P. Beyer

Theoretical understanding of turbulent transport in the SOL

Turbulence in the scrape-off layer (SOL) is investigated using a 2D fluid model for the interchange instability as a paradigm. A constant driving flux governs the dynamics of both the equilibrium and fluctuating parts of the density and electric potential. The turbulent flux exhibits intermittent bursts, called avalanches. These events account for a significant part of the total transport, and are manifested as poloidally localized density fingers, extending towards the far SOL. The time averaged density profile looks exponential, and the SOL width increases weakly with the driving source (scaling exponent 2/9). Viscosity is found to govern the characteristic radial size of convective cells, which in turn control the transport magnitude. The larger ν, the larger the turbulent transport. Finally, the impact on turbulence of local biasing is investigated, possibly modeling Langmuir probe measurements. For a too large extent of the theoretical probe, the density drops by factors at the probe, due to the local build up of a screening vortex. The ambient density is recovered for a sufficiently small probe. In this case, fluctuations exhibit a similar Fourier spectrum at and next to the probe, though the probe still misses a significant number of large bursts. Finally, the experimental probe characteristics are recovered qualitatively when varying the biasing potential.

Turbulence simulations of transport barriers with toroidal velocity

The effect of a sheared toroidal velocity on a transport barrier is studied. This analysis is done by using three-dimensional global fluid simulations of electrostatic ion temperature gradient driven turbulence in tokamaks. The barrier is produced with a reversed magnetic shear. For a flat density profile, and at low collisionality, co-rotation leads to an outward motion of the barrier, whereas counter rotation leads to an inward displacement. However, the barrier displacement saturates when increasing the torque at fixed heat source. This saturation is attributed to the onset of Kelvin–Helmholtz modes. Also the central temperature is larger without external torque because the width of the transport barrier is wider. The consequence is that better confinement is obtained in absence of external torque.

Bursty transport in tokamak turbulence: Role of zonal flows and internal transport barriers

Large scale transport events are studied using two different 3-D simulation codes related to resistive ballooning and ion temperature gradient turbulence. The turbulence is driven by a constant incoming flux. In the case of resistive ballooning simulations, the underlying structures are found to be radially elongated on the low field side and distorted by magnetic shear in the parallel direction (streamers). The non-linear character of these structures is emphasized. Bursty transport is investigated in the presence of zonal flows and internal transport barriers generated either by a strong shear flow or with a magnetic shear reversal. In deriving a low dimensional model that captures the main features of bursty transport dynamics, it is found that E × B shear flow is necessary to trigger the bursts.

Electrostatic turbulence and transport with stochastic magnetic field lines

Electrostatic turbulence, associated convective transport and poloidal plasma rotation at the edge of a tokamak plasma are strongly modified in a layer of stochastic magnetic field lines. Experimental observations during ergodic divertor operation show a decrease of density fluctuations but there is no evidence of a change of the turbulent cross field diffusivity. In this paper, the underlying mechanisms are studied using three-dimensional numerical simulations of flux driven resistive ballooning turbulence. Three key elements are found to determine the characteristics of transport due to fluctuations in the stochastic layer: first, long-lived stationary eddies appear due to modified equilibrium pressure and potential. Second, large scale pressure fluctuations decrease but small scale velocity fluctuations tend to increase. Third, the poloidal plasma rotation is suppressed and zonal flows are reduced by an anomalous friction due to stochasticity. In total, the level of convective flux associated with fluctuations is not quenched by the magnetic field perturbation. The impact of stochastic field lines on electrostatic turbulence is of interest for many experimental situations such as the stochastic boundary of stellarators and transport in the vicinity of the separatrix of standard tokamak divertors.

Edge turbulence during the static dynamic ergodic divertor experiments in TEXTOR

The influence of the magnetic ergodization on edge turbulence and turbulence-induced transport has been investigated by Langmuir probes in TEXTOR under three different static DED configurations. Common features are observed. With DED, the edge equilibrium profiles are altered and the resultant positive Er is in agreement with modelling. In the ergodic zone, the potential fluctuations are strongly reduced and the local turbulent flux changes direction from radially outwards to inwards. In the same zone, the turbulence properties are profoundly modified by energy redistribution in frequency spectra, suppression of large-scale structures and reduction of the radial and poloidal correlation lengths for all frequencies. Meanwhile, the fluctuation poloidal phase velocity changes sign from the electron to ion diamagnetic drift, consistent with the change of the Er × B flow, whereas the slight radially outward propagation of fluctuations is hindered by the DED. In the laminar region, the turbulence correlation is found to react to the observed reduced flow shear. Before the DED the Reynolds stress displays a radial gradient at the plasma edge while during DED the profile is suppressed, suggesting a rearrangement by the DED on the flow momentum profile.

Edge turbulence during ergodic divertor operation in Tore Supra

We report new measurements of turbulence during ergodic divertor (ED) operation. At low density, some de-correlation of the turbulence is observed with a decrease of the long timescale structures. It is shown that the typical time involved is compatible with a de-correlation mechanism through radial separation of the B field lines by the ED, with an associated parallel length of the order of the distance between two modules of the ED. This observation reinforces the conclusion drawn in [1] and based on computer simulations. The situation changes when the density is increased: the turbulence level is found to increase. At the highest density, the structure of the turbulent signal is modified and the bursty behaviour suppressed by the ED at low density reappears. These observations lead to the conclusion that the turbulence measured at high density is not sensitive to the ED stabilization effect. This indicates that it could be carried by the ions.

Reduction of the turbulent blob transport in the scrape-off layer by a resonant magnetic perturbation in TEXTOR

During the static 6/2 Dynamic Ergodic Divertor experiments in TEXTOR, a significant influence of the edge resonant magnetic perturbation (RMP) on the turbulent blob transport in the scrape-off layer (SOL) has been observed. In ohmic discharges without the RMP, the blobs extend 4–5u2009cm deep into the SOL with a radially outward moving speed of about 1u2009kmu2009s−1 and hence constitute a strong outflow of mass. With the application of the RMP, the blob amplitudes and their radially moving velocity are both reduced, resulting in a significant reduction of the blob transport in the SOL. The reduction effect of the RMP on blobs is found to be robust to changes in the operational regime and to phasing variations of the RMP as well. The blob dynamics appears to be consistent with the paradigm of the radial motions of the blob structures driven by the interchange instability.

Edge issues in ITB plasmas in JET

This paper documents critical issues in internal transport barrier (ITB) plasmas in JET, namely the transition from type III to type I edge localized modes (ELMs), and the subsequent impact of large amplitude ELMs on the ITB. Benign type III ELMs are observed in ITB plasmas at input powers much larger (up to a factor 3) than the empirical threshold for type III/I transition derived from standard H-modes. Various measurements indirectly suggest a larger fraction of plasma current at the edge of ITB plasmas. Experimental results look consistent with a type III ELM regime controlled by a large fraction of edge current. Especially, the transition to type I ELMs does not occur for a broad current profile (li≈0.78) characterized by low edge magnetic shear (s95≈2.6), and a back transition from type I to type III has been found to well correlate with an increase of the edge current. When large ELMs occur, strong perturbations δTe on electron temperature are generated, and propagate inwards on a ballistic timescales, at vburst≈160 m s−1. It is of the order of one third (respectively one ninth) of the curvature (respectively diamagnetic) drift. This propagation looks reminiscent of non-local transport experiments. The perturbation induced by large ELMs can reach the ITB. In this case, δTe increases in the vicinity of the ITB before being strongly damped further inside. Such ELMs also lead to a transient increase of Te gradient at the ITB, which then moves inwards on a diffusive timescale (χ≈3×10−2 m2 s−1) while degrading.

2D and 3D boundary turbulence studies

Pressure driven curvature instabilities at the boundary of a tokamak plasma are studied. First, three-dimensional turbulence simulations are presented including the case where magnetic field lines are stochastic. Three main features are observed: (i) the level of pressure fluctuations decreases in the ergodic layer. (ii) This is essentially due to a suppression of large-scale structures. (iii) The turbulent heat diffusivity does not decrease in the stochastic layer due to an increase of electric field fluctuations. These observations are in agreement with turbulence measurements on Tore Supra. Second, particle flux driven turbulence in the scrape-off layer (SOL) is studied using a two-dimensional code. The transverse transport is found to be ballistic and intermittent. Bursts propagate outwards with a radial velocity of the order of one tenth of the parallel velocity. Test particles undergo outward and inward trajectories. The order of magnitude of the e-folding SOL length is in agreement with experimental data.

Turbulence simulations of transport barrier relaxations in tokamak edge plasmas

A promising operational regime of future fusion reactors is characterized by an edge transport barrier, i.e. a localized steepening of density and temperature gradients. Typically, such a barrier is unstable and relaxes quasi-periodically. In this work, we show that complete barrier relaxation cycles can be reproduced by three-dimensional turbulence simulations. In these simulations, a barrier forms due to an imposed E × B shear flow. This barrier relaxes intermittently on the confinement time scale, even if fluctuations of the E × B flow are suppressed. It is found here that if the E × B shear increases faster than linearly with heating power, the relaxation frequency decreases with power. A relaxation event has a complex dynamical behaviour, characterized by the intermittent growth of a mode at the barrier centre. A crucial ingredient in this non-linear dynamics is a time delay for an effective E × B velocity shear stabilization.