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 $ κ$ and parameter $ α$ which reflects the relation of toroidal $ B_ϕ$ and poloidal $ B_T $ magnetic fields , has led to the conclusion that the achievement of theoretical maximum limit of Lorentz factor value $ γ_m=κ^{-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 $γ_m = κ^ {-2/3} $, in case when toroidal field becomes smaller in comparison to poloidal field the maximum Lorentz factor value does not exceed $γ_m = κ^ {-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.