Estimating the properties of single positive air streamers from measurable parameters

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 degree, 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. We do this by first analytically approximating the electron dynamics in different regions of a uniformly-translating streamer head, then we match the solutions between the different regions and finally we use conservation laws to determine unknown quantities. We find good agreement with numerical simulations for a range 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 easily measurable quantities and our approximations. The theoretical approximations also form a stepping stone towards efficient axial multi-streamer models.