  Using magneto-optical imaging the phenomenon of dendritic flux penetration in
superconducting films was studied. Flux dendrites were abruptly formed in a 300
nm thick film of MgB2 by applying a perpendicular magnetic field. Detailed
measurements of flux density distributions show that there exists a local
threshold field controlling the nucleation and termination of the dendritic
growth. At 4 K the local threshold field is close to 12 mT in this sample,
where the critical current density is 10^7 A/cm^2. The dendritic instability in
thin films is believed to be of thermo-magnetic origin, but the existence of a
local threshold field, and its small value are features that distinctly
contrast the thermo-magnetic instability (flux jumps) in bulk superconductors.
