Dependence of streamer propagation on background field conditions

Positive and negative electric streamers are column-shaped discharges which are an important stage in lightning development. The mechanism, by which the streamer acquires a certain velocity and radius of its head, had been a long-standing puzzle. In [1], we proposed a parametric streamer model (PSM), which may explain this mechanism, as well as the mechanism of the streamer threshold electric field. The PSM results for a positive isolated streamer in constant uniform external electric field are verified by comparing with hydrodynamic calculations of a `steady-state' streamer, namely a streamer whose length is kept constant by synchronizing the position of the electrode to which it is attached with the moving streamer head. For this particular streamer configuration, we found that both velocity and radius of a streamer increase with its length, a results which was also observed in previously performed hydrodynamic calculations and experiments. Beside the velocity and radius of the streamer, PSM allows to quickly estimate all other streamer parameters, such as the maximum field at the streamer tip and the field inside the streamer channel. The relatively low, compared to, e.g., hydrodynamic or particle-in-cell (PIC) models, computational costs of PSM suggest that generalizion of PSM principles to more complicated streamer structures may be very valuable. In the present work, we generalize PSM to evaluate how different background conditions affect streamer propagation. In particular, we find that, unlike the uniform-field case described above, (1) for the non-uniform electric field such as that of a spherical electrode, the streamer velocity decreases with length; (2) for a streamer propagating parallel to other similar streamers (as in a streamer ``bunch''), both velocity and radius stabilize to an approximately constant value. [1] N. G. Lehtinen, ``Physics and mathematics of electric streamers,'' Radiophysics and Quantum Electronics, 2021, in print [Russian version: DOI: 10.52452/00213462_2021_64_01_12].