Centrifugal acceleration of protons in the vicinity of a supermassive
  black hole
  Acceleration of protons in the active galactic nuclei is considered. The
largest energy is achieved by protons during centrifugal acceleration in the
magnetosphere of the central machine. When the proton accelerated in the
magnetosphere of a black hole approaches light cylinder surface, acceleration
occurs mainly in the azimuthal direction, i.e. the acceleration is centrifugal.
In this paper the acceleration of a proton having smaller synchrotron losses
compared to the electron is considered. As a proton experiences the highest
energy increase while accelerating near the light surface, a partial solution
for the maximum Lorentz factor can be obtained there. In the analysis the
obtained dependence of the maximum energy on the parameter of particle
magnetization $ \kappa $ and parameter $ \alpha $ which reflects the relation
of toroidal $ B_\phi $ and poloidal $ B_T $ magnetic fields , has led to the
conclusion that the achievement of theoretical maximum limit of Lorentz factor
value $ \gamma_m=\kappa^{-1}$ is not possible for an accelerated particle in
the magnetosphere of a black hole due to restrictions of the topology of
toroidal and poloidal magnetic fields imposed. The analysis of special cases of
the relation of toroidal and poloidal magnetic field has shown that in the
presence of magnetic field that is significantly more toroidal the maximum
Lorentz factor value reaches $\gamma_m = \kappa^ {-2/3} $, in case when
toroidal field becomes smaller in comparison to poloidal field the maximum
Lorentz factor value does not exceed $\gamma_m = \kappa^ {-1/2} $. For a number
of objects, such as M87 and Sgr. A *, maximum Lorentz factor values for
accelerated protons for scenarios of existence or lack of toroidal magnetic
field have been derived. The obtained results for magnetosphere of Sgr. A * has
confirmed by the experimental data obtained on the massive HESS of Cherenkov
telescopes.
