We recently have proposed that a reduced interfacial model for streamer propagation is able to explain spontaneous branching. Such models require regularization. In the present paper we investigate how transversal Fourier modes of a planar ionization front are regularized by the electric screening length. For a fixed value of the electric field ahead of the front we calculate the dispersion relation numerically. These results guide the derivation of analytical asymptotes for arbitrary fields: for small wave-vector k, the growth rate s(k) grows linearly with k, for large k, it saturates at some positive plateau value. We include a physical interpretation of these results.

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Modelling, Analysis and Simulation [MAS]
Multiscale Dynamics

Arrayás, M, & Ebert, U. (2003). Stability of negative ionization fronts: regularization by electric screening?. Modelling, Analysis and Simulation [MAS]. CWI.