Numerical convergence of the branching time of negative streamers

Discharge streamers in experiments branch frequently. Arrayas et al. [Phys. Rev. Lett. 88, 174502 (2002)] presented simulations of branching streamers and interpreted them as physical branching events. The numerical results were criticized by Kulikovsky [Phys. Rev. Lett. 89, 229401 (2002)]. Using an adaptive grid algorithm, we here present numerical experiments on the effect of grid resolution on streamer branching. The convergence of branching time with stepwise finer grid sizes provides a quantitative correction on the earlier, low-resolution results in overvolted gaps. Furthermore, streamers can branch even in undervolted, but sufficiently long gaps, but fewer branching modes are accessible than in higher fields