Stability of negative ionization fronts: regularization by electric screening?

Abstract

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 give a physical interpretation of these results.

11 pages, 2 figures

References in corpus (6)

• Front propagation into unstable states: Universal algebraic convergence towards uniformly translating pulled fronts
• Propagation and Structure of Planar Streamer Fronts
• Branching of negative streamers in free flight
• Streamer Propagation as a Pattern Formation Problem: Planar Fronts
• Universal algebraic relaxation of fronts propagating into an unstable state
• Breakdown of the standard Perturbation Theory and Moving Boundary Approximation for "Pulled" Fronts

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