  We study radiation from charged particles in circular motion around a
Schwarzschild black hole immersed in an asymptotically uniform magnetic field.
In curved space, the radiation reaction force is described by the DeWitt-Brehme
equation, which includes a complicated, non-local tail term. We show that,
contrary to some claims in the literature, this term cannot, in general, be
neglected. We account for self-force effects directly by calculating the
electromagnetic energy flux at infinity and on the horizon. The radiative field
is obtained using black hole perturbation theory. We solve the relevant
equations analytically, in the low-frequency and slow-motion approximation, as
well as numerically in the general case. Our results show that great care must
be taken when neglecting the tail term, which is often fundamental to capture
the dynamics of the particle: in fact, it only seems to be negligible when the
magnetic force greatly dominates the gravitational force, so that the motion is
well described by the Abraham--Lorentz--Dirac equation. We also report a
curious "horizon dominance effect" that occurs for a radiating particle in a
circular orbit around a black hole (emitting either scalar, electromagnetic or
gravitational waves): for fixed orbital radius, the fraction of energy that is
absorbed by the black hole can be made arbitrarily large by decreasing the
particle velocity.
