Journal of Statistical Physics, Vol. 106, Nos. 3/4, February 2002. p. 653-662.
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) and random walker model
for the case of external magnetic field. It is shown that fractal dimensionality of the discharge saturates with magnetic fields. It is conjectured that nonlinear current interaction is responsible for the experimentally observed "spider-legs" like streamer patterns.