When a strong electric field is applied to nonconducting matter, narrow channels of plasma called streamers may form. Branchlike patterns of streamers have been observed in anode directed discharges. We explain a mechanism for branching as the result of a balance between the destabilizing effect of impact ionization and the stabilizing effect of electron diffusion on ionization fronts. The dispersion relation for transversal perturbation of a planar negative front is obtained analytically when the ratio $D$ between the electron diffusion coefficient and the intensity of the externally imposed electric field is small. We estimate the spacing $\lambda$ between streamers and deduce a scaling law $\lambda \sim D^{1/3}$.

• Received 18 May 2005

DOI:https://doi.org/10.1103/PhysRevLett.95.165001