  It is well known that supermassive black holes in the centers of galaxies are
capable of accelerating charged particles to very high energies. In many cases,
the particle acceleration by black holes occurs electromagnetically through an
electric field induced by the source. In such scenarios, the accelerated
particles radiate electromagnetic waves, leading to the appearance of the
backreaction force, which can considerably change the dynamics, especially, if
the particles are relativistic. The effect of the radiation reaction force due
to accelerating electric field of the central body in curved spacetime has not
been considered previously. We study the dynamics of radiating charged
particles in the field of the Schwarzschild black hole in the presence of an
electric field associated with a small central charge of negligible
gravitational influence. We start from the flat spacetime description, solving
the Lorentz-Dirac equation reduced to the Landau-Lifshitz form. In curved
spacetime, we use the DeWitt-Brehme equation and discuss the effect of the
self-force, also known as the tail term, within the given approach. We also
study the pure effect of the self-force to calculate the radiative deceleration
of radially moving charged particles. In the case of bounded orbits, we find
that the radiation reaction force can stabilize and circularize the orbits of
oscillating charged particles by suppressing the oscillations or causing the
particles to spiral down into the black hole depending on the sign of the
electrostatic interaction. In all cases, we calculate the energy losses and
exact trajectories of charged particles for different values and signs of
electric charge.
