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Abstract We develop an axial model for single steadily propagating positive streamers in air. It uses observable parameters to estimate quantities that are difficult to measure. More specifically, for given velocity, radius, length and applied background field, our model approximates the ionization density, the maximal electric field, the channel electric field, and the width of the charge layer. These parameters determine the primary excitations of molecules and the internal currents. Our approach is to first analytically approximate electron dynamics and electric fields in different regions of a uniformly-translating streamer head, then we match the solutions on the boundaries of the different regions to model the streamer as a whole, and we use conservation laws to determine unknown quantities. We find good agreement with numerical simulations for a range of streamer lengths and background electric fields, even if they do not propagate in a steady manner. Therefore quantities that are difficult to access experimentally can be estimated from more easily measurable quantities and our approximations. The theoretical approximations also form a stepping stone towards efficient axial multi-streamer models.
Bouwman et al. (Sat,) studied this question.