We study the interaction of an ultra-high intensity laser pulse with plastic flat-top cone targets with curved walls and cone targets with straight walls. We find the appropriate type, dimensions of the cone target, and the ultra-high intensity laser pulse parameters for which the accelerated ions have the maximum energy and their number is the highest for a lower angular divergence and a better laser absorption. This numerical study will allow one to prepare and optimize first laser-ion acceleration experiments on CETAL using micro-cone targets.
