Three-dimensional plots of the evolution of the space-charge layers of two interacting negative streamers show how the electrostatic repulsion between the two heads affects the charge distribution in the heads and drives them apart. Index Terms-Corona discharge, photoionization, streamers. T HE THEORETICAL investigation of streamers-thin plasma channels that propagate through a nonionized gas suddenly exposed to high electric fields [1]-until very recently, has concentrated on single streamers

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... nly. But very often, streamers are observed in bunches propagating close together and in similar directions, either because they have branched from a single source or because the geometry and initial conditions favor the formation of multiple channels. Arrays of streamers are, e.g., created in the laboratory by means of multiple electrode needles [2], [3] . In addition, in sprite discharges above thunderclouds, one can observe multiple streamers [4], [5] , where the interaction between them is probably the reason behind the "carrot-shape" of sprites. In [6] , it was shown that 2-D streamers, arranged in a periodic array, converge toward a uniformly translating state with the shape of the well-known selected Saffman-Taylor finger. In [7], a first study of the physics of interacting streamers in three dimensions was presented. It was shown that there exist the following two competing mechanisms: electrostatic repulsion of their heads and photoionization in the region between them, which tends to make them merge. In this paper, we illustrate these results with figures showing the geometrical aspects of the streamer evolution, in particular, the shape of the space-charge layer in full three dimensions. The streamer model for oxygen-nitrogen mixtures that we use is detailed, e.g., in [7] and [8]. A major challenge in studying 3-D streamer dynamics is the high computational power required. In order to perform accurate simulations in present computers and manageable times, several numerical advances were needed. First of all, a proper refinement scheme that allows us to finely resolve the thin concentrated space-charge layer while not wasting time on the much coarser structures of Manuscript