Nuclear fusion is one of the most promising options to produce zero-carbon energy on large scales. For the stable operation of fusion reactors it is essential that we understand and are able to control the many plasma instabilities arising in the reactor. ELMs in particular are instabilities that can be detrimental to the energy confinement and lifetime of the reactor. While ELMs have been successfully modelled with MHD, this approach neglects important details of the underlying plasma kinetics. However, to achieve the project aim of studying the turbulent transport and plasma instabilities near the walls of fusion devices, the current Particle-in-Cell codes for kinetic simulations are not well adapted. Therefore, we will first need to develop a grid-based Vlasov code. Using the novel idea of split adaptive mesh refinement we will, for the first time, be able to fully kinetically model the onset and evolution of the instabilities.