Mechanisms of propagation and branching of electric discharges

When a strong external electric field is applied to a nonionized gas, an ionization process may take place leading to the appearance of patterns in the form of sparks. There are many processes involved in these phenomena, being two of the most relevant the ionization of the medium through impact with accelerated electrons and diffusion of electrons inside the medium.

Planar, cylindrical and spherical ionization fronts can exist as solutions of a minimal model taking into account both processes. We study how the combination of electron impact ionization and electron diffusion does affect the stability of planar fronts, leading to the formation of finger-like patterns, and deduce characteristic lengths for the thickness of sparks as a function of the parameters of the problem. The phenomenon can be viewed as an analog to the appearence of fingers in Hele-Shaw cells and dendritic growth.