  Using a time dependent selfconsistent model for vertical sequential
tunneling,we study the appearance of charge instabilities that lead to the
formation of electric field domains in a weakly coupled doped superlattice in
the presence of high magnetic fields parallel to the transport direction. The
interplay between the high non linearity of the system --coming from the
Coulomb interaction-- and the inter-Landau-level scattering at the domain walls
(regions of charge accumulation inside the superlattice) gives rise to new
unstable negative differential conductance regions and extra stable branches in
the sawtooth-like I-V curves.
