Onset of treelike patterns in negative streamers

Area of Science:

• Physics
• Plasma Physics
• Electrical Engineering

Background:

• Electric discharges exhibit complex branching, treelike patterns.
• Understanding the initial stages of discharge branching is crucial for various applications.
• Existing models often simplify the three-dimensional nature of streamer dynamics.

Purpose of the Study:

• To investigate the initial stage of electric discharge branching in a fully three-dimensional context.
• To develop and analyze an interface dynamics streamer model for discharge evolution.
• To compare simulation results with experimental observations and derive analytical expressions for growth rates.

Main Methods:

• Analytical and numerical studies of streamer dynamics.
• Development of an interface evolution equation based on charge production and balance laws.
• Full numerical simulations to observe pattern formation and splitting.
• Comparison of simulated patterns with experimental data.

Main Results:

• An explicit expression for the growth rate of harmonic modes in a symmetrically expanding discharge was derived.
• Numerical simulations successfully reproduced characteristic treelike patterns of electric discharges.
• The model accurately describes the interface evolution between ionized and nonionized regions.
• Observed splitting and formation of complex discharge structures.

Conclusions:

• The interface dynamics streamer model provides a robust framework for studying 3D electric discharge branching.
• The study elucidates the fundamental mechanisms behind the formation of treelike discharge patterns.
• The derived growth rate expression offers predictive capabilities for discharge evolution.