  We present numerical and analytical studies of coupled nonlinear Maxwell and
thermal diffusion equations which describe nonisothermal dendritic flux
penetration in superconducting films. We show that spontaneous branching of
propagating flux filaments occurs due to nonlocal magnetic flux diffusion and
positive feedback between flux motion and Joule heat generation. The branching
is triggered by a thermomagnetic edge instability which causes stratification
of the critical state. The resulting distribution of magnetic microavalanches
depends on a spatial distribution of defects. Our results are in good agreement
with experiments performed on Nb films.
