Streamer branching rationalized by conformal mapping techniques

Abstract

Spontaneous branching of discharge channels is frequently observed, but not well understood. We recently proposed a new branching mechanism based on simulations of a simple continuous discharge model in high fields. We here present analytical results for such streamers in the Lozansky-Firsov limit where they can be modeled as moving equipotential ionization fronts. This model can be analyzed by conformal mapping techniques which allow the reduction of the dynamical problem to finite sets of nonlinear ordinary differential equations. Our solutions illustrate that branching is generic for the intricate head dynamics of streamers in the Lozansky-Firsov limit.