Multiscale Modelling for Tokamak Pedestals

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 Lo- calised Modes, 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 an asymptotic expansion in appropriate small parameters. The derivation exploits the narrowness of the pedestal region, the smallness of the thermal gyroradius, and the low plasma $\beta$ typical of current pedestal operation to achieve its simplifications. The relationship between this framework and gyrokinetics is analysed, and possibilities to directly match this framework 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 discussed.