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Publication# Turbulent transport regimes in the tokamak boundary

Résumé

The overall performance of a tokamak strongly depends on phenomena that take place in a thin region between the main plasma and the vessel wall, which is denoted as tokamak boundary. In fact, the formation of transport barriers in this region can significantly improve plasma confinement and, therefore, the tokamak fusion performance. In addition, the tokamak boundary determines the peak heat flux to the wall, an essential quantity for the design and the operation of fusion power plants, as well as the level of impurities in the core, the removal of fusion ash and the dynamics of neutral particles.The dynamics in the plasma boundary is strongly nonlinear and characterized by a wide range of length and time scales as well as by a complex magnetic field geometry that mayfeature one or more nulls of the poloidal magnetic field. Large-scale, three-dimensional turbulence simulations are therefore often required to disentangle the complex physicalmechanisms that govern this region.The thesis is focused on the analysis of the different turbulent transport regimes present in the plasma boundary as they appear from three-dimensional, flux-driven, global, two-fluid turbulence simulations carried out by using the GBS code, which is significantly extended here to allow the self-consistent simulation of the plasma dynamics coupled to a kinetic single-species neutral model in arbitrarily complex magnetic geometries. Considering single-null magnetic configurations, three turbulent transport regimes are identified: (i) a regime of suppressed turbulent transport at low values of collisionality and large values of heat source, (ii) a regime of developed turbulent transport at intermediate values of collisionality and heat source, and (iii) a regime of very large turbulent transport at high value of collisionality and density, which can be associated to the crossing of the density limit. By leveraging the results of GBS simulations, theory-based scaling laws of the pressure and density decay lengths in the near and far scrape-off layer are derived in the developed transport regime from a balance among heat source, turbulent transport across the separatrix and parallel losses at the vessel wall. The theoretical scaling of the pressure decay length in the near scrape-off layer is successfully validated against a multi-machine database of SOL width measurements at the outer target.By carefully analysing the transition to the regime of large turbulent transport, we show that the density limit can be explained by an enhancement of turbulent transport at thetokamak boundary when the density increases. This analysis leads to a theory-based scaling law of the maximum edge density achievable in tokamaks, which is in better agreement with a multi-machine database than the widely used Greenwald empirical scaling, thus significantly improving our understanding and predictive capability of thedensity limit, with important implications for the design and the operation of future fusion power plants.The thesis concludes by presenting the first turbulent simulations carried out in various snowflake magnetic configurations, which are used to investigate the effect of turbulenceand equilibrium flow on the heat flux distribution among the different strike points.

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Maurizio Giacomin, Paolo Ricci, Louis Nicolas Stenger

The power exhaust through the scrape-off layer (SOL) in fusion reactors is expected to be significantly higher than in ITER, thus questioning the extrapolation of the ITER exhaust solution to these devices. The snowflake (SF) magnetic configuration is one of the alternative exhaust configurations being considered to mitigate the heat vessel loads in fusion reactors. The SF configuration features a second-order null of the poloidal magnetic field, i.e. a point where the poloidal magnetic field and its spatial derivatives vanish. As a consequence, the null-point is connected to the wall through four legs, which define four strike points. The presence of the four strike points allows for a heat flux distribution on a larger area compared to standard divertor configurations that feature two strike points. SF configurations are obtained experimentally by generating two first-order X-points close to each other. When the two X-points coincide, a second-order null point is obtained. However, in practice, the two X-points never coincide perfectly and, according to their relative position, we distinguish between the snowflake plus (SF+) and snowflake minus (SF-). The configuration with the two X-points coinciding is usually referred to as ideal SF. All these configurations have been experimentally investigated in the TCV, NSTX, EAST, and DIII-D tokamaks and are considered for the DTT tokamak. Numerical simulations of SF configurations, carried out by means of the EMC3-Eirene and the SOLPS codes, are unable to reproduce the heat flux distribution observed experimentally, calling for detailed investigations of the turbulence and flows in the SF plasma boundary. We present the first global turbulent simulations of the plasma dynamics in SF configurations, including the ideal SF, the SF+ and SF- configurations [1]. These simulations carried out by using the GBS code [2], evolve self-consistently the fluctuating and equilibrium quantities, as they result from the interplay of a heat and particle source in the core, turbulent transport, and parallel losses to the vessel wall. The simulations allow us to disentangle the mechanisms behind the heat flux distribution among the different strike points. As pointed out by our simulations, the heat flux can be reduced by a factor of two in the SF configurations, with respect to single-null configurations. The activation of the unconnected strike points in the ideal SF and in the SF+ configurations, also observed in the experiments, is due to the presence of a steady ExB equilibrium flow in the null region that provides a cross-field transport mechanism towards the private flux region. The origin, the properties and the effects of this steady ExB equilibrium flow are carefully analyzed and described as well as its dependence on the direction of the toroidal magnetic field and on the distance between the two X-points.

2020The turbulent plasma dynamics in the periphery of a fusion device plays a key role in determining its overall performance.
In fact, the periphery controls the heat load on the vessel walls, the plasma confinement, the level of impurities in the core, the plasma fuelling and the removal of fusion ashes.
Hence, understanding and predicting the plasma turbulence in this region is of crucial importance for the success of the fusion program.
The GBS code has been developed in past years to simulate plasma turbulence in the periphery of limited tokamaks.
The goal of the present thesis is to extend GBS to the treatment of diverted scenarios. Such configurations are of interest for present state-of-the-art experiments and future fusion reactors.
For the implementation of this geometry, we express the model in toroidal coordinates, abandoning the flux coordinates previously used in limited configuration, and overcoming the singularity that this coordinate system presents at the X-point of diverted configurations.
The accuracy of the numerical scheme is improved by upgrading the second order finite differences scheme to fourth order on staggered grids.
The resulting version of GBS is carefully verified
through a series of tests (i.e.,
a benchmark with the previous version of GBS in limited configuration,
a rigorous check of the correctness of the code implementation with the method of manufactured
solutions, and a convergence study on a relatively simple diverted configuration).
The results of a GBS simulation is then used to investigate the dynamics of
coherent turbulent structures, called blobs, that characterise plasma
turbulence in the periphery of fusion devices. A diverted double-null
configuration is considered, and the blob motion is studied using a pattern
recognition algorithm. The velocity of the blobs in the presence of an X-point matches
the analytical scaling that we derived by considering the different
blob properties in the divertor and main SOL regions, retaining the
correction terms that account for blob density and ellipticity.
In addition, we show that the blob current pattern observed
in the simulation results match the theoretical expectations.
Finally, the new version of GBS is run with a
realistic diverted magnetic equilibrium, taken from an experiment carried out
on the TCV tokamak. First insights of the turbulence properties
are in good agreement with the current physical
understanding of plasma dynamics in the periphery of diverted tokamaks.

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The turbulent plasma dynamics in the periphery of a tokamak plays a key role in determining its overall performances. In particular, it governs the confinement properties of the device, through the formation of a transport barrier associated with the L-H transition, and it controls the heat load on the vessel walls. GBS [1] is a three-dimensional two-fluid turbulence code, based on the drift-reduced Braginskii equations, which allows the simulation of plasma turbulence in this tokamak region. A non-field aligned algorithm has been recently implemented in GBS, to allow simulations in diverted configurations, such as the single- and double-null. Furthermore, simulations in innovative exhaust configurations, such as the snowflake, are being performed. The results of GBS simulations in single-null configurations are used to investigate the processes determining the radial electric field at the plasma edge and the related formation of a transport barrier. In particular, we show the presence of two different turbulent transport regimes driven by Kelvin-Helmholtz and resistive ballooning instability, respectively. A transition between the two regimes is obtained by changing the power source, which leads to a strong ExB shear and to the onset of a transport barrier at the plasma edge. The ExB shear provides a saturation mechanism for the resistive ballooning instability while destabilising a Kelvin-Helmholtz mode that becomes the main drive for turbulent transport. The transition between the two regimes leads to a steepening of the pressure profile and improved plasma confinement. We derive an analytical expression for the pressure gradient length in both regimes. The simulation and analytical results are in good agreement. The analysis is then extended to the SOL where we highlight the effect of edge turbulence on the SOL width and therefore on the heat load on the vessel walls. Finally, the results of simulations of alternative divertor configurations, which are considered for DEMO, are analysed. The analysis focuses on four different magnetic configurations: the ideal snowflake, the snowflake plus, the snowflake minus with the secondary X-point in the high field side and the snowflake minus with the secondary X-point in the low field side. For all the different geometries, the SOL width and the heat flux to the vessel walls are computed and the physics behind them analysed. A comparison between the single-null configuration and the four considered advanced configurations is shown.

2019