Contour dynamics model for electric discharges.

We present an effective contour model for electrical discharges deduced as the asymptotic limit of the minimal streamer model for the propagation of electric discharges, in the limit of small electron diffusion. The incorporation of curvature effects to the velocity propagation and not to the boundary conditions is a feature and makes it different from the classical Laplacian growth models. The dispersion relation for a nonplanar two-dimensional discharge is calculated. The development and propagation of fingerlike patterns are studied and their main features quantified.