Dynamics of a spark at small times: Self-similar hydrodynamic solutions
Phys. Rev. Fluids 11, 013202 – Published 12 January, 2026
DOI: https://doi.org/10.1103/c8cb-p95c
Abstract
We discuss the hydrodynamics of the radial expansion of an electric discharge (spark) channel at the early stage of the discharge process. Due to Joule heating, the strongly ionized gas in the channel expands and forms a cylindrical shock wave that, at the initial stage, controls its expansion. We show that such dynamics can be described approximately in terms of a self-similar solution to the hydrodynamics equations. We analyze the solutions in two regimes: for an ionizing shock front and for a nonionizing shock front. In the latter case, we find that the shock wave is followed by a sharp ionization wave that represents a sharp boundary between the strongly ionized gas (i.e., plasma) in the bulk of the channel and an outer shell region, where the gas is dense and relatively cold. We also analyze, qualitatively, the effects related to the heat transfer in the spark channel and discuss the influence of the heat production on the hydrodynamic profiles and the channel's expansion rate. We argue that the results of this paper can be used to assign the initial conditions for large-scale simulations of strong discharges in air gaps.
