The multiscale nature of streamers

Streamers are a generic mode of electric breakdown of large gas volumes. They play a role in the initial stages of sparks and lightning, in technical corona reactors and in high altitude sprite discharges above thunderclouds. Streamers are characterized by a self-generated field enhancement at the head of the growing discharge channel. We briefly review recent streamer experiments and sprite observations. Then we sketch our recent work on computations of growing and branching streamers, we discuss concepts and solutions of analytical model reductions and we review different branching concepts and outline a hierarchy of model reductions. (Some figures in this article are in colour only in the electronic version)