Magnetic Fractal Dimensionality of the Dielectric Breakdown Under Strong Magnetic Fields

摘要

The formation of breakdown pattern on an insulating surface under theinfluence of a transverse magnetic field is theoretically investigated. We havegeneralized the Dielectric Breakdown Model (DBM) for the case of externalmagnetic field. Concept of the Magnetic Fractal Dimensionality (MFD) isintroduced and its universality is demonstrated. It is shown that MFD saturateswith magnetic fields. The magnetic field dependence of the streamer curvatureis obtained. It is conjectured that nonlinear current interaction isresponsible for the experimentally observed 'spider-legs' like streamerpatterns.