Non-ionized media subject to strong fields can become locally ionized by penetration of finger-shaped streamers. We study negative streamers between planar electrodes in a simple deterministic continuum approximation. We observe that for sufficiently large fields, the streamer tip can split. This happens close to Firsov's limit of ``ideal conductivity''. Qualitatively the tip splitting is due to a Laplacian instability quite like in viscous fingering. For future quantitative analytical progress, our stability analysis of planar fronts identifies the screening length as a regularization mechanism.

Modelling, Analysis and Simulation [MAS]
Computational Dynamics

Arrayás, M, Ebert, U, & Hundsdorfer, W. (2001). Spontaneous branching of anode-directed streamers between planar electrodes. Modelling, Analysis and Simulation [MAS]. CWI.