Saffman-Taylor streamers: mutual finger interaction in spark formation

Area of Science:

• Physics
• Plasma Physics
• Electrical Engineering

Background:

• Current theories on electrical discharges like sparks and lightning often focus on single streamers or simplified breakdown trees.
• A gap exists in understanding the complex interactions within arrays of multiple streamers.

Purpose of the Study:

• To investigate the behavior of interacting streamer discharges in a uniform electric field using a two-dimensional fluid approximation.
• To analyze how streamer spacing affects their morphology and dynamics, particularly in relation to branching.

Main Methods:

• Simulations were performed on a periodic array of interacting streamer discharges in a homogeneous electric field.
• A density or fluid approximation was used in two dimensions.
• A moving boundary approximation to the density model was discussed and compared to Hele-Shaw flows.

Main Results:

• Streamers with sufficiently small periods exhibit uniform translation without branching.
• The enhanced electric field at streamer tips approaches twice the applied field (2Einfinity) near the branching regime.
• The simulated shapes of interacting streamers in uniform motion were accurately described by the analytical Saffman-Taylor finger solution.

Conclusions:

• The study provides a model for understanding interactions in streamer arrays, moving beyond single-streamer theories.
• The connection to Saffman-Taylor flow offers a new perspective on pattern selection in moving boundary problems.
• This research contributes to a deeper comprehension of electrical breakdown phenomena and fluid dynamics.