Recently we have reported on axisymmetric dielectric concentrator for Cherenkov radiation that focuses almost the whole radiation in the vicinity of the given point (focus) located on the trajectory of the charge. Here we continue investigation of this concentrating target and analyze in more detail the field in the focal spot depending on parameters of the target. We also discuss how the concentrating properties of this device depend on variations in velocity of a moving charge. (C) 2017 Elsevier B.V. All rights reserved.