We explain a mechanism for branching of a planar negative front. Branching
occurs 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 is obtained
analytically and reads: s=∣k∣/[2(1+∣k∣)]−D∣k∣2, where D, which is
assumed to be small, is the ratio between the electron diffusion coefficient
and the intensity of the externally imposed electric field. We estimate the
spacing λ between streamers in a planar discharge and deduce a scaling
law λ∼D1/3