Turbulence in the scrape-off layer of double-null tokamak configurations

Understanding the turbulent dynamics in the outermost region of the tokamak is essential to predict and control the heat and particle loads to the vessel wall, a crucial problem for the entire fusion program. In this thesis, the problem is approached via two-fluid simulations run with the GBS code. We leverage a recent code upgrade to employ coordinate systems independent of the magnetic geometry, allowing the simulation of diverted configurations. We focus on double-null magnetic configurations. A double null configuration is being considered for DEMO due to its practical advantages of spreading the heat load over more strike points than a single null configuration, having a quiescent high field side on which heating antennas can be placed and the possibility to radiate more heat in detached scenarios. From a theoretical point of view, it is simpler to analyse than a single null because the high and low field sides are topologically separated. Simulations with a balanced double null configuration are run for a range of resistivities and safety factors. The results are used to study the density decay at the outer midplane. A double decay length is observed and a model to predict the two decay lengths is developed. The decay length of the near scrape-off layer is well described as the result of transport driven by a non-linearly saturated ballooning instability, while in the far scrape-off layer the density decay length is described using a model of intermittent transport mediated by blobs. The analytical estimates of the decay lengths agree well with the simulation results and typical experimental values and can therefore be used to guide tokamak design and operation. Unbalanced double null configurations are then simulated using a new elliptical coordinate system developed for this purpose, allowing more realistic elongation of the magnetic field. The distribution of the heat flux between the four diverter legs is calculated and compared to previous experimental results. We explain the heat flux sharing in terms of the $E \times B$ , diamagnetic and parallel flows.

Turbulent transport regimes in the tokamak boundary

Maurizio Giacomin

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.

EPFL2022

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

The role of the sheath in magnetized plasma turbulence and flows

Joaquim Loizu Cisquella

Controlled nuclear fusion could provide our society with a clean, safe, and virtually inexhaustible source of electric power production. The tokamak has proven to be capable of producing large amounts of fusion reactions by confining magnetically the fusion fuel at sufficiently high density and temperature, thus in the plasma state. Because of turbulence, however, high temperature plasma reaches the outermost region of the tokamak, the Scrape-Off Layer (SOL), which features open magnetic field lines that channel particles and heat into a dedicated region of the vacuum vessel. The plasma dynamics in the SOL is crucial in determining the performance of tokamak devices, and constitutes one of the greatest uncertainties in the success of the fusion program. In the last few years, the development of numerical codes based on reduced fluid models has provided a tool to study turbulence in open field line configurations. In particular, the GBS (Global Braginskii Solver) code has been developed at CRPP and is used to perform global, three-dimensional, full-n, flux-driven simulations of plasma turbulence in open field lines. Reaching predictive capabilities is an outstanding challenge that involves a proper treatment of the plasma-wall interactions at the end of the field lines, to well describe the particle and energy losses. This involves the study of plasma sheaths, namely the layers forming at the interface between plasmas and solid surfaces, where the drift and quasineutrality approximations break down. This is an investigation of general interest, as sheaths are present in all laboratory plasmas. This thesis presents progress in the understanding of plasma sheaths and their coupling with the turbulence in the main plasma. A kinetic code is developed to study the magnetized plasma-wall transition region and derive a complete set of analytical boundary conditions that supply the sheath physics to fluid codes. These boundary conditions are implemented in the GBS code and simulations of SOL turbulence are carried out to investigate the importance of the sheath in determining the equilibrium electric fields, intrinsic toroidal rotation, and SOL width, in different limited configurations. For each study carried out in this thesis, simple analytical models are developed to interpret the simulation results and reveal the fundamental mechanisms underlying the system dynamics. The electrostatic potential appears to be determined by a combined effect of sheath physics and electron adiabaticity. Intrinsic flows are driven by the sheath, while turbulence provides the mechanism for radial momentum transport. The position of the limiter can modify the turbulence properties in the SOL, thus playing an important role in setting the SOL width.

EPFL2013