Plasmas in fusion reactors are highly prone to instabilities. For example, edge-localized modes (ELMs) occurring near the plasma edge are responsible for large energy losses and present a considerable potential for damage to the plasma-facing components. To understand the origin and evolution of these instabilities we must understand their plasma dynamics. However, since tokamak plasmas are a highly nonlinear system, we require numerical methods to properly address their behavior. While fluid approaches have been successful in reproducing ELMs, they do not capture the full physical description as the fundamental assumption in fluid methods is a Maxwellian velocity distribution. This assumption is not valid in the edge regions and further out, into the scrape-off layer (SOL). This provides the motivation to move to a kinetic approach where the velocity distribution is left free and solved for directly. Conventionally, particle-in-cell (PIC) codes have been used. However, these suffer from statistical noise in low-density regions such as the SOL. We are developing a finite-volume, 3D-3V Vlasov-Maxwell code that will be able to accurately model the plasma in the SOL without statistical noise. Historically, the six-dimensional phase space combined with the fine mesh that a finite-volume code necessitates, results in a large computational load where direct tokamak simulations become intractable. Therefore, we are also introducing an adaptive mesh refinement (AMR) scheme which will provide significant computational speedup. This will allow, for the first time, a feasible path to simulate the onset and evolution of ELMs in a tokamak using a fully kinetic description.
A simulation of the two-stream instability (left) and the corresponding reduced computational mesh generated with AMR (right).