  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.
