The onset of tree-like patterns in negative streamers

TL;DR

This paper investigates the initial branching behavior of negative streamers using a 3-D interface dynamics model, combining analytical and numerical methods to understand pattern formation in electric discharges.

Contribution

It provides the first analytical and numerical analysis of early streamer branching in three dimensions based on a fundamental interface evolution model.

Findings

Explicit growth rate for harmonic modes derived

Numerical simulations show formation of tree-like discharge patterns

Comparison with experimental patterns validates the model

Abstract

We present the first analytical and numerical studies of the initial stage of the branching process based on an interface dynamics streamer model in the fully 3-D 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 non-ionized 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 tree-like patterns of electric discharges is observed and described.