Growth model for filamentary streamers in an ambient field

Abstract

We have simulated the fast streamer stage of liquid dielectric breakdown as stochastic growth of a branching fractal tree. Breakdown and threshold properties of the fluid are represented in the random filter procedure. A range of fractal densities, from sparse to bushy, is approximated by the choice of power-law (4th-power to linear). The choice of threshold (cutoff) voltage also significantly affects the growth form. These parameters combine with the shape and concentration of the electric field, to regulate the distribution and directedness of the local discharge growth pattern. Inclusion of a voltage gradient along the streamer tree produces a secondary narrowing effect on the growth. A large grid (128 cubed) is used for the discretization. Diagonal growth paths to neighbor-vertices are included, increasing the choice of available directions for each discharge event. We use a combination of data-parallel programming and three-dimensional visualization. Complete growth histories, evolving from the voltage distribution, can be displayed in animation or in color banding against the "trials" variable, which simulates a time tick. Side views of the structures provide comparison against sub-microsecond snapshots from experiment. Results include sparse, directed trees evolving from a 4th-power-law filter; also dense trees from a linear filter, whose conical upper-envelope boundary is strongly influenced by the choice of threshold (cutoff) potential.