Onset of treelike patterns in negative streamers

Abstract

We present analytical and numerical studies of the initial stage of the branching process based on an interface dynamics streamer model in the fully three-dimensional case. This model follows from fundamental considerations on charge production by impact ionization and balance laws, and leads to an equation for the evolution of the interface between ionized and nonionized regions. We compare some experimental patterns with the numerically simulated ones, and give an explicit expression for the growth rate of harmonic modes associated with the perturbation of a symmetrically expanding discharge. By means of full numerical simulation, the splitting and formation of characteristic treelike patterns of electric discharges is observed and described.

Minimization of instabilities in growing interfaces: A variational approach

“…In the limit of small electron diffusion D 1, a contour-dynamics model have been utilized in Refs. [34][35][36]. The model describes an interface, with a negative charge density σ , separating a plasma region from a neutral gas.…”

“…(1) and (2), and as in Refs. [34][35][36] we can consider the limit of very high conductivity 1/ρ 1. To obtain the linear evolution of ζ n we keep terms up to the first order in ζ in the system of Eqs.…”

“…Now, by assuming the limit used in Ref. [36] [their Eq. (A6)] the unperturbed radius and the electric charge are related by…”

“…* jme@df.ufpe.br Distinct, but related types of interfacial patterns are formed in other physical systems. Two particular examples have received considerable attention over the past several years: (i) dendritic growth of a solid from a melt [18,19], linked to the celebrated Mullins-Sekerka instability [20][21][22][23][24][25][26][27][28][29]; (ii) the electric breakdown problem that studies the uprise and propagation of ionization waves through electric discharges [30][31][32][33][34][35][36]. These two systems and the viscous fingering problem have the common feature that there exists a moving boundary between two phases, on which competing stabilizing and destabilizing forces act.…”

“…Finally, it is also known that many industrial techniques (e.g., water purification, chemical processing of gases, etc.) could be improved if the emergence of treelike patterns due to electric discharges could be controlled or avoided [36]. Therefore, it is of scientific and technological importance to investigate how to control, minimize, and possibly suppress the growth of all these interfacial instabilities.…”