Magnetic Fractal Dimensionality of the Dielectric Breakdown Under Strong Magnetic Fields

The formation of breakdown pattern on an insulating surface under the influence of a transverse magnetic field is theoretically investigated. We have generalized the Dielectric Breakdown Model (DBM) for the case of external magnetic field. Concept of the Magnetic Fractal Dimensionality (MFD) is introduced and its universality is demonstrated. It is shown that MFD saturates with magnetic fields. The magnetic field dependence of the streamer curvature is obtained. It is conjectured that nonlinear current interaction is responsible for the experimentally observed spider-legs like streamer patterns.