Effect of an external magnetic field on particle acceleration by a rotating black hole surrounded with quintessential energy

We investigate particle motion and collisions in the vicinity of rotating black holes immersed in combined cosmological quintessential scalar field and external magnetic field. The quintessential dark-energy field governing the spacetime structure is characterized by the quintessential state parameter omega(q) is an element of(-1;-1/3) characterizing its equation of state, and the quintessential field-intensity parameter c determining the static radius where the black hole attraction is just balanced by the quintessential repulsion. The magnetic field is assumed to be test field that is uniform close to the static radius, where the spacetime is nearly flat, being characterized by strength B there. Deformations of the test magnetic field in vicinity of the black hole, caused by the Ricci non-flat spacetime structure are determined. General expression of the center-of-mass energy of the colliding charged or uncharged particles near the black hole is given and discussed in several special cases. In the case of nonrotating black holes, we discuss collisions of two particles freely falling from vicinity of the static radius, or one such a particle colliding with charged particle revolving at the innermost stable circular orbit. In the case of rotating black holes, we discuss briefly particles falling in the equatorial plane and colliding in close vicinity of the black hole horizon, concentrating attention to the interplay of the effects of the quintessential field and the external magnetic field. We demonstrate that the ultra-high center-of-mass energy can be obtained for black holes placed in an external magnetic field for an infinitesimally small quintessential field-intensity parameter c; the center-of-mass energy decreases if the quintessential field-intensity parameter c increases.