Fingering from Ionization Fronts in Plasmas

In this paper we describe the formation of fingers from ionization fronts for a hydrodynamic plasma model. The fingers result from a balance between the destabilizing effect of impact ionization and the stabilizing effect of electron diffusion on ionization fronts. We show that electron diffusion acts as an effective surface tension on moving fronts and estimate analytically the size of the fingers and its dependence on both the electric field and electron diffusion coefficient. We also verify and extend our results by direct numerical simulation of the model and compute finger-like travelling waves analogous to structures such as Saffman-Taylor fingers and Ivantsov paraboloid in the context of Hele-Shaw and Stefan problems respectively.