2007/08/31 by Alejandro Luque, Fabian Brau, Ute Ebert · 3 citations
Engineering · Materials Science · Physics and Astronomy · #Aerosol Filtration and Electrostatic Precipitation #High voltage insulation and dielectric phenomena #Lightning and Electromagnetic Phenomena #physics.flu-dyn #physics.plasm-ph
paper · pdf · doi:10.1103/physreve.78.016206
published as Phys. Rev. E 78, 016206 (2008) · 7 pages, 6 figures
arxiv created 2008/06/11 · openalex publication_date 2008/07/11 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/04
Bunches of streamers form the early stages of sparks and lightning but theory presently concentrates on single streamers or on coarse approximations of whole breakdown trees. Here a periodic array of interacting streamer discharges in a strong homogeneous electric field is studied in density or fluid approximation in two dimensions. If the period of the streamer array is small enough, the streamers do not branch, but approach uniform translation. When the streamers are close to the branching regime, the enhanced field at the tip of the streamer is close to 2Einfinity, where Einfinity is the homogeneous field applied between the electrodes. We discuss a moving boundary approximation to the density model. This moving boundary model turns out to be essentially the same as the one for two-fluid Hele-Shaw flows. In two dimensions, this model possesses a known analytical solution. The shape of the two-dimensional interacting streamers in uniform motion obtained from the PDE simulations is actually well fitted by the analytically known "selected Saffman-Taylor finger." This finding helps to understand streamer interactions and raises new questions on the general theory of finger selection in moving boundary problems.