  We study anode-directed ionization fronts in curved geometries. When the
magnetic effects can be neglected, an electric shielding factor determines the
behavior of the electric field and the charged particle densities. From a
minimal streamer model, a Burgers type equation which governs the dynamics of
the electric shielding factor is obtained. A Lagrangian formulation is then
derived to analyze the ionization fronts. Power laws for the velocity and the
amplitude of streamer fronts are observed numerically and calculated
analytically by using the shielding factor formulation. The phenomenon of
geometrical diffusion is explained and clarified, and a universal self-similar
asymptotic behavior is derived.
