Abstract
A levitated dipole reactor is a promising magnetic confinement fusion device design with the potential to solve some of the challenges associated with traditional fusion approaches. It is important to understand the transport of mass and energy within a levitated dipole device since these control confinement and thus fusion yield. Most of the levitated dipole's proposed advantages stem from the 'turbulent pinch' effect, whereby interchange turbulence drives centrally peaked plasma profiles. This is one of the key properties of a levitated dipole device and is advantageous in trying to achieve fusion, where high-pressure, centrally peaked plasma profiles are required. To advance understanding of the turbulent pinch, and the stability and turbulence in a levitated dipole, the hard-core Z-pinch is studied as a simple approximation that is valid in a levitated dipole device's central region.
This thesis begins by designing model equilibria for the hard-core Z-pinch. A linear theory for the hard-core Z-pinch is then developed to analyse and predict the stability of the model equilibria. WKB theory is applied to the linear theory to produce a dispersion relation for the system's eigenmodes, which gives expressions for growth rates of the axisymmetric and non-axisymmetric modes. I clarify the relation between the different instabilities and compare the WKB results to solutions for the full boundary value problem for several equilibria. The linear stability results are then tested in a full global geometry through non-linear simulations of the hard-core Z-pinch using the 3D Athena++ MHD code. In order to study transport in the steady state, I develop novel 'fueled' simulations, where the turbulence due to the instabilities and its impact on the equilibria in different regimes is studied. The turbulent pinch, driven by the interchange instability, is recovered at high ß (ß = 8πp/B²). The interchange turbulence drives the plasma toward interchange stability, resulting in the centrally peaked profiles of the turbulent pinch, which can be sustained in some simulations. When a threshold on the average ß of the system is exceeded, the non-axisymmetric ballooning instability is seen to drive 3D turbulence and much higher transport. This results in the destruction of the turbulent pinch, with important implications for levitated dipole fusion.