  We investigate the phenomenon of electron-positron pair production from
vacuum in the presence of a strong electric field superimposed by a weak but
fast varying pulse which substantially increases the total particle yield. We
employ a nonperturbative numerical technique and perform the calculations
beyond the spatially-uniform-field approximation, i.e. dipole approximation,
taking into account the coordinate dependence of the fast component. The
analysis of the main characteristics of the pair-production process (momentum
spectra of particles and total amount of pairs) reveals a number of important
features which are absent within the previously used approximation. In
particular, the structure of the momentum distribution is modified both
qualitatively and quantitatively, and the total number of pairs created as well
as the enhancement factor due to dynamical assistance become significantly
smaller.
