Perspectives of implementing QED cascade production with the next generation of laser facilities

QED cascade in an intense laser field can start developing if the electron proper acceleration expressed in Compton units χ becomes of the order of unity. We derive a general formula expressing the quantum dynamical parameter χ(t) of an initially slow electron in an arbitrary electromagnetic field, which is valid for a time range t 蠐 1/ω, where ω is the field carrier frequency. Using this formula, we identify a special field configuration of colliding focused laser beams, which provides cascade production at intensity of the order of 10²³W/cm². Such intensity is believed to become attainable with the new generation of laser facilities, particularly the ELI Beamlines, in the coming years.