Modeling Analysis and Simulation: Computing Complex Airy Functions by Numerical Quadrature

摘要

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 suffciently 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.