The Dimits shift, an upshift in the onset of turbulence from the linear instability threshold, caused by self-generated zonal flows, can greatly enhance the performance of magnetic confinement plasma devices. Except in simple cases, using fluid approximations and model magnetic geometries, this phenomenon has proved difficult to understand and quantitatively predict. To bridge the large gap in complexity between simple models and realistic treatment in toroidal magnetic geometries (e.g. tokamaks or stellarators), the present work uses fully gyrokinetic simulations in a Z-pinch geometry to investigate the Dimits shift through the lens of tertiary instability analysis, which describes the emergence of drift waves from a zonally dominated state. Several features of the tertiary instability, previously observed in fluid models, are confirmed to remain. Most significantly, an efficient reduced-mode tertiary model, which previously proved successful in predicting the Dimits shift in a gyrofluid limit (Hallenbert & Plunk, J. Plasma Phys., vol. 87, issue 05, 2021, 905870508), is found to be accurate here, with only slight modifications to account for kinetic effects.

The tertiary instability is believed to be important for governing magnetised plasma turbulence under conditions of strong zonal flow generation, near marginal stability. In this work, we investigate its role for a collisionless strongly driven fluid model, self-consistently derived as a limit of gyrokinetics. It is found that a region of absolute stability above the linear threshold exists, beyond which significant nonlinear transport rapidly develops. Characteristically, this range exhibits a complex pattern of transient zonal evolution before a stable profile can arise. Nevertheless, the Dimits transition itself is found to coincide with a tertiary instability threshold, so long as linear effects are included. Through a simple and readily extendable procedure, tracing its origin to St-Onge (J. Plasma Phys., vol. 83, issue 05, 2017, 905830504), the stabilising effect of the typical zonal profile can be approximated, and the accompanying reduced mode estimate is found to be in good agreement with nonlinear simulations.

Pedestal modelling is crucial to predict the performance of future fusion devices. Current modelling efforts suffer either from a lack of kinetic physics, or an excess of computational complexity. To ameliorate these problems, we take a first-principles multiscale approach to the pedestal.We will present three separate sets of equations, covering the dynamics of Edge Localised Modes (ELMs), the inter-ELM pedestal, and pedestal turbulence, respectively. Precisely how these equations should be coupled to each other are covered in detail. This framework is completely self-consistent; it is derived from first principles by means of an asymptotic expansion of the fundamental Vlasov-Landau-Maxwell system in appropriate small parameters. The derivation exploits the narrowness of the pedestal region, the smallness of the thermal gyroradius, and the low plasma β (the ratio of thermal to magnetic pressures) typical of current pedestal operation to achieve its simplifications.The relationship between this framework and gyrokinetics is analysed, and possibilities to directly match our systems of equations onto multiscale gyrokinetics are explored. A detailed comparison between our model and other models in the literature is performed. Finally, the potential for matching this framework onto an open-field-line region is briefly discussed.