**Publication date:** Apr 2016

**Abstract:**

We study the motion of charged particles in the field of a rotating

black hole immersed into an external asymptotically uniform magnetic

field, focusing on the epicyclic quasicircular orbits near the

equatorial plane. Separating the circular orbits into four qualitatively

different classes according to the sign of the canonical angular

momentum of the motion and the orientation of the Lorentz force, we

analyze the circular orbits using the so-called force formalism. We find

the analytical solutions for the radial profiles of velocity, specific

angular momentum, and specific energy of the circular orbits in

dependence on the black-hole dimensionless spin and the magnetic field

strength. The innermost stable circular orbits are determined for all

four classes of the circular orbits. The stable circular orbits with an

outward-oriented Lorentz force can extend to radii lower than the radius

of the corresponding photon circular geodesic. We calculate the

frequencies of the harmonic oscillatory motion of the charged particles

in the radial and vertical directions related to the equatorial circular

orbits and study the radial profiles of the radial, ωr;

vertical, ωθ; and orbital,

ωϕ, frequencies, finding significant differences

in comparison to the epicyclic geodesic circular motion. The most

important new phenomenon is the existence of toroidal charged particle

epicyclic motion with

ωr˜ωθ≫ωϕ

that could occur around retrograde circular orbits with an

outward-oriented Lorentz force. We demonstrate that for the rapidly

rotating black holes the role of the "Wald induced charge" can be

relevant.

**Authors:**

Tursunov, Arman; Stuchlík, Zdeněk; Kološ, Martin;