Toroidal and poloidal coordinates

The terms toroidal and poloidal refer to directions relative to a torus of reference. They describe a three-dimensional coordinate system in which the poloidal direction follows a small circular ring around the surface, while the toroidal direction follows a large circular ring around the torus, encircling the central void. The earliest use of these terms cited by the Oxford English Dictionary is by Walter M. Elsasser (1946) in the context of the generation of the Earth's magnetic field by currents in the core, with "toroidal" being parallel to lines of latitude and "poloidal" being in the direction of the magnetic field (i.e. towards the poles). The OED also records the later usage of these terms in the context of toroidally confined plasmas, as encountered in magnetic confinement fusion. In the plasma context, the toroidal direction is the long way around the torus, the corresponding coordinate being denoted by z in the slab approximation or ζ or φ in magnetic coordinate

Turbulence at the boundary of toroidal plasmas with open and closed magnetic flux surfaces

Fabio Avino

The control and confinement of fusion plasmas are currently limited by a lack of understanding of the physical mechanisms behind the evolution of the turbulent transport experienced by particles and energy. In-situ investigations of plasma turbulence in fusion experiments is strongly hampered by the high temperatures and densities. Basic plasma physics devices represent an alternative solution to perform turbulence studies with the possibility of rigorously validating numerical codes. One of these experiments is TORPEX, in which a comprehensive characterization of plasma turbulence has been conducted in the presence of open helical magnetic field lines in toroidal geometry. These reproduce the main features of the scrape-off layer (SOL), which is the open flux surface region at the edge of magnetically confined fusion plasmas. The SOL has a key role in the balance of the dynamics that determine the overall plasma confinement. The first achievement of this thesis work is a technical upgrade of TORPEX that consists in the installation of a copper toroidal conductor inside the TORPEX vacuum vessel. A poloidal magnetic field is produced by a current flowing inside the conductor, introducing a rotational transform. This allows studying plasma turbulence in magnetic geometries of increasing complexity, starting with the simplest configuration of quasi-concentric flux surfaces. The initial exploration of the main plasma properties, including plasma production mechanisms and particle confinement time, is followed by a detailed spectral characterization of the measured electrostatic quasi-coherent fluctuations. Measurements of the toroidal and poloidal mode numbers reveal field-aligned modes. These present a poloidal localization indicating a clear ballooning feature that is in agreement with the results of a linear fluid code. The first experimental measurements of plasma blobs in the presence of a single-null X-point are performed. Blobs radially propagating outwards across the X-point are conditionally sampled, which allows us to track and analyze in detail the corresponding dynamics. The ExB drifts induced by the background potential gradients and the fluctuating potential dipole are both responsible for the measured blob acceleration in the X-point region. The contribution of the potential dipole is explained on the basis of an analytical model, in which the variation of the magnetic field intensity close to the X-point plays a key role. This results in a blob speed scaling that is in good agreement with the measured values.

EPFL2015

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