Region of magnetic dominance near a rotating black hole

Processes of collimation of electrically charged particles near a rotating black hole are discussed. It is assumed that the black hole is immersed in a weak magnetic field aligned with rotation axis. This situation is relevant for understanding pre-collimation of astrophysical jets. The magnetic field affects the motion of material and restricts the validity of various scenarios which use the test-particle (cold plasma) approximation. A simplified criterion to estimate the relevance of this approximation is discussed in connection with the mechanism of the dissipative collimation, as proposed by de Felice and Curir.