Disentangling turbulence in the plasma boundary of diverted tokamaks

A non-field aligned coordinate system was recently implemented in GBS, a three-dimensional drift-reduced Braginskii fluid code to simulate turbulence in the plasma periphery of tokamaks. This avoids the singularity present in field-aligned coordinates at the X-point, thus allowing the simulation of any toroidally symmetric magnetic field configuration, with no separation between equilibrium and fluctuating quantities, therefore evolving self-consistently the formation of the plasma profiles. Simulations are carried out in the single-null and double-null configurations and first simulations in innovative exhaust configurations (such as the snowflake) are being performed. The talk will focus on the double-null configuration, which is of interest as a possible heat exhaust solution and for advanced heating schemes. The new insights obtained in the double-null configuration from the GBS simulations will be presented and thoroughly analysed. The different nature of the plasma dynamics in the low- and high-field sides will be pointed out, showing that turbulence is driven by a Kelvin-Helmholtz instability on the high-field side, and by an interchange instability on the low-field side. On the low-field side, a structure with two scale lengths forms. The wave-like nature of turbulence across the last closed-flux surface will be discussed and estimates of the narrow pressure scale length in this region will be given. It will be shown that blobs are generated across the last-closed flux surface, being responsible for the convective nature of the transport in the far SOL. The blob generation rate, size, and speed will be estimated, allowing the prediction of the far SOL width. Comparisons of the simulation results with previous and new analytical results will be presented, as well as with experimental results. Generalisation to other tokamak configurations will also be discussed.

Simulation of plasma turbulence in the periphery of diverted tokamaks

Paola Paruta

The 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.

EPFL2018

Properties of plasma turbulence in the periphery of diverted tokamaks

Carrie Fiona Beadle, Maurizio Giacomin, Paola Paruta, Paolo Ricci

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

A flexible numerical scheme for simulating plasma turbulence in the tokamak scrape off layer

Paola Paruta, Paolo Ricci, Fabio Riva, Christoph Wersal

Simulating the most external plasma region of a tokamak, the scrape-off layer (SOL), is of crucial importance in the way towards a fusion reactor as heat load on the vessel wall, impurity generation, and overall plasma confinement, all depend on the plasma dynamics in this region. In the last few years a numerical code, GBS, has been developed for solving the drift-reduced Braginskii equations, and describe turbulence in the tokamak SOL. In the present work, we re-formulate these equations in a general form that enables to treat diverted configuration with X-point. This is obtained by relaxing the requirement of using a coordinate system that follows the magnetic field lines. Within this alternative coordinate system, the drift-reduced Braginskii equations are then solved by using an high order numerical scheme. We show initial simulations carried out with GBS that describe well the expected field aligned turbulence structures.