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تسجيل مستخدم جديدCentrifugal acceleration of protons in the vicinity of a supermassive black hole
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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.
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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.
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