  An interplay of magnetic fields and gravitation drives accretion and outflows
near black holes. However, a specific mechanism is still a matter of debate; it
is very likely that different processes dominate under various conditions. In
particular, for the acceleration of particles and their collimation in jets, an
ordered component of the magnetic field seems to be essential. Here we discuss
the role of large-scale magnetic fields in transporting the charged particles
and dust grains from the bound orbits in the equatorial plane of a rotating
(Kerr) black hole and the resulting acceleration along trajectories escaping
the system in a direction parallel to the symmetry axis (perpendicular to the
accretion disk). We consider a specific scenario of destabilization of circular
geodesics of initially neutral matter by charging (e.g., due to
photoionization). Some particles may be set on escaping trajectories and attain
relativistic velocity. The case of charged particles differs from charged dust
grains by their charge-to-mass ratio, but the acceleration mechanism operates
in a similar manner. It appears that the chaotic dynamics controls the outflow
and supports the formation of near-horizon escape zones. We employ the
technique of recurrence plots to characterize the onset of chaos in the
outflowing medium. We investigate the system numerically and construct the
basin-boundary plots, which show the location and the extent of the escape
zones. The effects of black hole spin and magnetic field strength on the
formation and location of escape zones are discussed, and the maximal escape
velocity is computed.
