In AUG-W nitrogen seeded plasmas, a widening of the pedestal has also been observed, consistent with the JET observations. The absence of carbon can thus affect the pedestal structure, and mainly the achieved pedestal gradient, which can be recovered by seeding nitrogen. The underlying physics mechanism is still under investigation and requires further understanding of the role of impurities on the pedestal stability and pedestal structure formation.

Off-diagonal particle and toroidal momentum transport: a survey of experimental, theoretical and modelling aspects

In tokamaks, turbulent particle and toroidal momentum transport are both characterized by the presence of off-diagonal contributions which play an essential role in establishing the profile shapes of the density and the toroidal rotation under most conditions. In this paper similarities and differences between the two turbulent transport channels are pointed out and, thereby, interesting physical aspects which connect the two channels are identified. The main contributions to off-diagonal particle and toroidal momentum transport are reviewed by means of a rather simplified description, which aims at providing, when possible, a direct connection between theoretical, modelling and experimental research.

Advances in the physics basis for the European DEMO design

In the European fusion roadmap, ITER is followed by a demonstration fusion power reactor (DEMO), for which a conceptual design is under development. This paper reports the first results of a coherent effort to develop the relevant physics knowledge for that (DEMO Physics Basis), carried out by European experts. The program currently includes investigations in the areas of scenario modeling, transport, MHD, heating & current drive, fast particles, plasma wall interaction and disruptions.

Tungsten transport in JET H-mode plasmas in hybrid scenario, experimental observations and modelling

The behaviour of tungsten in the core of hybrid scenario plasmas in JET with the ITER-like wall is analysed and modelled with a combination of neoclassical and gyrokinetic codes. In these discharges, good confinement conditions can be maintained only for the first 2?3?s of the high power phase. Later W accumulation is regularly observed, often accompanied by the onset of magneto-hydrodynamical activity, in particular neoclassical tearing modes (NTMs), both of which have detrimental effects on the global energy confinement. The dynamics of the accumulation process is examined, taking into consideration the concurrent evolution of the background plasma profiles, and the possible onset of NTMs. Two time slices of a representative discharge, before and during the accumulation process, are analysed with two independent methods, in order to reconstruct the W density distribution over the poloidal cross-section. The same time slices are modelled, computing both neoclassical and turbulent transport components and consistently including the impact of centrifugal effects, which can be significant in these plasmas, and strongly enhance W neoclassical transport. The modelling closely reproduces the observations and identifies inward neoclassical convection due to the density peaking of the bulk plasma in the central region as the main cause of the accumulation. The change in W neoclassical convection is directly produced by the transient behaviour of the main plasma density profile, which is hollow in the central region in the initial part of the high power phase of the discharge, but which develops a significant density peaking very close to the magnetic axis in the later phase. The analysis of a large set of discharges provides clear indications that this effect is generic in this scenario. The unfavourable impact of the onset of NTMs on the W behaviour, observed in several discharges, is suggested to be a consequence of a detrimental combination of the effects of neoclassical transport and of the appearance of an island.