Recent progress in kinetic Monte Carlo modeling of streamers (and other types of discharges).

I discuss recent progress in using an alternative computational method of solving for drift-diffusion-reaction models that avoids the local density approximation. With kinetic Monte Carlo (KMC), electrons are tracked as drifting Brownian walkers and thus adhere to a microscopic drift-diffusion equation rather than a macroscopic one. Reactions within grid cells are resolved with KMC rather than with the deterministic reaction rate equation, while radiative transfer is treated with ray-traced Monte Carlo sampling of ionizing photons. The compound model maintains the efficiency of an explicit method but has no CFL constraint on the time step. The approach also has the benefit of eliminating numerical diffusion (which is especially problematic when dealing with cathode sheaths in fluid models). We have implemented this model on cut-cell Cartesian grids that scale to thousands of CPUs, and provide a few application examples. I also mention how the method can be used to obtain approximate solutions on very coarse grids, which are typically well out of reach of fluid models.