# Saffman-Taylor streamers: mutual finger interaction in an electric breakdown - Physics > Plasma Physics

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Abstract: Bunches of streamers form the early stages of sparks and lightning but theorypresently concentrates on single streamers or on coarse approximations of wholebreakdown trees. Here a periodic array of interacting streamer discharges in astrong homogeneous electric field is studied in PDE approximation in twodimensions. If the period of the streamer array is small enough, the streamersdo not branch, but approach uniform translation. When the streamers are closeto the branching regime, the enhanced field at the tip of the streamer is closeto $2 E {\infty}$, where $E {\infty}$ is the homogeneous field applied betweenthe electrodes. We discuss a moving boundary approximation to the set of PDEs.This moving boundary model turns out to be essentially the same as the one fortwo-fluid Hele-Shaw flows. In two dimensions, this model possesses a knownanalytical solution. The shape of the 2D interacting streamers in uniformmotion obtained from the PDE simulations is actually well fitted by theanalytically known selected Saffman-Taylor finger-. This finding helps tounderstand streamer interactions and raises new questions on the general theoryof finger selection in moving boundary problems.

Autor: Alejandro Luque, Fabian Brau, Ute Ebert

Fuente: https://arxiv.org/