Centrifugal acceleration of protons by a supermassive black hole
  The centrifugal acceleration is due to the rotating poloidal magnetic field
in the magnetosphere creates the electric field which is orthogonal to the
magnetic field. Charged particles with finite cyclotron radii can move along
the electric field and receive energy. Centrifugal acceleration pushes
particles to the periphery, where their azimuthal velocity reaches the light
speed. We have calculated particle trajectories by numerical and analytical
methods. The maximum obtained energies depend on the parameter of the particle
magnetization $ \kappa $, which is the ratio of rotation frequency of magnetic
field lines in the magnetosphere $ \Omega_F $ to non-relativistic cyclotron
frequency of particles $ \omega_c $, $ \kappa = \Omega_F /\omega_c << 1 $, and
from the parameter $ \alpha $ which is the ratio of toroidal magnetic field $
B_T $ to the poloidal one $ B_P $, $ \alpha = B_T / B_P $. It is shown that for
small toroidal fields, $ \alpha <\kappa^{1/4} $, the maximum Lorentz factor $
\gamma_m $ is only the square root of magnetization, $ \gamma_m = \kappa^{-1/2}
$, while for large toroidal fields, $ \alpha >\kappa^{1/4} $, the energy
increases significantly, $ \gamma_m = \kappa^{-2/3} $. However, the maximum
possible acceleration, $ \gamma_m = \kappa^{-1} $, is not achieved in the
magnetosphere. For a number of active galactic nuclei, such as M87, maximum
values of Lorentz factor for accelerated protons are found. Also for special
case of Sgr. A* estimations of the maximum proton energy and its energy flux
are obtained. They are in agreement with experimental data obtained by HESS
Cherenkov telescope.
