Self-organisation in tokamak turbulence

The research described in this thesis is part of the worldwide effort to realise nuclear fusion as a future energy source. Nuclear fusion, the merging of light atomic nuclei to form heavier ones, is an attractive option for large scale energy production. Fusion powers the sun and stars, and could on earth produce electricity from abundantly available fuels, without CO2 or other hazardous emissions. For the fusion reactions to occur, the fuel needs to be heated to 150 million degrees centigrade at several times atmospheric pressure. Under these conditions the atoms are fully ionised and form a plasma. In the most promising reactor concept, the tokamak, this hot plasma is contained inside a toroidal vessel by a strong magnetic field. Part of this magnetic field is generated by a current that runs in the plasma itself. In a working reactor, the energy generated by the fusion reactions helps to keep the plasma at the required temperature. Hence it is important to minimise the rate at which energy is lost from the plasma. This energy loss is mainly caused by chaotic plasma motions called turbulence. Perturbations of the density and temperature as well as of the electromagnetic fields play a role in plasma turbulence and show strong interactions. The strong magnetic field in a tokamak suppresses the dynamics directed along it, rendering tokamak turbulence more or less two dimensional. This type of turbulence is characterised by the formation of large structures from the merging of smaller ones, like for example the emergence of hurricanes from small disturbances in the atmosphere. In the tokamak the size of these structures is limited to intermediate scales, the so called mesoscales, by the shape of the magnetic field. Mesoscale structures may influence the transport, which in turn can modify the driving forces for the turbulence. Since the turbulence creates the mesoscale structures, a feedback loop is set up through which self-organisation can occur. This self-organisation is the object of study in this dissertation. The main questions addressed by this work are to what extend heat transport in the plasma is influenced by self-organisation, and whether self-organisation can explain certain observations in experiment that are not yet fully understood. Two coherent phenomena emerging from chaotic turbulent interactions are considered of prime importance: Current generated by the interaction of turbulent flows and turbulent magnetic fields, the dynamo current, and layered rotational flows emerging from small scale turbulent motions, the zonal flows. A model for tokamak turbulence is studied, the Cylindrical ElectroMagnetic 2 Fluid Turbulence (CEM2FT) model, which is arguably the simplest model to capture nonlinear interactions between turbulence, transport and plasma properties in a tokamak including the physics of dynamo currents and zonal flows. In order to compare the CEM2FT model with tokamak experiments, it is implemented in a numerical code, CUTIE. A simple one dimensional diffusive model for neutral particles was implemented in the CUTIE code to provide a better description of the particle source. However, the simulations show that in the small tokamaks this study is aimed at the situation is too complicated to be described by this simple model. The most important mesoscale structures emerging from CUTIE simulations are described and discussed. These are compared to actual observations in tokamaks. It is shown that the CEM2FT model not only describes generally observed phenomena such as magnetic islands and ballooning structures, but also reproduces specific self-organised structures such as off-axis sawteeth and flattened q-profiles. The dynamo current is shown to be of particular importance in the latter. The edge of a tokamak plasma can be cooled by injecting a hydrogen ice pellet. In such experiments, it is often found that the central temperature rises. In CUTIE simulations the pellet induces a zonal flow that decorrelates turbulent eddies and moves inward. This suppresses the turbulence over an area extending into the centre of the plasma. Although the magnitude and time scale of the effect do not correspond to the experiment, the suppression of turbulent heat loss could explain the rise of central plasma temperature. Another way of perturbing a steady-state plasma is by switching off the microwave heating of the plasma. In experiments, it is found that the central plasma retains its heat for some time after the switch-off, which is attributed to a reduction of turbulent heat loss. The simulations do indeed show such a reduction, but at a different position due to the fact that the magnetic configuration of the experiment could not be reproduced in detail. It is clear, however, that the suppression of the turbulence is caused by a zonal flow that is driven by enhanced magnetic fluctuations. In general it is concluded that self-organisation, in particular via the dynamo current and zonal flows, plays an important role in turbulent tokamak transport.