Contour dynamics model for electric discharges

Area of Science:

• Physics
• Plasma Physics
• Computational Physics

Background:

• Electrical discharges are complex phenomena involving plasma and electric fields.
• Understanding discharge propagation is crucial for applications like lightning and material processing.
• Classical models often simplify geometric complexities.

Purpose of the Study:

• To present an effective contour model for electrical discharges.
• To analyze the asymptotic limit of the minimal streamer model with small electron diffusion.
• To incorporate curvature effects into discharge propagation dynamics.

Main Methods:

• Deducing a contour model from the minimal streamer model in the limit of small electron diffusion.
• Incorporating curvature effects into velocity propagation, distinct from boundary conditions.
• Calculating the dispersion relation for nonplanar two-dimensional discharges.

Main Results:

• The model effectively captures the behavior of electrical discharges.
• Curvature effects are shown to influence propagation dynamics.
• Fingerlike patterns in discharge development and propagation are studied and quantified.

Conclusions:

• The proposed contour model offers an effective description of electrical discharges.
• The model's unique approach to curvature effects distinguishes it from Laplacian growth models.
• Quantification of fingerlike patterns provides insights into discharge morphology.