  To test the role of large-scale magnetic fields in accretion processes, we
study dynamics of charged test particles in vicinity of a black hole immersed
into an asymptotically uniform magnetic field. Using the Hamiltonian formalism
of charged particle dynamics, we examine chaotic scattering in the effective
potential related to the black hole gravitational field combined with the
uniform magnetic field. Energy interchange between the translational and
oscillatory modes od the charged particle dynamics provides mechanism for
charged particle acceleration along the magnetic field lines. This energy
transmutation is an attribute of the chaotic charged particle dynamics in the
combined gravitational and magnetic fields only, the black hole rotation is not
necessary for such charged particle acceleration. The chaotic scatter can cause
transition to the motion along the magnetic field lines with small radius of
the Larmor motion or vanishing Larmor radius, when the speed of the particle
translational motion is largest and can be ultra-relativistic. We discuss
consequences of the model of ionization of test particles forming a neutral
accretion disc, or heavy ions following off-equatorial circular orbits, and we
explore the fate of heavy charged test particles after ionization where no kick
of heavy ions is assumed and only switch-on effect of the magnetic field is
relevant. We demonstrate that acceleration and escape of the ionized particles
can be efficient along the Kerr black hole symmetry axis parallel to the
magnetic field lines. We show that strong acceleration of ionized particles to
ultra-relativistic velocities is preferred in the direction close to the
magnetic field lines. Therefore, the process of ionization of Keplerian discs
around Kerr black holes can serve as a model of relativistic jets.
