E. Fable

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.

Particle transport in tokamak plasmas, theory and experiment

The physical processes producing electron particle transport in the core of tokamak plasmas are described. Starting from the gyrokinetic equation, a simple analytical derivation is used as guidance to illustrate the main mechanisms driving turbulent particle convection. A review of the experimental observations on particle transport in tokamaks is presented and the consistency with the theoretical predictions is discussed. An overall qualitative agreement, and in some cases even a specific quantitative agreement, emerges between complex theoretical predictions and equally complex experimental observations, exhibiting different dependences on plasma parameters under different regimes. By these results, the direct connection between macroscopic transport properties and the character of microscopic turbulence is pointed out, and an important confirmation of the paradigm of microinstabilities and turbulence as the main cause of transport in the core of tokamaks is obtained. Finally, the impact of these results on the prediction of the peaking of the electron density profile in a fusion reactor is illustrated.

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.

Gyrokinetic modelling of electron and boron density profiles of H-mode plasmas in ASDEX Upgrade

Local gyrokinetic calculations of the logarithmic gradients at mid-radius of both electron and boron densities in ASDEX Upgrade H-mode plasmas are presented and compared with the experimental observations. The experimental results show that both the electron and the boron density profiles increase their peaking in response to the addition of central electron cyclotron heating over a background of neutral beam injection (NBI) heating. The boron density profiles are always less peaked than the electron density profiles in the confinement region, and are flat or even slightly hollow in the presence of NBI heating only. The experimental behaviours are well reproduced by the theoretical predictions. The agreement allows the identification, through theoretical modelling, of the transport mechanisms responsible for the observed dependences. In particular, the observed increase in the logarithmic electron density gradient with increasing central electron heating is explained by a concurrent reduction of the outward pure convection and an increase in the inward thermodiffusion. In addition, it is found that the plasma toroidal rotation velocity and its radial gradient play a non-negligible role in the turbulent boron transport, and allow the prediction of a decrease in boron peaking with increasing rotation velocity, which is consistent with the experimental observations.

Gyrokinetic simulations of impurity, He ash and α particle transport and consequences on ITER transport modelling

The transport of light and heavy impurities, as well as of energetic a particles, produced by the background electrostatic plasma turbulence is investigated by means of linear and nonlinear simulations with three gyrokinetic codes, GS2, GYRO and the recently developed GKW. The basic transport mechanisms of impurities and energetic alpha particles are elucidated, in combination with a simple analytical derivation. The relevance of these theoretical results in the transport modelling of the ITER standard scenario is assessed by means of ASTRA simulations, in which the transport of minority species like alpha particles and He ash is described by means of formulae which fit the gyrokinetic results.

Core momentum and particle transport studies in the ASDEX Upgrade tokamak

Core momentum and particle transport in ASDEX Upgrade (AUG) have been examined in a wide variety of plasma discharges and via several different methods. Experiments were performed in which ECRH power was added to NBI heated H-modes causing the electron and impurity ion density profiles to peak and the core toroidal rotation to flatten. Turbulence calculations of these plasmas show a change in the dominant regime from ITG to TEM due to the ECRH induced changes in the electron and ion temperature profiles. The impurity and electron density behavior can be fully explained by the changes in the turbulent particle transport. Momentum transport analyses demonstrate that in the TEM regime there is a core localized, counter-current directed, residual stress momentum flux of the same order of magnitude as the applied NBI torque. The initial results from momentum modulation experiments performed on AUG confirm that the Prandtl number in AUG NBI heated H-modes is close to 1 and that there exists a significant inward momentum pinch. Lastly, an intrinsic toroidal rotation database has been developed at AUG which can be used to test theoretically predicted dependences of residual stress momentum fluxes. Initial results show a linear correlation between the gradient of the toroidal rotation and both the electron density gradient scale length and the frequency of the dominant turbulent mode.

Particle pinch and collisionality in gyrokinetic simulations of tokamak plasma turbulence

The generic problem of how, in a turbulent plasma, the experimentally relevant conditions of a particle flux very close to the null are achieved, despite the presence of strong heat fluxes, is addressed. Nonlinear gyrokinetic simulations of plasma turbulence in tokamaks reveal a complex dependence of the particle flux as a function of the turbulent spatial scale and of the velocity space as collisionality is increased. At experimental values of collisionality, the particle flux is found close to the null, in agreement with the experiment, due to the balance between inward and outward contributions at small and large scales, respectively. These simulations provide full theoretical support to the prediction of a peaked density profile in a future nuclear fusion reactor.

The role of ion and electron electrostatic turbulence in characterizing stationary particle transport in the core of tokamak plasmas

A general feature of particle transport in the core of tokamak plasmas is that when core particle sources are small, a stationary peaked density profile is provided by a balance of outward diffusion and inward convection, driven by either neoclassical or turbulent mechanisms. The turbulent contribution to the off-diagonal elements of the transport matrix is very sensitive to the type of dominant instability of the background turbulence. We present here a detailed quasi-linear gyrokinetic analysis of stationary turbulent particle transport by means of analytical and numerical calculations to show how the actual parametric dependence of the stationary normalized density gradient can strongly vary between an ion temperature gradient (ITG) dominated turbulence and a trapped electron mode dominated turbulence regime. It is also shown how the maximal achievable normalized density gradient is reached when the turbulence regime is in a mixed state. This result is interpreted as the interplay of different physical mechanisms arising from (linear) wave–particle resonances. The results presented here are addressed to interpret some of the still unresolved issues in interpreting known experimental results.

Characterizing turbulent transport in ASDEX Upgrade L-mode plasmas via nonlinear gyrokinetic simulations

The nature and level of turbulent transport in the outer core of low-confinement (L-mode) discharges performed at the ASDEX Upgrade tokamak [Kallenbach et al., Nucl. Fusion 51, 094012 (2011)] are examined. Previously, it was found that for an L-mode discharge of the DIII-D tokamak [J. L. Luxon and L. G. Davis, Fusion Technol. 8, 441 (1985)] gyrokinetic simulations were unable to reproduce the experimental ion heat flux, underestimating it by almost an order of magnitude. In the present work, employing the GENE gyrokinetic turbulence code, an extensive nonlinear study is performed for L-mode discharges of ASDEX Upgrade in order to cross-check this observation. It is shown that no systematic underprediction can be found in these simulations—instead, discrepancies with respect to experimental transport levels are small enough to be resolved within the uncertainties of the experimental profiles. Moreover, it is shown that some turbulence properties resemble closely those of the underlying linear microinstabilities at least out to 90% of the minor radius, so that quasilinear transport models remain, in principle, applicable even for these parameters, provided that appropriate nonlinear saturation rules can be developed.