  We present a comprehensive analysis of longitudinal particle drifting in a
standing circularly polarized wave at extreme intensities when quantum
radiation reaction (RR) effects should be accounted for. To get an insight into
the physics of this phenomenon we made a comparative study considering the RR
force in the Landau-Lifshitz or quantum-corrected form, including the case of
photon emission stochasticity. It is shown that the cases of circular and
linear polarization are qualitatively different. Moreover, specific features of
particle dynamics have a strong impact on spatial structures of the
electron-positron ($e^-e^+$) density created in vacuum through quantum
electrodynamic (QED) cascades in counter-propagating laser pulses. 3D PIC
modeling accounting for QED effects confirms realization of different pair
plasma structures.
